bluuebunny/crossref_metadata_2025 huggingface dataset:
A note on determining operating strategies for probabilistic vehicle routing
Authors: Yee James R. , Golden Bruce L.
Published: May 2007

The stochastic vehicle routing problem is a problem of current importance and research interest. Applications include schoolbus routing, municipal waste collection, subscription bus scheduling, daily delivery of dairy goods, and a host of related transportation and distribution activities. In this paper, we assume that routes for vehicles have already been generated and we focus on determining operating strategies. That is, under what conditions should a driver return to the central depot in order to replenish his supply? We present a dynamic programming recursion which addresses this question and we show that the optimal policy is of a rather simple form. Finally, an algorithm and example illustrate the policy.
A note on integer linear fractional programming
Authors: Chandra Suresh , Chandramohan M.
Published: May 2007

This note consists of developing a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer linear fractional programs.
On the reliability, availability and bayes confidence intervals for multicomponent systems
Authors: Thompson William E. , Haynes Robert D.
Published: May 2007

The problem of computing reliability and availability and their associated confidence limits for multi‐component systems has appeared often in the literature. This problem arises where some or all of the component reliabilities and availabilities are statistical estimates (random variables) from test and other data. The problem of computing confidence limits has generally been considered difficult and treated only on a case‐by‐case basis. This paper deals with Bayes confidence limits on reliability and availability for a more general class of systems than previously considered including, as special cases, series‐parallel and standby systems applications. The posterior distributions obtained are exact in theory and their numerical evaluation is limited only by computing resources, data representation and round‐off in calculations. This paper collects and generalizes previous results of the authors and others.

The methods presented in this paper apply both to reliability and availability analysis. The conceptual development requires only that system reliability or availability be probabilities defined in terms acceptable for a particular application. The emphasis is on Bayes Analysis and the determination of the posterior distribution functions. Having these, the calculation of point estimates and confidence limits is routine.

This paper includes several examples of estimating system reliability and confidence limits based on observed component test data. Also included is an example of the numerical procedure for computing Bayes confidence limits for the reliability of a system consisting ofNfailure independent components connected in series. Both an exact and a new approximate numerical procedure for computing point and interval estimates of reliability are presented. A comparison is made of the results obtained from the two procedures. It is shown that the approximation is entirely sufficient for most reliability engineering analysis.
Solving incremental quantity discounted transportation problems by vertex ranking
Authors: McKeown Patrick G.
Published: May 2007

Logistics managers often encounter incremental quantity discounts when choosing the best transportation mode to use. This could occur when there is a choice of road, rail, or water modes to move freight from a set of supply points to various destinations. The selection of mode depends upon the amount to be moved and the costs, both continuous and fixed, associated with each mode. This can be modeled as a transportation problem with a piecewise‐linear objective function. In this paper, we present a vertex ranking algorithm to solve the incremental quantity discounted transportation problem. Computational results for various test problems are presented and discussed.
Auxiliary procedures for solving long transportation problems
Authors: Intrator J. , Berrebi M.
Published: May 2007

An efficient auxiliary algorithm for solving transportation problems, based on a necessary but not sufficient condition for optimum, is presented.
The role of internal storage capacity in fixed cycle production systems
Authors: Lev B. , Toof D. I.
Published: May 2007

The reliability of a serial production line is optimized with respect to the location of a single buffer. The problem was earlier defined and solved by Soyster and Toof for the special case of an even number of machines all having equal probability of failure. In this paper we generalize the results for any number of machines and remove the restriction of identical machine reliabilities. In addition, an analysis of multibuffer systems is presented with a closed form solution for the reliability when both the number of buffers and their capacity is limited. For the general multibuffer system we present an approach for determining system reliability.
Scheduling coupled tasks
Authors: Shapiro Roy D.
Published: May 2007

Consider a set of task pairs coupled in time: a first (initial) and second (completion) tasks of known durations with a specified time between them. If the operator or machine performing these tasks is able to process only one at a time, scheduling is necessary to insure that no overlap occurs. This problem has a particular application to production scheduling, transportation, and radar operations (send‐receive pulses are ideal examples of time‐linked tasks requiring scheduling). This article discusses several candidate techniques for schedule determination, and these are evaluated in a specific radar scheduling application.
Evaluation of force structures under uncertainty
Authors: Johnson Charles R. , Loane Edward P.
Published: May 2007

A model, for assessing the effectiveness of alternative force structures in an uncertain future conflict, is presented and exemplified. The methodology is appropriate to forces (e.g., the attack submarine force) where alternative unit types may be employed, albeit at differing effectiveness, in the same set of missions. Procurement trade‐offs, and in particular the desirability of special purpose units in place of some (presumably more expensive) general purpose units, can be addressed by this model. Example calculations indicate an increase in the effectiveness of a force composed of general purpose units, relative to various mixed forces, with increase in the uncertainty regarding future conflicts.
Reliability growth of repairable systems
Authors: Smith Stephen A. , Oren Shmuel S.
Published: May 2007

This paper considers the problem of modeling the reliability of a repairable system or device that is experiencing reliability improvement. Such a situation arises when system failure modes are gradually being corrected by a test‐fix‐test‐fix procedure, which may include design changes. A dynamic reliability model for this process is discussed and statistical techniques are derived for estimating the model parameters and for testing the goodness‐of‐fit to observed data. The reliability model analyzed was first proposed as a graphical technique known as Duane plots, but can also be viewed as a nonhomogeneous Poisson process with a particular mean value function.
On the distribution of the optimal value for a class of stochastic geometric programs
Authors: Ellnert Paul M. , Stark Robert M.
Published: May 2007

An approach is presented for obtaining the moments and distribution of the optimal value for a class of prototype stochastic geometric programs with log‐normally distributed cost coefficients. It is assumed for each set of values taken on by the cost coefficients that the resulting deterministic primal program is superconsistent and soluble. It is also required that the corresponding dual program has a unique optimal point with all positive components. It is indicated how one can apply the results obtained under the above assumptions to stochastic programs whose corresponding deterministic dual programs need not satisfy the above‐mentioned uniqueness and positivity requirements.
A class of continuous nonlinear programming problems with time‐delayed constraints
Authors: Reiland Thomas W. , Hanson Morgan A.
Published: May 2007

A general class of continuous time nonlinear problems is considered. Necessary and sufficient conditions for the existence of solutions are established and optimal solutions are characterized in terms of a duality theorem. The theory is illustrated by means of an example.
The bounded interval generalized assignment model
Authors: Ross G. Terry , Soland Richard M. , Zoltners Andris A.
Published: May 2007

The bounded interval generalized assignment model is a “many‐for‐one” assignment model. Each task must be assigned to exactly one agent; however, each agent can be assigned multiple tasks as long as the agent resource consumed by performing the assigned tasks falls within a specified interval. The bounded interval generalized assignment model is formulated, and an algorithm for its solution is developed. Algorithms for the bounded interval versions of the semiassignment model and sources‐to‐uses transportation model are also discussed.
An inventory model with search for best ordering price
Authors: Golabi Kamal
Published: May 2007

This paper presents a single‐item inventory model with deterministic demand where the buyer is allowed to search for the most favorable price before deciding on the order quantity. In the beginning of each period, a sequential random sample can be taken from a known distribution and there is a fixed cost per search. The decision maker is faced with the task of deciding when to initiate and when to stop the search process, as well as determining the optimal order quantity once the search process is terminated. The objective is to minimize total expected costs while satisfying all demands on time. We demonstrate that a set of critical numbers determine the optimal stopping and ordering strategies. We present recursive expressions yielding the critical numbers, as well as the minimal expected cost from the beginning of every period to the end of the horizon.
Preventive maintenance and replacement under additive damage
Authors: Chikte S. D. , Deshmukh S. D.
Published: May 2007

A system deteriorates due to shocks received at random times, each shock causing a random amount of damage which accumulates over time and may result in a system failure. Replacement of a failed system is mandatory, while an operable one may also be replaced. In addition, the shock process causing system deterioration may be controlled by continuous preventive maintenance expenditures. The joint problem of optimal maintenance and replacement is analyzed and it is shown that, under reasonable conditions, optimal maintenance rate is decreasing in the cumulative damage level and that beyond a certain critical level the system should be replaced. Meaningful bounds are established on the optimal policies and an illustrative example is provided.
A theoretical and computational comparison of “equivalent” mixed‐integer formulations
Authors: Meyer R. R.
Published: May 2007

This paper provides a theoretical and computational comparison of alternative mixed integer programming formulations for optimization problems involving certain types of economy‐of‐scale functions. Such functions arise in a broad range of applications from such diverse areas as vendor selection and communications network design. A “nonstandard” problem formulation is shown to be superior in several respects to the traditional formulation of problems in this class.
Stochastic models for spread of motivating information
Authors: Berg Menachem
Published: May 2007

In this work we consider spread of information which motivates the hearer to perform some specified action. The time to completion of an action is assumed to be a random variable and the main focus is on the number of completed actions by time t, X(t). Some models, which reflect different degree of centralization in the spread process, are analyzed and the distribution of X(t), as well as that of some other stochastic processes of interest, are obtained. The relevance to propagation of epidemics is pointed out.

All models are solved by employing two interrelated concepts, namely, the order statistics property of stochastic processes and the binomial closure property of collections of distributions. In this respect, the work also serves as an illustration of the application of these useful concepts.
Comparing alternating renewal processes
Authors: Chiang Dalen T. , Niu Shun‐Chen
Published: May 2007

Sufficient conditions are given for stochastic comparison of two alternating renewal processes based on the concept of uniformization. The result is used to compare component and system performance processes in maintained reliability systems.
An analysis of single item inventory systems with returns
Authors: Muckstadt John A. , Isaac Michael H.
Published: May 2007

Inventory systems with returns are systems in which there are units returned in a repairable state, as well as demands for units in a serviceable state, where the return and demand processes are independent. We begin by examining the control of a single item at a single location in which the stationary return rate is less than the stationary demand rate. This necessitates an occasional procurement of units from an outside source. We present a cost model of this system, which we assume is managed under a continuous review procurement policy, and develop a solution method for finding the policy parameter values. The key to the analysis is the use of a normally distributed random variable to approximate the steady‐state distribution of net inventory.

Next, we study a single item, two echelon system in which a warehouse (the upper echelon) supports N(N ⩾ 1) retailers (the lower echelon). In this case, customers return units in a repairable state as well as demand units in a serviceable state at the retailer level only. We assume the constant system return rate is less than the constant system demand rate so that a procurement is required at certain times from an outside supplier. We develop a cost model of this two echelon system assuming that each location follows a continuous review procurement policy. We also present an algorithm for finding the policy parameter values at each location that is based on the method used to solve the single location problem.
Systems defense games: Colonel blotto, command and control
Authors: Shubik Martin , Weber Robert James
Published: May 2007

The classical “Colonel Blotto” games of force allocation are generalized to include situations in which there are complementarities among the targets being defended. The complementarities are represented by means of a system “characteristic function,” and a valuation technique from the theory of cooperative games is seen to indicate the optimal allocations of defense and attack forces. Cost trade‐offs between systems defense and alternative measures, such as the hardening of targets, are discussed, and a simple example is analyzed in order to indicate the potential of this approach.
On nonpreemptive strategies in stochastic scheduling
Authors: Glazebrook K. D.
Published: May 2007

It is shown that there is an optimal strategy for a class of stochastic scheduling problems which is nonpreemptive. The results which yield this conclusion are generalizations of previous ones due to Glazebrook and Gittins. These new results also lead to an evaluation of the performance of nonpreemptive strategies in a large class of problems of practical interest.
An efficient algorithm for the location‐allocation problem with rectangular regions
Authors: Marucheck Ann S. , Aly Adel A.
Published: May 2007

The location‐allocation problem for existing facilities uniformly distributed over rectangular regions is treated for the case where the rectilinear norm is used. The new facilities are to be located such that the expected total weighted distance is minimized. Properties of the problem are discussed. A branch and bound algorithm is developed for the exact solution of the problem. Computational results are given for different sized problems.
A note on a maximin disposal policy under nwue pricing
Authors: Bhattacharjee Manish C.
Published: May 2007

For the classical disposal model for selling an asset with unknown price distribution which is NWUE (new worse than used in expectation) with a given finite mean price, this note derives a policy which is maximin. The gain in using the maximin policy relative to the option of selling right away is convex decreasing in the continuation cost to mean price ratio. The relevant results of Derman, Lieberman and Ross also follow as a consequence of our analysis. Our theorem provides a practical justification of their main result on the cutoff bid for the disposal model subject to NWUE pricing.
Monotone optimal preventive maintenance policies for stochastically failing equipment
Authors: Anderson Michael Q.
Published: May 2007

This paper examines various models for maintenance of a machine operating subject to stochastic deterioration. Three alternative models are presented for the deterioration process. For each model, in addition to the replacement decision, the option exists of performing preventive maintenance. The effect of this maintenance is to “slow” the deterioration process. With an appropriate reward structure imposed on the processes, the models are formulated as continuous time Markov decision processes. the optimality criterion being the maximization of expected discounted reward earned over an infinite time horizon. For each model conditions are presented under which the optimal maintenance policy exhibits the following monotonic structure. First, there exists a control limit rule for replacement. That is, there exists a number i* such that if the state of machine deterioration exceeds i* the optimal policy replaces the machine by a new machine. Secondly, prior to replacement the optimal level of preventive maintenance is a nonincreasing function of the state of machine deterioration. The conditions which guarantee this result have a cost/benefit interpretation.
Optimal selection from a random sequence with observation errors
Authors: Stewart T. J.
Published: May 2007

A form of sequential decision problem is introduced in which options are presented in sequence. with no recall of rejected options (as in the secretary problem), but in which the value of each option may only he inferred from experiments. Decisions have thus to be made concerning both the acceptance and rejection of each option and the degree of experimentation. General properties of the optimal policy are derived, and an algorithm is obtained for the solution in a special case. This special case suggests a heuristic rule for more general situations. the performance of which rule has been investigated by a Monte Carlo study.
Decomposition algorithms for minimal cut problems
Authors: Tufekci Suleyman
Published: May 2007

Consider a network G(N. A) with n nodes, where node 1 designates its source node and node n designates its sink node. The cuts (Zi, =), i= 1…, n ‐ 1 are called one‐node cuts if 1 ϵ Zi,. n q Zi, Z1‐− {1}, Zi ϵ Zi+1 and Zi and Zi+l differ by only one node. It is shown that these one‐node cuts decompose G into 1 m n/2 subnetworks with known minimal cuts. Under certain circumstances, the proposed one‐node decomposition can produce a minimal cut for G in 0(n2 ) machine operations. It is also shown that, under certain conditions, one‐node cuts produce no decomposition. An alternative procedure is also introduced to overcome this situation. It is shown that this alternative procedure has the computational complexity of 0(n3).
On queues with dependent interarrival and service times
Authors: Niu Shun‐Chen
Published: May 2007

AnM/G/1 queueing system is studied in which the service time required by a customer is dependent on the interarrival time between his arrival and that of his predecessor Assuming the two variables are “associated,” we prove that the expected delay in this system is less than or equal to than of a conventional M/G/1 queue This conclusion has been verified via simulation by Mitchell and Paulson [9] for a special class of dependent M/M/1 queue. Their model is a special case of the one we consider here. We also study another modified GI/G/1 queue. where the arrival process and/or the service process are individually “associated”.
Some properties of optimal control policies for entry to an M/M/1 queue
Authors: Rue Robert C. , Rosenshine Matthew
Published: May 2007

Customers served by an M/M/1 queueing system each receive a reward R but pay a holding cost of C per unit time (including service time) spent in the system. The decision of whether or not a customer joins the queue can be made on an individual basis or a social basis. The effect of increasing the arrival rate on the optimal policy parameters is examined. Some limiting results are also derived.
The construction of an optimal distribution of search effort
Authors: Wegener Ingo
Published: May 2007

Suppòse one object is hidden in the k‐th of n boxes with probability p(k). We know the probability q(t, k) of detecting the object if it is hidden in box k and we expend effort t searching box k. Our aim is to minimize the expected search effort of a successful search. Previously this problem has been solved only under the assumption that the functions q(·, k) are concave. We prove, without concavity assumptions, the existence of an optimal distribution of search effort and give a procedure for its construction.
On a shape estimator of weiss
Authors: Weissman Ishay
Published: May 2007

The problem of estimating the shape‐parameter of a distribution is considered. We introduce a class of estimators the distributions of which are independent of location and scale. An estimator proposed by Weiss [1] is a member of this class. We find the asymptotically most efficient estimator in this class which differs from that proposed by Weiss.
A note on integer solutions to linear fractional interval programming problems by a branch & bound technique
Authors: Agrawal S. C. , Chand Mam
Published: May 2007

This paper provides a method for solving linear fractional interval programming problems in integers with the help of a branch and bound technique.
A note on sojourn times in M/G/1 queues with instantaneous, bernoulli feedback
Authors: Disney Ralph L.
Published: May 2007

Queueing systems which include the possibility for a customer to return to the same server for additional service are called queueing systems with feedback. Such systems occur in computer networks for example. In these systems a chosen customer will wait in the queue, be serviced and then, with probability p, return to wait again, be serviced again and continue this process until, with probability (1 – p) = q, it departs the system never to return. The time of waiting plus service time, the nth time the customer goes through, we will call his nth sojourn time. The (random) sum of these sojourn times we will call the total sojourn time (abbreviated, sojourn time when there is no confusion which sojourn time we are talking about). In this paper we study the total sojourn time in a queueing system with feedback. We give the details for M/G/1 queues in which the decision to feedback or not is a Bernoulli process. While the details of the computations can be more difficult, the structure of the sojourn time process is unchanged for the M/G/1 queue with a more general decision process as will be shown. We assume the reader is familiar with Disney, McNickle and Simon [1].
A note on the two machine job shop with exponential processing times
Authors: Pinedo Michael
Published: May 2007

Consider two machines, labeled 1 and 2. A set of tasks has to be processed first on machine 1 and after that on machine 2. A second set of tasks has to be processed first on machine 2 and after that on machine 1. All the processing times are exponentially distributed. We present a policy which minimizes the expected completion time of all tasks.
Production planning for multi‐resource network systems
Authors: Leachman Robert C.
Published: May 2007

Production planning for large‐scale production systems requiring the allocation of numerous resources is considered. It is demonstrated how the dynamic activity analysis developed by Shephard leads to linear programming solutions of production planning problems. Three types of planning problems are formulated: maximization of output levels for a given time horizon; minimization of production duration for given output histories; and minimization of production costs for given output histories.
The variance of the coverage of a randomly located area target by a salvo of weapons
Authors: Schroeter Gerhard
Published: May 2007

We derive formulas for the variance of that proportion of the value of a randomly located, circularly symmetric area target that is destroyed by N independently fired weapons of identical type whose damage functions are circularly symmetric about the respective impact points. The probability density functions of the target center location and of the weapon impact points are also circularly symmetric. The general results are specialized to uniform and Gaussian functions. In the latter case a closed‐form solution (triple integral) for the variance of the coverage is derived. Similar to some well‐known results on expected coverage, this expression for the variance of the coverage can be easily evaluated by numerical quadrature. Numerical results are given which indicate the target coverage variability caused by the combined effects of random target‐locating errors and weapon impact point fluctuations.
An integer programming algorithm for portfolio selection with fixed charges
Authors: Cooper Mary W. , Farhangian Keyvan
Published: May 2007

A mean‐variance portfolio selection model with limited diversification is formulated in which transaction and management costs are incorporated as the sum of a linear cost and a fixed cost. The problem is a fixed charge integer programming problem solved by hypersurface search using dynamic programming. Fathoming is performed in the forward pass of dynamic programming so that values of the state variable which correspond to infeasible solutions are eliminated from the tables. This logic permits the solution of problems with 20–30 possible investments.
Scheduling of a single machine to minimize total weighted completion time subject to release dates
Authors: Bianco Lucio , Ricciardelli Salvatore
Published: May 2007

In this paper the n/1/rj Σj wj Cj problem under the assumptions of nonpreemptive sequencing and sequence independent processing times is investigated. After pointing out the fundamental properties, some dominance sufficient conditions among sequences are obtained and a branch and bound algorithm is proposed. Computational results are reported and discussed.
A note on splitting the bump in an elimination factorization
Authors: Helgaso R. V. , Kennington J. L.
Published: May 2007

This exposition presents a method for incorporating a technique known as “splitting the bump” within an elimination form reinversion algorithm. This procedure is designed to reduce fill‐in during reinversion and should improve the efficiency of linear programming systems which already use the superior elimination form of the inverse.
Transportation problems with aggregated destinations when demands are uncertain
Authors: Zipkin Paul
Published: May 2007

Transportation problems with uncertain demands are useful applied models themselves, and also they represent in a formal way the problem of estimating demands for use in deterministic models. We consider the effects of using a small, aggregate model of this type in place of a larger, more detailed one. Formulation of the aggregate objective function turns out to depend on how one chooses to use (disaggregate) the solution; several alternative methods are examined. Bounds are derived on the error induced by the approximation, thus facilitating comparison of alternative aggregations. We also consider the problem of estimating demands for an aggregate‐level deterministic problem. In a specific sense, it is often not the case (as one might expect) that such aggregate demands are easier to estimate than the detailed demands. This is because aggregation and centralization are not the same thing.
A class of parametric properties of transportation problems
Authors: Akinc Umit
Published: May 2007

This paper studies certain “second order” parametric relations in capacitated transportation problems. These relations concern the question of what happens to the effect of a parameter (first derivative) as another parameter is varied. These relationships have been found quite useful in the solution of many types of facility location and capacity expansion problems. The paper presents several results on the parametric behavior of the dual multipliers from which second order parametric relations can be derived.
Reliability applications of the relevation transform
Authors: Baxter Laurence A.
Published: May 2007

It is shown that Krakowski's relevation transform generates the nonhomogeneous Poisson process in an analogous fashion to the way in which Stieltjes convolution generates the renewal process. Properties of failure rates and of inter‐failure times are discussed and an application to warranty analysis is described.
Recruiters, advertising, and navy enlistments
Authors: Goldberg Lawrence
Published: May 2007

Regression analysis is used to estimate the effects on Navy enlistments of recruiters, advertising, unemployment and other factors. In measuring the effects of these factors on enlistments, changes in both the demand for and supply of enlistments are taken into account. Advertising is treated as a capital investment; its effect is estimated using a maximum likelihood technique that was developed for measuring the effects of capital investments. We find strong evidence that recruiters and unemployment increase enlistments. Advertising also seems to increase enlistments, but its effect is highly uncertain. The results suggest that increases in recruiting resources would have eliminated the enlistment shortfalls experienced by the Navy in FY 1978–79.
Periodic replacement when minimal repair costs vary with time
Authors: Boland Philip J.
Published: May 2007

A policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening system failures. The cost of a minimal repair to the system is assumed to be a nonde‐creasing function of its age. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the system. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited in the case where the system life distribution is strictly increasing failure rate (IFR).
Reliability of a single unit with k spares in case of the hyper‐exponential and the erlang failure distribution
Authors: Van Dam J. , Raaijmakers F. J. M.
Published: May 2007

In this paper formulas are derived for the reliability of a single unit to which identical spares in standby are allocated, with all of these units having a hyper‐exponential or Erlang distributed lifetime. Two advantages are obtained by using these distributions. First, the general procedure for calculating the effect of redundancy is applicable, in contrast with most of the common life distributions, such as Weibull. Moreover, both distributions are suitable for matching to observed curves and practical data by varying the values of the parameters, covering together most of the cases of practical interest.
Nonlinear integer programming for various forms of constraints
Authors: Cooper Mary W. , Farhangian Keyvan
Published: May 2007

A theoretical and computational investigation is made of the performance of a dynamic‐programming‐based algorithm for nonlinear integer problems with various types of constraints. We include linear constraints, aggregated linear constraints, separable nonlinear constraints and constraints involving maxima and minima. Separability of the objective function is assumed. The new feature of the algorithm is that two types of fathoming or pruning are used to reduce the size of tables and number of computations: fathoming by bounds and fathoming by infeasibility.
On patrolling a channel
Authors: Washburn Alan R.
Published: May 2007

A simple formula is found to be just as accurate as a complicated one for estimating the probability of detection achievable by an ingenious searcher patrolling a channel or barrier. The difference between “detection” and “closure” is emphasized in an extension.
The power of paired sample tests
Authors: Deutsch Stuart Jay , Schmeiser Bruce Wayne
Published: May 2007

The power of the component randomization test for the paired sample location test is compared to the power of the parametric test for paired comparisons using the sum of differences distribution. This analysis is presented in the form of operating characteristic curves for normal, exponential, uniform and absolute lambda observations over a range of small sample sizes.
A note on randomly evolving hazard rate functions
Authors: Schechner Zvi
Published: May 2007

Let τ be a finite stopping time with random hazard rate function (λt:t ≥ 0). We prove that στ λt dt is exponentially distributed with mean 1.
Nonadjacent extreme point methods for solving linear programs
Authors: Sherali Hanif D. , Soyster Allen L. , Baines Stafford G.
Published: May 2007

In this article we present some advanced basis or block‐pivoting, relaxation, and feasible direction methods for solving linear programming problems. Preliminary computational results appear to indicate that the former two types of simplex‐based procedures may hold promise for solving linear programming problems, unlike the third type of scheme which is shown to be computationally unattractive.
A simulation–optimization method: Its convergence and utility
Authors: Curry Guy L. , Hartfiel Darald J.
Published: May 2007

An optimization method is given for solving problems where a portion of the explicit mathematical form is unknown but can be evaluated. The solution scheme is an iterative process utilizing optimization and subsystem evaluation (such as via simulation). Conditions for the convergence of the iterative process are given. Several published application articles are noted as using this basic methodology. The method is superior to most other numerical optimization procedures. However, the class of problems for which the method is applicable is restricted to problems with enough known structure to generate a convergent iterative procedure. Three numerical examples are given and comparisons made with several other methods of optimizing unknown systems.
A bounded dual (all‐integer) integer programming algorithm with an objective cut
Authors: Austin Larry M. , Hanna Michael E.
Published: May 2007

In this article, we describe a new algorithm for solving all‐integer, integer programming problems. We generate upper bounds on the decision variables, and use these bounds to create an advanced starting point for a dual all‐integer cutting plane algorithm. In addition, we use a constraint derived from the objective function to speed progress toward the optimal solution. Our basic vehicle is the dual all‐integer algorithm of Gomory, but we incorporate certain row‐ and column‐selection criteria which partially avoid the problem of dual‐degenerate iterations. We present the results of computational testing.
Vehicle fleet refueling strategies to maximize operational range
Authors: Mehrez Abraham , Stern Helman I. , Ronen David
Published: May 2007

The focus of this research is on self‐contained missions requiring round‐trip vehicle travel from a common origin. For a single vehicle the maximal distance that can be reached without refueling is defined as its operational range. Operational range is a function of a vehicle's fuel capacity and fuel consumption characteristics. In order to increase a vehicle's range beyond its operational range replenishment from a secondary fuel source is necessary. In this article, the problem of maximizing the range of any single vehicle from a fleet of n vehicles is investigated. This is done for four types of fleet configurations: (1) identical vehicles, (2) vehicles with identical fuel consumption rates but different fuel capacities, (3) vehicles which have the same fuel capacity but different fuel consumption rates, and (4) vehicles with both different fuel capacities and different consumption rates. For each of the first three configurations the optimal refueling policy that provides the maximal range is determined for a sequential refueling chain strategy. In such a strategy the last vehicle to be refueled is the next vehicle to transfer its fuel. Several mathematical programming formulations are given and their solutions determined in closed form. One of the major conclusions is that for an identical fleet the range of the farthest vehicle can be increased by at most 50% more than the operational range of a single vehicle. Moreover, this limit is reached very quickly with small values of n. The performance of the identical fleet configuration is further investigated for a refueling strategy involving a multiple‐transfer refueling chain, stochastic vehicle failures, finite refueling times, and prepositioned fleets. No simple refueling ordering rules were found for the most general case (configuration 4). In addition, the case of vehicles with different fuel capacities is investigated under a budget constraint. The analysis provides several benchmarks or bounds for which more realistic structures may be compared. Some of the more complex structures left for future study are described.
Recurrence relations between moments of order statistics
Authors: Khan A. H. , Yaqub Mohd , Parvez Saud
Published: May 2007

A general result for obtaining recurrence relations between single moments of order statistics is obtained and has been used to establish the recurrence relations between moments of some doubly truncated distributions. The examples considered are Weibull, exponential, Pareto, power function, Cauchy, and logistic. Recurrence relations are also obtained for nontruncated gamma and beta distributions.
Solution of minisum and minimax location–allocation problems with Euclidean distances
Authors: Chen Reuven
Published: May 2007

A new method for the solution of minimax and minisum location–allocation problems with Euclidean distances is suggested. The method is based on providing differentiable approximations to the objective functions. Thus, if we would like to locate m service facilities with respect to n given demand points, we have to minimize a nonlinear unconstrained function in the 2m variables x1,y1, ⃛,xm,ym. This has been done very efficiently using a quasi‐Newton method. Since both the original problems and their approximations are neither convex nor concave, the solutions attained may be only local minima. Quite surprisingly, for small problems of locating two or three service points, the global minimum was reached even when the initial position was far from the final result. In both the minisum and minimax cases, large problems of locating 10 service facilities among 100 demand points have been solved. The minima reached in these problems are only local, which is seen by having different solutions for different initial guesses. For practical purposes, one can take different initial positions and choose the final result with best values of the objective function. The likelihood of the best results obtained for these large problems to be close to the global minimum is discussed. We also discuss the possibility of extending the method to cases in which the costs are not necessarily proportional to the Euclidean distances but may be more general functions of the demand and service points coordinates. The method also can be extended easily to similar three‐dimensional problems.
A performance comparison of empirical Bayes and Bayes estimators of the Weibull and gamma scale parameters
Authors: Canavos George C.
Published: May 2007

A mean‐squared error comparison of smooth empirical Bayes and Bayes estimators for the Weibull and gamma scale parameters is studied based on a computer simulation. The smooth empirical Bayes estimators are determined as functions of up to 15 past estimates of the parameter of interest. Results indicate that at best the mean‐squared errors of the empirical Bayes estimators are about 20–40% larger than those of the corresponding squared‐error optimal Bayes estimators.
A finite‐range distribution of failure times
Authors: Mukherjee S. P. , Islam A.
Published: May 2007

Properties of a finite‐range failure‐time distribution, that includes the exponential as a particular case, have been studied. The distribution is IFR when the shape parameter exceeds unity, but is IFRA always. For a given value of the shape parameter, the distribution is NBUE over a segment of its range. Estimators of parameters have been derived. Distributions of two‐component series, parallel, and standby system lives have also been worked out.
A heuristic procedure for allocating tasks in fault‐tolerant distributed computer systems
Authors: Mazzola Joseph B. , Neebe Alan W.
Published: May 2007

One way of achieving the increased levels of system reliability and availability demanded by critical computer‐based control systems is through the use of fault‐tolerant distributed computer systems. This article addresses the problem of allocating a set of m tasks among a set of n processors in a manner that will satisfy various task assignment, system capacity, and task scheduling constraints while balancing the workload across processors. We discuss problem background, problem formulation, and a known heuristic procedure for the problem. A new solution‐improving heuristic procedure is introduced, and computational experience with the heuristics is presented. With only a modest increase in the amount of computational effort, the new procedure is demonstrated to improve dramatically solution quality as well as obtain near‐optimal solutions to the test problems.
Optimal replacement policies with two or more loaded sliding standbys
Authors: Henin Claude , Perrakis Stylianos
Published: May 2007

This article defines optimal replacement policies for identical components performing different functions in a given system, when more than one spare part is available. The problem is first formulated for two components and any number of spare parts and the optimal replacement time y(x) at time x is found to have a certain form. Sufficient conditions are then provided for y(x) to be a constant y* for x > y*, and y(x) = x for x > y* (single‐critical‐number policy). Under the assumption that the optimal policies are of the single‐critical‐number type, the results are extended to the n‐component case, and a theorem is provided that reduces the required number of critical numbers. Finally, the theory is applied to the case of the exponential and uniform failure laws, in which single‐critical‐number policies are optimal, and to another failure law in which they are not.
Optimal advertising and inventory control of perishable goods
Authors: Balcer Yves
Published: May 2007

The primary goal of this article is to extend the results of a previous article to the case where the effect of advertisement on sales lasts more than one period. Monotonicity of the optimal advertising and inventory policies in the various factors is investigated. Also, attention will be focused on the relationship between the fluctuations over time of the optimal policies and the variations over time of the factors involved, such as demand distributions and holding costs. For example, if over a finite interval the demand decreases from one period to the next, reaches a minimum, and then increases, then the optimal advertising policy will produce the opposite effect. The period of minimum demand never precedes that of maximum goodwill; moreover, the optimal inventory level decreases while the demand decreases. Finally, when demand distributions are just translates of one another, the results of this article can be extended to nonperishable goods.
An optimum group maintenance policy
Authors: Okumoto K. , Elsayed E. A.
Published: May 2007

In this article we present an optimum maintenance policy for a group of machines subject to stochastic failures where the repair cost and production loss due to the breakdown of machines are minimized. A nomograph was developed for machines with exponential failure time distributions. The optimal schedule time for repair as well as the total repair cost per cycle can be obtained easily from the nomograph. Conditions for the existence of a unique solution for the optimum schedule and the bounds for the schedule are discussed.
One‐ and two‐stage scheduling of two products with distributed inserted idle time: The benefits of a controllable production rate
Authors: Buzacott J. A. , Ozkarahan I. A.
Published: May 2007

Consider the problem of scheduling two products on a single machine or through two machines in series when demand is constant and there is a changeover cost between runs of different products on the same machine. As well as setting batch sizes, it is assumed that the production scheduler can choose the production rate for each product, provided an upper bound is not exceeded. This is equivalent to permitting distributed inserted idle time over the production run. It is shown that characteristic of the optimum schedule is that there is no idle time concentrated between runs; it is all distributed over the run. If the inventory charge is based on average inventory then one product is always produced at maximum rate on the bottleneck stage; however, if there is an inventory constraint based on maximum inventory then in the single‐stage case it can occur that neither product is produced at maximum rate.
Optimality conditions for the bilevel programming problem
Authors: Bard Jonathan F.
Published: May 2007

The bilevel programming problem (BLPP) is a sequence of two optimization problems where the constraint region of the first is determined implicitly by the solution to the second. In this article it is first shown that the linear BLPP is equivalent to maximizing a linear function over a feasible region comprised of connected faces and edges of the original polyhedral constraint set. The solution is shown to occur at a vertex of that set. Next, under assumptions of differentiability, first‐order necessary optimality conditions are developed for the more general BLPP, and a potentially equivalent mathematical program is formulated. Finally, the relationship between the solution to this problem and Pareto optimality is discussed and a number of examples given.
Product moments of order statistics from the doubly truncated exponential distribution
Authors: Balakrishnan N. , Joshi P. C.
Published: May 2007

Recurrence relations for the product moments of order statistics from a doubly truncated exponential distribution are obtained. These relations allow us to evaluate the product moments for all sample sizes.
Periodic inspection policy with preventive maintenance
Authors: Nakagawa Toshio
Published: May 2007

This article considers a modified inspection policy with periodic check intervals, where the unit after check has the same age as before with probability p and is as good as new with probability q. The mean time to failure and the expected number of checks before failure are derived, forming renewal‐type equations. The total expected cost and the expected cost per unit of time until detection of failure are obtained. Optimum inspection policies which minimize the expected costs are given as a numerical example.