Analysis of optimal production and advertising policies

In this paper, the joint production and advertising control model proposed by Parlar is extended to include a time dependent depreciation rate of goodwill (sales), the salvage value of inventory unsold, and the salvage value of goodwill. For an arbitrary form for the production cost function, necessary conditions for optimal production and advertising rates are obtained using the maximum principle. For specific forms (quadratic and linear) for the production cost function, optimal production and advertising policies are investigated. In addition, the solution technique used by Parlar to deal with the pure state inequality constraint is shown to be incorrect, and thus correct analyses to the problem are presented. An alogorithm is developed to solve the necessary conditions and numerical examples are presented to illustrate the solution.