Production planning with variable demand

This paper presents an expanded version of the dynamic inventory model in which customer behavior is explicitly addressed. The intent is to give production planners a means of accounting for the inexact nature of demand as it varies over some mathematically defined set. The proposed model takes the form of a two-person, nonzero sum game or bilevel program. The manufacturer is considered the leader and announces a production mix and advertising strategy for the planning horizon. Using this information, the customer then tries to structure a response that will satisfy his demand at minimum cost. A basic property of the model is that the manufacturer can influence the choices available to the customer through advertising, but cannot control them. Both players try to maximize their individual objectives without violating the constraints of the system. Due to the inherent conflict in the game, this may give rise to non-Pareto-optimal solutions. Nevertheless, we feel that the approach offers new insight into the relationship between production planning and marketing, and offers management a powerful mechanism for coordinating inter-departmental activities. Results from a case study are presented to illustrate a number of these points.