This paper develops a novel mixed integer linear programming model (MILP) for decentralized factories scheduling problem where a set of transporters is used for shipping goods among parallel factories to minimize the production costs over all of the factories. Due to its typical features, such as multiple heterogeneous factories and transportation times, this problem is extremely difficult to solve especially in large-scale problems. In order to cope with this difficulty, the main purpose of this paper is to develop a new solving algorithm made by the interoperation of metaheuristics and mathematical programming techniques to minimize the production costs of jobs. The algorithm comprises an electromagnetism-like algorithm and variable neighborhood search. In this hybridization, by MILP relaxation, the guiding principle with ordering of neighborhood structures is used. The results of the proposed algorithm and MILP are analyzed and compared using various test problems.
