Majid Khalili - Islamic Azad University, Karaj branch,, Department of Industrial Engineering, Alborz, Iran
Mohammad Jafar Tarokh - Department of Industrial Engineering, K.N.Toosi University, Tehran, Iran
Bahman Naderi - Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

This paper studies the multi-stage supply chain system (MSSCM) controlled by the kanban mechanism. In the kanban system, decision making is based on the number of kanbans as well as batch sizes. A kanban mechanism is employed to assist in linking different production processes in a supply chain system in order to implement the scope of just-in-time (JIT) philosophy. For a MSSCM, a mixed-integer nonlinear programming (MINLP) problem is formulated from the perspective of JIT delivery policy where a kanban may reflect to a transporter. Since the adopted model is of MINLP type and solving it by branch and bound (B&B) takes time, a metaheuristic is presented. This metaheuristic is an electromagnetic algorithm (EA). The EA is compared against an existing algorithm and also B&B results to evaluate the proposed metaheuristic. Extensive experiments and statistical analyses demonstrate that our proposed EM is more efficient than B&B with regard to the objective functions considered in this paper

Kanban; Multi-stage supply chain system (MSSCS); Mixed integer non-linear programming (MINLP); Electromagnetism algorithm (EA)