Integration of Sales and Operations: A Dynamic Mixed-Integer Programming Game

We define a framework to investigate and assess the impact of prompt and dynamic reactions to market competition in production planning problems. It depicts two firms that produce and sell substitutable products over a finite time horizon. Each firm optimizes its sales and production costs, and has sufficient market power to affect the sales of the other firm. The framework can capture several production and market competition features. We model production plans using mixed-integer programs and market competition using sequential Stackelberg games. Under certain conditions, we can solve the models in our framework in polynomial-time. We provide examples to illustrate how the framework can match the requirements of production planning and sales. Then, we perform a computational study to analyze a planning problem that features the possibility of technological investments to reduce the variable production costs. We draw insights on the value of our polynomial-time method to compute subgame perfect equilibria by comparing its optimal production plans against a static model, where firms fix the entire production plan at the beginning of the planning horizon, and a myopic model, where firms ignore the impact that current decisions will have in future periods.