When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations

The simulations that many defense analysts rely upon in their studies continue to grow in size and complexity. This paper contrasts the guidance that the authors have received—from some of the giants of military operations research—with the current practice. In particular, the analytic utility of Hughes' simple salvo equations is compared with that of the complex Joint Warfighting System (JWARS), with respect to JWARS' key performance parameters. The comparison suggests that a family of analytic tools supports the best analyses. It follows that smaller, more agile, and transparent models, such as Hughes' salvo equations, are underutilized in defense analyses. We believe that these models should receive more attention, use, and funding. To illustrate this point, this paper uses two very simple models (by modern standards) to rapidly generate insights on the value of information relative to force strength. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Scheduling economic lot sizes in deteriorating production systems

The paper considers the economic lot scheduling problem (ELSP) where production facility is assumed to deteriorate, owing to aging, with an increasing failure rate. The time to shift from an “in‐control” state to an “out‐of‐control” state is assumed to be normally distributed. The system is scheduled to be inspected at the end of each production lot. If the process is found to be in an “out‐of‐control” state, then corrective maintenance is performed to restore it to an “in‐control” state before the start of the next production run. Otherwise, preventive maintenance is carried out to enhance system reliability. The ELSP is formulated under the capacity constraint taking into account the quality related cost due to possible production of non‐conforming items, process inspection, and maintenance costs. In order to find a feasible production schedule, both the common cycle and time‐varying lot sizes approaches are utilized. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 650–661, 2003     

Note: Dual sourcing with nonidentical suppliers

We analyze a dual-sourcing inventory model with exponential lead times and constant unit demand in which the order quantity is split in some proportion between two sources of supply. Unlike earlier studies, we do not require that the two sources be identical in terms of the lead-time parameters or the supply prices. We compare the expected total annual costs for the two-source and the traditional single-source models over a wide range of parameter values. We confirm the findings of earlier studies that, under stochastic lead times, dual sourcing yields savings in holding and shortage costs that could outweigh the incremental ordering costs. With this more general model, we demonstrate that savings from dual sourcing are possible even where the mean or the variability of the second source is higher. © 1993 John Wiley & Sons, Inc.     

The two-machine permutation flow shop with state-dependent processing times

If the processing time of each job in a flow shop also depends on the time spent prior to processing, then the choice of a sequence influences processing times. This nonstandard scheduling problem is studied here for the minimum makespan schedule in a flow shop with two machines. The problem is NP-hard in the strong sense and already contains the main features of the general case [10]. Restricting to the case of permutation schedules, we first determine the optimal release times of the jobs for a given sequence. Permutation schedules are evaluated for this optimal policy, and the scheduling problem is solved using branch-and-bound techniques. We also show the surprising result that the optimal schedule may not be a permutation schedule. Numerical results on randomly generated data are provided for permutation schedules. Our numerical results confirm our preliminary study [10] that fairly good approximate solutions can efficiently be obtained in the case of limited computing time using the heuristics due to Gilmore and Gomory [7]. © 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.     

Multiperiod capacity expansion and shipment planning with linear costs

In this paper we consider a multiperiod deterministic capacity expansion and shipment planning problem for a single product. The product can be manufactured in several producing regions and is required in a number of markets. The demands for each of the markets are non-decreasing over time and must be met exactly during each time period (i.e., no backlogging or inventorying for future periods is permitted). Each region is assumed to have an initial production capacity, which may be increased at a given cost in any period. The demand in a market can be satisfied by production and shipment from any of the regions. The problem is to find a schedule of capacity expansions for the regions and a schedule of shipments from the regions to the markets so as to minimize the discounted capacity expansion and shipment costs. The problem is formulated as a linear programming model, and solved by an efficient algorithm using the operator theory of parametric programming for the transporation problem. Extensions to the infinite horizon case are also provided.     

Longitudinal manpower planning models

A manpower planning model is presented that exploits the longitudinal stability of manpower cohorts. The manpower planning process is described. An infinite horizon linear program for calculating minimum cost manpower input plans is presented and found to have a straightforward solution in a great many cases and to yield an easily implemented approximation technique in other cases.     

On nash subsets and mobility chains in bimatrix games

This work is concerned with constructing, analyzing, and finding “mobility chains” for bimatrix games, sequences of equilibrium points along which it is possible for the two players to progress, one equilibrium point at a time, to an equilibrium point that is preferred by both players. The relationship between mobility chains and Nash subsets is established, and some properties of maximal Nash subsets are proved.