Production scheduling in a price competition

In this paper, we study the production scheduling problem in a price competition. Two firms produce the same product and compete with each other. The production capacity of each firm is random, due to random breakdowns. The demand process and its allocation are random and affected by the pricing strategies of both firms. We consider a finite planning horizon. The scheduling problem is formulated as a finite dynamic game. Algorithms are developed to determine the control policies of interest. Numerical cases are studied to observe the system behavior under those policies. We also construct a single-firm optimization model and demonstrate that the policy from the single-firm model may not perform well in a competitive environment.