Production scheduling to optimize the product assortment in case of constrained capacity and customer-driven substitution

This paper deals with the production scheduling problem by considering product assortment and demand substitution issues, along with capacity and production constraints. In this study we distinguish between long-term product assortment and short-term product assortment. The term long-term product assortment" is used here to indicate the whole set of alternative products that a company is able to produce over a long horizon of time. On the other hand, the "short-term product assortment" represents the products that the company is able to offer to its customers at a time. We assume that, in general, for reasons of capacity constraints and operative costs, the short-term product assortment is a subset of the long-term product assortment. Thus, the objective is to optimize the production schedule and, consequently, the short-term product assortment by considering capacity and production constraints, customer-driven demand substitution and production and inventory costs. In particular, a mixed-integer linear programming model is proposed in a multi-period and multi-product perspective. The validity of the model is proved by discussing a real-world case study from the brewery industry.