A MATHEMATICAL MODEL IN HYBRID MAKE TO STOCK AND MAKE TO ORDER ENVIRONMENTS WITH MAINTENANCE ACTIVITIES AND ITS SOLUTION BY META-HEURISTIC ALGORITHMS

In this paper, we present a mathematical model in Make to Stock (MTS) and Make to Order (MTO) production environments in order to entry stage. By solving this model, priceandleadtimeoforderswillbefavorablyobtained with respect to the maintenance activities. Also, in this study, scheduled preventive maintenance on assembly resources will be characterized. The proposed mathematical model is a mixed integer linear programmingmodel. Afterpresentingmathematicalmodel,solving methods and various numerical examples in dierent dimensions are given. To solve the proposed model, at rst, we use an exact method. The exact method is applied by optimization software, namely lingo 8.0. After solving the proposed model by Lingo 8.0 software, the results show that lingo software is not able to solve the model in medium- and large- sized problems in a reasonable time. The proposed model is classied among the NP-hard problems. In NP- hard problems, by increasing dimension of problems, the time taken for solving the models increases exponentially. It is also appropriate for our model. For solving NP-hard problems at the appropriate time, the metaheuristic algorithms are applied. Therefore, for solving the proposed model in medium and high dimensions, two meta-heuristic algorithms, namely genetic algorithm (GA) and particle swarm optimization (PSO) algorithms have been used. The comparison between the meta-heuristic algorithms and output of Lingo 8.0 software shows that the suit ability of the proposed algorithms for solving the model in medium and high dimensions. Finally, we consider the time and quality of solutions; the two algorithms are comparedbothgraphicallyandstatistically. Thegraphicalcomparisonshowsthatgeneticalgorithmisrelatively better than particle swarm optimization algorithm; and the statistical comparison between two metaheuristic algorithmsshowsthatthereisnodierentbetweengenetic algorithm and particle swarm optimization algorithm in solving the proposed mathematical model. It is shown that, with the help of a numerical example and with respect to the maintenance in the model, the total system costs are signicantly reduced.