Showing papers in "Naval Research Logistics Quarterly in 1977"
TL;DR: In this paper, the problem of simultaneously setting price and production levels for an exponentially decaying product was considered and the optimal ordering decision quantity was derived and its sensitivity to changes in perishability and product price was considered.
Abstract: This paper is concerned with the problem of simultaneously setting price and production levels for an exponentially decaying product. Such products suffer a loss in utility which is proportional to the total quantity of stock on hand. A continuous review, deterministic demand model is considered. The optimal ordering decision quantity is derived and its sensitivity to changes in perishability and product price is considered. The joint ordering pricing decision is also computed and consideration of parametric changes of these decisions indicates a non-monotonic response for optimal price to changes in product decay. Issues of market entry and extensions to a model with shortages are also analyzed.
172 citations
TL;DR: This work considers a single-item inventory system in which the stock level can increase due to items being returned as well as decrease when demands occur, and identifies those inventory levels where disposal is the best policy.
Abstract: 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.
161 citations
TL;DR: In this article, the authors decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs.
Abstract: This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case.
110 citations
TL;DR: It is empirically shown that batch means is superior to replication, but that neither method works well if n is too small, and it is shown that if m is chosen too small for replication, then the coverage may decrease dramatically as the total sample size n is increased.
Abstract: Suppose that we have enough computer time to make n observations of a stochastic process by means of simulation and would like to construct a confidence interval for the steady-state mean. We can make k independent runs of m observations each (n=k.m) or, alternatively, one run of n observations which we then divide into k batches of length m. These methods are known as replication and batch means, respectively. In this paper, using the probability of coverage and the half length of a confidence interval as criteria for comparison, we empirically show that batch means is superior to replication, but that neither method works well if n is too small. We also show that if m is chosen too small for replication, then the coverage may decrease dramatically as the total sample size n is increased.
95 citations
TL;DR: In this paper, a one-period two-echelon inventory model with one warehouse in the first echelon and n warehouses in the second echelons is presented, where at the beginning of the period, the stock levels at all facilities are adjusted by purchasing or disposing of items at the first level, returning or shipping items between the echeons and transshipping items within the second level.
Abstract: This paper presents a one-period two-echelon inventory model with one warehouse in the first echelon and n warehouses in the second echelon. At the beginning of the period the stock levels at all facilities are adjusted by purchasing or disposing of items at the first echelon, returning or shipping items between the echelons and transshipping items within the second echelon. During the period, demands (which may be negative) are placed on all warehouses in the second echelon and an attempt is made to satisfy shortages either by an expedited shipment from the first echelon to the second echelon or an expedited transshipment within the second echelon. The decision problem is to choose an initial stock level at the first echelon (by a purchase or a disposition) and an initial allocation so as to minimize the initial stock movement costs during the period plus inventory carrying costs and system shortage costs at the end of the period.
It is shown that the objective function takes on one of four forms, depending on the relative magnitudes of the various shipping costs. All four forms of the objective function are derived and proven to be convex.
Several applications of this general model are considered. We also consider multi-period extensions of the general model and an important special case is solved explicitly.
93 citations
TL;DR: In this article, the sum of a linear and linear fractional function is investigated in terms of quasi-convexity and quasiconcavity, and local optima of these functions are obtained.
Abstract: The sum of a linear and linear-fractional function is investigated in terms of quasi-convexity and quasi-concavity From this we obtain some insight into the nature of local optima of these functions useful in algorithms
73 citations
TL;DR: In this paper, the authors discuss the properties of a Bilinear Programming problem and develop a convergent cutting plane algorithm, which involves only a subset of the variables and preserves the special structure of the constraints involving the remaining variables.
Abstract: In this paper we discuss the properties of a Bilinear Programming problem, and develop a convergent cutting plane algorithm. The cuts involve only a subset of the variables and preserve the special structure of the constraints involving the remaining variables. The cuts are deeper than other similar cuts.
51 citations
TL;DR: It is desired to determine the number of repairmen and spares required over a multi-year planning horizon to provide for a service criterion of 90% availability.
Abstract: : A population of items which break down at random times and require repair are studied (the classic 'machine repair problem'). It is desired to determine the number of repairmen and spares required over a multi-year planning horizon to provide for a service criterion of 90% availability. When an item fails, it is transported to the repair depot, repaired, and then transported to the spares pool (which is constrained to be empty not more than 10% of the time). The first model considered treats transportation and repair as one service operation. The second model is a series queue which allows for the separate treatment of transportation and repair. Breakdowns are assumed Poisson and repair times, exponential.
50 citations
TL;DR: In this article, a job shop must fulfill an order for N good items, and if the number of good items falls short of the outstanding order, the shop must produce further lots, as necessary.
Abstract: 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.
47 citations
TL;DR: The 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.
Abstract: 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.
45 citations
TL;DR: The stochastic transportation problem (minimize shipping costs plus expected holding and shortage costs at demand points subject to limitations on supply) is shown to be amenable to the solution technique presented.
Abstract: A class of convex programming problems with network type constraints is addressed and an algorithm for obtaining the optimal solution is described. The stochastic transportation problem (minimize shipping costs plus expected holding and shortage costs at demand points subject to limitations on supply) is shown to be amenable to the solution technique presented. Network problems whose objective function is non-separable and network problems with side constraints are also shown to be solvable by the algorithm. Several large stochastic transportation problems with up to 15,000 variables and non-negativity constraints and 50 supply constraints are solved.
TL;DR: In this article, the authors examined all known special cases of the mXn flow shop problem and provided solution procedures to three new special cases along with the optimality proofs, based on the critical path concept.
Abstract: The paper examines all known special cases of the mXn flow-shop problem. It provides solution procedures to three new special cases along with the optimality proofs. The theory of the new special cases is based on the critical path concept.
TL;DR: In this paper, the authors investigate the effect of correlated exponential service times on the performance of two-stage queues in series and show that the system's behavior is sensitive to departures from the traditional assumption of mutually independent service times, especially at higher utilizations.
Abstract: An investigation via simulation of system performance of two stage queues in series (single server, first-come, first-served) under the assumption of correlated exponential service times indicates that the system's behavior is quite sensitive to departures from the traditional assumption of mutually independent service times, especially at higher utilizations. That service times at the various stages of a tandem queueing system for a given customer should be correlated is intuitively appealing and apparently not at all atypical. Since tandem queues occur frequently, e.g. production lines and the logistics therewith associated, it is incumbent on both the practitioner and the theoretician that they be aware of the marked effects that may be induced by correlated service times. For the case of infinite interstage storage, system performance is improved by positive correlation and impaired by negative correlation. This change in system performance is reversed however for zero interstage storage and depends on the value of the utilization rate for the case where interstage storage equals unity. The effect due to correlation is shown to be statistically significant using spectral analytic techniques. For correlation equal unity and infinite interstage storage, results are provided for two through twenty-five stages in series to suggest how adding stages affects system performance for ρ>0. In this extreme case of correlation, adding stages has an effect on system performance which depends markedly on the utilization rate. Recursive formulae for the waiting time per customer for the cases of zero, one, and infinite interstage storage are derived.
TL;DR: Computational experience with test problems whose corresponding linear programming formulation has over 400 rows and 2,000 columns is presented and efficient data structure techniques for exploiting the underlying network structure of this class of problems are presented.
Abstract: This paper presents the details for applying and specializing the work of Saigal [28] and Hartman and Lasdon [16] to develop a primal partitioning code for the multicommodity transportation problem. The emphasis of the paper is in presenting efficient data structure techniques for exploiting the underlying network structure of this class of problems. Computational experience with test problems whose corresponding linear programming formulation has over 400 rows and 2,000 columns is presented.
TL;DR: An algorithm designed to solve a large class of nonconvex max-min problems is described and its usefullness and applicability is demonstrated by solving an extension of a recently introduced model which optimally allocates strategic weapon systems.
Abstract: : An algorithm designed to solve a large class of nonconvex max-min problems is described. Its usefullness and applicability is demonstrated by solving an extension of a recently introduced model which optimally allocates strategic weapon systems. The extended model is shown to be equivalent to a nonconvex mathematical program with an infinite number of constraints, and hence is not solvable by conventional procedures. An example is worked out in detail to illustrate the algorithm.
TL;DR: In this article, an associated discrete (continuous) time Markovian decision problem for any given continuous (discrete) time decision model is formulated and a relationship between the continuous and associated discrete time discounted returns is obtained.
Abstract: An associated discrete (continuous) time Markovian decision problem for any given continuous (discrete) time Markovian decision model is formulated. A relationship between the continuous and associated discrete time discounted returns is obtained. This result is used to show the existence of a deterministic stationary policy that optimizes both discounted return functions. It is also proved that the same policy optimizes the average expected return for both continuous and the associated discrete time processes. The results obtained in this paper can be used to solve the continuous time Markovian decision problem by using the discrete time algorithms or vice versa.
TL;DR: This paper deals with the problem of finding the optimal dynamic operating policy for an M/M/S queue and the optimality criterion is the total discounted cost over a finite horizon.
Abstract: This paper deals with the problem of finding the optimal dynamic operating policy for an M/M/S queue. The system is observed periodically, and at the beginning of each period the system controller selects the number of service units to be kept open during that period. The optimality criterion used is the total discounted cost over a finite horizon.
TL;DR: In this article, the problem of finding a smallest set of nodes covering all edges of an arbitrary graph is solved by identifying partial covers associated with integer dual feasible solutions to the linear programming equivalent of node covering problem.
Abstract: This paper describes a node covering algorithm, i.e., a procedure for finding a smallest set of nodes covering all edges of an arbitrary graph. The algorithm is based on the concept of a dual node-clique set, which allows us to identify partial covers associated with integer dual feasible solutions to the linear programming equivalent of the node covering problem. An initial partial cover with the above property is first found by a labeling procedure. Another labeling procedure then successively modifies the dual node-clique set, so that more and more edges are covered, i.e., the (primal) infeasibility of the solution is gradually reduced, while integrality and dual feasibility are preserved. When this cannot be continued, the problem is partitioned and the procedure applied to the resulting subproblems. While the steps of the algorithm correspond to sequences of dual simplex pivots, these are carried out implicitly, by labeling. The procedure is illustrated by examples, and some early computational experience is reported. We conclude with a discussion of potential improvements and extensions.
TL;DR: In this paper, a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type attrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients).
Abstract: This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” attrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.
TL;DR: In this paper, the authors derived analytic expressions for the expected average cost associated with (s, S) policies for a continuous review inventory model with a compound Poisson demand process and stochastic lead time, under the (restrictive) assumption that only one order can be outstanding.
Abstract: Using Markov renewal theory, we derive analytic expressions for the expected average cost associated with (s, S) policies for a continuous review inventory model with a compound Poisson demand process and stochastic lead time, under the (restrictive) assumption that only one order can be outstanding.
TL;DR: In this article, it was shown that the monotone multivariate failure rates of Brindley and Thompson have no natural analog involving the multivariate fault rate function of Basu for continuous distributions.
Abstract: It is shown that the monotone multivariate failure rates of Brindley and Thompson have no natural analog involving the multivariate failure rate function of Basu for absolutely continuous distributions. Quantities related to the multivariate failure rate function are used to define monotone failure rates. It is shown that these are equivalent to the monotone failure rates of Brindley and Thompson. Based on these quantities, the loss of memory property of Marshall and Olkin is characterized.
TL;DR: The bounds on variables are used to compute bounds on the optimal value when the problem is being solved by the simplex method, and 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.
Abstract: 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.
TL;DR: In this article, an axiomatic formulation of a class of values for cooperative games is given, including the Shapley value and the Banzhaf index, which is related to the multilinear extension of a game.
Abstract: An axiomatic formulation is given of a class of values for cooperative games. This class includes the Shapley value and the Banzhaf index, and is related to the multilinear extension of a game.
TL;DR: In this article, the distribution of total units demanded can be considered as a compound distribution arising from the distributions of demand occurrence and individual demand size, where the number of demands is Poisson distributed.
Abstract: In an inventory model, the distribution of total units demanded can be considered as a compound distribution arising from the distributions of demand occurrence and individual demand size. Three such compound distributions are considered, where the number of demands is Poisson distributed. The demand size distribution will depend on the observed or desired variance-to-mean ratio. An approximation using the gamma distribution is given in terms of the cumulants of the compound distribution for both fixed and stochastic lead times.
TL;DR: In this article, a flow shop sequencing problem with ordered processing time matrices is considered and a convex property for the makespan sequences of such problems is discussed, and an efficient optimizing algorithm is presented.
Abstract: A flow shop sequencing problem with ordered processing time matrices is considered. A convex property for the makespan sequences of such problems is discussed. On the basis of this property an efficient optimizing algorithm is presented. Although the proof of optimality has not been developed, several hundred problems were solved optimally with this procedure.
TL;DR: In this article, interval estimation on the smallest of the θ's and related topics are studied, and applications are considered for location parameter, normal variance, binomial parameter, and Poisson parameter.
Abstract: There are given k (⩾ 2) univariate cumulative distribution functions (c.d.f.'s) G(x; θi) indexed by a real-valued parameter θi, i=1,…, k. Assume that G(x; θi) is stochastically increasing in θi. In this paper interval estimation on the ith smallest of the θ's and related topics are studied. Applications are considered for location parameter, normal variance, binomial parameter, and Poisson parameter.
TL;DR: In this article, an explicit steady state solution for the distribution of the number of customers for a queueing system in which Poisson arrivals are bulks of random size is determined for a queuing system where customer service is exponential.
Abstract: An explicit steady state solution is determined for the distribution of the number of customers for a queueing system in which Poisson arrivals are bulks of random size. The number of customers per bulk varies randomly between 1 and m, m arbitrary, according to a point multinomial, and customer service is exponential. Queue characteristics are given.
TL;DR: 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.
Abstract: 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.
TL;DR: Hirshleifer, Enzer, and Ronen and McKinney as discussed by the authors compared three different solutions to a very simple transfer pricing problem and pointed out weaknesses associated with each solution.
Abstract: 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.
TL;DR: The proposed algorithm finds the sequence (or sequences) with minimum total cost (sum of waiting, penalty and processor costs) when jobs have different available times, due dates, penalty costs and waiting costs.
Abstract: The problem of sequencing jobs on parallel processors when jobs have different available times, due dates, penalty costs and waiting costs is considered. The processors are identical and are available when the earliest job becomes available and continuously thereafter. There is a processor cost during the period when the processor is available for processing jobs. The proposed algorithm finds the sequence (or sequences) with minimum total cost (sum of waiting, penalty and processor costs.). A proof of the algorithm and numerical results are given.