Unlted States

,f

c

i Department of

Agriculture

Forest Service

Southern Forest

Experiment Station

New Orleans,

Lowslana

Research Paper

so-203

March 1984

L-O-S-T: Logging

Optimization Selection

Technique

Jerry L. Koger and Dennis 6. Webster
SUMMARY

L-O-S-T is a FORTRAN computer program that can be used to quantify,

analyze, and improve user selected harvesting methods. Harvesting times and

costs are computed for road construction, landing construction, system move

between landings, skidding, and trucking. Nonlinear harvesting relationships,

irregular boundary shapes, nonuniform timber densities, unequal distances

between multiple landings, variations in road construction conditions, changes

in trucking speeds, and harvesting restrictions (environmental, physical, and

time) can be analyzed. A linear programming formulation utilizing the relationships among marginal analysis, isoquants, and the harvesting methods is

used to estimate and select the harvesting procedure having maximum profits.

ACKNOWLEDGMENTS

The linear programming algorithm used in L-O-S-T is a modification of one

developed by Dr. A. Ravindran, Chairman and Professor, Department of

Industrial Engineering, University of Oklahoma, Norman, Oklahoma. The

input-output format modifications to Dr. Ravindran’s program were made by

E. Wade Culver, a computer engineer employed by the U. S. Forest Service at

Auburn, Alabama, at the time of this study.
CONTENTS

Page

INTRODUCTION ............................................................................................ 1

Existing Solution Techniques ...................................................................... 1

Objectives ..................................................................................................... 2

HARVESTING FUNCTIONS OPTIMIZED ..............................................2

Road Construction ....................................................................................... 2

Lading Construction and System Move ....................................................2

Skidding .................................................................................................. . ..... 3

Trucking ....................................................................................................... 3

SELECTING HARVESTING METHODS .................................................4

Method Selection .......................................................................................... 4

Types of Harvesting Plans ........................................................................... 4

OPTIMIZATION METHODOLOGY ........................................................... 5

Linear Programming Formulation .............................................................. 5

Formulation Explanation ............................................................................ 7

HARVESTING EXAMPLE PROBLEM ....................................................8

Problem Description .................................................................................... 8

Harvesting Methods for the Example Problem ..........................................8

Data Input .................................................................................................... 8

Output Analysis ........................................................................................... 9

LIMITATIONS ................................................................................................ 12

EXECUTING L-O-S-T .................................................................................... 12

RESULTS AND DISCUSSION ................................................................... 13

LITERATURE CITED .................................................................................. I3

APPENDICES

1. Harvesting Equations, Data, and Cost Relationships ..........................15

2. Determining and Using Skidding Distances .......................................... 23

3. Harvesting Example Problem Method Assumptions ...........................29

4. Equipment Specifications ....................................................................... 33

5. Data Card Types ...................................................................................... 35

6. H~&,ing Example Problem Input Data ............................................

.43

7. Harvesting Example Problem Output Data .......................................... 49

8. L-O-S-T Program Listing ........................................................................ 57

i
FIGURES

Figure

No. Page

1 The Tennessee VaUey Region (Tennessee, Kentucky, North Carolina,

Virginia, Georgia, Alabama, & Mississippi) .................................................................. 3

2 Truck road construction, system move between landings,

skidding, trucking, and landing construction times

are computed in L-O-S-T ................................................................................................ 4

3 Felling, bucking, skid road construction, and bunching

times are not computed in L-O-S-T ................................................................................ 3

4 Decking, loading, move-in, and unloading times are

not computed in L-O-S-T ................................................................................................ 6

5 Assumed harvest cost relationships with respect to

the optimum location of roads and landings ................................................................. 6

6 Relationships among isoquants, activity rays,

and harvesting functions ............................................................................................... 6

7 Error relationships involved in using the formulation .................................................7

8 Harvesting example problem ......................................................................................... 8

9 Stand densities and acres for the harvesting problem ..................................................9

10 Road, landing, and area locations used in method 1 ..................................................... 10

11 Road, landing, and area locations used in method 2 ..................................................... 11

12 Road, landing, and area locations used in method 3 ..................................................... 12

13 Road, landing, and area locations used in method 4 ..................................................... 13

I Relationship among average skidding distance, actual

travel distance, and fixed skidding distance ................................................................. 25

II Average skidding distance equations for areas with

simple geometric shapes ................................................................................................ 26

III Graphic method for determining average skidding distance

when landing is on boundary edge ................................................................................. 27

TABLES

Table

No. Page

I Harvest hours for the four methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..*.......................................... 10

1 Observed skidding volumes by horsepower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..I................ 17

2 Average truck speed versus road type . . . . . . . . . . . . . . . . . ..*..........................................*............. 18

3 Load characteristics for trucks hauling logs

(or tree length stems) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..I...................... 19

4 Load characteristics for trucks hauling pulpwood

(bolts, 21-foot stems, or tree-length material) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..*..*........... 19

5 Harvesting equipment assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..*....................................... 29

6 Road segment data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..*.................... 29

7 Landing construction data . . . . . . . . . . . .~............................“’..................“.................“..‘........ 29

8 Skidding data for method 1 . . ..*......................................................................................... 30

9 Skidding data for method 2 . . . . . . . . . . . . . . . . . . . . . . ..*..................................................*.................. 30

10 Skidding data for method 3 . . . . . . . . . . . . .*............................................*.................................. 31

11 Skidding data for method 4 . ..*.......................................................................................... 31

12 Equipment horsepower and weight characteristics for

selected crawler tractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . ..*........ 33

13 Equipment horsepower and weight characteristics for

selected rubber-tired skidders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..*...................... 34

ii
L-O-S-T: Logging Optimization

Selection Technique

Jerry L. Koger and Dennis B. Webster

INTRODUCTION

An age-old problem for timber harvesters is that of

selecting the location for roads and landings that will

maximize profits. This complex problem is partially

due to: 1) nonlinear harvesting relationships, 2) nonuniform terrain and timber characteristics, 3) irregu

lar tract boundaries with interior obstacles, and 4) the

lack of a general mathematical expression describing

total costs as a function of road densities, landing

spacings, skidding distances, and equipment mixes.

Existing Solution Techniques

One of the earliest mathematical attempts to minimize harvesting costs was by Matthews (1942). To

simplify the problem, he assumed: 1) the forest

boundary could be approximated by simple geometric

shapes, 2) linear cost relationships, 3) equal spacings

between multiple landings, and 4) uniform slopes and

timber densities. Using an indirect method, Matthews determined the optimum location of roads and

landings by using calculus to obtain the minimum of

unconstrained equations. Peters (1978) extended this

approach by developing a direct method to determine

optimum location of roads and landings. Although

Peters used most of Matthews’ assumptions, he

included landing costs and used a mathematically

accurate method developed by Suddarth (1952) for

determining average skidding distance. Corcoran and

Sammis (1975) developed a computer program to

solve the road and landing spacing equations developed by Matthews. Their computer program solves

two equations in two unknowns through a heuristically iterative procedure.

Operations research techniques were used very

early by Lussier (1960, 1961) to minimize harvesting

costs. He developed equations useful in determining

the optimum number of landings, the distance

between skid roads, and optimum skid road standards. Lussier also discussed several limitations on

using a strictly mathematical approach and in making simplified assumptions in solving harvesting

problems.

Gibson and Egging (1973) developed a locationallocation model for determining the optimal number

and location of landings when using rubber-tired skidders. A truncated enumeration algorithm was used in

the allocation phase to search systematically for a

local optimum solution. Dynamic programming and a

branch and bound methodology were used to find the

global optimal solution.

Dykstra (1976) used mathematical and heuristic

programming to determine the design of individual

cutting units and the assignment of specific logging

equipment to each cutting unit. He assumed that

timber within each “type island” was homogenous

and uniformly distributed and that only cable systems would be used to harvest timber on clearcuts.

He also developed a digital model to portray topography, timber conditions, and harvest restrictions.

Carter et al. (1973) developed a computer model to

determine the optimum spacings of roads and landings. Their work involved minimizing harvesting

costs in the Rocky Mountain area where timber was

accessible either by contour work-roads or switchbacks. An iteration solution technique was used to

find simultaneous zero points of the partial derivatives of the road and landing spacing equations.

Several simulation models have been developed to

analyze timber harvesting problems. However, most

simulation models consider only a single landing and

are not specifically developed to determine the optimum location of roads and landings. Several simulation models [Forest Harvesting Simulation Model

(FHSM), Harvesting System Simulator (HSS), Simulation Applied to Logging Systems (SAPLOS), and

Timber Harvesting and Transport Simulator

(THATS)] were evaluated by Goulet et al. (1980). 1

Weintraub and Navon (1976) developed a mixed

integer linear programming model to maximize disKoger is a Reqearch Engineer with the U.S. Forest Service in Auburn, Alabama. Webster is a Professor in the Department of Industrial

Engineering at Auburn University.

1
counted revenues from timber sales. Road construetion and maintenance, timber management, and

transportation were considered. The model was developed as a tool for decision in long range forest plan

ning. Constraints were allowed on available capital,

quantity of timber harvested, haul capacity of each

road, and stand access. Kirby (1974) and Newnham

(1975) also developed mathematical programming

models useful in the long-range planning of harvesting operations.

Objectives

Existing techniques have provided useful insights

into optimum timber harvesting strategies. For harvesting specific tracts of timber by ground-based

skidding systems, these models are limited. Realistic

harvesting costs often are not computed because

overly simplified assumptions are made concerning

stand boundary shapes, slopes, timber characteristics, and harvesting methods. The objectives of this

study were to: 1) develop a computer program capable of determining realistic harvesting times and

costs for highly individualistic conditions, and 2) utilize these harvesting times and costs, as well as harvesting constraints, in a unique linear programming

formulation to obtain maximum profits. This FORTRAN computer model is titled L-O-S-T, an acronym

for logging optimization selection technique.

HARVESTING FUNCTIONS OPTIMIZED

Although the methodology used to compute harvesting times and the linear programming formulation are general, the equations used to compute harvesting times are based on data collected in the Tennessee Valley Region (fig. 1). Harvesting times and

costs are only calculated for road construction, landing construction, system move between landings,

skidding, and trucking (fig. 2). Their relationships to

selecting harvesting methods and the linear programming formulation are discussed in later sections.

Costs are not calculated for felling, bucking, and loading (figs. 3 and 4) because those costs are not assumed

to be significantly affected by the locations of roads

and landings. The assumed general relationships

among various harvesting activities and harvesting

costs optimizations are shown in figure 5.

Road Construction

Construction of truck roads within the harvest

boundary reduces skidding costs, but increases road

construction, landing construction, system move,

and trucking costs. In L-O-S-T, a road is considered

2s a low volume, temporary structure constructed

solely for removing trees. If a high volume road is

constructed with a design standard or life expectancy

greater than that needed for timber harvesting, then

the cost of the road must be adjusted to reflect only

timber harvesting. The equation (Al, appendix 1)

used to compute road construction times was developed by Koger (1978) from data collected in the Tennessee Valley Region.

Due to irregular terrain, construction conditions

are seldom uniform over the entire road network. In

order to determine more accurately construction

costs, the road can be divided into short segments.

These segments reflect differences in bank cubic

yards, road slope (grade), or construction problems

caused by rock or dense timber.

Although the number of bank cubic yards removed

for making the roadbed is a variable, it does not have

to be computed by the user. However, the user must

supply roadbed width, side-hill slope, cut-slope ratio,

and fill-slope ratio. This information is used in an

equation reported by Bowman et al. (1975) to calculate bank cubic yards. Another variable, the number

of acres in the road right-of-way, is also calculated for

the user.

The construction of skid trails or skid roads for use

by rubber-tired skidders is not computed in L-O-S-T.

Skid road costs are assumed to be independent of the

locations of truck roads and landings.

Landing Construction and System Move

Landings are usually constructed in conjunction

with the road system, primarily as storage and loading areas for the skidded trees. Increasing landings

decreases skidding costs, but increases system move,

landing construction, and trucking costs. The equation used to compute landing construction times is a

modification of the road construction equation (Al,

appendix 1). The landing size in acres is converted to

an “equivalent” road length based on an assumed

cleared road width of 26.7 feet. An average cleared

road width of 26.7 feet was observed in a study of

logging roadsin the Tennessee Valley Region (Koger

1978). A road construction condition factor of 3,000 is

used (variable X6). In addition, the depth of the cut to

level the landing site is assumed to be uniform across

the landing area.

System move costs are those involved in moving

equipment such as loaders, crawler tractors used for

decking or landing maintenance, and shop trucks to

the next landing. These costs are related to the distance and road condition between landings, the

amount and type of equipment, and the hourly cost of

the equipment and associated labor. Skidders may be

included if they travel unloaded to the next landing

site. Haul trucks are not included. If only one landing

is used, system move costs are assumed to be zero.

Move-in costs are not considered because they are
Figure l.-The Tennessee Valley Region (Tennessee, Kentucky, Virginia, North Carolina, Georgia, Alabama, & Mississippi).

assumed to be approximately constant with whatever

the locations of roads and landings.

In the linear programming formulation, landing

construction and system move times are considered

together. Since a relationship exists between these

two costs, it is perhaps easier to think of them jointly

rather than separately. Equation A5 (appendix 1) is

used to compute a weighted time for landing construction and system move between landings.

Skidding

Skidding costs depend largely on skidding distance, which can be controlled through the locations of

roads and landings. Skidding costs decrease as the

density of roads and landings increases. The equation

(A3, appendix 1) used to compute skidding times was

developed by Koger (1976) for articulated, four-wheel

drive, rubber-tired skidders operating in the Tennessee Valley Region. The range of observed volumes

skidded in this region is shown in table 1 (appendix 1).

Techniques available to compute average skidding

distance are described in appendix 2. The differences

among average skidding distance, the distance

actually traveled by the skidder, and fixed skidding

distance are also discussed.

Trucking

Trucking over roads within the harvest boundary

reduces skidding costs but increases trucking, road

construction, landing construction, and system move

costs. The trucking speeds and load volumes shown

in tables 2 - 4 (appendix 1) are based on data collected

in the Tennessee Valley Region by Koger (1981). With

respect to the optimum location of roads and landings, it is not necessary to compute trucking costs

from the mill to the edge of the harvest boundary.

This distance remains constant and is not affected by

the road density or trucking pattern inside the harvest boundary. However, trucking costs are computed from each lauding to the mill or delivery point

because calculating these costs: 1) does not change

the optimum location of roads and landings, 2) may

alert the user to consider other routes from the mill to

the harvest boundary, and 3) provides the user with

an estimate of total trucking costs.

3
Figure 2.-Truck road construction, system moue between landings, skidding, trucking, and landing construction times are computed inL-O-S-T.

SELECTING HARVESTING METHODS

Method Selection

The user must determine either two, three, or four

different-but realistic-harvesting methods. These

different methods can be viewed as harvesting or

transportation plans. As a rule this requires drawing

the boundary, stand densities, harvesting restrictions, road and landing locations, and skidding patterns on a topographic map. The methods should be

selected so that road density (or road length) is at a

minimum for the first method and at a maximum for

the last method. Intermediate methods should be

between these limits. Truck roads can be divided into

segments to reflect differences in sidehill slope, road

slope (grade), road width, or other construction factors. The size, construction condition, and distance

from the harvest boundary is needed for each landing.

The skidding pattern must be determined for each

area and all landings. An area is a subdivision of a

stand and its boundary is used in determining average skidding distance. Areas should be numbered

consecutively within a stand and numbered so that

no two areas have the same area number. An area can

be subdivided into two or more new areas to reflect

changes in skidding patterns among landings for different methods. The complexity of harvesting problems and the level of detail or realism required by thf

user is reflected in the number of areas selected.

Types of Harvesting Plans

L-O-S-T is capable of analyzing most ground-based

plans including: 1) single road extension, 2) variable

landing spacings along a fixed road length, 3) parallel

roads, 4) multiple contour roads, 5) spur road extensions from major roads, and 6) climbing roads with

switchbacks. The only requirement for analyzing any

harvesting plan is that some relationship of road

4
Figure 3.-Felling, bucking, skid rood construction, and bunching times are not computed in L-O-S-T.

length and skidding exists between adjacent harvesting methods: From a silviculture perspective these

harvesting plans could be for individual tree selection, group selection, diameter limit, financial maturity, or clear cuts. Once a cutting practice has been

selected for an area in one method, it must remain the

same in all the remaining methods. More than one different cutting practice may be used within a stand or

harvest boundary.

OPTIMIZATION METHODOLOGY

Linear Programming Formulation

After the hours required for road construction,

landing construction, system move between landings,

skidding, and trucking have been calculated for each

method, they are utilized in a linear programming

formulation (equations 1 - 6). The formulation determines the proportion (X) of each method that should

be used. The formulation used in L-O-S-T is a slight

modification of McCarl’s (1979) and is also very similar to those developed by Allen (1956) and Chiang

(1974).

Maximize: Z = P&o - CC,H, (1)

Subject to: Qo- C&J,,, 20 t4

CXi,h, -Hi 50 (3)

Q” cx

=F (4)

= m 6)

Hi zbi (6)

Qo, Q,, ‘,, Hi ~ 0

where: Z = objective function

P = delivered price of the harvested timber (ie. $1

1,000 board feet)

5
Figure &-Decking, loading, move-in, and unloading times are not computed in LO-S-T.

TOTAL COST

MINIMUM COST POINT

TRUCK ROAD

CONSTRUCTION

SYSTEM MOVE

LANDING CONSTRUCTION

SKID ROAD CONSTRUCTIO

LOADING E UNLOADING

UCKING

LENGTH OF CONSTRUCTED ROADS (FEET)

Figure B.-Assumed harvest cost relationships with respect to the

optimum location of roads and landings (Note: fixed

costs lines are in an arbitrary order).

Figure C-Relationships among isoqunnts, activity rays, and hap

vesting functions.

6
QIt = volume of timber harvested (ie. board feet)

Ci = hourly equipment and labor cost for the i th

activity (i= 1 for road construction, i = 2 for

landing construction and system move, i= 3

for skidding, and i = 4 for trucking

Hi = the total number of hours of the i th activity

used by all harvesting methods

X, = the proportion of the m th method used to

harvest the total volume of timber (a decision

variable)

X,= the number of hours for the i th harvesting

activity of the m th method

bi = maximum number of hours allowed for the i th

harvesting activity

Formulation Explanation

The relationships among the formulation (equations 1 - 6), harvesting times, and harvesting methods are shown in figure 6. Assume that a boundary of

timber can be harvested by one of four methods (Ml,

M2, M3, or M4). For simplicity in graphing, only the

harvesting activities of skidding (the hours required

are mapped on the OS axis) and road construction

(the hours required are mapped on the OR axis) will

be considered. The volume of timber harvested is

constant and represented by the isoquant BC, Fewer

hours of skidding are required as the hours of road

construction increases. The harvesting methods can

be considered as activity rays (OMl, OM2, OM3, &

OM4) with four activity vectors:

Each activity vector shows a distinct input ratio

capable of yielding a constant volume of harvested

timber (isoquant BC). Thus, Pl indicates that method

1 (Ml) is used to harvest all of the timber. This formulation assumes that it is also possible to harvest timber in various convex combinations such as:

(%Pl + %P2).

This means that a new method can be determined

which uses l/4 of the skidding hours of method 1, plus

% of the skidding hours of method 2, plus ‘/4 of the

road construction hours of method 1, plus 3A of the

road construction hours for method 2. Graphically,

this means that the ratios for the combined processes

must lie on the dashed line segments (PlP2, P2P3,

P3P4). Assume that the optimum combination of

skidding and road construction hours is at point Kl

on activity ray OK. Due to the convex nature of the

production function represented by the isoquant BC,

point Kl is not on BC. The difference between Kl and

K2 on the activity ray OK represents the error

involved in attempting to solve a nonlinear convex

production function with a linear approximation.

0 ROAD CONSTRUCTION HOURS

:TION

Figure I.-Error relationships involved in using the formulation.

This error is not considered to be significant; its relationships to the formulation, harvesting methods,

and harvesting costs are shown in figure ‘7. The formulation will pick. only one method or a linear convex

combination of adjacent methods (Allen 1956; Chiang

1974).

The assumptions of linear ‘programming (additivity, linearity, divisibility, finiteness, and single-value

expectations) are basically those used in the traditional margi.nal analysis of the firm. For timber harvesting, a specific method has a constant and linear

proportionality between hours worked and volume

harvested. Fractional hours worked can result in a

fractional volume harvested. Finiteness means there

are limits to the number of hours permitted to harvest a boundary of timber. The single-value expectation assumption assumes realistically that the quantity of timber harvested and its selling price is

known. Another basic assumption is that the volume

of timber harvested is not dependent on the harvesting method. This results in a fixed output independent of the number of hours required for road construction, landing construction, system move, skidding, and trucking.

7
HARVESTING EXAMPLE PROBLEM

Problem Description

An example problem has been developed to help

illustrate the procedures used to select different harvesting methods, data input requirements, linear

programming formulation, and program output. Specifically, the problem is to maximize profit by determining the least cost harvesting method for the

boundary of timber shown in figure 8. The timber is

to be harvested by a crawler tractor, two rubber-tired,

cable skidders, and two trucks (table 5, appendix 3).

Selected equipment weight and horsepower characteristics are given in appendix 4. The problem is sufficiently realistic to be interesting and complex’enough

to prevent the formulation of a general mathematical

expression that could be differentiated to obtain minimum costs. The complexity of the problem is

increased by: 1) an irregular boundary, 2) nonuniform

timber densities or timber stands (fig. 9), 3) elevation

changes, 4) restrictions on streambed crossings, 5)

unequal costs for different road segments and landings, 6) unequal distances between landings, 7) nonlinear skidding costs, 8) decreases in truck travel

speeds as the length of the road constructed inside

the harvest boundary increases, and 9) restrictions on

the time permitted for road construction (120 hours)

and skidding (600 hours).

Harvesting Methods for the Example Problem

For the first method, a woods road was constructed 350 feet inside the harvest boundary and one

landing constructed at location A (fig. 10). All the

areas were skidded to this landing. Compared to the

other methods, this method minimizes costs for road

construction, landing construction, trucking, and

system move, but maximizes skidding costs. For the

second method, a woods road was constructed 2,525

feet inside the harvest boundary and landings constructed at locations A and B (fig. 11). Areas 1,3, and

4 were skidded to landing A and the remaining areas

skidded to landing B. It is important to recognize

that areas can be subdivided to reflect changes in

skidding patterns for different methods. For example, area 2 used in method 1 was subdivided into

areas 3 and 6 for method 2. Area 3 was skidded to

landing A, but area 6 was skidded to landing B. For

the third method, a woods road was constructed

3,875 feet inside the harvest boundary and landings

constructed at locations A, B, and C (fig. 12). Areas 1,

3, and 4 were skidded to landing A and areas 5,6,7,8,

and 9 skidded to landing B. The remaining areas were

skidded to landing C. For the fourth method, a woods

road was constructed 6,775 feet inside the harvest

boundary and landings constructed at locations A, B,

C, and D (fig. 13). Areas 1, 3, and 4 were skidded to

landing A; areas 5, 6, 7, 8, and 9 to landing B; areas

10, 11, 15, and 19 to landing C; and areas 16, 17, 20,

21,22, and 23 to landing D. Area 18 in methods 1 - 3

was subdivided into areas 19 and 20 to reflect

changes in skidding patterns for method 4. Compared

to other methods, this method minimizes skidding

costs, but maximizes road construction, landing construction, system move, and trucking costs. A summary of several calculated and assumed values for

each of these methods is given in appendix 3 (tables

6-11).

Data Input

For each method selected, specific input information is required on road construction, landing construction, system move between landings, skidding,

trucking, and equipment costs. Sixteen data “card

Acres: 283

Map Scale: 1”:660’

- - Bomd~ry Lin*

0 Boundary Comm (I-S)

0 Landinp Localion (propmod: A-D) I woodsYhdzsagmml(*--/)

“f z;ozMd Location (proposed) APumiWstnwnkd

Figure &-Harvesting example problem.

8
types” are required for each analysis of a boundary of

timber to be harvested. An additional card type is

required if constraints are placed on the number of

hours allowed for any of the pertinent harvesting

activities. These different card types are described in

detail in appendix 5. The complete input data used to

analyze the hypothetical example is shown in appendix 6. The values shown for average skidding distance

were based on the harvest patterns for the different

areas and landing locations in figures 10 - 13. Average skidding distances were determined using a

BASIC program written for use on an HP 9830A’

calculator and HP 9864A digitizer. ’

Output Analysis

The computer output for the harvesting example

problem is shown in appendix 7. The output consists

of: 1) an echo check of the input data, 2) harvesting

times and costs, and 3) the linear programming solution and sensivity analysis.

Road construction times and costs, the number of

bank cubic yards, and acres cleared for the road-rightof-way are given for each segment. Road construction

costs are: $170 for method 1 ($2,565 per mile); $1,061

for method 2 ($2,219 per mile): $1,625 for method 3

($2,214 per mile); and $2,910 for method 4 ($2,268 per

mile). The easiest way to modify road construction

costs without changing the road design or road construction equipment characteristics is through the

input variable ROADTY (card type 10, appendix 5).

Although guidelines are provided for estimating

ROADTY, a value should be selected that gives

‘The use of trade or corporate names is for reader association and

convenience. Such does not constitute an official evaluation, conclusion, recommendation, endorsement, or approval of any product

or service to the exclusion of others which may be suitable.

reasonable cost estimates based on the user’s experience or modeling needs.

Landing construction and system move times and

costs are computed for each landing. Landing construction costs are: $56.27 for method 1; $89.64 for

method 2; $118.73 for method 3; and $150.83 for

method 4. The simplest way to influence landing construction costs without changing the landing design

or landing construction equipment characteristics is

through the input variable EFFL (card type 12,

appendix 5). System move costs are: $0.0 for method

1; $101.26 for method 2;.$192.39 for method 3; and

$303.78 for method 4.

Skidding times and costs are computed for each

skidder on each area and summarized by area, landing, and method. The number of cycles and average

cycle time are also given. The skidding costs are:

$28,769.13 for method 1; $18,076.16 for method 2;

$15,471.31 for method 3; and $10,950.56 for method

4. The easiest way to modify skidding times without

changing skidder characteristics, skid load volumes,

or skidding distances is through the input variable,

AD (card type 13, appendix 5).

In addition to skidding times and costs, average

skidding distance, fixed skidding distance, and

weighted actual travel skidding distances are summarized by landing and method. In most cases the greatest potential for reducing skidding times is through a

reduction of average fixed skidding distance. In the

harvesting example problem, average skidding distance only decreased from 686 feet for method 1 to 550

feet for method 4. However, average fixed skidding

distance decreased form 4,296 feet for method 1 to

759 feat for method 4. This drastic reduction in average fixed skidding distance was largely responsible

for skidding times decreasing from 659.75 hours for

method 1 to 264.83 hours for method 4. Weighted

average travel skidding distance is computed by mulHarve*l Bolmdafy Line

f&eie: 1” 9 660’

TOId ma : 253

Total Harvest Volume: 567,500 Board Feet (#” ht.)

Figure O.-Stand densities and acres for the harvestingproblem.
Landing Construction:

Lendinp ot A

Figure lO.-Road, landing, and area locations used in method 1.

tiplying average skidding distance by the skidding

correction factor for each area. This product is added

to to the fixed skidding distance on each area and

then multiplied by the volume for that area in order

to obtain a weighted value.

The number of acres and volume of timber harvested for each method are provided as information

and as checks on the accuracy of data input. The

number of acres for each method must be the same

and the volume harvested for each method must be

the same. In this example, 283 acres and 567,500

board feet (VI ’ Int.) were harvested for each method.

The linear programming formulation requires that an

equal volume of timber be harvested in each method.

Trucking times and costs are shown for each truck

and are summarized by landing and method. In addition, cycle times and number of loads required for

each truck are given. Trucking costs for each method

are: $17,182.48 for method 1; $17,913.40 for method

2; $18,277.16 for method 3; and $18,774.91 for

method 4. In this case the construction of four landings and 6,775 feet of woods roads only increased

trucking costs by $1592.43.

A method summary giving the hours, costs per

harvesting unit for each function, total costs, and

total costs per harvesting unit is provided in the output. The total harvesting costs per thousand board

feet ( ‘/ ’ Int.) for road construction, landing construction and system move, skidding, and trucking are:

$81.37 for method 1; $65.62 for method 2; $62.79 for

method 3; and $58.31 for method 4. The hours

required for each harvest function considered in L-OS-T are shown in table I and are used to illustrate a

numerical example of the linear programming formu10

lation (equations 7 - 16). The formulation can also be

seen in the output (appendix 7) as the first iteration of

the linear programming tableaus.

Table I.--Harvest hours for the four methods

Harvest Method 1 Method 2 Method 3 Method4

Function (hours) (hours) (hours) (hours)

Road construction 7.86 49.07 75.12 134.65

Landing construction

& system move 0.78 2.64 4.31 6.29

Skidding 695.75 437.15 374.16 264.83

Trucking 429.56 447.83 455.68 469.37

After 18 iterations the optimum linear programming solution consisted of 24 ‘JJo of method 3 and 76%.

of method 4. The optimum method (not a global optimum) used 120 hours of road construction, 5.8 hours

of landing construction and system move, 292 hours

of skidding, and 466 hours of trucking. The linear

programming solution does not give the exact physical location of the roads, landings, and skidding patterns. However, the output Can be used to help locate

the road, landings, and skidding patterns for a new

method consisting of 24% of method 3 and 76% of

method 4. Since 102.2 hours were required to construct the road to the end of segment h-i, then 17.8

hours (120.0-102.2) or 909 feet of segment i-j can be

constructed. The road should be constructed 2,159

feet beyond landing C. Landing D would be located

6,034 feet from the harvest boundary; whereas it was

originally located 6,775 feet. The skidding patterns

would stay the same for landings A and B, and probably C. However, the skidding patterns would change

for landing D. If another computer analysis tiere

made in order to obtain a better estimate, then meth-
Figure 11 .--Road, landing, and area locations used in method 2.

Linear progr amming equations for the harvesting example problem:

Maximize 2:

$95.00 Qo ‘$21.63 H, - $72.26 H2 - $41.35 H,- $40.00 H,

1.00 Q,, - 567.60 Xc - 567.50 At - 567.50 A, - 567.50 A,

7.86 A, 49.07 x1 75.12 A, 134.55 A, - 1.00 H,

0.78 A, 2.64 A, 4.31 A, 6.29 A, - 1.00 Hz

696.75 A, 437.15 XI 374.16 X, 264.83 X, - 1.00 H,

429.56 A, 447.83 A, 455.68 A, 469.37 A,

1.00 Qo 0.00 A, 0.00 x2 0.00 A, 0.00 A,

1.00 x, 1.00 x2 1.00 A, 1.00 A,

2 0.00 (81

f 0.00 (9)

5 0.00 (10)

2 0.00 (11)

.I.00 H, 2 0.00 (12)

<

= 667.50 (13)

(volume)

5 1.00 (14)

(methods)

<

= 120.00 (15)

(road

construction)

2 600.00 (16)

(skidding)

1.00 H,

1.00 H,

where: Qo, &,,,, Hi 2 0

(7)

11
ods 1 and 2 should be eliminated. Two new methods

should be selected between the original methods 3

and 4. The original method 3 would become the new

method 1. By keeping two of the original methods,

the amount of new input data needed is reduced and

the search area can be systematically analyzed.

Harvesting costs for the optimum method were

$59.41 per thousand board feet ( M’ Int.). If the constraint on road construction (120 hours) were not

binding, then all of method 4 could have been used

and harvesting costs would have been $58.31 per

thousand board feet. Binding constraints always

cause an increase in costs. However, the optimum

method selected by the linear program (24% of

method 3 and ‘76% of method 4) is still better than the

method 1 ($81.37), method 2 ($65.62), or method 3

($62.79).

The sensivity analysis in L-O-S-T consists of penalty costs, shadow prices, and ranges on all the cost

coefficients and constraints. The formulation used in

L-O-S-T and the original input format of the linear

program algorithm make it difficult to correlate the

variable codes in the sensivity analysis with the correct harvesting costs and constraints. However,

users familiar with sensivity analysis should be able

to interpret these results in L-O-S-T. In this formulation shadow prices are always zero because all the

timber can be harvested by the number of hours computed for each method. The hourly costs of the harvesting functions are always non-basic. In this example, the hourly cost of road construction can increase

from $21.63 to $64.43 without changing the optimum

solution. This implies that the same road could have

been constructed to a higher standard or that more

roads should be constructed. The method summary

costs also indicated that more roads and landinns

LIMITATIONS

The linear programming solution calculated in L-OS-T is not a global optimum or the absolute best of all

possible harvesting methods. The program determines the “best” method based on the methods supplied by the user. Equipment interactions resulting in

production delays are not calculated by the program.

The effects of equipment interactions must be supplied indirectly by the user through equipment efficiency and area difficulty factors. Harvesting costs

are calculated only for road construction, landing

construction, system move between landings, skidding, and trucking. While this does not limit the

optimization process, an estimate of total harvesting

costs is not provided.

EXECUTING L-O-S-T

L-O-S-T is written in FORTRAN IV and is being

run under WATFIV on an IBM 3031 at Auburn University. With a modest amount of additional effort,

the program could be converted for use on similar

computer systems. The example problem described in

this report required 264K of storage, used 3.38 seconds of CPU time, and cost about one dollar to run.

The FORTRAN source statements used in L-O-S-T

are shown in appendix 8. A punched and interpreted

source deck (1,914 cards) can be obtained from: Engineering Research Unit, G. W. Andrews Forestry Sciences Laboratory, U. S. Forest Service, Devall Street,

Auburn Universitv, Alabama 36849. Phone (205) 887-

should be constructed. 7542, (FTS) 534-4ji8.

Figure l2.-Road, landing, and area locations used in method 3.

12
RESULTS AND DISCUSSION

A two-part methodology has been developed to

analyze user selected harvesting methods. The first

part of this methodology considers very specific and

realistic harvesting conditions: terrain features,

boundary shapes, roads, landings, skidding patterns,

and environmental restrictions. Harvesting times

and costs are computed for road construction, landing construction, system move between landings,

skidding, and trucking. The second part of the methodology uses these harvesting times in a linear programming formulation. The formulation utilizes the

relationships among the harvesting methods to estimate and select the harvesting procedure having

maximum profits.

Since the analysis performed by L-O-S-T depends

on the harvesting methods selected by the users, it is

important that users have some knowledge and

experience in developing harvesting plans. Time and

effort spent in selecting realistic harvesting plans will

enable the output from L-O-S-T to be used with

greater confidence by managers of harvesting operations.

L-O-S-T does not provide a global optimum with

each computer analysis. Theoretically, the procedures

used would, through repeated computer runs, find the

ultimate harvesting method having maximum profits. L-O-S-T does provide a local optimum and a

wealth of information for selecting a better harvesting method. Searching for the elusive global optimum

has some academic merit; however, selecting feasible

harvesting plans and then systematically quantifying, analyzing, and improving them has greater practical applications.

LITERATURE CITED

Allen, R. G. D. Mathematical economics. New York,

New York: MacMillan and Company, Ltd.; 1956. p.

618 - 632.

Bowan, John K; McCrea, Robert B; Fonnesbeck, Carl

I. A method of field design applied to forest roads.

Transportation Research Board, National

Research Council, National Academy of Sciences,

Washington, D.C., Special Report No. 160. In proceedings of Transportation Research Board Workshop, June 16- 19,1975. p. 186 - 197.1975.

Carter, Michale R; Gardner, R. B; Brown, David B.

Optimum economic layout of forest harvesting

work roads. Res. Paper INT-133. Odgen, UT: U.S.

Dept. of Agric., Forest Service, Intermountain

For. Exp. Station; 1973.13 p.

Chiang, Alpha C. Fundamental methods of mathematical economics. 2d ed. New York, New York:

McGraw Hi& 1974. p. 684 - 689.

Corcoran, T. J; Sammis, R. Optimized landing and

road spacing. Registry of Computer Programs,

American Society of Agricultural Engineers, St.

Joseph, MI, Program No. COM 0108,1975.

Dykstra, Dennis Peter. Timber harvest layout by

mathematical and heuristic programming. Ph.D.

dissertation, Oregon State University, Corvallis,

Oregon; 1976.‘299 p.

Gibson, David F; Egging, Louis, T. A location model

for determining the optimal number and location of

decks for rubber-tired skidders. Winter Meeting

American Society of Agricultural Engineers;

December 14 - 17; Chicago, IL. ASAE paper no.

73-1534. St. Joseph, MI, ASAE; 1973.14 p.

Goulet, D. V; Iff, R. H; Sirois, D. L. Five forest harvesting simulation models, Part II: paths, pitfalls,

Figure I%-Road landing, and area locations used in method 4.

13
and other considerations. Forest Products Journal,

30(8): p. 18 - 22.1980.

Greulich, Francis E. Average yarding slope and distance on settings of simple geometric shape. Forest

Science, 26(2): p. 195 - 202. 1980.

Kirby, Malcolm. Transportation systems and the

land use plan: a mathematical programming

approach. Engineering Technical Report NO. ETR

7700-g. Berkley, CA: U.S. Dept. of Agric., Forest

Service, Pacific Southwest; 1974.17 p.

Koger, Jerry L. Factors affecting the production of

rubber tired skidders. Division of Forestry, Fisheries, and Wildlife Development, Tennessee Valley

Authority, Norris, Tennessee, Technical Note No.

B18,55 p. 1976.

Koger, Jerry L. Factors affecting the construction

and cost of logging roads. Division of Forestry,

Fisheries, and Wildlife Development, Tennessee

Valley Authority, Norris, Tennessee, Technical

Note No. B27,95 p. 1978.

Koger, Jerry L. Transportation methods and costs

for sawlogs, pulpwood bolts, and longwood. Division of Forestry, Fisheries, and Wildlife Develop

ment, Tennessee Valley Authority, Norris, Tennessee, Technical Note No. B44,34 p. 1981.

Lussier, L. J. Use of operations research in determining optimum logging layouts. Pulp and Paper

Magazine of Canada, Convention Issue, 282: p.

32-41. 1960. (Woodlands Section Index No.

1947(A-2-a))

Lussier, L: J. Planning and control of logging operations. Forest Research Foundation, Universit’e

Laval, Quebec, Canada, Contribution No. 8, 135 p.

1961.

Matthews, D. M. Cost control in the logging industry. New York, New York: McGraw Hill; 1942.314

Pa

McCarl, B. A. Production function-convex approximation. Department of Agricultural Economics,

Purdue University, West Lafayette, IN. (unpublished lecture handout in Agricultural Economics

652) p. 48 - 52.1979.

Miyata, Edwin S. Determining fixed and operating

costs of logging equipment. General Technical

Report NC-55. St. Paul, MN: U.S. Dept. of Agric.,

Forest Service, North Central Forest Experiment

Station; 1980.16 p.

Newnham, R. M. LOGPLAN-a model for planning

logging operations. Canadian Forestry Service,

Department of the Environment, Ottawa, Ontario,

KIA OH3. Inf. Rep. FMR-X-77.59 p. 1975.

Nichols, Herbert L. Moving the earth: the workbook

of excavation. Second Edition. North Castle

Books. Greenwich, CT. 1962. 21 sections plus

appendix.

Peters, Penn A. Spacing of roads and landings to rninimize timber harvest cost. Forest Science, 24(2): p.

209 - 217.1978.

Peters, Penn A; Burke, J. Boyle. Average yarding

distance on irregular-shaped timber harvest settings. Res. Note PNW-178. Portland, OR: U.S.

Dept. of Agric., Forest Service, Pacific Northwest

For. Exp. Station; 1972.13 p.

Suddarth, S. K. Cost minimization in the primary

transport of forest products. Ph.D. dissertation,

Purdue University, West Lafayette, Indiana; 1952,

66 p.

Weintraub, A; Navon, D. I. A forest management

planning model integrating silvicultural and transportation activities. Management Science, 22(12):

p. 1299 - 1309.1976.

14
Appendix l-Harvesting Equations, Data, and Cost.Relationships

HARVESTING EQUATIONS AND DATA

road construction equation: (Koger, equation 3, pg 30, 1978)

e

0.5

xl

35 [ 1 X2/(X3X4) +

T =

x7

where : T = predicted road constructed time in hours

Xl = road length in feet

ii:

= number of bank cubic yards per 1,000 feet

= slope correction factor estimated by:

of road length

2

1.000 - (% road slope/lOO) - 0.0001952 (%

note: % road slope (+, -> is in direction

road slope/lOO)

of road construction

x4 = net horsepower of crawler tractor (Table 1 2, Appendix 4)

X5 = number of acres of cleared road width per 1,000 feet of road length

(Al)

x6 = road construction difficulty factor with suggested values of:

1 0 for high volume truck road or low volume road constructed

adverse conditions

500 for low volume truck road constructed under average

conditions

1,000 for low volume skid road constructed under average

conditions

2,000 for upgrading existing low volume skid road under average

conditions

3,000 for low volume landing constructed under average conditions

note: intermediate values (ie. 520, 750) can be used

x7 = (equipment availability)(equipment utilization), with suggested

values of:

0.50 for low availability and utilization

0.85 for average availability and utilization

0.95 for high availability and utilization

note: only the variables Xl, X4, x6, and Xi’ are required as user supplied

inputs . The variables X2, X3, and X5 are calculated by the program.

.

1 6
rubber-tired skidder equation (Koger, equation 2, pg 31, 1976)

T = (travel empty + travel loaded + fixed cycle tim)/efficency (A21

.

T=

a b c d e f g

A B C (l+D) E (l+sin(F)) G

h i

H I

j k 1

0.00005166 J A B (1-a~ En WsinMWO Gp +

q r s

H C I

K 11

L

(A31

-where : T = cycle time in minutes

A = one-way skidding distance in feet

B = radius of curvature in feet (used average study value of 483.99)

C = net skidder horsepower (Table 13, Appendix 4)

D = rut depth in inches (used average study value of 6.26)

E = harvest elevation in feet (used average study value of 1,547.13)

F= trail slope in degreestmeasured in travel loaded direction)

G = empty skidder weight in pounds (use constant of 20,400)

H= cone index of soil (used average study value of 192.23

I = arc length in feet (used average study value of 131.59)

J = board feet per cycle (l/4 *( Int.)

K = fixed time per cycle in minutes for hooking, decking, etc.

L = (equipment availability)(equipment utilization), or

equipment efficiency

exponents a through s:

a=l,022449; b=3.549048; ~~1.317563; dz0.223969; ez0.180727

fz2.156775; gsO.177384; hz0.183381; iz6.943695; j=O.l10305

k=1.098034; 1~3~472234; m=0.116935; n=0.098604; o=O.681159

p&234567; q=O.O67053; r=3.157504; s=7.456998

note: Variables B, D, E, G, H, and I remain constant in the program and do

not have to be supplied as inputs by the user.

16
Table l.--Observed skidding volumes by horsepower*

Horsepower

VOLUME PER CYCLE WHEN MEASURED AS:

Pounds Board Feet:+" Int. Cubic Feet Cords

LOW High Mean Low High Mean Low High Mean Low High Mean

70 2,205 7,080 5,266 87 617 410 29 117 83 0.3 1.21 0.90

80 3,141 7,129 5,278 233 741 471 43 120 8 1 0.54 1.21 0.90

92 4,032 6,921 4,987 350 666 464 67 108 82 0.69 1.18 0.85

94 815 19,188 8,124 23 2,403 861 14 294 119 0.14 3.28 1.39

112 2,983 25,450 8,416 141 2,260 715 51 361 128 0.50 4.35 1.44

120 5,005 20,226 12,822 5O3 2,142 1,334 al 310 199 0.86 3.46 2.19

147** 4,120 7,095 5,468 419 776 575 71 122 94 0.70 1.21 0.93

165++ 4,808 5,503 5,155 445 522 484 83 95 89 0.82 0.94 0.88

l (Koger, Table 6, pg 22, 1976)

** Did not observe &en stand conditions permitted high volu& skidding.
trucking equation

The following equation is used to calculate truck cycle time from landings

to the delivery point (mill).

Y. =o + 0 +

lj- -’

s;

‘i X i + Ki

J

where: Y. i =

1J

Fj

J

CEj’l+Ci)‘/2 (Lj(l+ciW2

round trip truck time in hours from the i th landing

for the j th truck

o=

sj =

F . =

J

xi =

E . = J

ci =

one-way distance in miles over roads outside the

harvest boundary

average empty travel speed in miles per hour for the j th truck

over sections outside the harvest boundary (woods to mill)

average loaded travel speed in miles per hour for the j th truck

over sections outside the harvest boundary (woods to mill)

distance in miles from beginning of harvest boundary to

the i th landing

empty travel speed in miles per hour over the woods road for

the j th truck

ratio of ending travel speed to beginning travel speed _ -

L.

as measured from beginning of harvest boundary to the i th landing

J

= loaded travel speed in miles per hour over the woods road for

the j th truck

Kj = fixed time per cycle in hours for the j th truck

(A41

trucking data

Table 2.-- Average truck speed versus road type*

Average Average

Empty Loaded

Speed Speed

Type of Road (mph) (mph)

woods 8 4

Gravel 16::3

5.35

13.89

Two-lane black top 38.76 33.78

Interstate 55.00 45.82

city 23.97 21.44

3 (Koger, Table 1, pg 5, 1981)

18
Table 3 .--Load characteristic for trucks hauling logs

(or tree-length stems)*

Truck Description

Average Average Average Average

Number Length VolurIE Volume

of logs (feet) (Doyle) (l/41f Wt.)

Single-Axle (1.5-ton) 8

:0

13.6 1,313 1,752

Tandem-Axle (1 drag) 12.9 1,937 2,584

Tri-Axle (1 drag) Tandem-Axle (2-ton) 25 15.2 13.0 2,018 2,643 ;';2

Four-Axle (&drag) 22 11.7 3,276 4:370

Tractor-Trailer (logs) 43 14.5 3,868 5,160

Tractor-Trailer (stems) 35 36.9 4,222 5,632

3 (Koger, Table 2, 6, pg 1981)

Table 4 .--Load characteristics for trucks hauling pulpwood

(bolts, 21-foot stems, or tree-length stems)*

Truck Description

Single-Axle (0.75-ton)

Single-Axle (l-ton)

Single-Axle (1.5 ton)

Tandem-Axle (I drag)

Tractor-Trailer

Tandem-Axle (2-ton)

Tri-Axle (I drag)

Tractor-Trailer

Type of Load

Pulpwood bolts (5' 3")

Pulpwood bolts

Pulpwood bolts

Pulpwood bolts

Tree-length

21-foot stems

21-foot stems

Pulpwood bolts

Average

vqaxne

(cords)

1.5

2.1

4.6

27'

* (Koger, Table 3, pg 6, 1981)

HARVESTING COST RELATIONSHIPS

Landing Construction and System Move

In the linear programming formulation, landing construction and system move

times and costs are considered together. The following equation is used to compute a weighted time for landing construction and system moving.

WH= (SL + SM)/(HL + HM) (A5)

19
Where: WH = weighted number of hours for landing construction and

sys tern move

- sum of

gi 5 sum of

HL = hourly

HM= hourly

landing construction costs for this method

system move costs for this method

landing construction costs

system move costs

Multiple Equipment

In many cases multiple crawler tractors, skidders, or trucks may be used.

For example, two rubber-tired cable skidders may be used on the same boundary to

skid trees to the landings. Equation A6 is used to compute total time under

these conditions. This equation is used for multiple equipment involved in road

construction, skidding, or trucking, but not for landing construction. Only one

crawler tractor is allowed to construct landings, although two or more are

involved in road construction.

T = 1

-

1 + -

1 +....+ 1

Hl H2 Hn

(A61

where: T =

H, =

H2 =

H, =

hours required if all equipment (ie. skidders) uorked together

hours required if this harvesting activity were done entirely by

the first machine

hours required if this harvesting activity were done entirely by

the second machine

hours required if this harvesting activity were done entirely by

the last machine

Equipment Interactions and Efficiency

Equipment interactions resulting in production delays are not directly considered. However, an equipment efficiency factor which considers utilization is

available and can be used to model indirectly the effects of delays caused by

equipment interactions. Equipment efficiency can be estimated or calculated by

the following equation.

E = AU

where: E = equipment efficiency (decimal value greater than 0)

A= equipment availability (decimal)

u = equipment utilization (decimal)

(A71

20
Labor and Equipment Costs

Harvesting costs computed in L-C-S-T are based on only the harvesting functions considered in the optimization analysis (road construction, landing

construction, system move between landings, skidding, and trucking).

Hourly labor cost includes the base wage rate plus social security and

workmen’s compensation. Hourly equipment costs include fixed and operating

costs based on a scheduled hour. Miyata (1980) discusses fixed and operating

costs for timber harvesting equipment and provides several examples of the different methods available. The following equation reported by Nichols (1962)

is a simple rule-of-thumb method that can be used to determine the approximate

scheduled hourly cost of timber harvesting equipment used in L-C-S-T.

c= O.o003(P> (AN

. where: C = hourly equipment costs (excluding labor)

P = purchase price of equipment or purchase price of an equivalent

piece of new equipment

J

21

Appendix Z-Determining and Using Skidding Distances

Determining Skidding Distance

In L-O-S-T, a distinction is made between average skidding distance (ASD),

average travel distance (ATD), and fixed skidding distance (Figure I). ‘Ihe

equations developed by Suddarth (1952) for average skidding distance on simple

geometric shapes are shown in Figure II. Greulich (1980) extended this and

included the influence of slope on the equations he developed for average

skidding distance on areas with simple geometric shapes. For irregular shaped

areas, average skidding distance can be accurately computed using a desk-top

programmable calculator and digitizer (Peters and Burke 1972).

In most cases there is very little difference between the values obtained

for average skidding distance using the mathematical equations derived by

Suddarth (1952) and those obtained by determining the straight line distance

from the landing to the centroid of the area. For example, if the landing is

located at the corner of a mile square area, then the average skidding distance

computed by Suddarth’s equation is 4,040.23 feet. The straight line distance

from the landing to the centroid (2640,264O) of the area is 3,733.52 feet. A

simple graphical method for estimating average skidding distance on irregular

shaped areas is shown in Figure III.

While average skidding distance has an exact mathematical definition

(Suddarth 1952), its use, nevertheless, represents a simplification of the

skidding process. If average skidding distance is used, then all the trees on

the area are essentially assumed to be located an equal distance (average

skidding distance) from the landing. However, trees are scattered over the area

and skidding usually starts near the landing and proceeds to the farthest boun-
dary of the harvest area. A more accurate estimate of skidding cycle time can

be obtained by integrating the skidding equation (A31 over the range of

skidding distances. Similarly, using an average skidding cycle volume rather

than the range of cycle volumes causes equation A3 to underestimate

skidding times. In L-O-S-T, users have the options of using average values for

skidding distance and volume or their ranges. For simplicity reasons, the

simplifed version (A101 of the skidding equation will be used to illustrate the

integration procedures (All) available in L-O-S-T, given below.,

Y = travel empty time + travel loaded time + fixed time

1.022 1 .og8 0.11

Y= 0.0027(X) + 0.00088(x) (VI +K

where: Y = cycle tima in minutes for articulated, four-wheel drive,

rubber-tired skidders in the 70 to 130 horsepower range

X = one-way skidding distance in feet

v= cycle volume in board feet (14 Int.); must be reasonable for

skidder size and skid trail conditions (Table 1, Appendix 1)

K = assumed fixed time (minutes) per cycle for hooking, decking,

/

b 1.022 b d 1 .og8 0.11

Y = 0.0027 (Xl dx + 0.00088 (Xl (VI dxdv

b-a a (b-a)(d-c) a //c

+K

where: Y = skidding cycle time in minutes

a = lower limit on skidding distance in feet

b = upper limit on skidding distance in feet

- lower limit on skidding volume in board feet (WI Int.)

:I- upper limit on skidding volume in board feet ( l/411 Int. )

x = skidding distance, feet

v= skidding volume, board feet (l/4*’ Int. >

d x = derivative of Y with respect to X

d v = derivative of Y with respect to V

K= fixed time per cycle in minutes for hooking, decking, etc.

(A91

(A101

etc.

(All)

Actual Travel Distance

Due to terrain features (steep slopes, streams, rocks, soft ground) and to

stand characteristics (large stumps, dead snags), the distance actually traveled

by the skidder from the landing to the tis is rarely ever equal to the

24
straight-line value computed for average skidding distance. Koger ( 1976) found

that a correction factor of 1.86 was needed to adjust average skidding distance

to the actual travel distance. The user can supply this correction factor

(1.86) or one pertinent to area conditions through the input variable, AC

(card type 13, Appendix 5). In most cases, if some correction factor is not

used, skidding costs will be significantly underestimated.

Fixed Skidding Distance

In most cases an area (Figures lo-131 will not be adjacent to a landing.

The distance traveled by the skidder from the landing to reach the area boundary is referred to as the fixed skidding distance. This value must be calculated or estimated by the user and coded in the input data (variabale AF, card

type 13, Appendix 5).

: Actual pml distance 8

8I

’ Harvest Boundary

25

Figure I .--Relationship among average skidding distance, actual travel

distance, and fixed skidding distance
AVERAGE SKIDDING DISTANCE (ASD)

FOR SIMPLE GEOMETRIC SHAPES

CIRCLE (Suddorth 1952) CIRCULAR SEGMENT (Suddarth 1952)

RIGHT TRIANGLE (Suddarth 1952) ANY TRIANGLE (Peters 1978)

LandingRECTANGLEBuddarth 1952)

Where. In = natural log. base e : tan = tangent : arcton = arctangent

Figure II. --Average skidding distance equations for areas with simple

geometric shapes

26
MAP BOUNDARY

e---a

I<wR;S;----4

/’

\

I

I

I

:

I

?

BOUNDARY i

\

\

\

\ HARVEST \

\ AREA

\

t

i

'4, LANDING 1

----,- c-----------1, 0' -0)

SMALL PLUM BOB

STEP 1: DETERMINE HARVEST BOUNDARY AND

LANDING LOCATION.

STEP 2: SEPARATE HARVEST AREA FROM MAP

BY CUTTING ALONG HARVEST

BOUNDARY LINE.

STEP 3:MAKE TWO SMALL HOLES NEAR

MARGIN OF HARVEST BOUNDARY

(AGB). SEPARATE FROM LANDING

BY ABOUT l/3 BOUNDARY CIRCUMFERENCE.

STEP4: PLACE A NEEDLE IN HOLE AT LOCATION (A) AND MAKE SURE THAT

HARVEST AREA CUTOUT ROTATES

FREELY ABOUT THE NEEDLE AXIS.

ATTACH A SMALL PLUM BOB TO NEEDLE AND MARK PLUM LINE ON

CUTOUT. REPEAT THIS PROCESS AT

@CATION (8).

STEP 5: THE CENTROID -OF THE HARVEST

AREA WILL BE AT THE INTERSECTION OF THE TWO PLUM BOB LINES

(C). MEASURE THE DISTANCE FROM

POINT C TO THE LANDING WITH A

RULER. THIS DISTANCE MULTIPLIED

BY THE MAP SCALE WILL GIVE A

CLOSE APPROXIMATION OF AVERAGE

SKIDDING DISTANCE~ASD).

LANDING

Figure III.--Graphic method for determining average skidding distance

when landing is on boundary edge

27

Appendix 3-Harvesting Example Problem Method Assumptions

Table 5 .--Harvesting equipment assumptions

Equipment

Efficiency

Equipment Description Fat tor

crawler tractor (72 hp)* 0.70

rubber-tired skidder (70 hp)* 0.80

rubber-tired skidder (90 hp)* 0.85

tandem-axle truck (2 ton) 0.80

tandem-axle truck (2 ton) 0.80

knuckleboom loader* N A

repair truck* N A

Cycle Volume

<MQt Int. Bdft)

400 - 5:

420 - 550

1,800

2,000

N A

N A

Scheduled

Hourly

costs ($1 +

$21.63

19.05

22.30

19.50

20.50

13.00

8.50

+ includes $5.50 per scheduled hour for labor costs

* equipment involved in system move between landings

Table 6.--Road segment data

Road Road Road Constructed Sidehill Cut Fill Building

Section Length Width Slope Slope Ratio Ratio Difficulty

(feet> (feet> (%I

a- b 2: 3; -10 '1; )

(feet> (feet>

1.5 1.5 100

b -c -8 1 5 1.5

c- d

E

1 5 -10 1 2 1.5 1:;

150

100

d -e 1 5 -10 1 2 150

e- f 600 1 4 -8 1 0 1:; ::; 100

f

f-i1;

700 1 4 -10 8 1.5 1.5 150

650

1,250

12 13 -15 -12 20 15 ::5" ::: 100 100

i-j 1,650 1 2 -6 1 0 1.5 1.5 100

Table 7 .--Landing construction data

Method

Number

Landing

Code

Letter

Distance Average Equipment

From Depth Sys tern

Harvest Landing of Construction Move

Boundary Size cut Difficulty Time

(feet> (acres> (feet> Factor (hours)

1 A

2 A

2 .B

:

A

B

t

C

A

t

B

C

4 D

350 5

350 A:6

2,525 1.5

350 0.6

2,525 0.8

3,875 350 x

2,525 0:s

3,875 0.9

6,775 1.2

0.3 1.00 0 0

0.3 1.00 0:o

0.4 0.90 2.0

0:4 E

1.00 0.0

0.90 1.00 2.0 1.8

0.3 1.00 0.0

0.4 0.90 2.0

0.4 1.00 1.8

0.3 0.80 2.2

4

29
Table 8 .--Skidding data for method 1

Average Fixed Fixed

Area Area Skidding Skidding Trail Cycle

Landing Area Volume Size Distance Distance Slope Time

Code Code (Q+Ynt> (acres) (feet) (feet> (%I Onin>

A 1 65,000 26 485 0 5

A 70,000 28 1,005 265 ;

A

2

40,000 1 6 525 2,080

r:

A

7"

22,500

459

415 3,700 -5 3

A 8 go, 000 4,000 2 1,180 1,200 -10

2:

4,000 -8 9'

A 9 15,000 1 0 3,000 -10 1 1

A 1 0 12,000 8 285 4,950 -2 1 1

A 1 1 24,000 16 1,095 4,550 5 1 1

A 1 2:z 27,000 16,000 2 71 6 625 990 6,230 5,050 1 0 1:

A 15,000 1 5 570 8,000 5 13

A 1 8 26,000 1 3 520 5,740 1 5

A 2 1 30,000 1 5 1,095 5,050 1 2 ;

A 6,000 170 7,700 1 0

A 105,000 900 7,225 1 0 z

Table 9 .--Skidding data for method 2

Average Fixed Fixed

Area Area Skidding Skidding

Landing Area Volume Size Distance Distance 2;: Cyc1e Tim!

Code Code (WInt> (acres) (feet) (feet> ($1 bin)

A 1 65 000 26 0 5 7

A 23

82: 40

A 43 ; h; 265

B 22:500

1 6

9 :;

2,080 2 ::

1 0 7

B

ii

12,500 190

go"

1 2

B 7

10 :

B go, 000 4,000 4552 630 0 -2

285 CE

1,300 -8 i

i 15,000 990

12,000

10 8

24,000 16

1,680

-10 -10 11 11

B 11

B

::

16,000 16 YE

1,290 -2

1,780 5 1:

B 14 27,000 27 990 2,670 1 0

18

15,000 570 5,050 10 ;;

B 26,000 ;; 520 2,080 5

B 2 3”61g; 15 1,095 1,880 1 5 99

B 23 105:OOo 3: 900 170 3,660 4,260 1 01 2 5"
Table 1 0 .--Skidding data for method 3

Average Fixed Fixed

Area Area Skidding Skidding Trail Cycle

Landing Area Volume Size Distance Distance Slope TiUE

Code Code (WInt) (acres> (feet) (feet) (46) Onin)

A 1 65,000 26 485 0 5

A 57,500 23 820 265

::

A t 40,000 1 6 525 2,080 2 7

B ii 22,500 12,500 ; 415 '90 iii: 1 01 2 s

BB ii go, 000 4,000 452 630 zz; 1,3000 -2-8 ;

B 9 15,000 10 990 -10 1 1

C 1 0 12,000 8 285 790 -10 1 1

C 1 1 24,000 1 6 1,095 -2 1 1

C 1 2 16,000 1 6 625

30:

5 13

C 13 27,000 27 990 1,390 1 0 13

C 1 4 15,000 570 3,660 1 0 13

C 18 26,000

1;

C 2 1 30,000 1 5 1,095 520 790 30 1: x

CC 2223 105,000 6,000 3: 900 170 2,480 2,870 1 21 0 z

Table 11 .--Skidding data for method 4

Average Fixed Fixed

Area Area Skidding Skidding Trail Cycle

Landing Area VoluuE? Size Distance Distance Slope TiltE

Code Code (WInt) (acres) (feet) (feet) (%I bin)

A 1 65 000

;p;

26 405 0 5 7

A

2

23 820 265

A 16 2,080 ;

B

B ii

22;500

E y;

12,500 ii '90 iii: 1 2 ::

B ii go,ooo 4,000 452 630 1,3000 2 ;

B 9 15,000 1 0

1,095 g;

990 -10 1 1

: 10

1:

24,000 12,000 16 8 790 0 -10 -2 1 1

C 6,000 6 490 :;

C

:;

10,000

37

270

z: 1;

D 37,000

zii:

500 1:

D 17 15,000 1; 13

DD 202 1 30,000 16,000 '21 5 1,170 335 2,noO200 43 x

D 2223 105,000 6,000 3: 720 170 2,820 150 z

Appendix 4-Equipment Specifications

Table 12 .-Equipment horsepower and weight characteristics

for selected crawler tractors

Equipment

Make &Model

Case 350

450

850

1450

Caterpillar D"f-;;

D5-DD

D6-DD

John'Deere JDJD;$

JD550

International TD-7EPS

TD-8E-PS

TD-15c-PS

Kormtsu D'+5A-1

zz

Massey-Ferguson MFE

MFSWB

Equipment

Horsepower

(net engine)

3 9

z

130

FE

105

140

z;

72

65

7 8

140

90

110 140

65

85

136

Equipment

Weight

(bare, pounds)

%O 05

13:OOo

23,800

l~,~O

13,990

19,200

24,000

8,160

11,600

12,300

10,459

13,834

24,153

18,340

22,200 28,220

14,700
Table 13 .--Equipment horsepower and weight characteristics for

selected rubber-tired skidders

Equipment

Make & Model

Athey S-97D

Caterpillar 518

528

Clark Ranger 664B

666~

. 668~

Equipment Equipment

Horsepower Weight

(net engine) (bare, pounds)

9 7 l6,250

120 20,400

175 28,300

82 15,890

112

166

17,855

24,480

Franklin 531

132

170

185

International ~8

John Deere JD440-B

JD540-A

JD640

JD'i'40

io” 12,000

17,840

112 18,740

775 24,140

86 13,100

'9::

12,250

16,150

110

145

19,900

26,700

Pettibone 100 93 14,950

Timber Jack 208D 67

225

12,300

92 12,784

Tree Farmer C5D 90

C6D

15,890

120 18,180

34
Appendix &Data Card Types

The following 17 data card types are used in L-O-S-T to describe organized

input data for the harvesting methods, areas, road segments, landings, and

equipment. Unless otherwise stated, all input data is to be right justified.

Input variable names beginning with INTf3GER letters (I,J,K,L,M, or N) do not

require decimal points. Input variable names beginning with REAL letters (A-H,

& O-Z) do require a decimal point in the input field location shown. Although

harvest volume units of pounds, l/4” Int. board feet, cubic feet, or cords may be

used, once a unit has been selected it must be used throughout the analysis.

The input data for the harvesting example shown in Appendix 6 should be used

to supplement the data card type descriptions given below.

Card Type 1: (required; one card)

64 cc

/-I ATITLEO harvesting problem title --_I- w-w

Card Type 2: (required; one card)

2 cc

'-'

5 cc

u

NDZR

7 8cc

/// NSKD - -

10 11 cc

/// NTRK - -

13 cc

/-I ICTRAT

15 cc?

l-1

17 cc

/,I,

ILPANA

LPCDE

number of methods analyzed

(minimum of 2 and a maximum of 4)

number of crawler tractors (l-5)

number of rubber-tired, cable skidders

(l-10)

number of trucks (l-10)

number of user supplied constraints

(O-4); allows limits on number of

hours permitted for harvesting

functions considered

linear programming option code:

= 0 if linear prograazning analysis

is performed

= 1 if linear programming analysis

is not performed

= 0 if no intermediate matrices are

printed; the normal case

= 1 if intermediate matrices are

printed; is helpful in understanding

sensivity analysis

36
Card Type 3: (squired; one card)

1 cc

/-,

/3/ / / / / / / / /

12 cc

,--------I/

1 4 18 mcc

/------- / / / /./ / /

26 28 cc

12?----A-- / / / / / /

35 cc ,3; / / / /

,--AIUNIT

HARVOL

PRODPC

SYSMHC

DFTBTM

Type 4: (required; one card for

4 cc

/'/---A/ / /

6 9 cc

1---- /./ / /

14 16

/'J-,-I-, / / / / /

; NDZR cards required;

each crawler tractor building roads

cards adjacent)

DZRHPO net horsepower of crawler tractor;

(Table 12, Appendix 4)

DZREFO crawler tractor efficiency (ie. 0.80)

cc

DZRHCO hourly crawler tractor and operator

cost ($/hr)

Type 5: (required; one card for

cards adjacent)

4 cc

/'/---I/ / / XDHPO

11 cc

/T----,A / / / / / smwT( 1

/7 / /

16 cc

-I,-/ SUXFO

36

unit code for volume;

= 1 for pounds

= 2 for 1/4" Int. board feet

= 3 for cubic feet

= 4 for cords

total volume of harvested timber

in same units as coded for IUNIT

selling or delivered price in normal

selling units tie. $/l,OOO board feet)

hourly cost ($/hr) to move pertinent

equipment to the next landing; not an

hourly move-in cost

distance in miles from mill to'harvest

boundary or start of constructed woods'

roads (can be zero if analyzing trucking

within harvest boundary)

each skidder; NSKD cards required;

net skidder horsepower;

(Table 13, Appendix 4)

weight of unloaded skidder in pounds;

(Table 13, Appendix 4)

skidder efficiency (ie. 0.75)
1 8 21 23 cc

/_I----- / / /./ / / s(DHC ( ) hourly skidder and operator cost ($/hr)

Card Type 6: (required; one card for each truck; NTRK cards required;

cards adjacent); note: travel speeds must be > 0.

A / /

4 cc

--L-/

6 9 cc

/_I--- / /./ /

14 cc

1’:m-z-/ / /

1 6 19 cc

/--c- / /./ /

,‘: / /

24 cc

,-A-/

26 29 cc

/ /./ / /

--we

3 1 38 40 cc

/_)--------- / / / / / / /./ / /

42 45 47 cc

/m-m--- / / /./ / /

lKTENw( >

llmAJw( >

TKTEMD()

TKTLWDO

TKPTPC ( )

TKEFO

TKVOL( )

TKHCO

empty truck travel speed in mph over

non-woods road (Table 2, Appendix 1)

loaded truck travel speed in mph over

non-woods road (Table 2, Appendix 1)

empty truck travel speed in mph over

woods road (Table 2, Appendix 1)

loaded truck travel speed in mph over

woods road (Table 2, Appendix 1)

fixed time per cycle in minutes; can

include delays, stops for fuel, etc.

truck efficiency (ie. 0.80)

average truck volume (Tables 3 & 4,

Appendix 1); same units as IUNIT in

card type 3

hourly truck and operator cost ($/hr)

ad type 7: (required; one card for each method; NMETH cards required;

cards adjacent)

1 cc

lJ IMmio method number (l-4)

4 cc

//I - -

IRDSEG() number of road segments for this method

(O-20)

7 cc

Li ILANDN() number of landings for this method

(1-N

Type 8: (required; one card for each landing for each method;

cards adjacent)

method number--not number of methods

(l-4)

3 7
4 cc

‘-’

7 cc

///--

10 cc

/// - -

JNA

Card Type 9: (required; one card)

1 cc

'-'

m-~-A me-- 4n- I---..1 -e-i. l;ara lype IV; (reyurreu; UIlt: --- USI-u ---2 O-- LUI each road segment for each method;

cards adjacent)

1 7 cc

/----m-s / / 1 / / 1.1 ROAJXL length of road segment in feet; if

there are no road segments code a

0 (zero) in card coluum 6 and then

skip other variables on this card type

landing number--not number of landings

(l-8)

number of areas for this landing

(l-25); not area code number

maximum value of any area code number

for this landing; is equal to JNA only

if areas are numbered consecutively

control card which follows the last

card type 8 and must have a 0 (zero>

coded in card column 1

9 12 cc

/---- / 1.1 1

14 18 cc

/---me / / 1 1.1

ROADSW

ROADSP

20 24 cc

/---we / / / 1.1 ROADSS

26 28 30 cc

/--a-- / /./ / / ROADCR

32 34 36 cc

/----- / /./ / / ROADFR

38 42 cc

/--m-w / / / /./ ROADTY

segment road width in feet

percent slope (+,-I or road segment in

direction of construction

percent slope

adjacent road

(+ only) of side-hill

cut ratio; rise in cut per 1 foot of

base (ie. 1.50)

fill ratio; drop in fill per 1 foot of

base (ie. 1.50)

road construction difficulty code;

= 10 for road constructed under

adverse conditions or for high volume

truck traffic

= 500 for road constructed under average

conditions

= 1000 for road constructed under

favorable conditions

38
= 2000 for road constructed under

very favorable conditions, or the

up-grading of an existing road

= 3000 for landing constructed under

average conditions

note: intermediate values (ie. 520, 760)

can be used; trial and error

techniques may be required to obtain

desired or expected times and costs

Card Type 11: (required; one card)

1 cc

/.l ILDZR input order number of crawler tractor

in card type 4 that will be used to

construct all landings (ie. if the

second crawler tractor in card type 4 is

used, then code a 2 in card column 1);

only one crawler tractor is permitted

to construct landings

Card Type 12: (required; one card for each landing for each method; cards

adjacent; input all landings for first method, then all

landings for second method, etc.)

DSFTBO distance in feet this landing is from

harvest boundary as measured along

woods road

13 cc

,'"/ - -/JJ ACRESL landing size in acres

15 18 cc

/ / /./ /

----

20 23 cc

/e--w/./ / /

CUTL

EFFL

average depth in feet of earth removed

in constructing this landing

landing construction difficulty factor;

must be greater than 0.0; suggest:

= less than 1.00 for difficult sites

= 1 .O for average sites

= greater than 1 .O for favorable sites

29 cc

,‘F,,-I- / / / / SYSMHR number of hours required to move

equipment to this landing; not a move-in

time, but a system move between landing

time; should be 0 (zero) for the first

landing

Card type 13: (required; one card for each area for each method;

cards adjacent)

1 cc

lJ method number

39
3 cc

'-'

5 cc

/// - -

6 14 cc

/ / / / / / / / /./ ---------

1 5 20 cc

/ / / / / /./

------

21 28 c~

/

-------- / / / / / / 1.1

36 cc

/"9/ ,,-----A / / / / / /' /

3 7 44 cc

/ / / / / / / /./ --------

46 48 50 CC

/--m-B / /./ / /

56 cc

/5'/ ,---' / / / /

58 61 cc

/---- /./ / /

ILN

IAN

A C

landing number

area code number

area volume in same units used for

variable IUNIT in card type 3

area acres

average or minimum skidding distance in

feet for this area; if AN=AX (next

variable) average skidding distance

option is assumed and skidding time

is not based on integration (dx)

average or maximum skidding distance in

feet for this area; if AX=AN (last

variable) average skidding distance

option is assumed and skidding time

is not based on integration (dx)

fixed skidding distance in feet from

landing to start of harvest area; is 0

(zero>. if landing is located on edge or

inside of harvest area; this is actual

travel distance and not straight line

distance (Figure I, Appendix 2)

correction factor adjusting straight

line skidding distance to actual

distance traveled by skidder inside an

area; suggest 1.86; use 1.00 for no

correction

slope of skid trail (+,-> in percent,

measured in travel loaded direction

difficulty factor code used to

provide more sensitivity for actual

skidding conditions on each area; can

be used to model increased skidder

interactions, multiple skidders on

small areas, or adverse skidding

conditions;

= less than 1 .OO for adverse skidding

conditions or high skidder interaction

= 1.00 for average skidding conditions

and no significant skidder interaction

= greater than 1 .OO for very favorable

skidding conditions and no skidder

interactions

40
63 66

/ / /.//

-B-v

C C

AT average fixed skidding time per cycle in

minutes (ie. hooking, unhooking, decking)

Card Type 14: (required; one card)

1 cc

Li control card which follows the last card

type 13; must have a 0 (zero> coded in

card colufi

Card Type 15: (required; one card for each method, for each landing, for each

area, for each skidder; cards adjacent)

1 cc

1-1

4 cc

/-I

KM method number ( l-4)

KL landing number (l-8)

7 cc

/// - - K A area code number; same as IAN in

card type 13 8

10 cc

/// - - KS skidder input order number; must be in

same sequence as coded in card type 5.

20 cc

/%//////// --------A- SKVMN average or minimum volume skidded per

cycle; if SKVMN=SKVMX (next variable)

average skid volume is assumed and

skidding time is not based on

integration (dv); volume ranges (Table 1,

Appendix 1); volume must be in same

units as used for variable IUNIT in

card type 3

/‘:--------A- / / / / / / / ,#: cc

SKVMX average or maximum volume skidded per

cycle; if SKVMX=SKVMN (last variable)

average skid volume is assumed and

skidding time is not based on

integration (dv); volume ranges

(Table 1, Appendix 1); volume must be in

same units as used for variable IUNIT in

cat-d type 3

Card Type 16: (required; one card for each landing for each method; cards

adjacent)

1 cc

l-1

4 cc

/-I

ITMN

ITLN

mathod number (l-4)

landing number-( l-8)

41
6 9 cc

/

---- /./ / / TKTVCF truck speed correction fat tor ; ref lee ts

change in truck travel speed as a

function of distance traveled over

woods road; ratio of ending travel speed

on woods road to beginning travel speed

on woods road; a value of 1.00 would

indicate the use of average travel speed

Card Type 17: (optional; use only if adding constraints for number of hours;

use only if value of ICTRAT in card type 2 is greater than zero;

one card required for each constraint; cards adjacent; most

often used after one computer analysis has been made without

upper bound constraints; upper bound values are usually not

know in advance of an initial unconstrained analysis

1 cc

/-I

I31 / / / / / /

10 cc

-,--,--A/

ICSTFO constraint code:

= 1 if supplying upper bound on road

construction hours

= 2 if supplying upper bound on landing

construction and system move hours

= 3 if supplying upper bound on skiding

hours

= 4 if supplying upper bound on trucking

hours

upper bound value of constraint in hours

4 2
Appendix 6-Harvesting Example Problem Input Data

HYPOTHETICAL HARVESTING EXAMPLE: 4 METHODS

4 12 2201

2 567500. 95.00 50.63 30.5

72. 0.70 21.63

70. 14175. 0.80 lg.05

90. 16675. 0.85 22.30

34.0 28.0 8.3 5.3 15.0 0.80 1800.00 lg.50

34.0 26.0 8.3 5.0 15.0 0.80 2000.00 20.50

111

2 5 2

3 7 3

4 9 4

1 11623

213 4

2 21423

3 13 4

3 2 5 9

3 3 923

413 4

4 2 5 9

4 3 419

4 4 623

0

350. 15.0

350. 15.0

450. 15.0

325. 15.0

800. 15.0

600. 14.0

350. 15.0

450. 15.0

325. 15.0

800. 15.0

600. 14.0

700. 14.0

650. 13.0

350. 15.0

450. 15.0

325. 15.0

800. 15.0

600. 14.0

700. 14.0

650. 13.0

1250. 12.0

1650. 12.0

1

-10.

-10.

-8.

-10.

-10.

-8.

-10.

-8.

-10.

-10.

-8.

-10.

-15.

-10.

-8.

-10.

-l"ai

-10:

-15.

-12.

-6.

10. 1.50 1.50 100.

10. 1.50 1.50 100.

15. 1.50 1.50 150.

12. 1.50 1.50 100.

12. 1.50 1.50 150.

10. 1.50 1.50 100.

10. 1.50 1.50 100.

15. 1.50 1.50 150.

12. 1.50 1.50 100.

12. 1.50 1.50 150.

10. 1.50 1.50 100.

8. 1.50 1.50 150.

20. 1.50 1.50 100.

10. 1.50 1.50 100.

15. 1.50 1.50 150.

12. 1.50 1.50 100.

12. 1.50 1.50 150.

10. 1.50 1.50 100.

8. 1.50 1.50 150.

20. 1.50 1.50 100.

15. 1.50 1.50 100.

10. 1.50 1.50 100.

350. 1.5 0.3 1.00 0.0

350. 0.6 0.3 1.00 0.0

2525. 1.5 0.4 0.90 2.0

4 3
350.

2525. ;.i

o:g

;.;

0:4

;A;

0.0

3875. I:OO

2.0

1.8

6775. 1.2 0.3 0.80 2.2

1 1 i112

114

115

1 1 '7

118

119

1 110

1 111

1 112

1 113

1 114 I 118

1 121

1 122

1 123

211 3

225

226

227

228

229

2 210

2 211

2 212 ; %

2 21E

2 221

2 222

2 223

311

313

314

325

326

;zi ; ;1: 3 311 3 312 ; $43 3 318 3 321 3 322 3 323

65000.

70000.

40000.

22500.

90000.

4000.

15000.

12000.

24000.

16000.

27000.

15000.

26000.

%i: l

105000:

65000.

zEt*

22500:

12500.

90000.

4000.

15000.

12000.

24000.

16000.

27000.

15000.

26000.

3Ei*

105000:

65000.

zE*

22500:

12500.

g:::i*

15000:

12000.

24000.

16000.

27000.

15000.

26000.

?E*

105000:

26.

28.

16.

4;:

2 .

10.

8 .

16.

ii?

15.

13.

15.

2 .

2:

23.

16.

59:

45.

2 .

10.

8 .

16.

16.

27.

15.

13.

15.

2 .

2:

23.

16.

;:

45.

2 .

10.

8 .

16.

16.

27.

15.

:;:

3::.

485.

1005.

525.

415.

1180.

z?

285:

1095.

625.

990.

570.

520.

1095.

170.

900.

485.

820.

z:;*

190:

630.

z;*

285:

1095.

625.

990.

570.

520.

1095.

170.

I2

820.

525.

415.

190.

630.

z;*

285:

1095.

625.

990.

570.

520.

1095.

170.

900.

485.

1005.

525.

415.

1180.

Go5:

285.

1095.

625.

990.

570.

520.

1095 l

170.

900.

485.

820. E

190:

630.

F-E:

285.

1095.

625.

990.

570.

520.

1095.

170.

900.

485.

820.

525.

415.

600.

630.

2255'

285:

1095.

625.

990.

570.

520.

1095.

170.

900.

0.

265.

2080.

3700.

1200.

4000.

3000.

4950.

4550.

5050.

6230.

8000.

5740.

5050.

7700.

7225.

0 .

265.

2080.

990.

600.

0 .

1300.

990.

1680.

1290.

1780.

2670.

5050.

2080.

1880.

3660.

4260.

26;:

2080.

990.

600.

0.

1300.

990.

790.

3000:

1390.

3660.

790.

300.

2480.

2870.

1.9 5. 1.00 7.0

1.9 -2. 1.00 7.0

1.9 -3. 1.00 7.0

1.9 -5. 1.00 7.0

1.4 -10. 1.00 9.0

1.4 -8. 0.90 9.0

1.4 -10. 1.00 11.0

1.4 -?. 1.00 11.0

1.4 +5. 0.95 71.0

1.5 +10. 0.85 13.0

1.5 +lO. 0.90 13.0

1.5 +5. 0.90 13.0

1.5 +15. 0.80 9.0

1.7 +12. 0.90 9.0

1:; +lO. 1.00 1.00 5.0 5.0

1.6 5 . 1.00 7.0

1.6 5. 1.00 7.0

1.6 -3. 1.00 7.0

1.6 10. 1.00 7.0

1.6 12. 1.00 7.0

1.6 -2. 1.00 9.0

1.6 -8. 1.00 9.0

1.6 -10. 1.00 11.0

1.4 -10. 1.00 11.0

1.4 -2. 1.00 11.0

1.4 5. 0.95 13.0

1.4 10. 0.85 13.0

1.9 10. 0.90 13.0

1.5 5. 0.90 9.0

1.5 15. 0.80 9.0

1.5 12. 1.00 5.0

::; 10. 5. 1.00 1.00 7.0 5.0

1:; -3. 5. 1.00 1.00 7.0 7.0

1.6 10. 1.00 7.0

1.6 12. 1.00 7.0

1.6 -2. 1.00 9.0

1.6 -8. 1.00 9.0

1.6 -10. 1.00 11.0

1.7 -10. 1.00 11.0

1.7 -2. 1.00 11.0

1.7 5. 0.95 13.0

1.7 10. 0.85 13.0

1.8 10. 0.90 13.0

1.8 5. 0.90 9.0

1.8 15. 0.80 9.0

1.8 12. 1.00 5.0

1.8 10. 1.00 5.0

44
411 65000.

4 1 3 57500.

414 40000.

EZ 22500- 12500.

427 90000.

428 4000.

429 15000.

4 310 12000.

4 311 24000.

4 315 6000.

4 319 10000.

4 416 f7xItI.

4 417

4 420 16000:

4 421

4 422 3Ec4 423 105000: 0

1111

1112

1121

1122

1141

1142

1151

1152

1 1 7 1

117 2

I 181

118 2

1191

1192

1 110 1

1 110 2

1 111 1

1 111 2

1 112 1

1 112 2

1 113 1 : :1::

1 114 2

I 118 1 1 118 2

1 121 1

1 121 2

1722 1

1 122 2

1 123 1

1 123 2

2111

2112

2131

213 2

2141

214 2

26.

23.

16.

59:

45.

2 .

10.

8 .

16.

6.

n5:

15.

8 .

15.

3;:

400.

460.

450.

:;:-

470:

450.

z-.

E:

420.

510.

550.

Et

Fig:

490:

450.

490.

450.

490.

450.

go"-

490:

450.

490.

450.

490,

400.

460.

450.

470.

450.

470.

485.

820. E

190:

630.

ZE285:

1095.

490.

270.

900.

450.

335.

1170.

170.

720.

2:

450.

:::-

;;i$ : g :.

?i::

420.

510.

550.

$2

~~:

450.

490.

450.

490.

450.

490.

450.

490.

450.

490.

450.

490.

450.

490.

E:

450.

470.

450.

470.

485. 0. 1.9 5. 1.00 7.0

820.

600.

265.

600.

630. 0.

285: zz;-

1300.

2::- .

790. 990.

1095.

2080. 990. , 0.

490. 300.

270. 790.

900. 500.

450. 0.

1.6 12.

1.4

1.00

5.

7.0

1.6

1.00

-2.

7.0

1.00 9.0

1.9 1.6

1.6

-3. 10.

-8.

1.00 1.00

1.00

7.0 7.0

9.0

1.6 -10. 1.00 11.0

1:; -10. -2. 1.00 1.00 11.0 11.0

1:; -5. -5. 0.95 0.90 13.0 9.0

::; -4. -5. 0.90 13.0 13.0

335. 2370. 1.5

1170. 200. 1.5

li0. 2820. 1.5 4 . 1.00 5.0

720. 150. 1.5 6. 1.00 5.0

4 5
2 2 51

2 2 5 2

2 2 61

2 262

2 271

2 272

2 281

2 282

2 2 91

2 29 2

2 2101

2 210 2

2 211 1

2 211 2

2 212 1

2 212 2

2 213 1

2 213 2

2 214 1

2 214 2

2 218 1

2 218 2

2 221 1

2 221 2

2 222 1

2 222 2

2 2231

2 223 2

3111

3112 3 1 3 1

31 32 3 1 4 1

3142

3 2 51

'3 ; 56 :

3 2 6 2

3 27 1 ; ; ii :

3 2 8 2 3 2 9 1 3 2 9 2 3 310 1 3 310 2 3 311 1 3 311 2 3 312 1 3 312 2 3 313 1 ; ;143 : ; ;:i : 3 318 2 3 321 1

4 6

400.

420.

400.

420.

460.

Ek

420.

510.

550.

460.

490.

Z:

450.

490.

450.

490.

450.

490.

450.

490.

450.

490 l

450.

490.

t/g

400:

460.

450. E

470:

400.

420.

400.

420.

460.

E?

420:

510.

550.

460.

490.

g::

450.

490.

450.

400.

420.

400.

420.

460.

Eii:

420.

510.

550.

460.

490.

500. E

490.

450.

490.

450.

490.

450.

490.

450.

490.

450.

490.

:5:*

400:

460.

450.

z;;*

470:

400.

420.

400.

420.

460.

E:

420.

510.

E:

490.

2%

450.

490.

450.

490.

450.

490.

450.

490.

450.
3 321

2

3 322 1 3 322 2 3 323 1 3 323 2

4 111

4 112

4131

413 2

4141

474 2

4 2 5 1

4 2 5 2

4 2 61

4 2 6 2

4271

zx:

4 2 8 2

4 29 1

4 292

4 310 1

4 310 2

4 3111

4 311 2

4 315 1

4 3152

4 319 1

4 3192

4 416 1

4 416 2

4 4171

4 417 2

4 420 1

4 420 2

4 421 1

4 421 2

4 422 1

4 422 2

4 423 1

4 423 2

1 1 0.95

2 1 0.95

2 20.90

3 1 0.95 ; : :*g

4 1 0:95

:: : ti%

4 4 0:80 :

120.0

600.0

//

490.

450.

490.

450.

450.

400.

460.

450.

470.

450.

470.

400.

420.

400.

420.

460.

500.

400.

420.

510.

E:*

490:

%:

450.

490.

420.

470.

430.

460.

440.

480.

450.

490.

490.

520.

450.

F$*

510:

490.

450.

490.

E*

400:

460.

450. E

470:

400.

420.

400.

420.

460.

ZC:

420.

510.

550.

460.

490. 2

450.

490.

420.

470.

430.

460.

440.

480.

450.

490.

490.

520.

450.

E:

510.

47

Appendix LHarvesting Example Problem Output Data

TITLE 14-S-T RUN= HY”OTHETICA1 HARVESTING EXACPLE: 4 HETHCOS

NUUBER OF RETHODS= 4

NUMBER OF r)DZERS= 1

NUMlER OF SKIDOERS= 2

NUMBER OF TRUCKS= 2

LP ANlrlYSIS CODE= 0

LP CUTf’UT CODE= 0

a USER CCNSTRAIMS= 2

HARVEST VOLUME’= 567500. INT. BOARC FEET

PRICE IN SELLING UNITS (St= 95.00

HOURLY LANDING POVE COST fs)= 50.t3

DISTAYCE F”OM WOODS EDGE TC FILL I%tILES)= 39.5

*,*********t********+**********

DOZE’? EOZEP DOZER W-NJRLY

LUMBER UP EFFIC COST

1 72. 0.70 21.63

t***~**k**f*i*~***+***+t*++L*

21.63

***+*,*******r**i************************$*********

SKI!lDER

SKIDDER SK IODER SKII?DER SKIOOER Hawit

vU*RFp WORSF~DWER WE I GHT CFFIC COST

: 90. 70. 16675. 14175. o.es G.80 22.30 19.05

*+*****+********+**********************************

41.35

*++*****+ t** ***+***o******************************************************

** fl(lf+WOODS ** ***** yf.lQljs  

TRAVEL TRAVEL TRaVEl TRAVEL F IXFD

FM”TY LOAOEO Et4pTY LOdOE T IrlC CYCLE TRUCK

TP{JCK SPEED SPEED SPEED SPEED FER ‘IRUCY 1 RUCK HOURLY

NUHR ER NPH H=H N@H WH I.040 EFFIC VolUnE cos 1

: 34.00 34.00 26.00 28.03 8.30 6.30 5.003lJ 15.00 15.00 o.ao 3.83 2GO0.W’ 1800.00 20.50 19.56

** ***+**t +** ***************+***************************************

40.00

49
NUMBER NUMBER

NETHOO ROAO O F

NVNBER SEG”ENTS LANDINGS

1 1

2 5 :

3 I 3

4 9 4

,F,*BE9

YFTHO!, LANDING O F *4xiriJ* 4REA

NUYBFR NUWER AREAS CGCE hUWeER

RObC OCbC

YIOTI! SLCFE

CUT FlLL aCAD

ZLCPE SLOFE 7YFE

RAT10 OATJO CCDF

13.c -JO. I”. I.50 1.50 lOi?.

13.0 -JO. JO. 1.30 1.30 lC3.

J3.0 -9. J5. 1.30 1.52 130.

J3.0 -JO. 12. 1.50 1.50 Inn.

15.0 -13. JZ. 1.30 1.50 130.

14.0 -e. JO. 1.50 1.50 100.

15.0 -JO.

13.3 -3.

1s.u -10.

15.0 -JU.

14.0 -e.

14.0 -JO.

13.u -15.

JO.

15.

:::

10.

a .

20.

1.33 1.50 100.

1.50 1.50 150.

1.30 1.3a 1ro.

1.3” 1.30 13”.

I.50 1.5r) 100.

1.50 1.30 150.

1.50 1.50 LOO.

JS.0 -10.

J3.C -e.

J5.J -10.

13.0 -10.

14.0 -2.

14.3 -JJ.

13.0 -1s.

12.0 -12.

12.0 -6.

10.

15.

12.

12.

JP.

2::

:::

1.50 1.5tl 100.

1.50 1.50 130.

1.50 1.30 100.

1.W 1.50 150.

1.30 1.30 100.

1.30 1.30 150.

1.50 1.50 1p.

1.30 1.50 lQ0.

1.53 1.30 100.

CUBIC ACFES SEGNEPlI

Vl“DS CLLAFFP HOURS

46.9 0.J 1.9

46.9 0.1

170.177

7.9 173.n7

7.8 lOY.JU

7.1 167.38

12.7 274.t.r

13.0 286.23

7.9

7.n

7.7

12.7

13.0

1:::

170.07

169 .oo

167.38

274.67

280.23

202.73

360.69

::I: 7.1

12.7

1J.U

63.J 0.3 9.4

138.8 n.7 16. r

176.3 0.4 27.1

141.3 0.3 32.3

943.3 2.6

J70.07

169.W

167.38

274.61

280.23

202.73

340.69

3a7.16

698.43

METMOO HC-lkol~

HOUPS LGSl

1.9 170.

I

2

330.

450.

223.

ROD.

600.

2525.

46.9

99.2

54.2

1 :::

1

7

3

‘

C.1

0.3

0.2

1.0

133.3

rn.n

403.6

3

49.1 IOaJ.

33’1. 46.9 0.1

95.2 0.2

54.2 (1. 1

133.3 G-5

70.0 0.2

e3.J 0.3

138.8 0.3

623.5 1.6

J

2

3

‘

?25.

3QO.

600.

7PO.

,553.

7473.

5

6

I

73.1 1ci3.

350.

&WI.

‘0.9 0. I

0.2

0. J

0.3

0.2

c

4

__.

99.2

34.2

133.3

iis:

300.

690.

703.

650.

1230.

1430.

6113.

4

4

e

‘

4

5 70.5

6

I

3

P

1

4

4

4 134.6 ZYJO.

60
Cl SIIKCC “““I’mz Clvenrct HCUPLl CALCING 1IYflIMG S7SlfP rvstcli :::t:::

airrciw

wvt c

*ETwPfI LAuntNG IRlW CUT OCZEl OOZER EFFIC BUILOIYG OUILOlkG WOVE

rdups

COVE L WVING

NIJWEA NWRER nolJwYA~V ACRES OEPlh “F CCST COCE CPSl halYf CDS1 HOUP s ‘““X

: I 1%. 1.q 0.3 II. 21.63 1.an Z.bQ 56.27 4.P u.00 3.71 SO.27

2 1 YSQ. 0.6 0.3 72. 21.63 I .oo 1.04 22.51 0.0

2 2 2525. 1.5 (1.4 72. 21.63 O.yO 3. IF b7.13 2.0

2 2.b4 ‘90.90

3 1 15’1. c.15 0.3 72. 21.63 1.00 l.U4 22.S‘ 0.0 0.W

3 ? 2szs. 0.8 C.4 72. 21.63 0.u 1.66 35.QO 2.Q IO‘.26

3 Y 3875. 1.5 0.4 72. 21.63 1.00 2.19 40.42 1.0 PI.13

1

2

:

0.b c.3

0.3 G.4

0.5 0.4

1.2 0.3

4.31 311.13

72. 21.t3 1.00 1.04 22.51 0.0 0.W

72. 21.6’. 0.9Q 1.bt 35.QQ 2.0 ‘01.2b

I?. ‘1.63 I.&B l.CC 34.23 91.13

72. ,?I.*? 0. P9 2.eo 54.27 1‘1.39

4.29 4Y4.62

NETtMn

NlJWRF~

:

:

:

:

1

:

:

1

:

:

:

:

:

:

2

:

:

:

:

3

:

:

3

:

3

:

:

3

3

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

lANolNG

WmfP

t

:

:

I

:

:

I

:

I

:

:

2

:

2

:

2

2

2

2

1

:

7

:

:

f

:

:

3

3

I

3

1

:

1

:

?

2

2

2

2

3

3

1

1

4

I.

4

4

4

4

PRE A

PUnaEC

I

2

4

5

7

s

9

I**

::

::

::

::

:

4

5

b

7

i

:t

12

::

18

21

.? :

a3

:

‘

5

6

1

I

1:

II

12

13

::

21

2?

23

1

3

4

5

;

9

1::

1‘

:;

::

20

2 ‘

23

23

ACEA

vl?Lu*E

bSQ10.

70000.

4wno.

22500.

9ooon.

4000.

1 SO00 .

IPQOO.

24noa.

1aono.

21CGO.

1 sooo.

ztloon.

3GQGG.

LOCO.

105nn0.

CSOQO.

57500.

40030.

ZZYW.

‘2SOQ.

WOOF.

4000.

15000.

12000.

24000.

IbCW.

270~10.

15000.

26009.

wnoo.

4QQO.

lQ!iO7Q.

b$QOi’.

57!!00.

4OOr)G.

?ZYw.

12’00.

WCJO.

4GW.

1 sow.

12EW.

24C00.

16000.

27Qnn.

1 SW?.

26039.

?CFOO.

bOOtI,

‘OWW.

65000.

~75’)O.

40030.

22son.

12500.

WOQG.

4000.

15080.

12000.

24000.

bO9Q.

lGO’)O.

37oon.

15000.

1bOCO.

3ccon.

6000.

10s000.

AREA

ACPES

2t.

20.

le.

9 .

45.

1::

e .

le.

:‘;:

IS.

Ii.

‘5.

3::

:::

It.

9 .

3.

45.

1::

1::

:::

IS.

13.

IS.

3;:

:::

lb.

5.

Y.

45.

1;:

2".

lb.

27.

‘3.

13.

IS.

2 .

33.

zt.

33.

it.

5 .

5 .

43.

,r:

1::

t .

5.

31.

IS.

a.

‘5.

2.

3s.

*INIKC* MAXIPW

SKICCING SKICOING

UISTAYCE OISTAhCE

415.

WJS.

s25.

415.

IIRO.

275.

F4Q .

285.

109s.

625.

590.

575.

520.

1095.

110.

9-m.

4e5.

C20.

52s.

41s.

‘90.

630.

PTS.

445.

267s.

1095.

621.

990.

570.

520.

IGaS.

‘70.

900.

495.

czo.

525.

415.

190.

t30.

27S.

445.

235.

1095.

tzs.

WV.

L70.

520.

‘095.

l7C.

Ma.

4ns.

etrl.

52S.

415.

190.

b30.

275.

445.

205.

1095.

49G.

no.

WV.

450.

335.

1170.

170.

120.

4CI.

1005.

S2S.

415.

Itan.

27s.

840.

2e5.

1095.

425.

990.

5-m.

‘120.

1095.

‘IO.

900.

4er.

820.

52s.

43s.

‘90.

630.

275.

445.

2Q¶.

1095.

625.

9vn.

57G.

SZG.

1095.

‘76.

900.

405,

820.

52s.

4‘5.

690.

630.

21s.

449.

2cs.

1095.

625.

SW.

570.

520.

1099.

170.

ecn .

4e5.

920.

s24.

415.

MO.

alo.

2Y5.

441.

265.

109s.

49G.

270.

306.

450.

Go’:

17n.

720.

FlXfO

SKICOING

DISTANCE

0 .

2t5.

2oQG.

3710.

LOW.

4000.

3Qh).

49SG.

4550.

snso.

t.230.

aooo.

5740.

soso.

7700.

7225.

0 .

205.

2oQQ.

990.

LOO.

130::

1X”,:

1290.

1710.

2670.

5nSQ.

ZllPO.

11100.

364G.

4260.

:I.

2t5.

20110.

990.

(100.

1 w::

990.

740.

n.

300.

139n.

3tbO.

79fi.

JW .

24PO.

iQW.

0.

2t5.

2 c to.

990.

bon.

130::

2:

n.

300.

790.

Yrn.

237::

2lw.

2?20.

SKIOOlNG WAIL SLlm!

COPPEClICN ItlAViL Liiikij

f AC IUR OlREcrlcY 111

.

5 .

1.90

::2

1.40

1.w

1.4a

I.40

1.50

1.50

1.50

1.h)

1.70

1.70

1.70

l&O

I.60

l&Q

::2

‘.bO

1.w

::2

3.40

1.4*

::,”

1.w

1.5Q

1.50

::,”

1.W

I.90

::!z

1.66

I.40

::2

1.70

1.71

I .70

‘.biI

1.m

1.00

l.RO

1.80

1.90

1.90

1.90

l.bO

1.60

‘.bO

l.QU

::z

I.70

l.fO

1.70

1.50

I.50

1.50

1.50

1.50

1.w

-2.

-3.

-5.

-16.

-*.

-10.

-2.

I.

lb.

10.

5.

:::

:::

3.

5 .

-3.

‘0.

12.

-2.

-6.

-10.

-2.Y.

:b’:

1::

6:

5.

5.

-3.

:;:

-2.

-I).

-10.

-10.

-2.

1::

IU.

5.

‘5.

12.

‘0.

I.

5 .

-3.

IO.

‘2.

-2.

-d.

-10.

-IO.

-2.

-5.

-5.

-4.

-3.

3.

4 .

46

b .

APCA fIXLO

OIFC ICUL?V 1 WE

FAClCl E1bf.t

1.00

1.00 :::

1.00 14

1.00 1.5

Ii:2 :::

1.00 IArc)

1.00 IA.0

0.90 rl.il

0.80 13.e

0.90 13.3

0.w I3.Y

o.ao 090 2,”

PC . :*:

::ii

1:o

1.00 2:

1.w 1.0

1.00

1.00 ::I:

:*z . I:::

::c

‘1.0

IA.0

0.90 11.0

0. co I,.0

0.w l3.G

a.vo 0.3

o.eo ~.o

1.00

1.00 ::t

1.00 :-:

1.00 r:c,

1.00

:::

:*:

9:*

::: 9.Q

II.0

I.00 l1.d

I .oo I&.*

6.50 l1.U

O.CP Il.0

0.90 13.0

n.90

o.eo :::

1.30 5.b

l.CG 5.0

‘*ao l.W i-8

::iZ 110

1.00 :::

1.00 9.Q

1.00 9.J

1.00 11.0

::z

1A.J

AI.0

0.90 13.0

0.90 9.9

o.on lY.O

U.90 L1.J

be0 9.~

61
62

11:224‘455q?77ms3991

1J

:‘j

::

1‘

12

‘ 2

12

13

13

13

‘4

‘ 4

14

14

1R

lr)

21

::

22

::

23

::

1212121212121212:1712::121212

nlrlMur

VOLUHE

SK IDOFD

4’)o.n

463.0

45fl.0

470.0

45n.0

47C.O

*sn.n

470.11

46”.0

5na.r

coo .o

420.0

510.F

550.n

460.0

49O.P

500.0

92F.P

450.0

49P.O

450.0

490.0

450.0

490.0

450.0

49o.c

450.0

490.0

450.0

490.0

450.0

490.n

1141 IMU’1 CYCLE NIJMSEQ

VCLUPE T‘NE O F

SK‘OJEO NIhUTES CYCLES

400 .J ‘9.91

460.5 lC.51

450.2 ?2.45

470.0 27.21

450 .J 42.8‘

470.0 35.43

450.5 5P.7‘

470.0 47.F7

460.3 40.C5

5OU.J 33.4’)

41X.3 .J 64.2‘

420.0 62.82

510.J 57.N

f5Q.O 47.7‘

460.0 76.40

490.5 62.58

500.0 102.74

520.0 e4.3tl

450.C 121.8R

490.0 ‘61 .Cb

450.0 136.69

490.0 112.57

450.0 148.72

490.0 121.35

450.0 131.56

49O.J 10.5.37

450.0 120.2fl

490.0 98.73

450.0 117.11

490.0 95.19

450.0 Iza.61

490.0 104.40

‘63.

141.

‘56.

‘49.

09.

95.

50.

4a.

196.

110.

‘0.

14.

2c.

27.

26.

24.

48.

4c.

?b.

33.

60.

55.

?3.

31.

5R.

53.

67.

Cl.

13.

‘2.

233.

214.

dREA

SKI0

IiME

ncdJRS

51.21

38.89

e4.13

67.54

63.42

50.25

48.93

3e.27

130.54

‘00.4H

10.70

8.38

28.23

21.69

33.25

25.7‘

a2.19

64.9‘

72.23

55.00

136.69

‘03.38

82.34

61.91

126.69

55.84

‘33.56

100.75

26.03

19.43

500.16

372.85

AREA LANDING LANOING rEwa0 rre1noli

SK‘COIRG SKlfl01hG iK 1UOlt.G

kaws nouas C‘JSTS

22.10

37.46

28.04

21.47

56.79

4.10

12.27

‘4.50

36.27

31.22

cE!.ec

33.34

!4.56

57.43

‘1.12

213.61

695.75 20769.13

695.75 287S9.13

(lETRonw2:2:2:2::22::22:::22:2222:222:::2:::33

L 4w

YOt11::11:22722:2:2:2::2:22:2:2:2::2::11

AREA

NP:13:444555646777

8”a9i

10

:!i

11

::

if

12

13

::

14

14

::

19

:‘:

::

::

22

::

2311

SK10

Ml

11212121212::12:1212:12b212::

M‘MIUUN CLX ‘Mu* CYCLE NUWWI

VOLUME VOl.U*E TIME O F

SK IDOFO SKl0OE0 HlhUTES cYclES

AREA

SK10

Tl ME

HOURS

400.0

VJO.0

450.0

470.0

45n.n

470.0

400.0 17.19

460.3 15.12

450 .o 27.N)

470.0 22.Sb

163.

141.

‘28.

‘22.

44.57

35.62

57.49

46. R2

450.3

470.0

40.53

33.53

CO.bS

4a.13

400.0 400 .o 28.95

420.0 420.0 24.t2

.

9’;.

56.

54.

27.14

21.99

400.0 400.0 19.55 3‘. 10.18

420.0 420.0 ‘7.05 30. P.46

460.0 4elI.0 21.t1 196. 70.47

500.0 500.0 18.94 180. 56.a2

400.0 4oo.a 21.39 10. 4.73

420.0 420.11 24.26 10. 3.n5

5‘0.0

550.0

46O.ll

490.0

3oo.n

520.0

510.5 30.36 29. 14.88

550.1 26.17 27. 11.89

4bE.O 34.21

490.0 29.22

26.

24.

48.

4t.

‘4.@7

11.93

500.0

520.0

450.6

490.0

45.4.1

38.22

36.32

29.4D

450.0

490.0

450.0

490.0

450.0

490.0

53.58

45.66 :;:

60.

55.

33.

31.

58.

53.

67.

61.

:::

233.

233.

31.75

24.a5

450.0 c7.09

490.0 73.10

450.0 IlD.lfl

490.0 91.73

450.0 50.99

490.0 42.el

450.0 74.tb

490.0 62.47

450.0 5e.a?

490.0 48.47

450.0 82.00

450.0 66.70

87.09

67.14

t1.5n

46.60

450.0

490.0

450.0

49n.o

450.0

490.0

450.0

450.0

49.10

37.36

82.96

t3.74

13.07

9.89

318.99

259.37

wo.0

4b0.0

wo.0 le.91

460.0 16.51

163.

141.

51.21

38.09

AREA LANDING LANDING MEW00 nt 1 t,co

SKIOOlNG

lfaURS

SKlC”W(;, SKIOD‘NG SKlOOlhG SKlUlJl*G

CGSTS nouns LIJSTS

20.18

25.80

26.83

72.02 3011.06

‘2.15

4.62

31.46

2.12

6.61

t.62

‘6.25

‘3.94

37.91

26.58

il.37

3t.05

5.63

‘43.03

364.33 15065.10

437.15 18076. l b
:

I

2

:

1

,

I

*

1

I

:

1

2

t

2

I

2

I

2

:

:

:

:

:

:

I

‘IO.0

470.0

30.0.

P5.“

179.

122.

‘50.0

‘W.0

52.91

35.43

89.

05.

63.32

%I.25

‘OP.0 ‘t%l.O 71.55 16. 27.12

42F.F ‘20.0 ZI.C2 s.. il...

.nn.n

420.0

40u.0

‘20.0

2?.E.

l...h

3‘.

30.

‘2.P)

9.90

660.0

‘100.0

‘40.0

soa.

?I.(1

1C.G‘

L.C.

1.3.

WO.0

‘13.0

‘W.0

.,!,.n

29.29

24.26 :II:

4.73

3.M

lO.?b

26.11

75.

7T.

tc.de

“.*.

4W.J

‘90.0

‘60 .o

5VO.3

25.El

?2.%

26.

2‘.

II.22

9.2,

3gn.o 503.5 I? .5’* .e. 27.1.

520.” ,Z”.O 29.1‘ ‘6. 22.3.

‘SO.0 ‘5O.J 35.33 ?b. 2O.W

‘9V.b ‘W.J Il.02 33. Lb.19

‘TO.0 ‘51.0 69.8. 60.

590.0 ‘90.0 59.23 $5.

‘90.0

‘PO.@

4QY.n

‘.O.il

‘SO.0

‘90.0

‘50.0

‘50.0

‘SO.0

‘50.0

‘50.0

‘90.V

‘SO.0

‘5P.O

“1.39

13.0‘

34.e.

25.83

81.

II.

50.

13.

‘SO.0

‘.O,(’

‘50.0

r.lf.0

‘50.0

‘9O.F

Sl.9. 67.

‘4.03 61.

+2.11 13.

33.57 ‘2.

65.15 233.

53.79 233.

65.03

56.39

5’e.ss

37.2s

33.55

26.39

51.6‘

‘4.93

9.4.

7.2.

‘00.0 ‘00.0 Il..1

‘60.0 ‘60.0 lb.¶l

‘50.0 ‘50.0 30.01

163.

‘41.

128.

21*+00

20.. ‘(1

S1.2‘

39.99

b..OI

C‘K l”“”

VCLUME

SXI‘WEV

- -

mtt LINU‘NG L‘NVING MEW00 MlI~CO

sK1*o,hG sxloolht JKIWlhG

wu*s WULS ‘“SIS

22.13

79.C6

2ll.OC

ii.15

5.43

?,.‘b

2.,2

C.6‘

l .a

12.27

0.39

30.511

2l.OI)

L4.77

25.2s

4.11

llY.13

22.10

5

1t.90 3259.22

51.11 23ee.b‘

237.59 5b24..9

37‘. lb 15‘71.31

“EIYO” LWO

Na

.

4

‘

‘

.

‘

‘

4

.

.

.

‘

4

4

‘

4

.

‘

.

.

‘

.

4

4

.

4

.

‘

.

.

4

‘

.

‘

‘

4

.

‘

.

‘

:

.

.

‘

.

.

‘

4

.

4

.

.

.

I(

N O

:

I

1

:

:

2

:

7

:

2

:

2

2

:

2

3

:

1

3

:

:

3

:

3

‘

4

.

.

.

.

.

5

.

.

‘

.

4

‘

.

4

4

.

.

2

:

:

1

2

:

:

:

:

:

:

I

,

:

1

2

1

2

I

2

:

:

LUIVING L4NOlNG NEW00 rKlW

S”W~IW4~ SK‘OOING SKlOOlhC S~lUOlhG

cosrs HOURS COSIS

‘70.0

‘10.0

41a.o

570.0 5l.bb

2 9 .bb

‘50.2

47O.J

25.w

42.9‘

?S.O

‘22.

Y..

11. 2::.

27.1+

21.9.

28.0.

79.90 32S0.22

:

9

t

*

6

:

1

e

9

9

9

”

9

‘00.0

42n.o

‘00.0

‘20.0

211.5’1

24.t2

36.

3‘.

‘00.0 ‘UO .o .23.0.

*LO.0 420.0 lP..b :::

12.03

9.90

12.1s

5.43

‘60.0 ‘60.0 2l.Cl 196. 70.51

500.0 YPP.0 1e.r. 180. ‘16. 82

.00.*

‘20.0

‘00 .O

4W.b

5‘9.0

550.0

5lO.d

S50.U

;p;:

.

30.36

26.17

LO.

10.

29.

27.

4.73

3. e3

31.a

2.12

14.81

‘1.J.

h.61

57.77 23dO.61

‘9

‘0

‘9

‘1

::

1s

IS

::

::

‘40.0 ‘C0.U 2l.b‘

699.0 S90.0 22.36

11.22

9.21

5.06

5OO.J

s20.0

5PO.O

?Zd.J

33.9.

29.11

21. ‘I

22.3.

12.27

‘5O.E

‘90.0

‘50.3

‘90.0

30.61

21.0’1

t.eo

1.53

3.05

‘20.0 420.5 26.30

l 7a.n 670.0 22.93

LO.47

e.13

4.911

25.9s ‘031.06

I*

3 6

lb

17

‘1

::

2 0

::

::

:t

2;

::

23

‘30.” ‘35.0 39.96

460.0 ‘60.0 34.23

56.7‘

‘5.89

25.37

‘W.0

‘0O.P

‘SO.0

‘90.0

590.0

n20.0

‘50.0

100.0

l 70.0

110.0

“0 .a

‘10.0

455.0

‘90.0

‘90.0

(20.0

450.0

$00 .o

470.0

5‘0.0

21.23

22.17

w-55

‘1.4‘

42.63

lb.26

‘3.26

35.1+

20.52

17.31

:::

‘8.

‘(1.

13.

‘2.

:::

2

3‘.

3‘.

36.

33.

61.

31.

:::

!23.

206.

‘4.33

‘I.96

33.51

25.82

‘?.30

34.06

9.6‘

1. “I

76.04

59.6‘

6..9

‘4.59

‘9.35

4.10

33.41

103.31 4211.99

2*4..3 lO950.56

....*...*..“*~.**...~......*.*....*..*....................*..~.....“...........~“*.*.*...*..**.*.......~........I****..
PVEPAGE

LANDlNG L 4NO ING LANOING HE 7hUO HETHOO SKIllDING

YUf4RfR VOL WE PCRE5 VCLWE AC&ES i?lSrANCE

I ?f.,5n?. 493. 686.

5clSCP. 283.

1 162~lm. 65. Cl@.

2 4J”‘iYl~,. ZIP. 586.

5675AC. 2R3.

I 1t..,50’1. 63. Lllh

2 1+40P!l. 432.

3 2tlOo~l.

,2::

tv4.

C-61500. 2a3.

PEP LANCITC

AVEP AGf

FIXED

SKICDlhC

PI STAVCF

‘296.

732.

201t.

YEIGHlFO

AVf94GF

lR4VEL

SKIGOING

CISIANCE

bhll.

15P7.

3212.

782. 1111.

116. 1221.

13sr. 3204.

.....I...OEK ‘IE,H(JO .A.......

bfIG~lL5

AVEK AGE AVYkAirt

AVERAGE FIAEO l*aVtL

SKICUING SKlCCfhC SKlUJl*U

01 STANCE OISl4NCE CIIIANLE

bfb. b29b. 4871.

554. 1399. LIAI.

579. 985. i!Mt.

6 I 102500. 65. 61th 722. 1771.

I 1hCOJ. Il. 432. I?#. l221.

c

3

5zaar. 35. 535. 470. 1524.

4 6 2O9403. 112. CZL. 1057. lSR3.

‘ 5bi100. 293. 550. ?5P. 1540.

. ..~.~..*.*...*..~.**.~*~*.*.*..*.~.*..~..~~~~~..~.*.****~...*.~*.**~.~*.~*...,..*..**.*~.*.~*.**~***..*.**.....*.*,**,*.*~~~

*.,**..*.** . . . . . . . . ********

1IlIlCY

rP4veL

;ynQ; L:$;;; COsctCTION

FACTOR

: :

‘1.99

0.9s

2 2 0.w

3 I 0.95

: : u.90

0.95

4 1 0.85

. 2 0.90

A 3 0.15

A A 0. dP

.**. ..** *..*~..*...*.*.

METHOD LANOlNG TRt.JC K

NUMBER NIJJ’BER NIJWBEP

:

1

1

2

5

2

2

2

2

3

3

3

3

3

3

3

1

3

4

4

4

4

4

4

4

4

4

4

4

4

4

:

1

1

:

:

I

2

:

1

2

1 2.99 80.0 239.20

2 3.10 72.0 223.33

CYCLE NUMbER

TINE O f

WQURS CCJAOS

2.e2

2.93

215.3

2e3.8

TRUCK

TIME

HIURS

889.62

830.C5

2.82 90.3 254.74

2.93 t1.3 237.85

2.95 225.5 b72.74

3.10 202.5 626.12

I.82 eo.3 254.14

2.93 61.3 237.E5

2.99 30.0 239.20

?. 10 12.0 223.33

3.10

3.22

145.0

130.5

449 -80

4 19.s5

2.82 90.3 2’14.74

2.93 81.3 237.85

3.10 28.9 a9.t1

3.22 26.0 03.ir7

3.35 116.1 368.55

3.47 104.5 362.75

**++* ALL TRUCKS WOPKINC TOGETHER I)++**

LANOINC LAN0 INC METHOD

TRUCKING TRIJCKING TRUCKING

wJns COST HOURi

METbIOO

TRUCKING

COST

429.56 17182.48

429.56 17182.48

123.00 4520.13

324.e3 12993.30

447.e3 17913.40

123.00 4920.10

115.50 4619.34

217.18 8687.21

455.68 18227. lb

123.00 4920.10

115.50 4619.04

43.21 1730.79

lE7.60 7504.20

469.37 18774.91

LI*******+**~+***oo**

CONSlR4INl

COOE

I- RO40 HR

29 L4NO M\ UPPER

39 SKI0 HR BOUNO

4= TRUK Ho VALUE

1 120.

3 600.

64
PFTWCD sl,l*PPY

.*..t*l**..t**.*.***..~~*~*.*.*~*.~~***~*~..~*.~.*******~*~*~*~**~*~*...*~*~.*~~~*~.*******.****~*,~**..~.~~**~..*********..**~

La*4DIVi CCNSTRLC110N TCT.lL N6THUJ

RrJ4” COPISlRuCTIOh( AN” !YllEH 90\, IhC SKICCINC TRbCKILG ,tET*CJ ~~RVflIlllt

NET,, ______--_-------.--- ---- ---- ----------- -em----me-- -_--- --- _------_-_------___ nlE”tSTIr,G UNIT

N J HOURS fll f /V(rL HCIJF 5 04 IIVCl muds IS3 TIVCL bCUPS 1,s ,,"CL CCSTS COSTa

1 9. 170. 0. 1. 56. (1. 6F6. 20169. 51. 430. 17137. 35 . 46177.95 6i.ji

2 49. 1061. 2. 3. 101. 0. 431. 1eo7t.. 32. 448. L7913. 32. 37241.81 BS.62

3 15. 1625. 3. 4. 311. I. ,74. 15471. 27. 456. 18227. 22. ?563S. 38 0.. 19

4 135. 2~10. 5. 6. 45’. I. 265. ICSII. 14‘. 465. lb775. 33. 33lwc.44 id.31

*~***.*******t*******.**~*.******~**~.**.~**~*~~~**.*.~**.~*~*.**~*~**.*~.**~.~***.*~*.*.***~**~***,~*****~*****.***~**...*.~*

IlFRATl~N WI- 1

.~.~*.**.***.**.**.*.~~~*..*.***~~**~**.**,.~**.~**~~***~.~****.~*.**.~**..*.******~=**~ ~** *.*~*~*.**~***~.~***.***,****~.*~

l . . . t *

l . l CJ * 95.JJ -;I.t? -72..?e -41. f 5 -4P.Od I RlLhI -

l tg. . . .

. .a* ~.*~*~rt**+*t..****~~*~*~~.,~**~~**,~~***~~*~~~~~~~*~~*~*****~*.**.******~**.. ..** ~.*.***~.****** mnu *

l *s* l SElLIí,G * PETHCO * *E?HGO * “ETb*O . nETno l . IlHR * %,rR * I/W l ,IHR * l

. CB l I* * PRICE 5 l 1 * 2 1 2 * 4 * * CCIO, l L4hC t SKiL * TWCK * Ccnrlnhrs *

l t s+ l cm, l lr-1) l 122) . (M3l * lF4i * t 1211 * IL21 * 1131 * li4, l t

..*..**~*.*~,**~***t.*.~*~~*~*~..~*.~~*.~**.~~~*..~,~~***~*~**.***.**~*.**.~..*.~.~***~*******.*.~*.**.*.*~****~*~***~******.***

. l l

+ **.I-n l x,0* 1.w -567.50 -561.50 -567.50 -567.50 n .@O U .OiJ 0 .no MO:

l

i.au *

I n.7o l rll* 0.00 7.86 49.01 75.12 134.55 -1.03 0.00 0 .JO 0.00* 0.J.J *

* 0.00 l x12* 9.30 0.70 i.t4 4.31 6.25 0.00 - 1 .,h, n.oo 4.00* 0.60 *

* o.‘),, * ‘(13. 0 .UF 655.,5 437.15 374.16 264.F3 0.00 0.w -1.nu U .n0* 5.03 *

l n.oo * x14* *.on 429.55 447-E: 455.bR 469.37 0.m 0.00 0.00 -,.oo* O.OJ *

. -21.03 * x15* 1.W O.CO 0.00 a .w ll.J” *.,w 0.w 0 .I30 P.JO* 541.50 l

l -72.26 * X16’ O.OQ 1.00 i -00 1.m l.GJ 0.03 0.6%) 0 .oí) 0.00” i.03 .

l -41.35 l XL?+ 0.00 0.00 0.00 J .u3 J .JO 1.03 @.OO 0.30 *.dl** LZlJ.DLl l

c -4o.cfj l X18í o.up 0.00 o.ao ~~.OO c.w C.ìil 0.00 I .t+o O.GQí ti*cl.w * . l l t I

*.*~..**.**t.t**t**f ~~** ~****~~~..***. .~** .*********~*******~~.**~****~*.~***.***.~**.*******~*.**.**..***********.*.*.~

l . * 7; *

l c-am PCW : 35.50 r).ilJ O.CG 0.00 a.co -21.t3 -72.20 -41.35 -40.03* I).*

ttt.t***t****...*~..***..**..****.*.**.*.~**~.~.~*.*.*~~****~**~ ~** .~~~***~*************..~~~*.*..**..**.*.*.*.**~**....*..*

bFTEe 1E IIEPbTlCNS 71-f OPllWJP SCLulICN CCLSISTEC OF:

~..*.*.~**.t.**.~t~****..*.*.*~~***..**~~.~~,~,,.*~*.~~~.**~.~~~... ~** *..*~~*******..*..*.****.****************. ..** ..~*

1040 9OSO LAhCIhG CChST LAkClhG CCNST TUTAL

PF WOO w7niltu COQST CCNST AKC SYSTEP &ND IYSTEY SX1001hG Sh IDOIhC IPUCK ING TRUCKIhG METNOD

I PRrlPOC7 10~~ HOURS COSTS COUP5 COSTS HOUP 5 COSTS HOURS COSTS C(rST 5

___--- ---m-v

OIFFEPEYCE: ,A)-,#,: zu199. 35.59

*,“..~..L.**..*.*..*t*..~*.*.****t.C**.*L*,,~,*~~~l.***~*.l**t*~~***.~.*..******..~~~*.*.

___ _

. 0.4~ l Y e* - 0 .co -197.09 -15.05 O.OU -0.00 -O.DO -0.00 I .oo -o.o*+ L91.59 *

l 0.9î * x v* -il.on LO.62 1-a* 0.00 -0 .co -0.00 -0.00 -0.00 I.009 ‘.bb.J.? s

l -4J.JQ * x19* -@.I?0 197.83 15.08 4.0” -4.00 -4.ou -0.00 -0.00 -u.oil* 30b.M *

l 0.00 l ‘( 5. -* .w -1.13 -0.44 b .00 1 .co -3.00 -O.JO -0.k.30 -o.ao* 0.76 +

. 0.00 l x l * 0.03 2.13 1.44 1.00 0 .oo 0.00 0.00 0.00 o.oo* Il.24 *

* -72.26 l X16. -@.Otl -0.F0 a.00 o.nn -n.nn -0.00 -n .oo -0.00 -O.UO* 0.40 l

l n.oc l x 6í -@ .03 0.00 -0 .oo 0.00 -0.00 1.00 -0.03 -0.30 -o-00* 113.05 *

l l l . l

.~~.~..*~~~*~.~~~~~~..~~~=~~~~~~~.~~~~~*~~~~.~.~~*.~~~~*~.~~~~~~~~*.*~~~.~.~~.~~~~~~~~.~~~~.**~~~*~~~~~*.~.*~~~**~*~~~.~*~~**.~~

. * * 7=

, c-e** WY * 3.03 -76615.56 -49i.fe 1.00 ;I.co 0 . 00 0.00 0.00 0.091 .wm.=

*~..*~.....*.~**~.*l*..***.*.**..*~~.*.**...~.*****~.~*.*****.*.*~..*.*..***..*.*~******..*.***.*.********.*****..**.~.~**~***

.*.********.**** *.* L****LL.C***

..,*****t***.**. l .* l t**LCL.*.*L

l .**.***..**.*** #HOVE VALUES IN C-BAY COY l .* A80VE VALUES IN C-84R ROW l *****.*.***

**ì**L******.*. ARE DEhALTY CCSTS ..* APE Snlook PRlCES ****.*.**.**

,******L*.**t**l I .** **.*..*

.****.***.***..* **. **********.*

,**~t*~*.*****.~.*..*.~*******~*~~***~~~*~~.*.~.***~~.**.**...*.~*.*..~***.*...~~***.*~.***~**...~ .** ***********.*****~****~
SENSilIV!TV ANdLYSIS

USEXS FAMILIAR WlTH C? SHOULC BAKE C#AhGES Ik

INPUT COSTS ICJI PXD DESOUaCE LIMITS te.,, TO

rECOWE Ea"IL149 WITH Tt‘F SENSITIVIII AhALYSlS AS I,

APPLIES 70 THE CONVEY-ISCCUAhl-~EldGn FCQP~LPTIOY

CSFI ,*I L-0-S-T

PENALTY COSTS AQC CH4U;E IN OUJECTIVE FUhlClICh VALUE FER VCIT

INCREA5F lhl NO+DPSIC VARIAb165.

IO -67.947

11 -t*.42t

1 2 -72.260

13 -41.350

14 -4a.cca

15 -27.053

17 -42.756

2 -7669.563

3 -492.084

P”d SHACOY

NUNSER PRICES

a.000

a.cca

a.coo

0.000

0 .noo

0.000

a.000

0.000

0.000

RANGES RN NO’,-BISICCIJI

"9914RLF LOWFF L,WIT

10 b7.541 il

12

13

::

I?

b4.426

72.2eD

k1.3Sl-l

40.500

27,053

42,7Sh

2 lhC5.563

3 492.8rz4

RbNGES c-N A&SIC CIJI

VdRllBLE 1WFF LIMIT

1 6 -38559.d50

I!? -22.2&l

1 67.54,

4 -34i.br.4

5 -2543.590

-64.425 ,L737?.P*.O

-hQ3.4?5 Q.POO

-71.Y32 -13.3fl?

-74.dtI ~.O!-l~I

RANGES ON t)tIl

,

50?.500

'74.124

-559999.000

504.219

-99s999.300

-a.c.on

I .OIlD

274.,24

504.ZlY

Is352.7op

30 . 5 4 6

9~C79~.llO4

2543.590

1124.I23

66
Appendix 8-L-0-S-T Program Listing

L-o-S-T IS DIVIED INlU2 ICTIWS; lIEFIRST§CTIOH

C4mAlESLDGGIffimPH)MsmnCTrwuss

TESEOE~SASIKWFCRMLI~PRWW

_._._ __.. --_-. .~ ~. W.R?=QMRSIUdFKU4tl5ICFEETTOBWWFBT

nEsE cxNmsIcN5 #IE QCY !Bo IN xIIDIffi n& Epr\TI(M

WWR.7O~ (AnllE(IIR),ITR=1,16)

07200 7OFUWT(lW)

073%' YIX~KW.KJ) (ATIlLE(IlW,IMl,l6)

07403 81 FW%T(H~~/.M.'TI~LE L-U-S-T w)1='.4X,16W

07503 Gu

Ez

1lX,‘LIlZERS=‘,2X,13./,2X,‘~ CT %IIZB=‘,2X,I3,/,

24X,%.MER ff TMU='.2X.I3)

fi%

HW’EW 125WpN9,LFW ICTWT

crml

125 FCMTt4; ‘u, AIy\LtSIS f.&=’ 3X 12 / 6X ‘LP OVWT a=‘,

13X,I2,/,2;,‘# USER mMIw\IHTs=‘:3X:Ii) * mm_ _ _ _ _ bbIClRATt5 __. . .

ii%

t@tWIWICIPAT+lO

cQ7wcx zE3oalrKiEAul.LtEiwAY

%K

if%

0 3 I50 Iimw1.m

w 140 IzAK=l,B

Ei

al 133 Ii!AW1,25

REAVwAw,IzAK.IzAVAb0.o

lo4al l3=lo%TIME

1m 14oaxTIME

1o6oo.lBCMIHE

107al cx

108oow(

uJ9wc.x

ll0mC.K ZOMairZELECEDiWAKLEDINLPSECITO(ffLOSl

lllca w(

1l.m ill 170 ILul~1.25

11Jx) Ill 160 ILs?-1;25

114al A(Ia22,ICUlbO.o

11503 160 axrIME

llml 170 OxTIME

llxa a, ls 12om=1,11

11830 m I83 mJT2d.m

llwo LoxT(Izam,IzalT2bo.o

l2u.B lfBaINTIKE

12100 lB5o.xTIM

E

0 3 190 mrr3-1.25

cI(ImJI3mo .~-

%

CtIZM3&O.O

P(IZCUT3bO.O

I2603 crpcIzaJT3)~.o

zJtizaJT3,40

Ivm(Izan3)d).o

KosTuzar3)~.0

w(Izm3)=0.0

af1zon3bo.o

aM12am3bo.0

OP(IZCUT3bO.O ao(Izanwi.0

WIZCW3bQ.O

ao~UaJr3,~.0

B(IZClJT3bO.O

203 F1RM(T(II.1X,FlO.0.1X.F7.2,1X,F7.2,lX,F5.1)

IFWNIT.EQ.l)I#UTE(kW,250)tWNr

25DFOMT~2X.‘HRWST WArrrW='@

DWNIT.EQ.2)I

33 FoI(Fy\T(ZX,'tbW

fit%

3 % FCIWTt2X ‘WMST WriW ZtX Fll.O,Zx,‘~IC FEY)

IF(IWIT.kJ 4)tRIIEW 3E&Wi

16100

360 FlRWT(2X YiWiT Kl.k=' 22X,Fil.O,2X,'~',

Km(KIJ.~m)m.s~,h

162m 400 FcRFy\T(PX.'FRIE IN SU.116 tMl5 W='.l5X.P8.2./.2~.

1693 m-475 IdlB=l.Nm

17ozsl IF~ILNIT.EO.lKOMET~l,IR~~~~.O in03 B(I~IT.EP.P)UXFET(l,Ia00)L)(sRW1000.0

17200 B~Iu(IT.EQ.3~uMI~1,I~~)~~.O

17x0 ff~I~HIT.EQ.4~~~1,t~oo~LHaR~1.o

17400 47?imTxt4.E

1750l 95ZtC=O.O

6’7
17cIll m 6x1 1a01=1,wR

177WW

178COw(

17933w(-MpE4

EE

-

18203 lx DZIIpH()=mzB HRSEFWR; 0ziw0=axol EFFIcEIMx

183x W C DZlw,=mZER tKw.LY OMT; 3@x=SDlzEx

184arx taRlYcosT

l8mwc

ik%

REm(KR so)Dwp(Iaol) aP5(IaOl),(;mMffIaOl)

5co FoF3RTti4 0 1X F4 2 1X Fi 2)

163l.l 94mx&i&&inioii

18900 ~IT(KW,SM))Iam,cmbP(iuO1,,~(IaO1),~(~~01)

1Wll 550 FClWT(QX,I3,2X,F5.0,3X,F5.2,2X,F7.2)

19103 605 awIME

192cn bwTE(I(W,650)91DM:

19303 650 F~T(/,W.29(‘*‘)./,23X,F8.2)

194Ol WIlEWl,7CO)

19500 703 F~l~2~/~.2X,51~‘*‘~,/.46X.‘sKI~‘.~,

:F%

12x,'9(ImER'.6x,'sKIoDER',3x,'sI(IocER',2X,

2'SKI~R'.6X,'HM(LY'./.3X,'KM3ER1,3X,

19m ~'HRSEFDIER'.~X,'YI(;HT',~X,'~IC',~,'~KT~,/)

uwE(w,900)9aKH:

900 FCIMTU 2X R('*') /

mwW:95i)) "

45X,F8.2)

950 FClUMPU). .W 78('*')/,%'* NH-VCCB *'.

Ei 26fm

Ei

27100

27Xx)

-UUtDlWE6-

lKlEFuo=lRLKx lRAbEL SPEED EWTY (MR NB-box6 f@xD

xnrhviux m~ti groED UwED 0w wwac6 Ro40

lKTEwo=lluKK TIWEL SEED EMTY WiR km05 mm

xnw HIurx lR4KL SPEED LWED cbQ7 urn6 RCPD

lWlFCO=FIXED TIFE FfR TRUX CKLE IN MINJTES

lKfF( )=lNJX EFFICIEW UE 0.8))

lKHxo=lRLa KUM

2lKmIwJ3)

Urn FCHT(5(F4.1JX),F4.2,1X,FlO.2,1Xf;6.2)

!34IKHz~+~:(In(u) ~Ix~Kw,roso~~a03,~~~Iaw~,~~~Ia03~,

i~~(racu);ncnkMrao3),~(Iaw);iw(Iao3),

;7KwIaD3),1Mc(1~03)

1050 F~T(2X,14,3x.F6.2.3XJ6.2.3X.F6.2.4X,F6.2.2X,F6.2,2X,

lF6.2.1X,FlO.2.2X,F7.2)

1100 CONTIME

wx(Ku.ll5O)sMIKHc

1150 F~T(l(/).M.M(‘*‘),/.7W~6.2)

WlEW,1175)

1175 FU1MRT(M./,2X.26(‘*‘),/,1M.‘MEEER’,4X,’KMeER1,/,

1M,'FEMo',6X,'RwD'.8;1,'ff'./,2X.'~',2x,

2'SEQmTS'.2X.'LwIM'./)

27330 CX

27403 Rwl(m,m)Im,IRosEG,IuwD(I~o4)

27503 1200 FcIFy\T(Il,1X,12,lX,I2)

27603 ItftS&uao1)=IFsEG

27703 WI~~KW,12L5~I~MTH,IR,I~~IaM~

27800 M5 FUWT(4X,I4,6X,14,6X.I4)

27905 125JONIKE

WEW 1275)

itit l275 FUMTU'2X 26('*'),//)

2am WUlECKW:1&

28350 1Bl F~T(2(/),21,43('*')./.~X,'NuuBER'./,

E

~~x,'~',~X,'WIDIE',~X,~X,'CF',~X,'EYWIMM MEA',/,

~X,'NVIBER',4X,'~',5X,'PREAS',5X.'CO[E H)IBER',/)

28ful lz25aMrIME

287mc.x

~k---VHD,,8-'----

m&K

malw(

29200 WC &?4Hmco NJ4ER; blA=wolffi m;

293cuw( Jm=ti.mRcFmEA5

294aJw( 3.wHwXIn.Mviu.LEffpRu\oxIKMBER;IsM~

29503C& ASJF#CKVIFPRWA7EEDIN?WfBiC&SEUEHE

EZ

298xJc.Jc

Ri3WR.1350)~wI.U,J*~

1350 F@W1T(fl,lX.I2,1X,I2,lX,12)

lFLJ#.q.om m 1400

.NwA(JH,~Lw)-3#y

wwEw,l375)~LIN,J,~

1375 FCWsT~4X.14.6X.14.6X.14.14X.13)

a,rntiseee. .

1400 bRIlEwu*1425)

1425 FUMT(/ 2X 43('*') 2(/l)

mEcm:l4ht '

145i) F(FWIT(~(/),~X.~~(‘*‘)~,~,‘~‘.~~X,’F~’.~X.’~’,

y,n,'Knm',zx.'~~',3X,'mzw',5x,'ROAD',3X.

2'IM9D',3x,'w#D',3x,'sIoE'.2x,'poR'.~,'~'.4x.'TIpE

31Xx.‘CiBIC’.

,

STPRTCFa,LWBYKnaoHHRWoWSTWTICNTIKS

DO u30 Iaab1.m

SfCE4-0.0

zMax=o.o

IERMR-o.0

93mR=O.O

slamo.0

mm=m(Iacm

Iam?=INcB4(Icu6)

If(lar3Jl.EQ.oHwB?=l

58
37aBwc

37103

37200

37333

~~

37600

377aJ

:Ei

38033

381CQ

E

3edul

E

387al

E

3wxJ

39100

39x0

39300

E

396ia

39700

z?l

iiz%z

iEKli

4oxllc.x

4mmw(

iEw(

iii%E

41003 W C

41103 w(

4l2ww(

41Jx) CJC

414CO c.x

415u) c&

41600 LK

41703 c.x

4l@lC&

blK0C.X

i-E

42zw

4ml

9R~=0.20

IWW = AT#(RolusS/loo.O)*

lWlX3 = ATAWUMUOiaaU)SF=l.aw0.Ol4wuSP)~O.~~~

KNFS = ATPNO@MW*cnxG

cm = mm(m)

m = __......._ rnvwanwaw)~ --.

ii = w*(1+sftlvF)

A? = OlTANWWWCIW)-

A 3 = scRTMl/A2)

A 0 = louw/2.0*(&1.0)

E K = A4/@3+1.0)

ff = ((R04LMJ/Z.O)~)/(a(~)~R)

DC = (KMMIW2.0)I@JTkW)TANoBW)CR)

llETA = 183.m

BASE1 = cC/IAN(R~cTw\D)

WTA = lBl.O-W’lFS

tV@V = (l.QI2.0)*(ROaDSW/2.O)*IIWfRTIN(THTA*CmA)

fE&2~=&~~&cw~’

IKmJa/TAN(R(WX3*CTIU\D)

aRU\C~(0.5*((RWOSW/2.0)~~~)~)-(0.5~~)

WUHR = (84sE*lo3l.ov435fao

ITYUKY = (MEPJ%XO.O)/~~.O

aEEMwpREpcaw6L)/27.0

tws=~ws=~~4~.0

iTiizzE=+

SWOSbO.0

STPRT ff O l LOOP FCR COW CBtSTRLCTICN TIFES

ml 160;1 IIL07=l,NlZR

XcRaffMRs m BUILD THIS Rw SE(MNI; WED oy EWVICN

B y JEARY mE.R ‘FKTau ATEcTIffi M -1cN ANI

COST I+ LoGGIffi f4WS” TVA lEWIW NllE 627, EMESSEE

VPLLEY AUMRITY, NJWS, TN, 37828 PPGE 30, 1978

EQJTICN KOIFIED BY LATER WLYSIS INKJ DIFFERENT f&WI

SEE FPEICR WMJTY F(R THIS W&lbENI

R(WW\-NIMBCFKRES~~C~&WEORIU~TCF~Y~

lOOPOPE OMECTICN FACVR m

FRXUE VALES GIKN IN FIURE 2-Z ff TVA lEM H)TE 827

42zia LRIK~Kw,155o~I~m,Iao5,I~o7,Ro4c6L.~.ldwDsp,

:$$ 1550llwr&sF(Y@W;rlXR@m?!,Xfuxfm 14 4icRWTY 14lX’F8 14 aIt3u,mEs,sm,~mF6.0.1X 1X F6 l lx 0

42831 ~6.0.2X.F~.2:2X~F5~2,~X,~6.~,~,~8.i.l~,~8.~,lX,F8.~,F9.2~

B(NOZR.GI.l)lRITE(KY.l625)Ia05,Iao6.~,~

1625 F@JW+T(4X,I4.5X.I4.8lX.F6.l,F9.2)

lmfmTINE

,/A

l8wOMIH+~ ..

lmEbJupa)

19Ol WT(/ .l27(‘*‘))

6’& HJUffi’.4X.‘uIH)Iffi’,

6/,2X,‘MMER’ ,3X,W%R’ ,2x. ‘my’ .5x.

7’pc~~s’,4~,‘cEpTH’.6X,‘Hp’,4X,‘cMF’.4X.’[ME’,5x.

8’HxRS’,6X,‘a)~‘,4X,‘Hw’,Sx,‘~‘,5x,’H3(RS’,

97X.‘msT’ ./I

469ac.K

47ixxl w( 1LKR=Itfw UUER N.MB (F OIZER us0 m BUILD

471fa w( LPNJItU... OKY OE DOZER IS PLLMII m WILD

472oow: WOWS

om,c+K

47400 c.x

47wlw

416% RfMKf&?wHLIl?R

47700 2033 FOWT(I1)

47803w(

47903&K

i!Ei

START W Ill LCOP FCR MlWK* LMIINi CMTRLCTICN Tim

48alciu

co 2m IRo3=1,tKTH

9M.A=O.O

YS&=O.O

94SW.O

48xX) 94X=0.0

iEzlw(

ma3=IlJva Ia.cB)

iii%2 STPRT 0: CO LOP FCR LAN)IN;s+m-o IN; OCIMWTICN T1f.b

49Knw(

493ooc.x

z&a

al 2150 10.09=1.1R@3

496Bcx

497cO

498Bw(

49mcx

Lx -c4ullwEI2 -

!D.Dl CX WTEO=OISTAM IN FEET FKJd TRKT LWKWY m MIS bWIG

50100 w( ME%= K?ES IN THIS LAMIN;... SIZE ff LANDIN

50203 W WlL=AWWE CUT OEPTH (+ EARTH KB4BED IN BJILDIffi LAN)Iffi

50303 w( E=FLKk’FFICIEEY FACXR FCR THIS WIN; (IE 0.80)

WOI w( SYSIRSYSTEN MM T&E IN HXRS m THIS LMtIffi; t@T A

50503 w( m I N TIM BuT A MlyE fEWEN uwIffi TIFE

ES

WLWR xM)KlWB(IDLoB ICLoS,J&Se OJIL

=20% FCMTC;8 0 1X F4 1 1X Fi 1 lX,F4.2,lX:F5.1;

EFFL,SWlff

51mO K+l.L+-&&4&:0,;28:6

511m pppCn=((ApRL*amYm.7/27.O)/(pppLL/1ocD.O~

51200 pppAcL=(((ppRc*aj.70)/43560.01)/(ApRL/100.0)

51303 w(

51400 W C LffiIC bPS m CONWIT LAMING SIZIN KRES m AN

51503 fix E@JIW~!BWTfffWOAWlliENl6ERW

51600 IX KNSTRUICN ECWTION IN TVA TEC-I WE 627

51703 w( pppcnesoxrw~ HEEfR (F amIc ypRD5

51800 W PJPKL+WWXIf4VEO M.MR CF PERES IF CONKWED

51903 w( FK?4uwD1ffiKRESmrouJLErGlHKRES

52mcF. tmEl.=KxRs m WILD L/WIN3

52103 cx

52mw

ii%

H(TB~(APRVJaO.O)‘(0.524~T(APPCW(ILCW))+

l(U.~(nPWYX/~(ILCW))))/(D~(IL~)~L)

5250 .cHiu52903 9Il4.m?L+a.

2E -w=

~~~~~.2rm)ra~,Ia09,087B(~ace,Iaos~garm,am,

u)zlbp~Iuw~.~~IupR~,~L,~TBL.ca,susrm.cK

g 2103 FtJWT(4X.14.5X.14.1X.F9.0.4X,F6.1.3X,F6.1.2X.F6.0.

llX.F7.2.2X.F6.2.lX,F9.2.lX.F9.2.2X,F7.l.lXJ=8.2)

53500 2lSOm;nrmi

ii%

Kffll~ZIwILDZR)+S(Smc

K0iu=(SMB+~)ni.B1

54axl w: KMIW H.ws FCR WILOIffi LANDINS ANI

54103 w( MMffi EMEN LAH)ItGS * MIS VALLE IS UWJ

54xJlcx INMELPtUJUOx~BYMmx,

54mc.K

5licxlti

54.m -+sbJb.

5ml bRIlEKu.21751IRCB.KRf&S.~

WOI 2175 F(3Fy\T(4X,I4.103x,F8.2.2X.F9.2)

54m imm3.*aa3bw3Rs

wol ;ToDawTIW
567cIlc.x

‘333% C.X IWW MMER, ILN=LPNNC M.MER,IpN2pREA m,

56903 w( AWREA VcLuq Iv\=mEA PnES, w4mItw SKIrnIffi

570x) CLK DISTAM, AXrmY1M.M SKImIffi DISTANI, PFfIXED SKImIN

57103 C& T o AJW MERE A N PN) Ax WXLD APRY; Ac=OZRREcTIcN FFCXR

57x0 C-X 00NVERTINi SIRAICHT LIhE XImIffi DISTAW -iD ACT%%

57303 w( DISTAN[E TRARAKLED BY WOOER; AS-SLOR CZ SKID W’.Ii IN

57403 C.X FlXfNf IN DIRCTIaY CF TRAKL LLMED; AD=f%A DIFF1CU.M

5750;) C.X CCE FfFEcTItG SKIIDIC TIE SIMIM xl XIaXR EFFICIEEEY

57@ll CX HE 0.83)

577io Lx

WC

2375cmTihw

RW)(KR,2400)IMN,ILN,IAN,AV,AA,AN,AX,W,AC,AS,AD,AT

24U.l F(REY\T(I1,12,12,F9.O,F6.O,FB.O,

lF8.0,F8.0,1X,F%!,F5.0,1X,F4.2,1X.F4.1)

IF(IMy.EO.OMl I D 25m

JW&W~IMY;ILN;~AN)~

MAFD(IMt,ILN,IPNW

W.E!G&bW,ILN,IAN)~

Aw3(IMY,ILN,IPHwS

PRW)I(IIUH,ILN,Iffl)=tW

i%WU~,ILN,IANbAT

~ITE~K~,~~~)~I~,ILN,IAN,AV,/~\,AN,A~.~,~C,~,~,A~

2450 F@6’#T(4x,14,5X,14,4X,14,1X,F10.0,2X,F7.0,2X.F9.0,

12x,F9.0,2X,F9.0,5X,F7.2,10X,F6.0,6X,F7.2,1X,F6.1)

mm2350

2503 aNTIME

KtIlEMu25D)

64x,wmIM

bRIlE(w,2Mo)

2603 F~T(6X,‘N0’,4X,‘M’,4X,‘~‘,4X,‘N3’,2x.

l’S(ICOED’,3X,‘SKIUED’,2X,‘Ml~‘,2X,’CYCl.W,

2sx,'~cc~s',9x,'HxRs',7x,'Hcu\S',5x,'ulsTS',6X,

3'tms',7x.'alsrs',/)

START (x m LCW FO? RTHXG++++S(ImIffi TIMES

9cImIis AWW~E VALW F~o4 TVA ~towfw. toTE 810, 1976

BY JWRY KXZR ‘WlKRS WFECTIffi ME f%tWTIoN Cf

RcflBER TIRED SKIOOERS” TVA. MRRIS, lN 37828

ltAEU3 = IWJJIUF 0: ClJtVAlLRE AKRAa VALLE CF 483.99 F T

RUDSIUID CEPTH aY SKID TRAIL; VACLE CF 2“ ASWED

aJEP= SOIL SrTwGlH BY axlE RETR(MIER, AseED 200

pRCLG= AX LENSTH 5 SKID TRAIL, USE0 AKRAa ff 15.

SEE NA TEaMlE BlB WEE 23 FCR TH% VALIES

lkaxwE3.99

Rkm6.3

ozrEPl92.2

fG&G==;.;

s

Ixl31m Ihl~l,wEIH

i.tEZI:::

fizzz%

sst&o

S6KD4.0

IclBo1=Iu\H)(I~lO)

STPRT ff m LOOP F(R LAWI- WmIC TIMES

ixl3& ~all=l,IaBn

5wM.i)

3w=o.o

ASiUR4.0

FSK@L=O.O

bfXFl.=O.O

AVUN4.0

Ia$&-~(IalO,Iall~

START ff m LCOP FOR MEA-%ImI& TIFES

00 m Ial2=1,IRtX6

~(~v(Ialo,Iall,IaO.w.o.o)m m m

ioe=mml KMEER; KL=w@Iffi N.MfR;rkwA N&Elk

KSsKICCfJt NMfR; SKWMINIMLM MCLM SKIDJZO F%R 0U.E;

si?u+tsa;mLwm KLLM SKIOOEO PER CYaE;

lF .SKW++tVKt MN INTEWnlW

EWTICN FIR SKImIH; TM IS WT USED

OWE SWHLS USED FGFPETCR; A...=?,= IN APPEHIIX

5 THIS REPCRT F(R SKImIffi EQMTION; E=SIMBX FCR

TR4EL FJWY . . . . . . . . . THIS APPLIES lD FHZ&,FIIcBE

WE CMEIffi LEED BELW

IF XN.K.XI IlEN INlEWTIcN EWTIUI IS IHO T D CWlJlE

VALE ‘3 FAW ++lRAbW. EWTY

5 XN.E.XX WN INTEUWCW EWTIQI IS UZED T D CMUIE

VALLE ff F/U.+++ 0ISM.Z FACTCR-IIWL UWED
759w Fwc~fwl.067%3

76aB F,WL=(SKKW(I~13))*3.157x#

761m FACIL=ma~7.4569%

76203 nME.0.~1395469*((F~*FACBETPCCE*FPUI'FPCEE*FPCFE)/

7Mo 1(FPEK*FPuE))

7640 nws).cQa5166*( (FPCJ_TW\LtfPCBLYPCCL*FPCEL*

76503 lFA@L*FpcGL)/(FtWL.~~*FpcIL))

766mCz

7670 c.x

766Olw T-~ImIffiCtUE TIE INMIMIIESAS CWUIEDBYEWTICN

76900 LX 2 PAZ 31 ff lVA TEEONIW NITE 618, 1976 BY &VY KWR

770 WC 'FiUCRS &=FECTIffi M RlocucTIcN @ !W?ER TIRED SKICIB7S"

77103 WC TVA, lW7IS, I, 37G-28

77mw(

77303 c.x TIf.E=lWKL TIK WTY; TIML=Iw\KL TPE L(wlED;

77403 c.x PfWFT()=FIXED Cyol TIFE; W=WmER EFFICIERY;

77YSlw( pREADI(,) =REA DIFFICUTYFACTWFG? WmIffi

77600 c%K

77700 c.K

:Ei

T=((TIFEE+Tl~+PREPFT(~,~,~))/9(m(KS))/PREADI(KM,kL,W\)

9(SFE=(FPCBEtFPUX*FPCOE+FPCEE)/(FPC~*FACIE)

:iE

9(SFL=(FPCBCTPCa*L)I(FPCKTPCIL)

CYCLEN=(PRFAV(KM,~,,W\))/(fSK~SCUMX)/Z.O)

78203 AW(T'CYClEN)/60.0

?z

WTF?(Kw 275W41~. KAKS,9(V13Y,9(W,T,CN,A~

2750 FWWT(4; I4 2X f4 iX i4,2X,I4,F9.1,1X,F9.l,lX,

78503 lF8.2,1X,F!.O:Flh.2; '

Y#+WW(l.D/A7H)

E% 2mlartrIW

7e#Jl~

7amc.x

79ax)CJc S'.WA= W TIFL ITWMDTPXEAU. SKICOERS IF MEY

;9% URKEDTamtERCNMISAREA

793BLx

79Ko s-wA=l.W%m

94LA~srwv\

IF(MKD.GT.l)IITE(Kw,285o)KM,KL,w\,~

79703 2&50 FLlHT(4X,I4,2X,14,2X,14,57X,FlO.2)

79833 29moJvrIFM

iti%

vcutm.lo,Iall)ew vaf44(Ialo0,1allw3w

mlm m(Iawallw3xbwmN

FSKJB.(ICllO.ICLll)f/~N

2% a6KDww wm.ualo,~all)~wswpL/sM9v

835Lll y\y(D~(Iaio,~all)

81CCll

81100 eRITE(W,29m)~,~,W,~C

8l20l 2950 FCIWT(~X,I~,~X.I~.~~X,F~O.~,F~O.~)

&WI 3oo3coNTIfkE

814Ul vam(~alowm4

81x0 u)GMEr(4,IWD)++I+J

IyLll=Ia.BDI

Aw04(Ialo).ll

FSKlBl(Iu1o)sFsKD/pal1 ldWBrlualobswfWw4

bRITf(Ku sob?4 sM*y\,sKIM:

$g a60 FtJWT(4;.14,93X:F11.2,1X,F11.2,//)

aaal 3lmawTIHE

a25m UWE(tW,3125)

.Z'&Xl ___ 3125 _-_ FtYWT(/ZX.126('*')) ._.-.-.. ~ ,

g

UWEW 3l50)

3W Fi,+,,T(& 2(/) ,,?$i("') / ax a'*') ' pifit i.-I~'&

19('*'),5X,k'*'j,' PER bl%lD~:lx.9c’~‘,,/,

~X,~\~EI~',~~X.'\+I~~~',,/,~~X,'A~',~X,'A~',

a3100 317x,'AyERpEE ',3x,'AKRpI;E',/,QX,'Aww;E'.6X.'FIxm',5x,

~'TRAKL',~X,'ALEWT+'.~X,'FIXED',~X,'TRAKL',/,~X,

5'FRHx)',2X,'LAH)Iffi',3X,'LAH)Iffi'.3X,'LAH)IN;',SX,

6'~',5X.'~',3X,'s(ImIffii,3x.'~ImIffi',3x,

7~~ImIH;~,5x,~~ImIffi’.3x,‘9(ImIffi’.3x,’sKImIffi’,/.

~,'~',3X,'NIFBER',4X,'vtcIM',5X,'~',5X,'ML~'.

~~X,‘~CRES’,~~,‘DISTMCE’ ,3X.‘DIsTpM’,3X,‘DIST~‘,

83gx) ~~x,'DISTPHCE',~X,'DISTAKE',~X,'DI~~',/)

axxn m32w IaWl.EERH

aim WC

~I~(~,~)Ial4,Ial~,~(Ial4,Ial4A),

iv~(3al4,Ia14A),AsKDBL(1a14,Ia14A),

mm(Ia14 Iam) biwmal4,Ial4A)

E ?ZQ F(IW\T(4X,14;5X,14,1;.F9.0,2X,F8.0.~X.F8.0,3X,F8.0,3X,F6.0)

652m 93laMIME

853JlccK

wmw(

85503CJc @JlFwrLAKJIffitwMEMmvcLIM.KREs AN)SKIrnIffi

85600 c& OISTANzfS BY t4cTH.m 0N.Y

65703 w(

85803w

Ei

cRIlf(~,3240)Ia14,~~(Ia14),~~(IaM),

~(Iai4i4),F~(Iaw),ldhI)BM(Ia14)

861m 940 F~T(4X,14,30X,F10.0,1X,F10.0,37X,F9.0,2X,F9.0,2X,F9.0)

e6m ?zWcoKlIN.E

% 3350 %l%i?% 27('*') / 24X 'TRLCK' I

86703 123X,'~KL:,/:2XX,'~',2;,'~II;G',2X

86&B 2WWTIO('./.2X.'NWR'.3X.'~R'.6X.'FtClO7'./)

86m m35u Ialj.i,rkni '

87Wl Iatrfam(Ia15)

87100 m 34m Ialf+l.Iam

a72w (;1(

873mKu-uwTwf-16-

874m WK

a7w GI(

a7fm w( 1lb~=ElHB WER; IRN=bWIffi tUER Ftl7 MIS t4PW

877m w( lKlW=lRucI(SPfEOOBRECTICN FnClU? lWTEOX;NIZES

87803 c&K TWTTR4KLSPEEOM9YIECREASEASWMSTAMWll

8790) WC CEUWSESASAFWTIONCFR@DLENilH

it%%

(IE O.mW.I.DFVWMATTf'.AbEL SFEEDATTtE EN,

M 83% (r BEGIFNIGTRAKL SPEED)

rn(I(R 3363)Ilbw IRNTKW

E 3360 FOWT(il 1X 12 1; F4 i,

E

TxTcrcIai5,iaisGti

wITE(KW,3370)Ilw,InN,lKlw

88933 3370 FUU+?T(4X,I4,5X,I4,6X,F6.2)

88903 34moBTIN+

89ooo 35aJccNrINlE

89103 WITE(Kw,3%D)

892Ol 35% FW39T(/.2X.27('*').//)

69m cR1lEclw;3eJ,

&kl@l 3EOl FCIFnAT(lHl,/.2X,94("'),/,57X,5('*'),lX,'W. TRLCKS',lX,

69500 lwwffi ToGETtER . . 1x 51”‘) *./

Et

228X,‘CYCLE’,4X,‘M);EER’,5X,‘TRUCK’,5X,’WU)IN;’,

33X.‘LAMIffi’.5X,‘FETKx)‘,5X.‘~‘/.

EEt

42X,‘FEMOD’,2X,‘U\N)Iffi’,3X,‘~~’.4x.’TI~’,6x,

5'ff',6X.'TIlrE'.4X,'TRUXIN;',2X,'~~Iffi',3x,

WE?

6'TRuHN?,3x,'lRuxIffi',/,

E

72X,'HMBER',3X,'NCMBR',2X,'NIMBER',3X.'HXRS',5X,

a'~',sx.~HxRs',7x,'~s',hy,~m9',

%X.'tKYJ?S',7X,'msT',/)

z!lzE-z

fXHllw( ST/V?TWm LCWFCRWW?W+lRLCKIffiTIMtS

907mw(

scaa,cx

%zz F34lm+oo

m3950 Iaif+l,t+fni

91100 Iam7=bacrai6)

91ml w(

913a) w(

914mCK STPRTCF mLmPFO7W01NB+++lRLCKIffiTIMS

915co w:

91605 WC

917aJ m 38x) Ial7=l,fam7

9lm 94lMMl.O

915cu

i7zL.x

92mc.x

923JlCiK STARTCfmLWF(RTRUXS+++IRUXIffiTIMS

92401) c.x

!+2mw(

E-i

7+mfwmmw(IalB)

Tuwmmwn~(IalB)

iEz

~=(mFiB(Ia16.Iai7)/5285.0)/

;E

l((TKTCIID(Ialsf*(i.OclKTCF(Ia16,Ia17)))/2.0)

IKR~(MFTB(Ial6,Ial7)/5280.0)/

93mlw

l~~TKRwo~Ia~~+(l.~~Tff~Ial6,Ial7~~~~2.o~

933mw

934mc.x lKCT=lRUX CKlE TIE; lKlEW=lR4W’lY TIE

93503&K O'ERKmWnmRo4D; TKlLb+blRWLLWnOTIff

9xcQw OKRt@tKm6R(u\o; IUEBR=TRAKLTI~EFJWY

93700 Lx DWWaaS(RBUILTW@; lKnW=lRAbELTIbE

93mJLx L(WJEDWR BJILTCRW3306RWD

9mc.x

9moc.x

94103

i%tz

1K~=(~KmJr)tlKnWl(r1KTEBR+1KRW+(mTPC(Ia~)/m.o))

mfmaw

IKCYC~(Iai6,Iai7)/IKML(Ials)

E

lKH=lKcrvKcYc

34KeMwcl.QI1KH)

www 37omai6 Ia Ia rm m ~KH

= 37m F@MT~4~,14.5X.14,~X,14,iX.F7.i.1X,i9.1,Fi0.2)

94x0 375oowrItE

iTi%Ez

95103 c.x WIKH.=MTIbf 1TKM.D TPKE IFW.lRLWWWD

95M)c.K nrntfR
9553 34lKH=l.O/WlKH

rn~~P4lKH

53lTKlcmm

9cml WrnH

lF(NlF& T;I.l)~ITE(KIJ,3&O)Ia16,Ia17,SMnaH,9JmaC

s Xtl F~T(iX,I4,5X,14,38x,F10.2,F9.2~

----- -._. _ .

izl

94wJcw

LC@ET(~,IR~~)-SMIK~

%wl WIlEWi,39mlICL16,9rllkm,SMIYm:

96503 33C1l F~T(4X,I4,67X,F11.2,F~~.2,/)

%ml 395oor(TIKE

96703 WIlE(KYl,~)

%KIl 4033 FcREI9T(/ 2X !%('*'))

96Y.x IFwlRAi.E~.o,m m 45(;0 CmTn _ , _ tnlTFfKu.42501 .- - . , 97103 4250 FwIwT(2(/),2x,21(‘*‘)./,

972ca U K ‘coMTRAINT’,/,5x,‘coEE’,/,2x, ‘I= lam M’J.

973.x ax”% w ~',6X,'WW,/,2X,'3= WD HR',6X,'mD'./,

9mm _. .__ nx:'rr- mu( W'.6X,'VPlE',/)

97503 ~3'4403 Ia2~l,fcW4T

97m

97700

9mxl

97903

98ooo

9aml iEPD(m,4m)ImO,csTVAL

s 45)3 FWWT(Il,lX,F9.1)

mxtx=JMYSC-(4-1C0)

93axc.x

99lCIlW(U%RaXNDRWDCQNSTR~TICNHXRS

93mcx

E

IFWSlFO.Ea.I)P(K).

B(ICSIFO.~.l!NK,M)=l.D

ilzk.x

BwsTFo.Ea.lv.w(Ko=1

9970)Wc~aXNDFCRKIGHTEDWYOIffiCOMT.&MhrIffi

9woom

999al IFwsrFO.Ea.2)P(KbCSTVPi.

:z

IF(tCjTFD.Ea.2)A(K,EmfsC)I1.0

lF(ICWD.Ea.2hTVWK)~

1OCLK

;al%l~::lPRRDF(RSKIODIffiHXRS

lOZ6Ol JFwsTFD.Ea.3)P(KwSTVAl

Es%

!F(ICSTFO.Ea.3)A(K,M)=l.o

~F(ICSTFO.Ea.3U!FfGKoJ

1cMBLaW

1lWCOW UPPER tUNDFcRTRLCKIffiHl~

lOlCRl

lOllal

lOl20l

1013x

1014m

iOl6ol

101600

101700

10111x)

101900

:E

lomx,

lo23J.l

lD24Dl

102500

l(32600

102700

LK

lFwxFO.m.4)P(KkcsTV~

lF(IUlFO.Ea.4)A(K,MXWrjC)d.O

IFUCSTFO.E1).4U’WK)=4

IIlEwu,435o1imo,CSTVAL

4350 F@Y.WT(~X,I~,~X,F~.D)

4403 OMIKE

LAlE(I(W,4450)

4450 FCIWTU 2X Zl(‘*‘)

4!mcmTIKE' ' ’

/)

IwwT.~a.l~mnu=t+ww~.o

5w+iT.Ea.2~mnu=~w~.o

IF(IUYIT.Ea.3)mnK.~~.o

~~IwrT.~o.4~mnu=wu.~l.o

1oSlol 2F&O,lX,F6.0,2X,F12.2,2X,FlO.2)

1052uJ 49ooawrINlE

m!mJw

1056iuW

1057al WC ##w####KIwYsEcrIcN 2~~~~

1058;ow(

105903 WC

lo6aJW

1061OJOX FCfWTSTATbWl'SUSEO INRAVIN~IN'SPRCLRAM

1o62oo(wc

lFOWT(lHl / 3X 'ITERATION Nl=' IS)

:% C 112 FCIWT(lX i2x’ 4iIN13X 4112h3X 4Il2)/(13X 2112))

lC6Wl C 121 F@U44Td12.k2.3X.4i2.2/(14X.‘&.2)/(14X:412.2)/

iofxu3 c 2(14x,mi2)j

106700 C 122 F(RM4T(5X,4F13.U(5X,913.1))

lo6805 C 123 FaFy\T(W.F12.1,1X,~u.v~4X,412.1~/~4X,41.1)/~

lc693lC 34X,z=l2.1))

107CXX C 325 FC+U#T( lx/ 7X,B1Y;LUTICN,IOX,MIABUW)

10710 C 326 FWiT( lX.14HvpAIABE ~~,2X.3F15.4/(2X,4F15.4)/(M

107Mo c 4,4F15.4)lcX,sl5.4))

1073X 102 FLTWT(lX,5X,37HM OtUECTIK FINZTION IS NIT WMED)

107403 335 FCIWT0tW

107503

107Em

107703 IX

107eJxl WC

107900 OdC

108oo;)ax:

lC8lol

1092iu

:Ez

108Mo

1086u)

1087ffl MC

lC@BoJc

108903WC

losm,Mc

109103

lD92fXl

E

1095ooaC

l@%JlMc

1037Lmix

1098ooMc

lC9WJaK:

IlIxyx OJC

11olal aJc

1102oo

IlMoD

IPl=l

IP2 = 1

M=NlMEK(rCIMM61NBc\SIS

N = NUB3 CF CIYJS IN "A" WRIX

M= IClP.AT+7

R=#!ElH+lO

N=t#CFH+W

tQ=tHlH+5

t43 = Mtl

I$=t#WliM

I~P=offDYFIRSTrAaEAUISmERIIHlED

=l IFALLTAEEAL6W.l.DEFWlED

IRfP=l

ITi

WIlEwQ35)

EF=.%6

"~"PRW\YCaCfAIMA~R~EYWYDIffimEACHOOL~

IN M "'A" MRIX. IlJt TD M MRXX, W IWUT INl'O M

NRIX, M FIRST M aXW6 W’SIS) U = M HWtIX MUST

EhWBZREDmREFLECTlHEFPETT#%TIT9011DAPPFIY\

ATM ED CF M WRIX.

t.0 3 I=l,M

&W(I) * N2+1

ilO4CO 3 CONTINUE

llC#l MC

fDgO$ MMeROlW?OLXUWSASMW;HTWkDlEATFRCNTfft4QRIX

lloaxf 004 1+0,N

11Ceal J#R(I)=I-!4

11100;) 4oxTiM

llllal

lll2lx Lx

111433 MC

1114crl UC

lll%U

lll@l

111703 M:

lmal an:

1119al lx

:iE

llzzul OJC

1123x3 MC

13240 cx

lL?Y.-RMc

112MoMc

112703

:sa

11m WC

113103 C+K

1132c0 w(

113xX) WC

113403 C.x

113xQ

11WB

1137aJ

113803

113903 lx

1140x ax:

114103 MC

114.m OK

1143x

K+43

SETFfWJZTAiICE INOtMCTIKFWTI'&

C(K) = PkWf'C

K*WTHW+l

SfTR@DE~F+WHWlYCOST INC&ECTIYFlWTICN

C(K) = -SC!ZK

K =K+l

C(K) = -D.?lWILiZR)-S)sMc

K =K+l

C(K) = -94WC

K =K+l

C(K) = -9llWK

K =K+i

114900

114503

1143x 778 LwrIrw

1147itl A(l,t43)=1.0

ll‘lax K9+UWWl

62
114900 K8=M+2

llw33 OIC

115105 MC STORE D(\TA IN “WT” HRIX IN “A” t+URIX lo E @LYD

115200 MC IN LP

ll53m W C

115400 a, 317 H&K9

115503 CO 242 J=l,M

115603 K=I-M-1

115701) A(J,I) = UWT(J,K)

1158x) 242 WTINLE

115903 317 ONTINE

116ml MC

;;6E& 2 STOE 2 VALES INTO “A!’ MRIX

1163m K9=K9+1

1164m KB = K9+3

116500 J;l

116600

116700

117105 MC STUtE CCNSTRAINT RELA’TW To lFJXZK UXME INTO 'A" WIRIX

117al MC

117xa A(6,W.l.O

117400 MC

117503 (M: STCRE lRa KLlw INro “8” WRIX

1176u) MC

117700 p(6)=mnv..

117800

117900 iY)=zY *

iltao;l ax:

118100 MC ST~E ~MTRAINT RFsmIcnffi 3.kd ff tattz m fwu. OhE

ll62moJc

ll87m OJC

ll8rm (WC STW 1.0 INm ‘B” WvRIX

1umlMc

119ml P(7) = 1.0

119lm B(7) = 1.0

1192m m 5 J=l,N

119303 JhAbWJ)

119400

119500 5 EkY(J)

119600 m 301 1d.N

1WDl CI(I)Z(I)

119830 IwI)IJw((I)

1193m 331 OHIME

l2umMc

mlrn 01~ sw aws Item t4vRIx

l2umM

Eli

m 444 I=l,n

A(1,I)d.o

l2wl 444mFTIHE

1206M l94 Wt+-9.EJ)

uo7mM:

1208o)Mc c&aJAlxcBpRRcw

laul ax: @JER m LW aZNIRflS UN+6 IN W WRIX

121oxoc IrwtmuwainasSIPNIH;wwaEFENTwm+.M

12llm fx

2%

m 74 dG1.N

24.0

l214u) OJC Y? Is p(MoLcT CF W WAY OwlMy TIlrES CE ELEWNrS (T: WRIX

l215u.l MC

l21603 m 75 1=1d

121703 75 z=z+Au,JwcI(I)

iii%% ENTISC-WWEKIF~TIY\T’=~EH

l22UlloJc WIsAWAYlWTtSDFCC-BPRaEFENTS

l22lmoc

Ez ELzi%

lmcoan:

).22!33loJc FIM)L%fSTW.LlE INC-BPRRCWTOIMASPIWTOCLW

L?BBM:sTCF~VALLE(FVV\GESTC~~NTIN(TPM~~

l227Ol& PlKITMtbNKElfR INKWI

iE2.F BWB4.GT.ENT)GO m 74

Ei2 ii!iFz

E%x

74 OBTIW

moo w 1ta7wta ~mv\nat ~cuaTu7 AH) *ITE Irawm busa

l235mM

i%i

IbIT+

uWEW.l)IT

izzL3x

I F ~~~P.EO.OKO m 25

l2403l (y: rJiLlJAlE Z WE Ml SXRE IN ,WIAIU “Vk(T*

124100 ti

l242w m1vPlE.o.o

l24xrl m 110 I-1.M

l244m 110 VPLlE=Viu.CE+P(I)FI(I)

l246moc

l24KXlC4 WRITE DJT “A” f4URIX As IWUTTED INIO LP F%CUWl

124703 ax:

l248)oc.x

l249mcx OEBU;FawTBTICN:::: MISF(RMRT IS twul m

12%XBw( FU.LWBJTSih5lBZIWUTFu\~iXINMEF'JM

125105 w( USED BY RAVANRIM :: wx AN) zJ.wl.16 FIRST

12yo3 w( MN NlRlrpL LP VPLLTS

l2mwI(

1254m IFU.PUZ.EO.l)IAITE~KW,6a)l)M,N

l25Ka W.ll FW#T(25X,'RQJS 1 lH7U ',13,' PM COLWS 1 lHUJ ‘,13,

Ez

1 ’ IN RAVIW LP WIRIX ,/)

m 2456 K=~,M

lFWCE EQ.l)WWKW,6456) (A(K,JW,W=l,N)

;E 6456 FGWTh0.2)

1260x, 24% COYTINE

l261rn 2457 OWTINLE

l262cooJc

l263UlD.K bRITEo111TDPTWfE m FO.RLINSW TABJWWIICHDB

1264rna.c NlTvPRYBYNMfR~bEETH3c6

lE5maK:

m ~1lE~w.60331

1267m 6x0 FClW%/'lX l28('*'))

126833 uwEcw:miD,

1269CXl 6’310 FGWT(lX,‘*‘,4X,‘* l ‘,7X,“‘,99X,‘“,11X,‘*‘)

127030 K2=aWlH+2

127lm K-1

127200 WTEW,W'J) C(M31.(C(I),IX2,N)

127300 6020 F(By\T(lX,‘*‘,4X,‘* *‘,2X,‘CJ’,2X,‘*‘,lX,F8.2,49X,4(lX.F9.2),

127403 11X ‘*’ 3X ‘R&H-r 3X ‘*I)

1275C0 w&&.koa) ’ ’

127603 603) FOHTW.,'*',4X,'* R *‘,5x,‘*‘,99X,‘*‘,llX.‘*‘)

127700 WlEE(ta,mo)

1278133 6D?3 F;)D49T(lX,‘*‘,4X.‘* A *‘.4X.101(‘*‘),3X.‘HAH)‘,4X,‘*‘)

iizkx

N3=tfElH-1

128lmoJcwwimsTAmiE~tueR~aww~urrmrpcuRDIffi

L~~M~M:~MEMMERcFNIK~G

_-__ _._

iEl&x

m m uaq7010,7aa),~3

129lmw(

129205ax:

1293031X UWECU~TAEEAIJF(R~WPJU~~NWMJKM~I~

1296cx) 6060 Fw\y\T&'*',5X,'* S * *',a'*- *MMJ) **

1,29x.1* s&R * s/If2 * s/k * s/la *’ 11x ‘*I)

. 3

129903 6070 FClWT(lX,‘*‘.2X, ‘CB’.ZX,‘*‘.2X,’ I l l (Yo) *' 4x ‘1’ 4x

1"' 4X '2' 4X '*',29x,'* K$(@ * m * y& ;I, ' ' II 9

2' lilk * m(sTPM'S*')

lI3lm wuE(W.60BO)

13(ua 6083 Faw\T(lx,‘*‘.7X.‘* S * *‘,9X.‘* (M1) * (R)

slit

l’* (Zl) l (22) * (23) * (24) *‘,11x*‘*‘)

*‘,29x,

wrE0a,6050)

1306(a f3Hl Fow\T(lX l2%'*'))

lx17m wwEDw.h5)

13’HXl 6115 F(IPY\T(lX.‘*‘,9X,‘*‘,4X.‘*‘,99X,’*’,llX,’*’)

lwwO(M:

1310ooM mL~awllEaSllWTIffiCF VICHRCW INWURIX

l3llm MC

:ziz

m BXT) I=l,M

K=IVAR(I)

131400 ax:

131500 wc wd71pa~s ~90 m arrrmx owur. w i+w m ni~tu

1318x)Mc mFIGkRECuTTHEv&LuTH(\T~DmsEt6sIwom

131700 Lx THE VPRIAE.ES

13lml MC

l319a) t&t@+1

Ei LEE

1-w

132-W DUITWFOU#ITF(RLPINCUMXFC~+~~Y~

L?WJJcXAH)WRSPWNEATtfADIHJ

13i?yD CK

1326m

%t

KUlEW,6090) C(K).IWUI),AAfI.M).V\(I.J),J=t4l,S)

UN6 N) P(I)

@30 F&TCiX

132wo

'*',1X.F7.2,1X,'*',W,'X',I2,'*',310.2,

129X.Qll).i,‘*‘.lX.F9.2,1x.‘*‘)

13X03 &XXI CONTINLE

wlm WlEWW.6115)

WUEW 6100)

:i%!! 6100 FUWT& Ii?&'*'))

133400 u1xcw,i1lo,

133xX) 6110 ~T~lX,‘*‘,14X,‘*‘.99x,‘*‘.4X.‘Z -‘.4X.‘*‘)

133mDK

1337CIlMc LRIlEC-BIyIRMWTINTAMAlJ

1338ooIyc

SA(1.J).

WITEW 6120)

:% 6l20 FWWTCl;

(CWJ).J=%N),WLLE

wlm

,'*',W,'C-BM RM'.3X,'*'.310.2,'*',28x.4F10.2.1X.

lFll.o,‘*‘)

l342m mm7wo
134Bl 7010 bRITE(I(w,6130)

1344mMc

143503 IF(lWTA.LT.THHl T D 812

13m 6140 ~T(lx,‘*‘,2x,‘CB’,2X,‘*‘,W,‘I * * RICE $ *‘,4x,‘l’dx,

13510;) I'*' 4X '2' 4X '*a 4x '3',4X,'*'JOX.'* Km * LAW *I%

1352iYl 2’ ‘$0 : iI&& *‘mrST+WTS “)

1353al HIlEW,61W

135103

135503

135603

135703 ox

135w chc

135933 cidc

lw35)

Ixdrn

1362o;)WC

1363CDW

136WWC

:s

136703

13Eal

a) ml0 I=l,M

K = IVA’?(Il

W9+1

%=wl

t4W.W

W7ITf(KW,6160) C(K1,IVPR(I),A(I,~O),(A(I,J),~,~).(A(I.J).

136!3x IM6,N),P(I)

137ccO 6160 F@HT(lX,‘*‘,1X,F7.2,1X,‘*‘,1X,‘X’,12,’*’,4FlD.2,~x,410.2~

1371m lFlo.2,1X,‘*‘)

1372m ml0 (DNTINE

137303 WIEWI,61l5)

137403 !4IfE(KN,61rn)

137s.l WTE(Kw,6110)

137600 0%

1377ooaK RINTsmTc-wllw

1378113 M

137900 WEW,6190) (UWJ),3;M3,N),WLE

13WB 6190 FCRMtT(lX,‘*‘,2X,‘C-W ~‘,3X,‘*‘,~lO.2,~,~10.2,

1381m lFll.o,‘*‘)

ram7wo

138403 WC WTE GUI TAEEAU F@? D.WWW Cf F0.R bETH%

1386mM

13860 7020 uwE(al,62rn)

133700 6203 FCFWT(lX,‘*‘,5X,‘* S *’ 3X ‘* ELLIffi ’ 4(‘* FRHX] ‘),‘*‘,

19x,4(‘* $/HI ~,,~**,ll;,h ’ wIlE(Kw,62lDo)

139m) 6210 F~T(lX,‘*‘,W,‘CE’,2X.‘*‘,2X,‘I l * FRICE S *’ 4x 2 ‘I’,4 x. I )

139103 1'" 4X '2' 4X I*' 4X '3' 4X '*I 4x '41,4X '*',9x

139203 2” ‘& *’ ‘I.&‘* ‘xi0 : kCK : CCdNTS *‘)

139303 L4wmw,6220)

* y’ *‘. (22) (23) *I,

13%0 ~ITE(W,6l151

139903 m fBD I=l.M

14amax: -~ .

fma& of$ wJ7IAEES LEO T D aMma. Mllwr

:s

K = IVpR(I)

N i = N9+1

14oMa K, = N5+1

i4c#l M=K3+1

140703 UUTE(KW,62W C(K),IVPA(I~~(I.FO~.(A(I,J~,~.~~,(A(I.J~.

14CSXl lM6,N),P(I)

14CWJ 6230 F~T(IX,‘*‘,iX.F7.2,1X,‘*‘.1X.‘X’,12.’*’.~lO.2.~.~lD.2,

141Lm l’*‘,lX,F9.2.1X.‘*‘)

1411m 8320 (DNTINLE

i4l2cil WITE(tsf,6l15)

14l3xl WIIEW,6lW

1414a IRIlEW,6llO)

141fal arc

1416000& FfwrsaJrctlwI(M

141703 aJc

14laxJ UUTE(iG’.6?6D) (U4Z(J),J+%N),VRLI):

141903 6260 FmT(lX,‘” ,2X,‘C@.Nt iU%” ,3X,‘*’ ,5F10.2,9&4=2.‘*‘.

142033 IF11.0 ‘f’)

142103 7W DBTItilE

142x0 PIlEW,6131)

142Bl 6131 F@WT(lX,IzI)( ‘*’ ))

142400 MC

142503aK

142600

1427CU

1423zl

142wl

Mxco

143103

143203

143xJl

143403

14?.Ym

143603 m 8l2 I-1,M

143703 IF(A(I,tWTUE.EPW x) 812

14x0 Tti=P(I)/A(I,KIxIT)

144033 (WC

1441m C-!C VARIAEE RETA CDNTAINS VW! CF PIw)T ELEIENT AFTER DIVISIor(.

144203 (x: IRIN CONTAIN5 THE NHER (F lHE PI\DT @I.

144300 M:

:z

MTA=lH

IRIN=I

1446m 812 mKFINLE

1447m W C

144870 Cwc DECK FCR LW?3UED SCUJTIOJ. IF FO WITE WI bESS%

1449tocdC fwlEN)k%aw4

145cul MC

1451m IF(TtETA.LT.9.fEWl T o 597

1452ol wm0?4,lo2)

145300 m m 192

1454m 191 IF(IRP.EQ.O)GO T D 601

145503 WC

145603 GJC VPfW&E PIulT aMAIM PIWT El.@EM

1457013 OJC

145800 507 PIWT=A(IRIN,WT)

145903 P(IRINfP(IRIN)/PIWT

141im . _ _ _ cl&- _ _

1461m OIX: DIVIE PIWT Rf& 8Y PIKIT ELEI4ZNl

14EQlOit

M63.33 m 521 J=l,N

146W 521 A(IRIN,J)=A(IkIN,J1/PIUIT

1465mcuc

14fE0.l Ox m ECESS4QY WIRIX DIVISION #TER PIWT ELEMENT ANI O M

146703 ox: IS FWM. OUTER LCX)P mmhxS coLIM6: 1W.R LOOP

146ipxw LBmaslMJs

1469m ax:

147030 CI3 522 J=l,N

147103 ff(J.EWM)co TO 522

147aJl aJ 523 I=i,M

1473co ff(I.EO.IRINXU T o 523

147403 A(i,J,&I,JbA(I,kWT~‘A(IRIN,J~

147x0 523 UNTIW

147600 522 EM’INLE

1477m m 529 I=l,M

147803 ax:

14EUlW IF STATEt4WRQlEClS PIWJTELEMfNT

14am,aK:

14810 rfu.E(f.IRI~xx~ m 529

1482Dlax:

148333 (WC WeCUAlE RIGiT-WNI UtSTANTS

1484ooW

:EoJc

P(IkP(IbP(IRIN)*A(I.@UT)

148xX) Cwc ZERU iM PIWT aXLMy

14R3XO+C

A(1 tWWl.0

:E 529olNilNi.E

149100 EP=EP+sE-6

1492m CI(IRINbC(WT)

14933 IVAQ(IRIN)=WQ(KDUT)

149403 w

14959 OK SET PIlDT ElEbENr m 1.0

149WoJc

1497m

149213)

yp&ur”1.0

149900 MC

15MaMc biWECUTWW#YEMM3E6PICEDFW4lP

1601m.w

l5mJl l92aMIN.E

l.WSUl& IlDTKEEFSlWKWNBERCfFEIWJSPICKED

150605cwC l5S.MISTtEMEffltfEIWWTION~WIiEmmPICED

1507m IM:

l5G33.3 IrnT-0

EE

IrnIP=D

ES1m flT?i%-“-I.25

151Mo 9431 awlIrv&

l513ll

1514m &~~~1y4

151503 RmELPYbo.O

l516m LDwEl.PY)~.0

151x0 9afwYbO.0

151800 ai1tw0=0.0

151900 9433alNTIraE

152ooo wwH=O.o

152lm ilhFGO.0

SMOT=O.O

kRITE(Bd,65m1

EC0 FcRMI\T(lX 16('*'),57X,'m',40X,12('*')./.lX,16('*'),

157X,'m':40X,12('*')./,lX 16('*'),9x.

2'ABBE VALES IN C-BAR ROJ'.Z%,'m'.6X.

3'ABovE VALES IN C.&W RM’.9x.12(‘*‘)./.lx.l6(‘*‘).

49X,'KtE R~NOJSTS'~31X,'~~.6X, . .

5’pRE 9wM PRras’,17X.~(‘*‘,,/.lX,1~‘*‘~,57x~’~’,

64
6/ tk ‘I’ .2x, TbaxixTIM’

i,kJ4s~,4x,‘m’*12i ‘ms’,l2x,‘ms’

76X.‘H)IRS’.7x.‘(xKTs’.7X,~~S’.7X.’uKTS’,5i,’C0~‘./,

00'~)~ bi.MCO 1012 K=l.WTH

KM+1

1f;(~~(1uu2~ 00 m mu

s

LpRR(I1bIu4wbl

nS!M=lSsu4+P(I)

IlOT= ImT+l

l3x&vw~f’

rax12PbLoxT(2,I2ww(Il)

~XI~P~LIB~~(~,I~P)‘~W(I~)

%(12Pbul3ET(4,12Pww(11)

yw&o3$r(5,12P~ww1)

i7.w%&(12P)~tc

LpHMc=LDW1~D~(ILCZW%S4C)

zziz3%zz z

m(12p)

sERpc-9JFRpc+Rww:

swwwwiD(I2P)

sl4JJcmm

ggggggl~)

sHvwww+lK(I2P1

tiMlXIuMIpc+IRwc

mTliwwx+bv4x+3wc+ntuw

SMlUT=SU4lOT+~

LAIE(KW,BW~~IPRR(I~~.PROP(I~~,RC(I~P~,R(,LD(I~P~,

~.sK(I2p),9(IMc,~(I2p),TRu(m,lDM1M

8317 F~T(3X,14,6X.F6.2,1X,F9.1,1X.F8.0.8x,F9.1.9x.F8.0.~,

lF9.0,4x,F8.0.3X.F9.1.4XJ8.0,1X,F9.0)

lo12 OzNrIw

blwE(KII.BwB)

8048 ~T(12X,7(‘-‘),~x.9(‘-‘).1x.~‘-‘),8x,9(’-’).9x,

18(‘-‘),2X,9(‘-‘~,4x.B(‘-‘~,3x.9(’-’~.4X,8(!-’~,1X.9(‘-‘~~

~ITE(KW.LDd9)TSKM,S,~,~*~~.~*

lS.WC.9WTRI.9NllrC.SLMRTl

8009 ~w1y\~(1~,‘TDTkS:‘,5X,F6.2,1X,F9.1,1X.F8.0,8x,F9.1,9x,

lF8.0.2X,F9.0,4X,F8.0,3X,F9.1,4X,F8.0.1X,F9.0,/,

21x l28(‘*‘))

t3bksv-mnk

Q?wev-VALUE

WmYALmTLK

QNWZAM(pc-uNIMc

WITE(KII,BC65~V*RMCR:

855 F(IF39T(Z(/).lX,m(‘*‘,,/.lX,‘(A, TOTAL CELIKRD PRICE’.

1lX.W WWESlED TIWfR:‘,2X,F13.0,7X,‘lNIT lWE:‘,3X.F9.2)

lwlEwai.g)6o~.GwHu:

EIEO FUWT(1X.W) TDTR. HWESTIffi COSTS (THIZE CCNSIIEGEO):’

l.lX.F13.D.7X.‘WTT cOm:‘,3x.F9.2./.5oX.7~‘-‘~,~X, 2j(G))

kRIIE(Klt.8l7OwuE.Lrw

8D70 FUWT(26X,‘OIFFEREHI: (A)~B):‘,2X.F~.O,2lX,F9.2,/.

lolf'+'\\ --\

0l.L siikN.Nl

SrcP

1607m

Es&

t!&YJTI# §M(N.Ml

16103 -MIS ~~TINE IS M EX~JTIK ROUTINE m INITIPLIZE w

161100 C SENSITIVITY IWLYSIS.

16l2U.l C

161Xa mmrr C(~),P(~).~(25),A(25,25),25(25),IVAR(%),RX)S1(25)

:%i

i,9w13(25),a(25).w(a).ap(25),ao(25),8p)

2,WS),cC(25),JW25)

161600 3.IllRR(4).AMp(4)Rc(4)CD(4),9;(4),1K(4)

16l7olc

;;E IjcwneIW. lHE LIMITS (r( Wi C(J) A’tE FWI. IF X(L) IS A BASIC

iWAB.E, MN SWWTINE C84S IS @LlED, DllfRWSE SLBWFIFE

162iwc CNXfl IS L6ED FCR KtWSIC X(L). IF X(L) IS @SIC, NclE IS SET

162100 c m 1. OMwlIs HxE Rkt4w 0.

162ialc

162%Xl

2

5#J.E=0

:tEi

Kg+1

L=JwI(K)

zzi

B(K.GT.NXT) m 16

co lo I=l.M

:EE

KV=IVpR(I )

IF(L-+wlD0,20.10

163x0 2ONx-1

163303 l o wT1w.E

:i.%i 25 CPUIFoclE-I) CNWK,I;,M; 30 25

aTo5

32 C4.L CfWK,N,M)

16380;) 0Dms

164200 Cmr”Nh’,SJWOUTIE WIG IS WED m IXTEPMIN ME w\N;Es aU ME

1410 c RICH tW SICE WTANTS E(I).

lW200 c

1643)o 15 C4L fiW.3N.M)

1644alc

16wJl VrrE FIW’L STEP IS m UUTE M REKRT. FIRST, ME siwu FRIES

1646ooc AN) FWLTY COSTS ARE MITTEN. #XT, lHE RAGES ON M EWC

1647m c PM WWSIC C(J) ARE IRITEN. TEN, THE 8(I) IWGES PRE

1648ooc DISflAXD, PNl ME SEMITIVITY WLKIS IS CCFRETED. IXRIffi -ik!?

164900 c WTE ROUTIHS, ME SUBWUTIFC: OeCK IS WLED, W1IM CETEBlINES

169.Jxc IF X(J) IS @SIC CR Hx(BI\sIC IN M CPTIFIM TAB&W.

165lm c

iitz

YrlE(Ku.u))

tRIlE(Ky,lom)

:zE ;aBg;

185600 KS) ’

1667Ul 11 K&+1

:zz

F(K.6T.N) GD m 31

‘XL ‘XXXW,W.N.M)

166ooo IFDQ&l) w1,2l

:EGK

21 UWE(KW,lO3U) JhWK:).FfBWK)

16h#x)&

166400 cx lRITES aJr KB-BASIC VHPAES AH) FWUTY axa

166Mow(

16mcolx

1667al W E

GD m 11

:EEE 3l uuTE(w,149)

167xow

167103 w:

167mcaK wINCuTMwERIW)wuxHPRIm

167Ja w:

167400 Cx

167Wl Dl 22 I=l,H

167700 167600 2 2 UWW&,~~,’ I.ZJ(I)

167800 uulE0&05)

167933 K=O

168300 UK=K+l

F(K.6T.N) W m 60

WI OEO((K,NaE,N,M)

5oa.G1) 50,~.~

50 YITE(tW.1061 JWK).O_(K)

1-w:

16%oJceK

166703 w( WIN CM RANZS 01 NIN-WSIC C(J). V#IIAlX.E amE

;z E AH) ITS LaLR LIMIT

16SCOlcX

163lOl oDm4o

:zEi

70 KK+l

F(K.6T.N) (I) m 90

1697W C4.I. 0iWK.HXL.N.M)

16wl FDaE) w%m

169SUl 80 LAI7E(I(W,109)3I1PR(K).aO(Kl:,.apoc,

17aa3 C.x

17Olol Cx

17CEW CX IRIlES OUT m CN BASIC C(J). WLRaE LDER LWT, AN1

17CW C,K ViWMlE LPPER LIMIT

lmux,CtK

17C6WClK

:z

wm7u

93 wlEw 110)

17Efo lRIlEwu:lll)

:E

al 95 I+4

IRIlED3l.1lz) I.luKIuwIp(I1

171103 CJc

17Eul w:

17laxw: WIlrSarVpRlAaEmEAH)~AH)La+RLD4ITff B(I)

171400 cx

17lB3w:

ma33 95mN.E

;7l70& 100 F(JW\T(ltil,26X,‘SZNSITIYTY #yvySIS’ ,2(/l,

llDX,‘NJlE:. &WARE CUE NJtERS UED IN S36ITIVITY’,/,

171903 2m,wms 4-a rm u\r( m awww unw amwd.

172030 31c#,‘ouI6 AH) rws faTI LP wvRIx’,//.

172lal 4lCR.‘lERS FPMIIH WITH LP 3UJ.D I#E ow&s IN’./,

818: ‘USED IN L-O-S-T’,//)

:fif% ml tiT(lOX ‘tJB-&WC l2X ‘PEW..TY’)

172703 M ~T(l(Ix:‘VpRIABEs’:~X:lcosT1./~

172830 lD3 FOWT(l3X.I2.l3X.Fl2.3)

1729D3 101 FaFla;r(4(/).3X,‘RPN;ES ON NhB’SIC C(J)‘./)

65
17Txu

173lcu

17900

1733rxl

173lal

173500

173ml

1737cll

173800

173903

174axl

174lol

174203

174300

17440

174500

174603

174700

1748x

174900

17m

17SlCfl

105 F~T(lOX,‘VpRIAkE’ ,llX.‘LMER LIMIT’ ./)

106 FwryITU3X,I2,14X,F11.3)

107 FClU+,T(#/),3X,‘RA%ES ON &SIC C(J)‘,/)

108 ~T(lOX,‘VARIAU’.llX,‘~ LIMIT’.llX,‘m LIMIT’ ,/)

109 FCW#T(1JX,I2,14X,Fll.3,1lX,F11.3)

1lO FC%4%T14(/1.3X.‘RAMS ON B(I)‘./)

111 FOU4U(14X.‘I’;14X,‘LoER LIMIT’,llX,‘1PPER LIMIT’ ,/)

112 ~T113X,I2,14X,Fll.3.llX,Fll.3)

149 F~l~3(/),13X,‘RQJ’.15X.‘YWOrl’,/,UX,’N~’.13X,

l’FRICE.S’,/)

lox) Fo7M4T(lX,‘wRmJ PRICES PRE C-WGE IN OfIJZcTIK FLNcII(Iy’,

llX,‘VALLE PER LNIT WWJ’./,6X,‘IN RIGHT HRN) SICJZ’,

21x,‘mwRAINTs.‘,2u).1X,‘Fwu.TY axis PRE owuz’ l

31X,‘lN DU!CTIK FLUION VALLE FfR UNIT’ ./,6X,

4'1N.REA.9 IN MKBASIC VpRIAEES.‘,2(/) .1X,

S’P.APGFS ON C(J) REPREYNT LIMITING VPMS CF Cosr’ ,

61X.‘CZFFICIENIS M9T’ ,/,6X,‘WIU MT wuIc;E THE CPT1M.M’ ,

71x,‘xLuTIcN’,2~//~.2X.‘RAHu CN B(I) REPREYNT LIMITIH;‘.

81X,‘VpLES CF RIGHT t+hD SICE ~lRAINTS’,/,6X.‘TwIT WILL’,

91X, ‘NIT O+NZE CPTIMM 8GIC VARIPRES. ’ .2(/l)

*,“.- ”

175803 -THIS i0JfIK OiEW iU SEE IF lliE INEX ff X(L) FRTD1Es M

17XOC IKEX CF PHY ff l?E UPTIMlM RSIC VAQIAkES. IF m

178w) c ISAFU\TM,NWISKTR)l,~ISAVALCEQZBMIS

176100 C REnRNED.

17@o.l c

176B3 L-JWR(K)

1764al wEdI

17&m co 10 I=l,M

176au KV=IVAR(I )

176703 lF(L-w 10,20,10

176800 20 m-1

177im .9JIRMlE CNHK,N,M)

177111 C

1775al c

mm c

1777alc

1774Ul WlHIS ROOTIIY: CflE@#NES THE m LIMIT FCR haJ84slC C(J).

M tETHI0 LEED IS m FIND 7HE MINIHJ4 VN..LE CF C(J) Y.K+i Tw\T

CL&Q(J) IN M CF’T1bU.l TAEEAU fiB#INS kEG4TIK, ‘INUS MINTAININ;

wTIl4kITY CF l?E aFm%T SUTICH.

in+m ~(25).~(251,(XL(25)~A(25,25),ZJ(a),IW\R(25),~(25) 1,9w1)(25),a(25),w(a).ap(25).ao(25).8p)

2,B(25),CCG?&Jw1(25)

3.1AllR(4),RMp(4),Rc(4)CDf4).9((4),7K(4)

J=l

10 t!i%bR( J)

~~~(KV)‘A(J.K)

IF(J.6T.M) Go m 20

mmm

-. _-- _

C

20 a(K)=zz

UK)-.

1tic

179330 om”“INZlUHl IN THIS f@UFIEE IS ME IOENTIFYING ff W FftU4el-Y

17wooC mSrCrMMNBAsICVARlAB.ES. ITgaclDBE

179xoc N)7EDTW\TIFMR~NuKIffANY~ICX(J)ISZWO,

1796JBc M IR’BEM HAS PN PLlERMIvE Cf’TMIM SCluTICN USING X(J).

1797al c

KOSUKbCIG!(K)

:tiitifI ENIN

lma FM

l8UlCl.l 9JBROUTIK C@S(K,N.M)

lt33XOC

ii%%

THIS S.B0IfIH DElEl@UtG ME RANZ ON CPTIFly @SIC C(J)

lizi

DIl@HCN ZS(@o)

OcMrcN c(25),P(25),(Mz(25)J\(a.25),ZJ(25),IwIR()

181CSO C

l811C0 CmmsIPST, A mWIMlM LIMIT IS YT ON ME UPPER AH) LckER gxN0

l8l2WC FIR C(J). IF M FIt& @UT IN Itif OJIF+JT IS THIS

l8l3llC HRXIMLM VALlL IT U w 8E mTW\T M LIMIT mEs HIT EXIst.

181400 C

Ei

OHKb939993.

CLO(K)=-999999.

l817al c

l8ltXK1 C”M*lHE LIMITS ON BASIC C(J) llRE D+lEiU4pED BY M @‘US CF ll+Z

l8l9WC NCNBRSIC C(J)‘S. WH NxQnsIC C(J) IS lRZAlED YPARATELY. PH)

182cmc A LIMIT CM C(J) IS CElEBlPED BY FINOIG ME BU CR MIN VAUE

la2100 c C(J) f#Y t%E IN cwu( m MNTAIN lH4T @‘R(J) ECATIK.

l82EQlC

l827Olcmf*zs(J) ~STHVALLECFME~MCFMEI~-%R~~~CTS~FCB~\N,

PEW. bxawffi M wu4 INHxVIffi M @SIC C(J).

ZS(J)=O.

l5 I:+1

ff(1.a.~) a, m 20

IFUWt(J).EQ.IV0R(I)) GD m 10

03 m 15

20 L=o

22 L-L+1

25 IF(L.GT.M). M m 30

LV-IwuL)

IF(LV.EQ.J\RR(K)) I3.l m 35

zs(J)=ZS(J)~cc(LV)‘A(L,J)

alTo22

35 NI=L

oom22

I&WI -IF A(N1.J) IS %@U, IT IS IGKRED BECAUSE IT PB’EMS IN I&

lwol c

18483lc

DEHMIw\IoR. OTtfRdISE. IF IT IS FOSITIK, A LaER LIMIT IS

184Srn c

FCU@, PN) IF IT IS EEGRTIK, A N UPPER LIMIT IS FOND. m

VPLES IRE MN WmD m M PRESENT LIMITS.

ZiE

IF MEY lIRE FZRE

RSTRICTIK Tww TH PRESENT LIMITS, 7HE FRESENT LIMITS &

REVISED.

EC 3l BGBS(A(NI J)) LT 1 E-OB) @.I m 10

ifi%?

IF(A(NI J))‘40 i0 !k,’

40 lUJ= CCiJb&iACNI J)

z?%z

IF(TCU.LT.CLP(K)) C&HOJ

(0 m lo

- LB5803 50 lU= (C(JbZS(J))/A(NI.J)

z% wTuT.ao(K)) sow-m

83 m lo

E 75c0NT1NLT IETWN

Es

EN)

SBOUTIE E5WXN.M)

l86XUC

186600 -IHIS ROiJTIEE OEmFlW THE w\Ms aY AL B(I).

lwm c

l8ml

iE%

187103

EE

187403 aG+1

l8m lF(K.(;I.M)GD m 36

l87W3C

f38 ~RillT’“” WER AH1 LMR IfZdNS OI E(K) ARE SET.

l879a BJP(Kb@3999%

ii% %(K)---

l89zw 20 i=Itl

lw3xl 5u.8~~4) 6x1 m 30

IBJlalc

188500~PIEISTHVALLEffMSLHffTtrEI~~TB-1~

ZE

TMS B(I). EXUDING THE TE@4 ImVIffi M B(K) Y F@E FINlIffi

LIMITS FO7. l88emc

WIFE(Iko.

E MJ

I89lw lDJ+l

EC-i

IF(J.GT.I.0 80 m 25

IF(J.EQ.KXD m 15

ii-k2

PPRIM(I)~IME(I)~A(I.J)‘B(J)

Bornlo

l8WD 15 NI*J

l89703 mm10

l89BBC

I89933 @--IF A&NH IS 94U, IT IS IGHIM). F?ESENT LIMITS I% nul

19OXklC REVISED IF IEFwMMHls ME lQSS1R.R.

C

25 lF(ABS(A(I.NI)).LT.l.E-8) M

lF(A(I.NI)) 26.20.27

26 lRJ=-fff@UI)/A(I.NI)

F(lBJ.LT.RP(K)1 @U’(K)=IBJ

oomm

27 lB=-F?RIFE(I )/A(I.NI 1

!f(rB.Gl.&.O(K)) 64.01KbTB

am20

191afl 33 IETIRN

l911ol w

19l2al /a,

data ca-ds go hwe

m20

lo z-i+1

IF(J.6T.N) a, m 75

66
Koger, Jerry L. and Webster, Dennis B. 1984. L-O-S-?‘: Logging Optimization Selection Technique. U. S. Dept. of

Agric. For. Serv. Res. Pap. SO-203, 66 p. South. For. Exp.

Stn. New Orleans, La.

L-O-S-T is a FORTRAN computer program developed to

systematically quantify, analyze, and improve user selected

harvesting methods. Harvesting times and costs are computed for road construction, landing construction, system

move between landings, skidding, and trucking. A linear

programming formulation utilizing the relationships among

marginal analysis, isoquants, and the harvesting methods is

used to estimate and select the harvesting procedure having

maximum profits.

Additional keywords: optimization, harvesting, computer

program, roadbuilding, skidders, hauling.

*U.S. CO”ERNHENT PRINTING OFFICE: 1984-769-089:32