A cooperative game approach to a production planning problem

This paper deals with a production planning problem formulated as a Mixed Integer Linear Programming (MILP) model that has a competition component, given that the manufacturers are willing to produce as much products as they can in order to fulfil the market's needs. This corresponds to a typical game theoretic problem applied to the productive sector, where a global optimization problem involves production planning in order to maximize the utilities for the different firms that manufacture the same type of products and compete in the market. This problem has been approached as a cooperative game, which involves a possible cooperation scheme among the manufacturers. The general problem was approached by Owen (1995) as the "production game" and the core was considered. This paper identifies the cooperative game theoretic model for the production planning MILP optimization problem and Shapley Value was chosen as the solution approach. The results obtained indicate the importance of cooperating among competitors. Moreover, this leads to economic strategies for small manufacturing companies that wish to survive in a competitive environment.