Optimal capacity expansion in the presence of capacity options

This paper studies optimal long-term capacity strategies when there exist markets for capacity options. The essential ingredients of the problem derive from the strategic interaction of contract markets with spot markets. This interaction provides the foundation for the short-term pricing and contracting strategies for market participants. Sellers in this market can sign long-term (e.g., forward) contracts with Buyers, where such long-term contracts take the form of capacity options that may or may not be executed by Buyers at some pre-speci ed maturation date. Capacity not o ered in the options market, or for which options by Buyers are not executed, can then be o ered in the spot market. As in our earlier work, Wu et al. (2001a,b,c), we assume that there is some residual risk that such capacity may not nd last-minute buyers. This risk of not being able to sell in the spot market, together with the bene ts of long-term contracting, lead to an equilibrium in the pricing and demand for capacity options. The details of this equilibrium have been fully worked out in Wu et al. (2001c). However, this equilibrium is a short-term equilibrium and assumes that capacity of each Seller in the market is xed. The purpose of this paper is to derive the optimal capacities for Sellers, given full knowledge of the short-term equilibria that would result from any set of capacity decisions they might take. We determine the best response strategies for each Seller in the game derived from the short-term outcome resulting from capacity decisions. We then characterize the long-run equilibrium, when it exists. This allows us also important insights into the nature of technologies that can survive in the long run. As we show, the factors determining such survival depend on the characteristics of both the costs of the technologies as well as the structure and volatility of the markets in which they operate. Numerical examples show that computing long-run equilibrium capacities (and associated short-run market equilibrium) are straightforward using algorithms developed in this paper. We thank helpful discussions and comments from Dimitris Bertsimas, Tim Mount, and Shmuel Oren. Financial support by a mini-Summer research grant, a research fellowship by the Safeguard Scienti cs Center for Electronic Commerce Management, LeBow College of Business at Drexel University as well by Project ADVENTURES and the German Ministry for Education and Research (BMBF) are gratefully acknowledged. Corresponding author is Dr. D.J. Wu, 101 North 33rd Street, 324 Academic Building, Philadelphia, PA 19104. Tel.: +1-215-8952121; fax: +1-215-8952891. Email address:[email protected] (D.J. Wu).