Using Lagrangian Relaxation Decomposition With Heuristic to Integrate the Decisions of Cell Formation and Parts Scheduling Considering Intercell Moves

Cell formation and parts scheduling are two important correlated processes in a cellular manufacturing system; however, the decisions involved in these processes are typically made individually. Determining how to integrate these decisions effectively to pursue a productive and lower cost system has become an important issue. This paper focuses on providing an effective solution to integrate the decisions of cell formation and parts scheduling, while considering intercell moves by using a Lagrangian relaxation decomposition method. A mixed integer nonlinear programming mathematical model (CFPSP) is proposed to determine which part families and machine groups are assigned to cells and in which sequence the parts are processed in the machines to minimize the total tardiness penalty cost. To effectively solve the model, a Lagrangian relaxation decomposition method with a heuristic (LRDH) is developed. Using the LRDH, the CFPSP model is solved by decomposing the model into two subproblems, i.e., the cell formation subproblem (CFPSP-FD) and the parts scheduling subproblem (CFPSP-SD). After linearizing the CFPSP-FD model, the subproblem CFPSP-FD is solved by the MIP optimizer CPLEX. A scatter search approach is developed to solve the subproblem CFPSP-SD. Combined with the Lagrange multipliers, the CFPSP-SD model takes into consideration the assignment of part families and the associated machine groups to each cell, when it sequences the processing of the parts on each machine in cells. An illustration of the application of the CFPSP model in an electronic appliance cellular manufacturing enterprise in China is presented.