Lateral capacity exchange and its impact on capacity investment decisions

We study the problem of capacity exchange between two firms in anticipation of the mismatch between demand and capacity, and its impact on firm's capacity investment decisions. For given capacity investment levels of the two firms, we demonstrate how capacity price may be determined and how much capacity should be exchanged when either manufacturer acts as a Stackelberg leader in the capacity exchange game. By benchmarking against the centralized system, we show that a side payment may be used to coordinate the capacity exchange decisions. We then study the firms' capacity investment decisions using a biform game framework in which capacity investment decisions are made individually and exchange decisions are made as in a centralized system. We demonstrate the existence and uniqueness of the Nash equilibrium capacity investment levels and study the impact of firms' share of the capacity exchange surplus on their capacity investment levels.© 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A note on the constrained shortest-path problem

The subject of this note is the validity of the algorithm described by Aneja and Nair to solve the constrained shortest-path problem.     

Scheduling stochastic jobs on a single machine subject to breakdowns

A single machine is available to process a collection of stochastic jobs. There may be technological constraints on the job set. The machine sometimes breaks down. Costs are incurred and rewards are earned during processing. We seek strategies for processing the jobs which maximize the total expected reward earned.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

On the aggregation of preferences

The article attempts to show how network theory may be applied to gain new and better insights into basic economic problems. Starting with a precise definition of what is meant by acting and, in particular, by economic acting, we direct the line of argumentation toward solving the problem of how to aggregate economic decisions. Results indicate that network theory might well prove itself to be a powerful instrument in developing a theory of human behavior much more comprehensive than currently used models.     

A targeting model that minimizes collateral damage

This paper considers the problem of allocating weapons to achieve targeting objectives while simultaneously minimizing aggregate damage to surrounding nonmilitary facilities, each of which has an upper limit to the damage it is permitted to incur. A model is formulated which assumes only that damage to individual targets or associated facilities does not decrease as the number of allocated weapons increases. An implicit enumeration algorithm, based on that of Lawler and Bell is described that yields optimal integer solutions. An example is presented.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

A characterization of the value of zero-sum two-person games

For the family D, consisting of those zero-sum two-person games which have a value, the value-function on D is characterized by four properties called objectivity, monotony, symmetry and sufficiency.     

Joint determination of preventive maintenance and safety stocks in an unreliable production environment

In this article we formulate an analytical model of preventive maintenance and safety stock strategies in a production environment subject to random machine breakdowns. Traditionally, preventive maintenance and safety stocks have been independently studied as two separate strategies for coping with machine breakdowns. Our intent is to develop a unified framework so that the two are jointly considered. We illustrate the trade-off between investing in the two options. In addition, we provide optimality conditions under which either one or both strategies should be implemented to minimize the associated cost function. Specifically, cases with deterministic and exponential repair time distributions are analyzed in detail. We include numerical examples to illustrate the determination of optimal strategies for preventive maintenance and safety stocks. © 1997 John Wiley & Sons, Inc.     

Multiple-facility loading under capacity-based economies of scope

Multiple-facility loading (MFL) involves the allocation of products among a set of finite-capacity facilities. Applications of MFL arise naturally in a variety of production scheduling environments. MFL models typically assume that capacity is consumed as a linear function of products assigned to a facility. Product similarities and differences, however, result in capacity-based economies or diseconomies of scope, and thus the effective capacity of the facility is often a (nonlinear) function of the set of tasks assigned to the facility. This article addresses the multiple-facility loading problem under capacity-based economies (and diseconomies) of scope (MFLS). We formulate MFLS as a nonlinear 0–1 mixed-integer programming problem, and we discuss some useful properties. MFLS generalizes many well-known combinatorial optimization problems, such as the capacitated facility location problem and the generalized assignment problem. We also define a tabu-search heuristic and a branch-and-bound algorithm for MFLS. The tabu-search heuristic alternates between two search phases, a regional search and a diversification search, and offers a novel approach to solution diversification. We also report computational experience with the procedures. In addition to demonstrating MFLS problem tractability, the computational results indicate that the heuristic is an effective tool for obtaining high-quality solutions to MFLS. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 229–256, 1997