Linear Programming Models for Production-Advertising Decisions

Abstract

This paper studies the problem of simultaneously smoothing production and inventory and setting advertising levels. The models given are linear programming models, assuming a deterministic demand-advertising-price relationship. The formulations include both one period and multiperiod models. Advertising has a decreasing effect within each period with a saturation level of advertising included and advertising also has a decreasing effect through time, allowing a build up of a stock of goodwill. A decomposition approach is given which is very efficient computationally due to the simplicity of the subproblems. Other computational aids are discussed; the pricing problem is examined briefly; and a numerical example is given to indicate the possible effect of considering production and advertising (and pricing) decisions together.