a b s t r a c t This paper considers a multi-product problem with non-identical machines. This manufacturing system consists of various machine types with different production capacities, production costs, setup times, pro- duction rates and failure rates. One of the major issues in the planning phase of a manufacturing system is to take the best decision about which machines must be utilized to manufacture which items. As a result, the decision makers face three critical questions: what machines must be purchased, which items should be allocated to each machine, and what is the optimal cycle length. These decisions must be made to minimize system costs including utilization, setup, production and scrap costs. The multi-machine multi-product economic production quantity (EPQ) problem for an imperfect manufacturing system is formulated as a mixed integer non-linear programming (MINLP) , where the convexity property of multi- product single machine EPQ model is used to convert the problem into a bi-level decision-making prob- lem. In the first level, decisions about machine utilization and items allocation are made. After, in the second level the optimal cycle length for each machine is determined. To solve the problem at hand, a hybrid genetic algorithm (HGA) is proposed integrating genetic algorithm and derivatives method. In the proposed HGA, the solutions of the first level are obtained randomly and then, for the second level, the derivatives method is applied to obtain optimal cycle length based on solutions of the first level. Finally, the results of HGA method are compared to the results of general algebraic modeling system (GAMS) and it is found that HGA method has better and more efficient results. Also, a numerical experimentation and a sensitivity analysis of the model are done.
A multi-machine multi-product EPQ problem for an imperfect manufacturing system considering utilization and allocation decisions(2016- مقاله + ترجمه)