A production control problem in competition

In this paper, we study a production control problem in a competitive environment. Two firms produce the same product and compete against each other. The demand is random and so is the production capacity. Each firm needs to decide how much it will produce daily without knowing what the competitor is doing. If it produces too much, the firm has to pay an inventory cost. If it produces too little, unsatisfied customers are turned away to its competitor. The daily demand is randomly allocated between the two firms. We consider a finite planning horizon. The control problem is formulated as a finite dynamic game. Algorithms are developed to determine the control policies of interest. Numerical examples are presented. Comparisons are made with the control policies from a single-firm optimization model.