Heuristics for the multi‐resource generalized assignment problem

The well‐known generalized assignment problem (GAP) involves the identification of a minimum‐cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi‐resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three‐phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near‐optimal solutions. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 468–483, 2001     

Attrition modeling in the presence of decoys: An operations-other-than-war motivation

Under various operational conditions, in particular in operations other than war (OOTW) or peacekeeping, an intervening force, here Blue, must occasionally engage in attrition warfare with an opposing force, here Red, that is intermingled with noncombatants. Desirably, Red armed actives are targeted, and not the unarmed noncombatants. This article describes some simple Lanchesterian attrition models that reflect a certain capacity of Blue to discriminate noncombatants from armed and active Red opponents. An explicit extension of the Lanchester square law results: Blue's abstinence concerning the indiscriminate shooting of civilians mixed with Red's is essentially reflected in a lower Blue rate of fire and less advantageous exchange rate. The model applies to other situations involving decoys, and reflects the value of a discrimination capability. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44 : 507–514, 1997     

Testing or fault-finding for reliability growth: A missile destructive-test example

A new piece of equipment has been purchased in a lot of size m. Some of the items can be used in destructive testing before the item is put into use. Testing uncovers faults which can be removed from the remaining pieces of equipment in the lot. If t < m pieces of equipment are tested, then those that remain, m₁ = m − t, have reduced fault incidence and are more reliable than initially, but m₁ may be too small to be useful, or than is desirable. In this paper models are studied to address this question: given the lot size m, how to optimize by choice of t the effectiveness of the pieces of equipment remaining after the test. The models used are simplistic and illustrative; they can be straightforwardly improved. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 623–637, 1997     

Towards finding global representations of the efficient set in multiple objective mathematical programming

We propose and justify the proposition that finding truly global representations of the efficient sets of multiple objective mathematical programs is a worthy goal. We summarize the essential elements of a general global shooting procedure that seeks such representations. This procedure illustrates the potential benefits to be gained from procedures for globally representing efficient sets in multiple objective mathematical programming. © 1997 John Wiley & Sons, Inc.     

A stochastic air combat logistics decision model for Blue versus Red opposition

Technologically advanced aircraft rely on robust and responsive logistics systems to ensure a high state of operational readiness. This paper fills a critical gap in the literature for combat models by closely relating effectiveness of the logistics system to determinants of success in combat. We present a stochastic diffusion model of an aerial battle between Blue and Red forces. The number of aircraft of Blue forces aloft and ready to be aloft on combat missions is limited by the maximum number of assigned aircraft, the reliability of aircraft subsystems, and the logistic system's ability to repair and replenish those subsystems. Our parsimonious model can illustrate important trade‐offs between logistics decision variables and operational success.     

Risk pooling in a two-period,two-echelon inventory stocking and allocation problem

The object of this article is to investigate the risk-pooling effect of depot stock in two-echelon distribution system in which the depot serves n retailers in parallel, and to develop computationally tractable optimization procedures for such systems. The depot manager has complete information about stock levels and there are two opportunities to allocate stock to the retailers within each order cycle. We identify first- and second-order aspects to the risk-pooling effect. In particular, the second-order effect is the property that the minimum stock available to any retailer after the second allocation converges in probability to a constant as the number of retailers in the system increases, assuming independence of the demands. This property is exploited in the development of efficient procedures to determine near-optimal values of the policy parameters.     

Properties of a source location estimator in the plane

The statistical properties of an estimator of a source location were established by simulation for the case in which the source location is estimated—using transformation of lines to points—from the angles in which different observers see the source, and both the assumed locations of the observer points and the observed angles are subject to error. It was found that for normal error distributions the estimator is unbiased, and the resulting estimates are approximately normally distributed with a small standard deviation. An easy-to-use and reliable forecasting formula was suggested to forecast the parameters of the distributions of the estimates for different observer-source relationships. © 1993 John Wiley & Sons, Inc.     

On the equivalence of jit and mrp as technologies for reducing wastes in manufacturing

JIT (just-in-time) is widely regarded as an excellent tool for reducing costs and cycle times, and for improving quality in manufacturing operations. JIT follows a multistep procedure. First, it identifies and prioritizes wastes or non-value-adding activities. Second, it forces these wastes to be removed. MRP (materials requirements planning) can identify the same wastes and prioritize them in the same way that JIT does, by using data from the MRP database and master production schedule, and a waste identification model. In this article, a model is developed which describes the process by which the classic JIT system identifies and prioritizes waste. An equivalent MRP waste identification model is then developed for the production environment of the classic JIT system. (The classic JIT system was developed to produce many products having low to medium volumes.) The results developed here can be extended to other production environments where adaptations of the classic JIT system are used. An example, taken from an actual application, is presented to illustrate the models and the equivalence of JIT and MRP as systems for identifying and prioritizing wastes in manufacturing. © 1993 John Wiley & Sons, Inc.