The Capacitated Product Portfolio Mix-and-Allocation problem with integrity constraints

In this paper, we address the Capacitated Product Portfolio Mix-and-Allocation (CPPMA) problem, which arises where a decision-maker has to determine simultaneously (a) the optimal product mix; (b) its allocation to different production facilities; and (c) the capacities of the facilities given the product mix and clients/orders allocated. This problem is particularly important when customers orders may affect the whole product portfolio, due to some constraints limiting the overall flexibility of the system. Although it is possible to find models addressing these issues separately, no attempt seems to have been made in the literature for addressing all of them simultaneously. In this paper, we introduce a novel model which aims at maximising the operational profit by simultaneously addressing product portfolio, facility selection, capacities, and orders allocation decisions. Given the high computational complexity of the resulting formulation, we propose a greedy heuristic approach that is capable of producing high-quality solutions. Our computational experience has also yielded some interesting managerial insights.