bluuebunny/crossref_metadata_2025 huggingface dataset:
Insurance type item provisioning guidelines
Authors: Burton Robert W. , Jaquette Stratton C.
Published: May 2007

Policy decisions for insurance type items, where zero or one unit is maintained at the depot, are more difficult and more critical than decisions for common supply items. This report presents results of developing initial provisioning guidelines for insurance type items. The guidelines are based on examination of lifetime costs and benefits. Costs of stocking an item as compared with not stocking are developed through a sinking fund annual payment formulation. Benefits of stocking are developed as stationary reduction in time weighted backorders experienced. A resource allocation formulation yields an optimal policy for allocating a fixed budget. The guideline is presented with refinements based on a sample of items. A figure of merit is calculated for each item, and if it is large the item is stocked while if small it is not stocked. Empirical definitions for large and small are developed based on sample data. Estimation techniques are discussed for deriving all of an item's parameters needed to compute its figure of merit. A Bayes procedure is suggested based on family group Experienced Demand Replacement Factors. This and other techniques are discussed.
Periodic replacement with minimal repair at failure and adjustment costs
Authors: Tilquin C. , Cléroux R.
Published: May 2007

We investigate periodic replacement policies with minimal repair at failure, thereby, minimizing the average expected cost per unit time over an infinite time span. The standard cost structure is modified by the introduction of a term which takes adjustment costs into account.
A recursive branch and bound algorithm for the multidimensional knapsack problem
Authors: Thesen Arne
Published: May 2007

This paper presents an efficient branch and bound algorithm for the solution of certain multiconstrained knapsack problems. The key to this algorithm is a rigidly defined tree structure in which branching and bounding may be performed through recursive relationships. The algorithm is particularly useful when only limited amounts of core storage are available as only the current and one previous solution is saved at any one time. Execution speeds compare favorably with other algorithms. A numerical example and computational experience is given.
Parametric studies in transportation‐type problems
Authors: Fong C. O. , Rao M. R.
Published: May 2007

In this paper we present some results in parametric studies on several transportation‐type problems. Specifically, a characterization is obtained for the optimal values of the variables in the problem of determining an optimal growth path in a logistics system. We also derive an upper bound beyond which the optimal growth path remains the same. The results are then extended to the goal programming model and the prespecified market growth rate problem.
The static theory of transfer pricing
Authors: Enzer Hermann
Published: May 2007

An analysis of the literature of transfer pricing is presented. It is shown that, under assumptions that the firm and its divisions have full deterministic knowledge of their costs and demands, some form of average cost is the appropriate transfer price. What happens when a firm adopts an objective other than profit maximization is further examined.
An efficient cyclic coordinate method for optimizing penalty functions
Authors: Bazaraa Mokhtar S.
Published: May 2007

In this study, a simple and efficient cyclic coordinate search procedure is used to optimize penalty functions. Since the contours of the penalty function are very ill‐behaved, an accurate line search is very difficult to achieve. Due to accumulated errors in line search, this makes “simple‐minded” search directions just as good as more sophisticated directions, and actually better since they require a smaller effort per iteration. Of course this is only true if the search procedure is able to “ride” along steep ridges, and meanwhile move an appreciable distance towards the optimal, if at all possible. Computational results on the cyclic coordinate method seems to support this point of view, and shows robustness, reliability, and efficiency of the method.
On fractional programming and equivalence
Authors: Craven B. D. , Mond B.
Published: May 2007

Under fairly general conditions, a nonlinear fractional program, where the function to be maximized has the form f(x)/g(x), is shown to be equivalent to a nonlinear program not involving fractions. The latter program is not generally a convex program, but there is often a convex program equivalent to it, to which the known algorithms for convex programming may be applied. An application to duality of a fractional program is discussed.
Extensions and reductions in the von neumann model of an expanding economy
Authors: Bauer Leonhard
Published: May 2007

This paper introduces an extension of the v. Neumann model of an expanding economy. In addition to the conventional nonnegative input and output matrices A1, B1 representing technology, two matrices A2, B2 represent socio‐political evaluations and show that there exist solutions to the 4‐matrix model. The proof is based on an extension of a constructive proof given by O. Morgenstern and G. L. Thompson. It is shown that this proof is valid only under an additional assumption. The transformation of v. Neumann models (taking consumption into account) into 1 or 2 games is shown and adds an additional condition to M. Morishima's model to guarantee a solution. The equivalence of the v. Neumann model to a maximization problem under a (efficiency) constraint is presented. It is shown that E. Malinvaud's maximality and efficiency criterion ‐ if based on the same assumptions (model) ‐ are equivalent and specify the assumptions which will make the MT‐model efficient. The economic evaluation is considered to be of utmost importance.
Simulating stable stochastic systems, V: Comparison of ratio estimators
Authors: Iglehart Donald L.
Published: May 2007

The regenerative method for estimating parameters in a simulation requires the simulator to estimate the ratio of two means. Five point estimates and four confidence intervals for this ratio have been computed for three stochastic simulations. The jackknife method appears to be the most promising for both point and interval estimation.
One machine sequencing to minimize mean flow time with minimum number tardy
Authors: Emmons Hamilton
Published: May 2007

The problem of sequencing n jobs on one machine is considered, under the multiple objective of minimizing mean flow time with the minimum number of tardy jobs. A simple procedure is first proposed to schedule for minimum flow time with a specified subset of jobs on time. This is used in conjunction with Moore's Algorithm in a simple heuristic producing good and often optimal schedules. A branch‐bound algorithm is presented to produce the optimal schedule efficiently with the help of several theorems which eliminate much branching.
Optimal production growth for the machine loading problem
Authors: Balachandran V.
Published: May 2007

This paper investigates a production growth logistics system for the machine loading problem (generalized transportation model), with a linear cost structure and minimum levels on total machine hours (resources) and product types (demands). An algorithm is provided for tracing the production growth path of this system, viz. in determining the optimal machine loading schedule of machines for product types, when the volumes of (i) total machine hours, and (ii) the total amount of product types are increased either individually for each total or simultaneously for both. Extensions of this methodology, when (i) the costs of production are convex and piecewise linear, and (ii) when the costs are nonconvex due to quantity discounts, and (iii) when there are upper bounds for productions are also discussed. Finally, a “goal‐programming” production growth model where the specified demands are treated as just goals and not as absolute quantities to be satisfied is also considered.
A note on the relationship between some specialized binary algorithms and the algorithm of land and doig
Authors: Taha Hamdy A.
Published: May 2007

This note examines the relationship between several specialized binary algorithms and the pioneering work of Land and Doig. This relationship may provide new ideas which could enhance the effectiveness of these algorithms.
A game theoretic approach to a two firm bidding problem
Authors: Cook W. D. , Kirby M. J. L. , Mehndiratta S. L.
Published: May 2007

In this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view.
Multilinear extensions and the banzhaf value
Authors: Owen Guillermo
Published: May 2007

It is shown that the Banzhaf value can be obtained by differentiating the multilinear extension of a game at the midpoint of the unit cube. This gives us a composition theorem for the value of compound games. As an example, the values of the electoral college and presidential election “games” are approximated by the method of extensions.
Transportation problems with some xij negative and transshipment problems
Authors: Dwyer Paul S.
Published: May 2007

The general solution process of the Hitchcock transportation problem resulting from the application of the method of reduced matrices may give solutions with some negative xij values. This paper is devoted to a review of the reduced matrices method, an examination of suitable interpretation of sets of xij which include some negative values, and ways of interpreting these values in useful modifications of the Hitchcock problem. Such modifications include a) the reshipment problem, b) the overshipment problem, and c) the transshipment problem. Techniques are developed for determining and eliminating cij which are not optimal. These techniques and results are useful in solving the problems indicated above. The natural applicability of the simple and general method of reduced matrices is emphasized.
An improved branch and bound procedure for n × m flow shop problems
Authors: Panwalkar S. S. , Khan A. W.
Published: May 2007

This paper considers the classical nXm flow shop sequencing problem. An improved branch and bound procedure is proposed. Computational experience shows that the proposed procedure is more efficient compared to the existing optimizing procedures.
Implicit enumeration based algorithms for postoptimizing zero‐one programs
Authors: Piper Christopher J. , Zoltners Andris A.
Published: May 2007

It has been shown by G. Roodman that useful postoptimization capabilities for the 0‐1 integer programming problem can be obtained from an implicit enumeration algorithm modified to classify and collect all fathomed partial solutions. This paper extends the the approach as follows: 1) Improved parameter ranging formulas are obtained by higher resolution classification criteria. 2) Parameters may be changed so as to tighten the original problem, in addition to relaxing it. 3) An efficient storage structure is presented to cope with difficult data collection task implicit in this approach. 4) Finally, computer implementation is facilitated by the elaboration of a unified set of algorithms.
A note on allocating jobs to two machines
Authors: Rothkopf Michael H.
Published: May 2007

A recent article in this journal by Mehta, Chandrasekaran, and Emmons [1] described a dynamic programming algorithm for assigning jobs to two identical parallel processors in a way that minimizes the average delay of these jobs. Their problem has a constraint on the sequence of the jobs such that any group of jobs assigned to a processor must be processed in the order of the sequence. This note has two purposes. First, we wish to point out a relationship between this work and some prior work [2]. Second, we wish to point out that Mehta, Chandrasekaran, and Emmons formulation, slightly generalized, can be used to find the optimum assignment of jobs to two machines in a more general class of problems than they considered including a subclass in which the jobs are not constrained to be processed in a given sequence.
A modified block replacement policy
Authors: Berg Menachem , Epstein Benjamin
Published: May 2007

A well known preventive replacement policy is the block replacement policy (BRP). In such a policy the item undergoes a planned replacement at a sequence of equally spaced time points independent of failure history. The main advantage of a BRP is its simplicity, because under this policy it is unnecessary to keep detailed records about times of failures or ages of items. The main drawback of a BRP is that at planned replacement times we may be replacing practically new items. In this paper we study a modified BRP which is free of this drawback. We calculate the expected cost of following a modified BRP for lifetime distributions possessing a special structure and illustrate it for the case of an Erlang distribution. A numerical comparison is made between a modified BRP and a standard BRP for the special case of a two stage Erlang distribution.
Project scheduling: The effects of problem structure on heuristic performance
Authors: Patterson James H.
Published: May 2007

Individual characteristics of multiple‐constrained resource, project scheduling problems are examined in an attempt to predict the solution obtainable with heuristic methods. Difficulties encountered in performing this type of research are described, and several multiple regression models are developed for predicting heuristic performance. Both single and multiple project data are examined, and results reported demonstrate the efficacy of determining beforehand the method used for problem solution.
A class of distributions generated from distributions of exponential type
Authors: Elandt‐Johnson Regina C.
Published: May 2007

A class of exponential type distributions with special exponential parameters is defined. It is assumed that the exponential parameters vary according to some (known) probability law. It has been shown in this paper that the compound distribution can be easily represented in form involving moment generating function of the mixing distribution. The results obtained in this paper provide an efficient and simple method of obtaining compound failure time distribution with known mixing distributions (uniform, exponential, gamma).
A markov chain version of the secretary problem
Authors: Albright S. Christian
Published: May 2007

This paper deals with the Secretary Problem where n secretaries are interviewed sequentially and the best k must be hired. The values of the secretaries are observed as they are interviewed, but beforehand only the distributions of these values are known. Furthermore, the distributions of two successive secretaries' values are governed by a Markov chain. Optimal hiring policies for finite n and limiting optimal policies as k and n approach infinity are obtained.
Transportation type problems with quantity discounts
Authors: Balachandran V. , Perry Avinoam
Published: May 2007

It is known to be real that the per unit transportation cost from a specific supply source to a given demand sink is dependent on the quantity shipped, so that there exist finite intervals for quantities where price breaks are offered to customers. Thus, such a quantity discount results in a nonconvex, piecewise linear functional. In this paper, an algorithm is provided to solve this problem. This algorithm, with minor modifications, is shown to encompass the “incremental” quantity discount and the “fixed charge” transportation problems as well. It is based upon a branch‐and‐bound solution procedure. The branches lead to ordinary transportation problems, the results of which are obtained by utilizing the “cost operator” for one branch and “rim operator” for another branch. Suitable illustrations and extensions are also provided.
Longitudinal manpower planning models
Authors: Grinold Richard C. , Marshall Kneale T. , Oliver Robert M.
Published: May 2007

A manpower planning model is presented that exploits the longitudinal stability of manpower cohorts. The manpower planning process is described. An infinite horizon linear program for calculating minimum cost manpower input plans is presented and found to have a straightforward solution in a great many cases and to yield an easily implemented approximation technique in other cases.
On the assignment and sequencing of operations on a crew‐served project
Authors: Bulfin R. L. , Parker R. G.
Published: May 2007

This paper is concerned with assigning and sequencing a set of activities for some or all members of a crew of operators so that the completion time of all such operations is minimized. It is assumed that each of the operators in the crew possesses, initially, certain tasks that only he can perform. A branch‐and‐bound scheme is proposed to treat the problem, and suitable computational experience is provided.
A measure of effectiveness for sensors and strategies
Authors: Antoniak Charles E.
Published: May 2007

This paper discusses a possible measure of effectiveness for information sensing equipment, such as radar or sonar, based on its ability to provide information. It is shown that such a measure is particularly appropriate for situations where a sequence of similar limited engagements may occur, as on antisubmarine patrol, for example. In this case the measure expresses the expected rate of gain per engagement of the relative resources of the participants. Rates are calculated for the optimal and certain simpler, but suboptimal, strategies. The measure is illustrated by an exact analysis of a gambling problem and a qualitative treatment of an anti‐missile missile allocation problem.
On nash subsets and mobility chains in bimatrix games
Authors: Heuer G. A. , Millham C. B.
Published: May 2007

This work is concerned with constructing, analyzing, and finding “mobility chains” for bimatrix games, sequences of equilibrium points along which it is possible for the two players to progress, one equilibrium point at a time, to an equilibrium point that is preferred by both players. The relationship between mobility chains and Nash subsets is established, and some properties of maximal Nash subsets are proved.
On the core and competitive equilibria of a market with indivisible goods
Authors: Kaneko Mamoru
Published: May 2007

We consider a generalization of the assignment game of Shapley and Shubik [4]. In the market which we consider, s kinds of indivisible goods are exchanged for money. The market consists of buyers and sellers. Each buyer wants to buy at most one unit of the goods, and each seller may sell more than one unit. First, we show that the set of all competitive imputations is given by the solutions of a certain linear programing problem dual to the optimal problem. Second, we show that the core of the market coincides with the set of all competitive imputations under some condition, and consider the core of the market where s=1 and the condition does not hold.
On the relationship between the force ratio and the instantaneous casualty‐exchange ratio for some lanchester‐type models of warfare
Authors: Taylor James G.
Published: May 2007

A “local” condition of winning (in the sense that the force ratio is changing to the advantage of one of the combatants) is shown to apply to all deterministic Lanchester‐type models with two force‐level variables. This condition involves the comparison of only the force ratio and the instantaneous force‐change ratio. For no replacements and withdrawals, a combatant is winning “instantaneously” when the force ratio exceeds the differential casualty‐exchange ratio. General outcome‐prediction relations are developed from this “local” condition and applied to a nonlinear model for Helmbold‐type combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. Conditions under which the effects of the supporting fires “cancel out” are given.
AN ALGORITHM FOR THE SEGREGATED STORAGE PROBLEM
Authors: Neebe A. W. , Rao M. R.
Published: May 2007

The segregated storage problem involves the optimal distribution of products among compartments with the restriction that only one product may be stored in each compartment. The storage capacity of each compartment, the storage demand for each product, and the linear cost of storing one unit of a product in a given compartment are specified. The problem is reformulated as a large set‐packing problem, and a column generation scheme is devised to solve the associated linear programming problem. In case of fractional solutions, a branch and bound procedure is utilized. Computational results are presented.
Determining adjacent vertices on assignment polytopes
Authors: McKeown Patrick G.
Published: May 2007

To rank the solutions to the assignment problem using an extreme point method, it is necessary to be able to find all extreme points which are adjacent to a given extreme solution. Recent work has shown a procedure for determining adjacent vertices on transportation polytopes using a modification of the Chernikova Algorithm. We present here a procedure for assignment polytopes which is a simplification of the more general procedure for transportation polytopes and which also allows for implicit enumeration of adjacent vertices.
Suboptimal decision rule for attacking targets of opportunity
Authors: Kisi Takasi
Published: May 2007

A player having only a definite number of weapons is hunting targets. His total hunting time is also limited. Targets of opportunity with various values arrive at random, and as soon as a target arrives the player observes the target value and decides whether or not to shoot it down. The issue is what the decision rule is which guarantees him a maximum expected gain during the hunting time. Poisson arrival of the targets, uniform distribution of the target value, and the shoot‐look‐shoot scheme qre assumed. A decision rule is derived which is not optimal but has a very simple form and gives almost as good value as the optimal decision rule does.
Armor configurations via dynamic programming
Authors: Shear R. E. , Arbuckle A. L. , Kucher V. B.
Published: May 2007

The problem of selecting materials, their thicknesses and order for armor designed for the defeat of shaped charge threats, has been formulated as a constrained optimization problem. The mathematical model provides an optimal order and thickness of each layer of material such that the resulting armor configuration will be of minimum mass per unit area subject to constraints on total thickness and shaped charge jet tip exit velocity.
The conjugate gradient technique for certain quadratic network problems
Authors: Leblanc Larry J.
Published: May 2007

We consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large‐scale versions. It is shown that finding a saddle point for the Lagrangian of an m constraint, n variable network problem requires only the solution of an unconstrained quadratic programming problem with only m variables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum‐cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 computer.
Solving quadratic assignment problems with rectangular distances and integer programming
Authors: Love Robert F. , Wong Jsun Y.
Published: May 2007

The problem considered involves the assignment of n facilities to n specified locations. Each facility has a given nonnegative flow from each of the other facilities. The objective is to minimize the sum of transportation costs.

Assume these n locations are given as points on a two‐dimensional plane and transportation costs are proportional to weighted rectangular distances. Then the problem is formulated as a binary mixed integer program. The number of integer variables (all binary) involved equals the number of facilities squared. Without increasing the number of integer variables, the formulation is extended to include “site costs” Computational results of the formulation are presented.
State‐dependent gap acceptance
Authors: Harris Carl M.
Published: May 2007

This paper considers a traffic problem in which vehicles queue up according to a Poisson process on a single‐lane entrance ramp prior to merging into a major stream of vehicular traffic. In order to then prevent the ramp queue from becoming too large, a model is proposed which considers a lowering of the critical gap as the ramp queue size increases. With the critical gap assumed to be a nonincreasing function of the number of vehicles on the ramp at instances that correspond to departure times of lead vehicles from the ramp queue, the resultant model is an M/G/1 queue with state‐dependent service times. Some general results are obtained for this model and a specific case discussed in moderate detail.
Confidence bounds and propagation of uncertainties in system availability and reliability computations
Authors: Shaw L. , Shooman M. L.
Published: May 2007

This paper develops bounds on the uncertainties in system availabilities or reliabilities which have been computed from structural (series, parallel, etc.) relations among uncertain subsystem availabilities or reliabilities. It is assumed that the highly available (reliable) subsystems have been tested or simulated to determine their unavailabilities (unreliabilities) to within some small percentages of uncertainty. It is shown that series, parallel and r out of n structures which are nominally highly available will have unavailability uncertainties whose percentages errors are of the same order as the subsystem uncertainties. Thus overall system analysis errors, even for large systems, are of the same order of magnitude as the uncertainties in the component probabilities. Both systematic (bias type) uncertainties and independent random uncertainties are considered.
A semieconomic method for the determination of optimal lot sizes
Authors: Massa Larry
Published: May 2007

The construction of lot sizes usually depends upon factors influencing homogeneity. When these factors are not a function of lot quantity, it is possible to determine an optimal lot size. The optimization process balances the cost of sampling against the expected cost of lot rejection for some specified procurement quantity. The rationale for balancing the two costs is contingent upon the fact that rejection criteria waivers frequently occur when the lot size is large. This concept implies that the lot size should be as small as possible, whereas the cost of sampling drives the lot size up. Hence, trade‐offs may be made. The formulation is termed a semieconomic one because it combines a pure economic objective function with a pure statistical constraint. This constraint is necessary because the nature of the items under study dictates that the cost of accepting defective material cannot be explicitly stated. The paper presents the formulation, describes when it should be used, derives a good analytical approximation under certain assumptions and gives various ramifications when it is used.
Optimal reject allowance with constant marginal production efficiency
Authors: Beja Avraham
Published: May 2007

A job shop must fulfill an order for N good items. Production is conducted in “lots,” and the number of good items in a lot can be accurately determined only after production of that lot is completed. If the number of good items falls short of the outstanding order, the shop must produce further lots, as necessary.

Processes with “constant marginal production efficiency” are investigated. The revealed structure allows efficient exact computation of optimal policy. The resulting minimal cost exhibits a consistent (but not universal) pattern whereby higher quality of production is advantageous even at proportionately higher marginal cost.
A chance‐constrained distribution problem
Authors: Reese Richard M. , Stedry Andrew C.
Published: May 2007

The transportation model with supplies (Si) and demands (Di) treated as bounded variables developed by Charnes and Klingman is extended to the case where the Si and Di are independently and uniformly distributed random variables. Chance constraints which require that demand at the jth destination will be satisfied with probability at least βi and that stockout at the ith origin will occur with probability less than αi are imposed. Conversion of the chance constraints to their linear equivalents results in a transportation problem with one more row and column than the original with some of the new arcs capacitated. The chance‐constrained formulation is extended to the transshipment problem.
Johnson's approximate method for the 3 × n job shop problem
Authors: Szwarc Wlodzimierz , Hutchinson George K.
Published: May 2007

The effectiveness of Johnson's Approximate Method (JAM) for the 3 × n job shop scheduling problems was examined on 1,500 test cases with n ranging from 6 to 50 and with the processing times Ai, Bi, Ci (for item i on machines A, B, C) being uniformly and normally distributed. JAM proved to be quite effective for the case Bi ⩽ max (Ai, Ci) and optimal for Bi, ⩽ min (Ai, Ci).
Optimal dynamic rules for assigning customers to servers in a heterogeneous queuing system
Authors: Winston Wayne
Published: May 2007

We consider a queuing system in which both customers and servers may be of several types. The distribution of a customer's service time is assumed to depend on both the customer's type and the type of server to which he is assigned. For a model with two servers and two customer types, conditions are presented which ensure that the discounted number of service completions is maximized by assigning customers with longer service times to faster servers. Generalizations to more complex models are discussed.
Computing bounds for the optimal value in linear programming
Authors: Kallio Markku
Published: May 2007

Consider a standard linear programming problem and suppose that there are bounds available for the decision variables such that those bounds are not violated at an optimal solution of the problem (but they may be violated at some other feasible solutions of the problem). Thus, these bounds may not appear explicitly in the problem, but rather they may have been derived from some prior knowledge about an optimal solution or from the explicit constraints of the problem.

In this paper, the bounds on variables are used to compute bounds on the optimal value when the problem is being solved by the simplex method. The latter bounds may then be used as a termination criteria for the simples iterations for the purpose of finding a “sufficiently good” near optimal solution. The bounds proposed are such that the computational effort in evaluating them is insignificant compared to that involved in the simplex iterations. A numerical example is given to demonstrate their performance.
The divisionalized firm revisited—A comment on Enzer's “the static theory of transfer pricing”
Authors: Jennergren L. Peter
Published: May 2007

Three different solutions to a very simple transfer pricing problem are outlined and contrasted. These are labeled by their authors: Hirshleifer, Enzer, and Ronen and McKinney. Weaknesses associated with each solution are pointed out.
Optimal disposal policies for a single‐item inventory system with returns
Authors: Heyman Daniel P.
Published: May 2007

We consider a single‐item inventory system in which the stock level can increase due to items being returned as well as decrease when demands occur. Returned items can be repaired and then used to satisfy future demand, or they can be disposed of. We identify those inventory levels where disposal is the best policy.

It is shown that this problem is equivalent to a problem of controlling a single‐server queue. When the return and demand processes are both Poisson, we find the optimal policy exactly. When the demand and return processes are more general, we use diffusion approximations to obtain an approximate model, which is then solved. The approximate model requires only mean and variance data. Besides the optimal policy, the output of the models includes such characteristics as the operating costs, the purchase rate for new items, the disposal rate for returned items and the average inventory level. Several numerical examples are given.

An interesting by‐product of our investigation is an approximation for the steady‐state behavior of the bulk GI/G/1 queue with a queue limit.
Probability density function of a stochastic linear programming problem
Authors: Hsia Wei Shen
Published: May 2007

A stochastic linear programming problem under the “wait‐and‐see” situation is studied. After the conditions for the interchange of the order of integration and differentiation are surveyed, an explicit form of the probability density function of the stochastic linear programming problem is found. An example is also given to illustrate the result.
Probabilistic priorities in the M/G/1 queue
Authors: Matthews D. E.
Published: May 2007

A simple method is presented for deriving the mean and variance of the queueing time distribution in an M/G/1 queue when the priorities assigned to customers have an assignment probability distribution. Several examples illustrate the results. The mean and variance of the queueing time distribution for the longest service time discipline are derived, and its disadvantages are discussed.
Characterization of the nucleolus for a class of n‐person games
Authors: Owen Guillermo
Published: May 2007

An inductive procedure is given for finding the nucleolus of an n‐person game in which all coalitions with less than n‐1 players are totally defeated. It is shown that, for such a game, one of three things may occur: (a) all players receive the same amount; (b) each player receives his quota, plus a certain constant (which may be positive, nerative, or zero); (c) the weakest player receives one half his quota, and the other players divide the remaining profit according to the nucleolus of a similar (n‐1)‐person game. It is also shown that the nucleolus of such a game yields directly the nucleolus of each derived game. An example is worked out in detail.
A note on the relationship between correlation and circular error probability (CEP)
Authors: Olsen Dale E.
Published: May 2007

This note investigates the effects of ignoring correlation (p) as is sometimes done when estimating or placing confidence intervals on circular error probability (CEP). It is shown that better estimates of CEP can be made if the axis is rotated [5] so that the estimate of p is zero. It is also shown that ignoring variability in estimating correlation can affect the confidence intervals on CEP or the placing of a lower bound on the probability content of a circle.
Replacement models under additive damage
Authors: Zuckerman Dror
Published: May 2007

A production system which generates income is subject to random failure. Upon failure, the system is replaced by a new identical one and the replacement cycles are repeated indefinitely. In our breakdown model, shocks occur to the system in a Poisson stream. Each shock causes a random amount of damage, and these damages accumulate additively. The failure time depends on the accumulated damage in the system. The income from the system and the cost associated with a planned replacement depend on the accumulated damage in the system. An additional cost is incurred at each failure in service. We allow a controller to replace the system at any stopping time T before failure time. We will consider the problem of specifying a replacement rule that is optimal under the following criteria: maximum total long‐run average net income per unit time, and maximum total long‐run expected discounted net income. Our primary goal is to introduce conditions under which an optimal policy is a control limit policy and to investigate how the optimal policy can be obtained. Examples will be presented to illustrate computational procedures.
A bayesian approach to evaluating military investments in product improvement and testing
Authors: Robinson R. T.
Published: May 2007

Two issues of frequent importance in new product development are product improvement and reliability testing. A question often faced by the developer is: Should the product be distributed in its present state, or should it be improved further and/or tested before distribution? A more useful statement of the question might be: What levels of investment in further improvement and testing are economically permissible? Products for which this question is relevant may vary widely in type and intended use. This paper presents a model for determining these levels for one such product—an equipment modification procedure. The model presented makes use of present value analysis to compare cost streams and of Bayesian statistics to relate the costs to various outcomes under conditions of uncertainty. The model is applied to an actual military problem and a method is described for examining the sensitivity of the results to changes in the prior probabilities and discount rate.
The cyclic separation scheduling problem
Authors: Armstrong Ronald D. , Sinha Prabhakant
Published: May 2007

This paper deals with the problem of scheduling items (tasks, employees, equipment, etc.) over a finite time horizon so as to minimize total cost expenditures while maintaining a predefined separation between certain items. The problem is cyclic, because the same schedule will be repeated over several consecutive time periods of equal length. Thus, requirements are present to maintain the separation of items not only within the individual time periods considered, but also between items in adjoining periods. A special purpose branch‐and‐bound algorithm is developed to solve this scheduling problem by taking advantage of its cyclic nature. Computational results are given.
A primal simplex algorithm to solve a rectilinear distance facility location problem
Authors: Armstrong Ronald D.
Published: May 2007

This paper considers the problem of locating m new facilities in the plane so as to minimize a weighted rectangular distance between the new facilities and n existing facilities. A special purpose primal simplex algorithm is developed to solve this problem. The algorithm will maintain at all times a basis of dimension m by m; however, because of the triangularity of the basis matrix, it will not be necessary to form a basis inverse explicitly.
An analytical minefield evaluation model without space averages
Authors: Mjelde K. M.
Published: May 2007

The paper describes an approach to the evaluation of the effectiveness of a minefield in terms of the number of mines that are detonated by a convoy of sweepers and ships and the corresponding number of vessels that are immobilized. The positions of the mines and the tracks of the vessels are assumed to be known, which means that the evaluation measures are dependent on a large number of disjoint events, each event being the immobilization of particular vessels by particular mines. This may render combinatorial methods computationally infeasible, but by introducing approximations in the assumptions, the difficulty can be overcome, specifically by modelling the arrival of each individual vessel in the neighborhood of a mine by an inhomogeneous Poisson stream for which the arrival rate is nonzero only over a short time interval. The plausibility of the approach is supported by results of a critical‐event simulation model.
A procedure for generating time‐dependent arrivals for queueing simulations
Authors: Fishman George S. , Kao Edward P. C.
Published: May 2007

This paper presents a method for modeling cyclic inputs to a congested system in a discrete event digital simulation. Specifically, we express the mean of the interarrival time conditional on the last arrival as a linear combination of harmonic components whose coefficients can be determined by stepwise regression. We also assume that the conditional interarrival time normalized by its corresponding mean follows a distribution that is independent of time. The result can, in turn, be used to generate the desired input for a simulation, An example based on a set of actual data is used to illustrate the process of parameter estimation for the model.
Estimating reliability growth (or deterioration) using time series analysis
Authors: Singpurwalla Nozer D.
Published: May 2007

In this paper we propose a method for estimating reliability growth (or deterioration) using time series analysis. Our method does not call for the specification of a particular model, and estimates the growth in the presence of periodicity. We illustrate our procedure by considering some binomial failure data generated during the testing of a large system of the U.S. Navy.
General trigger‐off replacement procedures for two‐unit systems
Authors: Berg Menachem
Published: May 2007

A trigger‐off replacement policy, suggested and analyzed in [1], for two‐unit systems composed of identical units, is generalized and extended in this work in several ways. In the first part of the paper we obtain the appropriate integral equations for nonidentical units and then use them for a complete solution of the case of two units, whose lifetimes are distributed according to general Erlang distributions. In the second part of the paper we extend the trigger‐off policy itself by allowing preventive replacements of units which reach a certain critical age. The system stops working if either one of the two units fails or reaches its critical age. Both cases present natural replacement possibilities for the remaining unit, provided that its age exceeds a predetermined critical age.

Finally, we consider the question of which policy parameters, i.e. control limits and critical ages, to choose when facing a real‐life situation. Using the criterion of expected costs per unit time in the long run, we show how to find the optimal parameters which minimize this objective function. The fact that a restricted optimization, within the class of trigger‐off replacement policies, leads to the global optimal policy has been proved in [2] by a different approach.
A linear programming approach to geometric programs
Authors: Dinkel John J. , Kochenberger Gary A. , Elliott William H.
Published: May 2007

A cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.
Nonstationary stochastic gold‐mining: A time‐sequential tactical‐allocation problem
Authors: Hall Gaineford J.
Published: May 2007

This paper presents an extension of gold‐mining problems formulated in earlier work by R. Bellman and J. Kadane. Bellman assumes there are two gold mines labeled A and B, respectively, each with a known initial amount of gold. There is one delicate gold‐mining machine which can be used to excavate one mine per day. Associated with mine A is a known constant return rate and a known constant probability of breakdown. There is also a return rate and probability of breakdown for mine B. Bellman solves the problem of finding a sequential decision procedure to maximize the expected amount of gold obtained before breakdown of the machine. Kadane extends the problem by assuming that there are several mines and that there are sequences of constants such that the jth constant for each mine represents the return rate for the jth excavation of that mine. He also assumes that the probability of breakdown during the jth excavation of a mine depends on j. We extend these results by assuming that the return rates are random variables with known joint distribution and by allowing the probability of breakdown to be a function of previous observations on the return rates. We show that under certain regularity conditions on the joint distributions of the random variables, the optimal policy is: at each stage always select a mine which has maximal conditional expected return per unit risk. This gold‐mining problem is also a formulation of the problem of time‐sequential tactical allocation of bombers to targets. Several examples illustrating these results are presented.
The queue G/M/m/N: Busy period and cycle, waiting time under reverse and random order service
Authors: Rosenlund Stig I.
Published: May 2007

The busy period, busy cycle, and the numbers of customers served and lost therein, of the G/M/m queue with balking is studied via the embedded Markov chain approach. It is shown that the expectations of the two discrete variables give the loss probability. For the special case G/M/1/N a closed expression in terms of contour integrals is obtained for the Laplace transform of these four variables. This yields as a byproduct the LIFO waiting time distribution for the G/M/m/N queue. The waiting time under random order service for this queue is also studied.
Steady state waiting time in a multicenter job shop
Authors: Kapadia Asha S. , Hsi Bartholomew P.
Published: May 2007

This paper analyzes the waiting‐time distribution of a specific job as it moves through a job‐shop with multiple centers and exponential service times. The movement of the job through the shop is governed by a Markovian transition matrix and ends with the job's exit from the shop.