Competitive production scheduling: A two-firm, noncooperative finite dynamic game

In this paper, we study the production scheduling problem in a competitive environment. Two firms produce the same product and compete in a market. The demand is random and so is the production capacity of each firm, due to random breakdowns. We consider a finite planning horizon. The scheduling problem is formulated as a finite dynamic game. Algorithms are developed to determine the security, hazard, and Nash policies. Numerical examples are discussed. A single-firm optimization model is also analyzed and it is observed that the production control policy from the single-firm optimization model may not perform well in a competitive environment.