The Product-Mix Problem under Stochastic Seasonal Demand

Abstract

The product-mix problem of production planning is to determine the best quantity of each product to manufacture, over a complete range of products competing for a number of limited resources. This paper examines the problem when uncertainty of demand is a major factor, making any differences between the penalties of over- and under-production important. In these circumstances the basic linear programming technique is insufficient, and a model has been developed as a multi-item newsboy problem in which a number of linear resource constraints affect the decision variables. The formulation is one of linear programming under uncertainty. A marginal analysis approach is used to obtain a detailed insight into the structure of the solution and to develop an effective computational procedure. Very little additional data is required, beyond that needed for a conventional linear program.