A market game with the characteristic function according to the MRP and input–output analysis model

Abstract

In recent papers (Grubbström and Molinder, IJPE 1994; Bogataj and Horvat, IJPE 1996) the material requirements planning and input−output analysis have been studied using z-transform for discrete time models, Laplace transform for continuous time models and elements of decision theory for stochastic demand in the model. In the above models a single decision maker, i.e. a company, chooses an optimal decision, i.e. production level, without reference to the effect that the decision has on other decision makers and vice versa. In many business situations (also with an MRP model), however, two or more decision makers, i.e. companies, choose an action, i.e. production level, simultaneously, and the actions chosen by each player affect the rewards, i.e. profits, earned by other companies. We have determined the optimal policy for each company in a three-person game derived by the theory of the Shapley value, where the objective function is estimated by the expected value of the annuity stream using MRP theory (for a detailed coordination case for a two-level model).