Optimal sizing of production units for goods subject to stochastic demand

This paper presents a general framework to handle the optimal sizing of singlestage multi-product units incorporating demand uncertainty. This problem consists on the determination of the type, number of units and their capacities, chosen from a set of standard equipment sizes. The objective function is the profit expectation maximization, involving five components: i. revenue; ii. production cost; iii. equipment depreciation cost; iv. storage cost; v. cost due to non fulfillment of the demand target. The multiple dimension integral representation of the expectation is approximated through cubature formulae. With linear process models, an overall MILP problem formulation is obtained. The approach is applied to the design of the furnace section of a ceramic tile industrial plant, where different products are obtained.