David P. Rutenberg

Preempting an Alert Rival: Strategic Timing of the First Plant by Analysis of Sophisticated Rivalry

This paper examines the strategic rivalry in a duopoly where firms must correctly time the construction of the first plant in a growing market. We explicitly model rivalry for market share. Firms recognize the effect of the rivals actions on their profits; they behave noncooperatively to maximize discounted profits over the infinite horizon. For the timing problem we develop an appropriate solution concept. It is a Nash equilibrium in the space of sequential decision rules which specify each firms correct action as a function of the state of the world. We then show how the equilibrium can be computed by backward induction dynamic programming. Numerical examples illustrate the sequential Nash solution and characterize the rivalry to be the first to build. Parametric analysis of the example enables us to explore the competitive dynamics of capacity choice in new markets.

Design Commonality to Reduce Multi-Item Inventory: Optimal Depth of a Product Line

The problem of commonality is posed as a problem of economic balance. It involves the disutility of refusing to provide each segment of customers with an item fitting its exact requirements versus economies of scale achieved in producing and inventorying each item. The depth of the product line the optimal number of items to produce is determined by finding the minimum concave cost flow through a network. An efficient dynamic program developed in production smoothing is used to find this flow. Many products consist of interacting subassemblies; such multistage problems of finding the number of types of each subassembly can also be solved; a computational procedure is developed and an example presented. Along with modularity and cannibalization, multistage commonality is an essential component of a theory of efficient engineering design.

Managing Exchange Risks in a Floating World

Dr. Shapiro is an Assistant Professor at The Wharton School of the University of Pennsylvania. He has published a number of articles related to international financial management and is a consultant for several banks and multinational corporations in this area. Dr. Rutenberg is an Associate Professor of Industrial Administration at Carnegie-Mellon University. He is completing a book Multinational Tactics which brings together his research in multinational finance, production, and marketing. Rutenberg has been a consultant to numerous corporations on questions of strategy and competition.

Computation in Discrete Stochastic Programs with Recourse

This paper presents a solution procedure for discrete stochastic programs with recourse linear programs under uncertainty. It views the m stochastic elements of the requirements vector as an m-dimensional space in which each combination of the discrete values is a lattice point. For a given second-stage basis, certain of the lattice points are feasible. A procedure is presented to delete infeasible points from the space. Thus, the aggregate probability associated with points feasible for this basis can be enumerated, and used to weight the vector of dual variables defined by the basis. Finally, the paper presents a systematic procedure for changing optimal bases so that a feasible and optimal basis is found for every lattice point.

Planning for a multi-national synergy

Abstract If the headquarters of a multi-national company is to justify its existence, it must plan movements of products, ideas, money and people so that synergistic benefits of multi-national co-ordination exceed the behavioral costs of intervening in the affairs of subsidiaries. Planning in the corporate headquarters of a multi-national company is more complex than in a domestic company in any one nation, so it appears sensible to use analytical tools developed in operations research and organization theory. The benefits from global movements can be estimated by formulating operations research models; these benefits provide bounds against which to gauge the behavioral costs. That is to say, the base case for analysis is that of independent national subsidiaries, with a passive holding company headquartes. It is a geographically diversified portfolio; there are no communication problems for nothing is communicated, neither are there control problems; the stigma of nationalism is minimized.

Technical Note-Risk Aversion in Stochastic Programming with Recourse

In stochastic programming with recourse the objective is to maximize the expected net payoff. This assumes implicitly no aversion to risk. With risk aversion, the objective becomes to maximize the expected concave utility of the net payoffs. Because of the special structure of the problem with risk aversion, a number of computational short cuts are possible in the mathematical program that results. All the second-stage problems can be solved as linear programs. Unfortunately, whether with or without risk aversion, it is necessary to solve the first-stage problem as a nonlinear program. This note shows that the latest representation of the gradient is but a simple modification of the latest representation of the linear objective function without risk aversion.