Two-level optimization for decentralized production and advertising planning

Production and advertising decisions are often made in a decentralized fashion; that is, the decisions are made somewhat independently by the corresponding departments of a firm, and these decisions are modified gradually to cope with the best interest of the firm. We treat the joint production and advertising problem as a serial system, where the advertising expenditure is an input to the production level, and we present a two-level optimization algorithm for this problem. With this approach the original is first divided into two subproblems and then the solution to the overall problem is obtained by solving the subproblems iteratively. We later show numerically that the decisions made by this approach are consistent with those planned in a centralized fashion.