Use of Game Theory and Stochastic Programming for Supply Chain Optimization

This thesis investigates managerial decisions related to the design of a supply chain with the goal of maximizing profits. The work is divided into two parts, the first focusing on the use of game theory and the second focusing on the use of stochastic programming. In the first part, we study competition and coordination in a supply chain in which a supplier both operates a direct channel and sells its product through independent retailers. We find that the supplier generally prefers to have as many retailers as possible in the market, even if the retailers' equilibrium retail price is lower than that of the supplier, or if, at equilibrium, there are no sales through the direct channel. We also find that contracts known to coordinate a traditional supply chain do not coordinate the two-channel supply chain; thus we propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the two-channel supply chain with symmetric retailers. We study numerically the supply chain with asymmetric retailers and find that our key qualitative results are unaffected by retailer asymmetry. We then extend our investigation of the two-channel supply chain to that in which the supplier has limited capacity, subject to probabilistic constraints. We develop conditions under which the supplier should sell through the indirect channel, in spite of the risk that direct channel demand will go unfulfilled. In the second part, we present a case study of a large-scale stochastic optimization problem for USG, a building supplies manufacturer with plants and customers throughout North America. USG seeks to minimize total delivered cost, subject to capacity constraints and cost uncertainty. We first demonstrate that demand uncertainty, rather than production cost uncertainty, is the main cause of month-to-month variations in total cost. We then use the chance constraint method to optimize the network for the 50th percentile of demand, and reduce theoretical costs by approximately 4.8% (1.6% as implemented), as compared to the base case using a single month's demand and cost data.