In this paper, to integrate the decisions of parts scheduling, Material Requirement Planning (MRP), Production Planning (PP) and Transportation Planning (TP) for designing a Cellular Manufacturing System (CMS) under a dynamic environment, a Mixed-Integer Nonlinear Programming (MINLP) mathematical model is formulated. The proposed mathematical model integrates extensive coverage of significant manufacturing characteristics in designing a CMS to be implemented in a three-layer supply chain. The considered features include markets demands, heterogeneous vehicles, raw materials requirements planning, parts due dates, cell size limits, machines capacity, intra/inter cell material handling time/cost, transportation time/cost, operation time, alternative processing routes in addition to the main decisions of parts scheduling, PP, TP and dynamic cell formation. Also, some novel characteristics are incorporated based on a three-layer supply chain that make the presented model remarkable respect to the literature including 1) In the first layer, planning the orders of raw materials with different lead times and usage coefficients is performed, 2) In the second layer, decisions of dynamic cell formation and parts scheduling are made, and 3) In the third layer, optimal vehicles are selected as a generalized fixed-charge TP based on transportation time and cost to satisfy multi-markets with different demand volumes. The components in the objective function to be minimized include total costs of holding the parts inventories in the markets, backorders, tardiness, transportation of the parts from the plant to the markets, purchase of raw materials, keeping raw materials in the plant warehouse, intercellular/intracellular movements and machine relocation. An illustrative numerical example is solved by the CPLEX solver to illustrate the achievements obtained by the incorporated characteristics in the integrated model. Furthermore, a sensitivity analysis is performed to assess the effects of important parameters on the model performance. Since the proposed model is NP-hard, a Simulated Annealing (SA) algorithm is improved by an elaborately-designed matrix-based chromosome representation is applied to represent all decision variables, as well as a sequential procedure generating initial solutions. Several test problems either generated randomly or taken from the literature with various sizes are solved and the results are compared with the solutions gained using CPLEX solver. The comparisons results show that the designed SA is capable of evolving optimal or near-optimal solutions with reasonable relative gaps in a computationally satisfactory manner.
A bi-level bi-objective mathematical model for cellular manufacturing system applying evolutionary algorithms