Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management

This paper presents a new mathematical model for integrating the virtual dynamic cellular manufacturing system into supply chain management with an extensive coverage of important manufacturing features. The considered model regards multi-plants and facility locations, multi-market allocation, multi-period planning horizons with demand and part-mix variation, machine and labor time-capacity, labor assignment, training and purchasing or selling of new machines for an increased level of plant capacity. The main constraints are market demand satisfaction in each period, machine and labor availability, production volume for each plant and the amounts allocated to each market. To validate and verify the proposed model is explained in terms of an industrial case from a typical equipment manufacturer. Some of the hard constraints of the proposed model are relaxed in order to obtain a lower bound on the objective function value. In fact, the number of machines and workers allocated to each cell are restricted to yield feasible solutions and tight upper bounds on the objective values for medium size instances in a shorter time. The relaxed model yields tight lower bounds for medium instances in a reasonable computational time. Furthermore, a Benders decomposition is developed for solving the upper bounding model.