Monday, July 19, 2010

Supply Chain Network Design and Redesign, Game Theory, and Nash Equilibria

There is a wonderful interview (but too short) by Ron Howard, the Director of the Academy Award winning movie, "A Beautiful Mind," with John F. Nash Jr., the 1994 Nobel laureate in Economic Sciences, in a trailer that accompanies the DVD of this movie. I had the pleasure of recently seeing both.

As John Nash walks away at the end of the interview, bundled up in a warm overcoat and knit cap, he ruefully comments that he has lost so many years and he needs to get back to research since that is what matters.

John Nash's contributions to game theory earned him the Nobel Prize. His work has influenced numerous disciplines, in addition to economics, notably, operations research and management science, political science, applied mathematics, and computer science.

I cite Nash's classical (1950) and (1951) papers in many of my papers that deal with competition.

For example, in a paper, "Supply Chain Network Design Under Profit Maximization and Oligopolistic Competition," which was published recently in the journal, Transportation Research E (2010), I devised a model in which firms seek to determine their optimal supply chain network designs in terms of manufacturing, storage, and shipment capacities, as well as product flows so as to maximize profits. The governing concept is that of a Nash - Cournot equilibrium. This model extends my earlier model in which a firm seeks to design (or redesign) its supply chain network so as to minimize its total costs associated with capacity enhancements (even from scratch) as well as the operational costs. In the latter, no competition was assumed. That study, "Optimal Supply Chain Network Design and Redesign at Minimal Total Cost with Demand Satisfaction," is in press in the International Journal of Production Economics.

High tech companies, including Samsung, Hewlett Packard, and IBM, as well as apparel companies from Benetton to Zara well understand the competitive advantages of careful cost control in supply chains. In addition, more and more companies, including Frito-Lay, Tesco, P&G, and Colgate are being recognized for their supply chain performance.

The analytical challenges of identifying not only the optimal capacities associated with various supply chain network activities, coupled with the optimal production quantities, storage volumes, as well as shipments are tremendous, since the possibilities of where to site manufacturing plants and distribution centers, for example, and at which capacities, may be great. Furthermore, the determination of the optimal supply chain network design (or redesign if a supply chain network already exists with some capacities) needs to be done in a rigorous manner that captures the system-wide nature of the problem.

I've also recently made use of the Nash equilibrium concept in devising a model to capture the gains of possible mergers and acquisitions of firms which are competitors. That paper, "Formulation and Analysis of Horizontal Mergers Among Oligopolistic Firms with Insights into the Merger Paradox: A Supply Chain Network Perspective," is in press in the journal Computational Management Science.

The algorithms that can be applied to determine the optimal designs of supply chain networks, operating either in a centralized manner or in a competitive, decentralized manner, are also reported in the above papers.

I agree with Nash that it is imperative to carve out the necessary time to do research.