A stock redistribution model

Multi-depot supply systems are subject to stock distribution imbalances; i. e., the fraction of total system stock located at a depot may be too small to support the fraction of system demand expected to be placed on it. In the supply system of concern, a cutomer is always satisfied if there is stock anywhere in the system. Stock redistributions to correct imbalances may reduce both transportation costs and customer waiting times. A model for determining optimum redistribution quantities is formulated, and a practical method of solution for the two depot case is described. Selected numerical illustrations are given.     

Three ways of obtaining the average cost expression in a problem related to joint replenishment inventory control

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.     

Hyperbolic integer programming

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.     

Geometry and resolution of duality gaps

In this study we interpret the exterior penalty function method as a generalized lagrangian metliod which fills duality gaps in nonconvex problems. Geometry and resolution of these gaps from a duality point of view are highlighted.     

An explicit general solution in linear fractional programming

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-Minkowki 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.     

A Bayesian approach to demand estimation and inventory provisioning

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.     

On max-min problems

Necessary and sufficient conditions for max-min problems are given here. In addition to characterization of directional derivatives of the relevant functions, subdifferentiability set for such functions is characterized.     

An n-step, 2-variable search algorithm for the component placement problem

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.     

Sequential bid selection by stochastic approximation

Suppose that a contractor is faced with a sequence of “minimum bid wins contract” competitions. Assuming that a contractor knows his cost to fulfill the contract at each competition and that competitors are merely informed whether or not they have won, bids may be selected sequentially via a tailored stochastic approximation procedure. The efficacy of this approach in certain bidding environments is investigated.     

Stochastic duels involving reliability

The reliability of weapons in combat has been treated by Bhashyam in the context of a stochastic duel characterized by fixed ammunition supplies. negative exponentially distributed firing times and weapon lifetimes, and a fixed number of spare weapons for each duelist. The present paper takes a different approach by starting with the fundamental duel of Ancker and Williams, characterized by unlimited ammunition and by ordinary renewal firing times, and adding to it weapon lifetimes which can be functions of time or of round position in the firing sequence. Probabilities of winning and tieing are derived and it is shown that under certain conditions the weapon lifetimes are equivalent to random time and ammunition limits.