Optimal control of production and/or marketingplanning

Abstract

This study deals with problems related to production and/or marketing system. Dynamic models are formulated from which the optimality conditions are derived through the application of the optimal control theory to the following three areas: Firstly, a production planning problem is considered for an item whose utility gradually loses with passage of time. A minimum cost scheduling of production output levels is determined during the finite planning period. Also, the production and inventory problem is presented that simultaneously determines the production policy and the planning length during a repetitive period over an infinite planning horizon. Secondly, we introduce a marketing planning problem in which the time delays exist between advertising expenditure and its sales rate. The objective is to find the optimal expenditure rate of advertising which maximizes the current value of net profits. Also, the problem of simultaneously determining the advertising policy as well as the product life is presented. Finally, a production and marketing problem is discussed which combines the first two problem. The objective is to simultaneously determine the production rate of a decaying item and the advertising rate recognizing the existence of the delays effects in a way that miximizes the current value of net profits during the finite planning period. Also, this problem is generalized by incorporating the some practical conditions. A hierarchical approach is presented to solve the problem and compared the combined solutions with the solutions obtained using separate models. These problems are to formulate the dynamic models determining or characterizing the optimal policies of the producting and/or marketing systems. For all the models developed, the explicit solutions are derived in closed form if possible and otherwise, the computational methods are suggested for finding the optimal solution.