Knowledge that Transforms

We present an inventory model, where the demand rate varies with an underlying state-of-the-world variable. This variable can represent economic fluctuations, or stages in the product life-cycle, for example. We derive some basic characteristics of optimal policies and develop algorithms for computing them. In addition, we show that certain monotonicity patterns in the problem data are reflected in the optimal policies.

Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions (L, W) is supplied. There are n types of demanded rectangles r1, r2, …, rn, with the ith type having length li, width wi, value vi, and demand constraint bi. It is required to produce, from the stock rectangle S, ai copies of ri, 1 ≤ i ≤ n, to maximize a1v1 + a2v2 + · + anvn subject to the constraints ai ≤ bi. Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.

A supply chain is a network of facilities that performs the functions of procurement of material, transformation of material to intermediate and finished products, and distribution of finished products to customers. Often, organizational barriers between these facilities exist, and information flows can be restricted such that complete centralized control of material flows in a supply chain may not be feasible or desirable. Consequently, most companies use decentralized control in managing the different facilities at a supply chain. In this paper, we describe what manufacturing managers at Hewlett-Packard Company (HP) see as the needs for model support in managing material flows in their supply chains. These needs motivate our initial development of such a model for supply chains that are not under complete centralized control. We report on our experiences of applying such a model in a new product development project of the DeskJet printer supply chain at HP. Finally, we discuss avenues to develop better models, as well as to fully exploit the power of such models in application.

A parameter adaptive decision process is a sequential decision process where some parameter or parameter set impacting the rewards and/or transitions of the process is not known with certainty. Signals from the performance of the system can be processed by the decision maker as time progresses, yielding information regarding which parameter set is operative. Active learning is an essential feature of these processes, and the decision maker must choose actions that simultaneously guide the system in a preferred direction, as well as yield information that can be used to better prescribe future actions. If the operative parameter set is known with certainty, the parameter adaptive problem reduces to a conventional stochastic dynamic program, which is presumed solvable. Previous authors have shown how to use these solutions to generate suboptimal policies with performance bounds for the parameter adaptive problem. Here it is shown that some desirable characteristics of those bounds are shared by a larger class of functions than those generated from fully observed problems, and that this generalization allows for iterative tightening of the bounds in a manner that preserves those attributes. An example inventory stocking problem demonstrates the technique.

Exploratory modeling is using computational experiments to assist in reasoning about systems where there is significant uncertainty. While frequently confused with the use of models to consolidate knowledge into a package that is used to predict system behavior, exploratory modeling is a very different kind of use, requiring a different methodology for model development. This paper distinguishes these two broad classes of model use describes some of the approaches used in exploratory modeling, and suggests some technological innovations needed to facilitate it.

This is the second of a pair of papers describing a two-sided game model of combat. In this paper, each side attempts to develop a force structure attaining the maximum of a prescribed merit function, subject to certain constraints expressed by a set of prescribed measures of effectiveness. These measures can be different for the two sides: furthermore, those of each side can depend on the other side's actions. A solution of the model is a generalized Nash equilibrium of this game, and such a solution also yields shadow prices that reveal the cost in merit paid by each side for requiring the specified level of performance on each measure of effectiveness. The first paper examines a special case in which the model has a linear structure, and shows that in a restricted case the shadow prices produced by that model are the classical eigenvalue weights familiar from Lanchester theory.