Multi-product multi-market model for co-ordination of marketing and production decisions

A multi-product multi-market segment optimal control model for coordinating marketing and production decisions in a firm is presented. On the marketing side, the model considers pricing and the rate of advertising expenditure for each product for each market segment as decision (i.e. control) variables. On the production side, the production rate for an individual product is considered as a decision variable. The model assumes that demand for a product in each market segment is subject to seasonal and other exogenous effects. The model includes the following two special cases: (a) single-product multiple-market segments, (b) multiple products having purely exogenous, time-varying demand. The production planning subproblem in the model represents a class of partially singular optimal control problems. A solution procedure using Pontryagin's maximum principle is designed to solve the partially singular control problem. A hierarchical approach is then used in designing the solution procedure for the overall model.