Showing papers in "Naval Research Logistics Quarterly in 1973"
TL;DR: In this paper, the authors presented several single-echelon, single-item, static demand inventory models for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 - b is lost forever.
Abstract: This article presents several single-echelon, single-item, static demand inventory models for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 - b is lost forever. Both deterministic and stochastic demand are considered. although the case of stochastic demand is treated heuristically. In each situation, a mathematical model representing the average annual cost of operating the inventory system is developed. and an optimum operating policy derived. At the extremes b=1 and b=0 the models presented reduce to the usual backorders and lost sales cases, respectively.
314 citations
TL;DR: A feasible one period model is constructed and the central theorem deals with the n-stage dynamic problem and demonstrates the appropriate cost functions are convex in the decision variable and also provides bounds on certain derivatives.
Abstract: This paper considers the problem of computing optimal ordering policies for a product that has a life of exactly two periods when demand is random. Initially costs are charged against runouts (stockouts) and outdating (perishing). By charging outdating costs according to the expected amount of outdating one period into the future, a feasible one period model is constructed. The central theorem deals with the n-stage dynamic problem and demonstrates the appropriate cost functions are convex in the decision variable and also provides bounds on certain derivatives. The model is then generalized to include ordering and holding costs. The paper is concluded with a discussion of the infinite horizon problem.
139 citations
TL;DR: The aim of this paper is to describe methods of handling problems of handling optimization problems numerically in an effective manner and indicate a number of applications.
Abstract: Many optimization problems occur in both theory and practice when one has to optimize an objective function while an infinite number of constraints must be satisfied. The aim of this paper in to describe methods of handling such problems numerically in an effective manner. We also indicate a number of applications.
107 citations
TL;DR: This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available.
Abstract: The applicability of critical path scheduling is limited by the inability of the algorithm to cope with conflicting resource demands. This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available. These heuristic rules are evaluated on their ability to solve a large multiproject scheduling problem.
98 citations
TL;DR: In this article, an efficient heuristic procedure for a special class of mixed integer programming problems called the uncapacitated warehouse (plant) location problem was introduced. But this procedure is derived from the branching decision rules proposed for the branch and bound algorithm by the author in earlier paper.
Abstract: This paper introduces an efficient heuristic procedure for a special class of mixed integer programming problems called the uncapacitated warehouse (plant) location problem. This procedure is derived from the branching decision rules proposed for the branch and bound algorithm by the author in an earlier paper. It can be viewed as tracing a single path of the branch and bound tree (from the initial node to the terminal node), the path being determined by the particular branching decision rule used. Unlike branch and bound the computational efficiency of this procedure is substantially less than linearly related to the number of potential warehouse locations (integer variables) in the problem. Its computational efficiency is tested on problems found in the literature.
84 citations
TL;DR: In this article, the authors show the equivalence of this problem to a single machine sequencing problem with earliest start and due date constraints where the objective is to minimize the maximum lateness.
Abstract: Recent efforts to improve lower bounds in implicit enumeration algorithms for the general (n/m/G/Fmax) sequencing problem have been directed to the solution of an auxiliary single machine problem that results from the relaxation of some of the interference constraints. We develop an algorithm that obtains optimal and near optimal solutions for this relaxed problem with relatively little computational effort. We report on computational results achieved when this method is used to obtain lower bounds for the general problem. Finally, we show the equivalence of this problem to a single machine sequencing problem with earliest start and due date constraints where the objective is to minimize the maximum lateness.
76 citations
TL;DR: This paper proves an optimal ordering rule, previously conjectured by Talwar, which is derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs.
Abstract: This paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.
66 citations
TL;DR: The formulations as well as the proofs and the transformations provided by the general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases.
Abstract: : A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transformation to canonical form, exploitation of the Farkas-Minkowski lemma and the duality relationships which emerge from the Charnes-Cooper linear programming equivalent for general linear fractional programming. The formulations as well as the proofs and the transformations provided by our general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases. The augmentation developing the explicit solution is presented, for clarity, in an algorithmic format.
63 citations
TL;DR: This paper deals with the stationary analysis of the finite, single server queue in discrete time and investigates the joint density of the queue length and the residual service time and the distribution and its mean.
Abstract: This paper deals with the stationary analysis of the finite, single server queue in discrete time. The following stntionary distributions and other quantities of practical interest are investigated: (1) the joint density of the queue length and the residual service time, (2) the queue length distribution and its mean, (3) the distribution of the residual service time and its mean, (4) the distribution and the expected value of the number of customers lost per unit of time due to saturation of the waiting capacity, (5) the distribution and the mean of the waiting time, (6) the asymptotic distribution of the queue length following departures
The latter distribution is particularly noteworthy, in view of the substantial difference which exists, in general, between the distributions of the queue lengths at arbitrary points of time and those immediately following departures.
56 citations
TL;DR: In this paper, a branch and bound technique is used to identify the global minimum extreme point of a convex polyhedron and a linear undrestimator for the constrained concave objective function is developed.
Abstract: A general algorithm is developed for minimizing a well defined concave function over a convex polyhedron. The algorithm is basically a branch and bound technique which utilizes a special cutting plane procedure to' identify the global minimum extreme point of the convex polyhedron. The indicated cutting plane method is based on Glover's general theory for constructing legitimate cuts to identify certain points in a given convex polyhedron. It is shown that the crux of the algorithm is the development of a linear undrestimator for the constrained concave objective function. Applications of the algorithm to the fixed-charge problem, the separable concave programming problem, the quadratic problem, and the 0-1 mixed integer problem are discussed. Computer results for the fixed-charge problem are also presented.
46 citations
TL;DR: An improved placement procedure is described which is demonstrated to be effective in generating near optimal solutions to the component placement problem and an assessment of performance of the class of near optimal algorithms.
Abstract: The component placement problem is a specialization of the quadratic assignment problem that has been extensively studied for a decade and which is of considerable practical value. Recently, interest in component placement algorithms has risen primarily as a result of increased activity in the field of computer-aided design automation. This paper deals with the methodology of component placement and is based on the results of considerable operational experience. A tutorial presentation of tree search placement algorithms is provided, and an improved placement procedure is described which is demonstrated to be effective in generating near optimal solutions to the component placement problem. These solutions are completely reproducible and are obtained at an acceptable expenditure of computational resources. An additional objective is an assessment of performance of the class of near optimal algorithms. In particular, the question- how close to optimal are the near optimal solutions- is examined.
TL;DR: The theoretical properties of this m-machine problem are explored, and the problem of determining an optimum scheduling procedure is examined; properties of the optimum schedule are given as well as the corresponding reductions in the number of schedules that must be evaluated in the search for an optimum.
Abstract: This paper deals with the sequencing problem of minimizing linear delay costs with parallel identical processors The theoretical properties of this m-machine problem are explored, and the problem of determining an optimum scheduling procedure is examined Properties of the optimum schedule are given as well as the corresponding reductions in the number of schedules that must be evaluated in the search for an optimum An experimental comparison of scheduling rules is reported; this indicates that although a class of effective heuristics can be identified, their relative behavior is difficult to characterize
TL;DR: The results of some numerical experiments designed to compare the performance of various strategies for finding the global solution of a nonlinear program are presented.
Abstract: When applied to a problem which has more than one local optimal solution, most nonlinear programming algorithms will terminate with the first local solution found. Several methods have been suggested for extending the search to find the global optimum of such a nonlinear program. In this report we present the results of some numerical experiments designed to compare the performance of various strategies for finding the global solution.
TL;DR: The problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel, and the cases of Weibull lifetime distributions are elaborated and illustrated numerically.
Abstract: : The problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Life time distribution is arbitrary but known. The optimization is carried with respect to two cost factors: the cost of inspection a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull life time distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.
TL;DR: It is shown that the general rule for optimal resource allocation requires simply that the absolute value of the marginal factor cost of repair services divided by the marginal product cost be equal to the arrival rate of end products to repair.
Abstract: : The paper demonstrates how to determine the minimal cost combination of end products and investment in repair service capability in order to maintain a given level of operating end products. The model is then applied to the problem of determining the optimal size of the Navy's F-4 aircraft pipeline. (Author)
TL;DR: In this paper, a general algorithm for solving the hyperbolic integer program which reduces to solving a sequence of linear integer problems is proposed, which is similar to the Isbell-Marlow procedure.
Abstract: The hyperbolic integer program is treated as a special case of a hyperbolic program with a finite number of feasible points. The continuous hyperbolic program also belongs to this class since its solution can be obtained by considering only the extreme points of the feasible set. A general algorithm for solving the hyperbolic integer program which reduces to solving a sequence of linear integer problems is proposed. When the integer restriction is removed, this algorithm is similar to the Isbell-Marlow procedure. The geometrical aspects of the hyperbolic problem are also discussed and several cutting plane algorithms are given.
TL;DR: The ability afforded the planner by this model to quantify the impact on inventory system costs of varying levels of system reliability or management uncertainty as to projected system performance will provide an economic basis for analysis of such alternatives as early deployment, operational testing, and equipment redesign.
Abstract: This article addresses the problem of explicitly taking into account uncertainty about the demand for spare parts in making inventory procurement and stockage decisions. The model described provides for a unified treatment of the closely related problems of statistical estimation of demand and resource allocation within the inventory system, and leads to an easily implemented, efficient method of determining requirements for spare parts both in the early provisioning phase and in later periods of operations when demand data have accumulated
Analyses of the model's theoretical foundations and of sample outcomes of the model based upon data on parts intended for use in the F-14 lead to conclusions of great importance to both support planners and operations planners
Finally, of particular significance is the ability afforded the planner by this model to quantify the impact on inventory system costs of varying levels of system reliability or management uncertainty as to projected system performance. This will provide an economic basis for analysis of such alternatives as early deployment, operational testing, and equipment redesign.
TL;DR: In this article, the authors describe a procedure for determining if constrained transportation problems with additional linear constraints can be transformed into pure transportation problems by a linear transformation involving the node constraints and the extra constraints.
Abstract: : The paper describes a procedure for determining if constrained transportation problems (i.e., transportation problems with additional linear constraints) can be transformed into equivalent pure transportation problems by a linear transformation involving the node constraints and the extra constraints. The results extend procedures for problems in which the extra constraints consist of bounding certain partial sums of variables.
TL;DR: A comparison of the complementary pivot method of Lemke-Howson and the more commonly used primal-simplex method for solving linear programming problems in symmetric dual form has been made.
Abstract: A comparison of the complementary pivot method of Lemke-Howson and the more commonly used primal-simplex method for solving linear programming problems in symmetric dual form has been made. In our tests the complementary pivot method shows a definite superiority over the simplex method both with regard to the number of iterations and computation time.
TL;DR: Although drawbacks to the use of search techniques in the computer simulation framework exist, these techniques do offer potential for “optimization,” and the modification of these techniques to satisfy the requirements of an “Optimizer” is discussed.
Abstract: Computer simulation has many advantages. However, one major disadvantage is that, in all too many cases, the attempt to use computer simulation to find an optimum solution to a problem rapidly degenerates into a trial-and-error process. Techniques for overcoming this disadvantage, i. e., for making optimization and computer simulation more compatible, are applicable at two points in the development of the overall computer simulation. Techniques which are used within actual construction of the mathematical models comprising the simulation will be labeled as internal methods, while those which are used after the simulation has been completely developed will be termed external methods
Because external methods appear to offer the largest potential payoff, discussion is restricted to these methods, which are essentially search techniques. In addition, the development of an “Optimizer” computer program based on these techniques is suggested
Although drawbacks to the use of search techniques in the computer simulation framework exist, these techniques do offer potential for “optimization.” The modification of these techniques to satisfy the requirements of an “Optimizer” is discussed.
TL;DR: Sufficient conditions are developed for the ergodicity of a single server, first‐come‐first‐serve queue with waiting time dependent service times.
Abstract: Sufficient conditions are developed for the ergodicity of a single server, first-come-first-serve queue with waiting time dependent service times.
TL;DR: In this article, the consequences of interchanging parts within a generalized coherent structure are investigated. But the authors focus on the case where each component can operate at several levels of partial performance and a representation theorem is derived to express the state of a system as a function of the number of working parts at each level.
Abstract: Using the theory of Hirsch, Meisner, and Boll, we study the consequences of interchanging parts within a generalized coherent structure. This procedure has been termed “cannibalization.” The theory of cannibalization is extended to the case where each component can operate at several levels of partial performance and a representation theorem is derived, which expresses the state of a system as a function of the number of working parts at each level. The stochastic theory of these systems is then investigated.
TL;DR: This work shows how to synthesize the optimal target selection policies from the basic optimality conditions and shows that whether or not changes can occur in target priorities depends solely on how survivors are valued and is independent of the type of attrition process.
Abstract: We develop the solution to a simple problem of target selection in Lanchester combat against two enemy force types each of which undergoes a “linear-law” attrition process. In addition to the Pontryagin maximum principle, the theory of singular extremals is required to solve this problem. Our major contribution is to show how to synthesize the optimal target selection policies from the basic optimality conditions. This solution synthesis methodology is applicable to more general dynamic (tactical) allocation problems. For constant attrition-rate coefficients we show that whether or not changes can occur in target priorities depends solely on how survivors are valued and is independent of the type of attrition process.
TL;DR: In this paper, Manpower planning models for a system consisting of many skill categories are formulated; the particular application is to the enlisted force in the U.S. Navy. Interactive computer models of these theoretical formulations have been developed and implemented to aid decision-makers who wish to test the effects of alternative manpower policies on staffing requirements and future manpower budgets.
Abstract: : Manpower planning models for a system consisting of many skill categories are formulated; the particular application is to the enlisted force in the U.S. Navy. Interactive computer models of these theoretical formulations have been developed and implemented to aid decision-makers who wish to test the effects of alternative manpower policies on staffing requirements and future manpower budgets.
TL;DR: In this article, the authors assume that effectiveness tables are given and show how to construct from them a system of weapon weights each of which is a weighted average of the effects of a given weapon against each of the enemy's weapons.
Abstract: Detailed combat simulations can produce effectiveness tables which measure the effectiveness of each weapon class on one side of an engagement, battle, or campaign to each weapon class on the other. Effectiveness tables may also be constructed in other ways
This paper assumes that effectiveness tables are given and shows how to construct from them a system of weapon weights each of which is a weighted average of the effects of a given weapon against each of the enemy's weapons. These weights utilize the Perron- Frobenius theory of eigenvectors of nonnegative matrices. Methods of calculation are discussed and some interpretations are given for both the irreducible and reducible cases.
TL;DR: In this article, the authors present decision procedures which can be used to handle this aspect of initial provisioning, which relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion.
Abstract: Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.
TL;DR: This paper provides a decision rule giving the least valued target that should be attacked as well as the resources thatShould be expended as a function of the attack element's remaining mission time.
Abstract: Frequently in warfare, a force is required to attack a perishable enemy target system - a target system where the targets are detected seemingly at random, and if not immediately attacked, will shortly escape from detection. A conflicting situation arises when an attack element detects a target of relatively low value and has to decide whether to expend his resources on that particular target or to wait for a more lucrative one, hoping one will be found. This paper provides a decision rule giving the least valued target that should be attacked as well as the resources that should be expended as a function of the attack element's remaining mission time.
TL;DR: This paper examines the long range costs of lot-by-lot sampling inspection of product which may be inspected on a dichotomoun basis and suggestions are made concerning the choice of parameters to minimize this cost.
Abstract: Military Standard 105D has been almost universally adopted by government and private consumers for the lot-by-lot sampling inspection of product which may be inspected on a dichotomoun basis
The plan specifies, for each lot size, a random sample size and set of acceptance numbers (maximum allowable number of defectives in each sample). The acceptance numbers are based upon the binomial distribution and depend upon the quality required by the purchaser. Where several consecutive lots are submitted, a shift to less severe (“reduced”) inspection or more severe (“tightened”) inspection is specified when the ongoing quality is very high or low. Further experience permits a return to normal sampling from either of these states
This paper examines the long range costs of such a sampling scheme. The three inspection types are considered as three distinct Markov chains, with periodic transitions from chain to chain. The expected sample size and the expected proportion of rejected product are determined as a function of the two parameters under control of the manufacturer, lot size and product quality. Some numerical examples are given which illustrate how to compute the overall cost of sampling inspection. Suggestions are made concerning the choice of parameters to minimize this cost.
TL;DR: This paper does not present a new result, rather it is meant to illustrate the choice of modelling procedures available to an analyst in a typical inventory control problem, where the same “average cost per unit time” expression is developed by three quite different procedures.
Abstract: This paper does not present a new result, rather it is meant to illustrate the choice of modelling procedures available to an analyst in a typical inventory control problem The same “average cost per unit time” expression is developed by three quite different procedures This variety of approaches, as well as the recounting of the author's chronological efforts to solve the problem, should be of interest to the reader The specific inventory problem studied is one where the controller of an item is faced with random opportunities for replenishment at a reduced setup cost; the problem is an integral component of the broader problem of inventory control of a group of items whose replenishments are coordinated to reduce the costs of production, procurement, and/or transportation
TL;DR: In this article, the availability function for an alternating renewal process with exponential failure and general repair times is given, and a bound on the error is also given, with the most practical consequence being the lower bound on availability.
Abstract: This paper gives bounds on the availability function for an alternating renewal process with exponential failure and general repair times. A bound on the error is also given. Several of the bounds with greatest practical consequence are worked out and illustrated. Repair distributions for which a lower bound on availability is easily computed are gamma (integer shape parameter), log normal, and Weibull. Finally, some simulation results for log normal repair versus gamma repair are given.