Combining genetic approach and integer programming to solve multi-facility economic lot-scheduling problem

Economic lot-scheduling problem (ELSP) has been studied since the 1950's. ELSP deals with the scheduling of the production of several items on a single facility in a cyclical pattern. The facility can only produce one single item at a time, and there is a set-up cost and set-up time associated with each item. Because of the rapid development of many emerging markets nowadays, many common items are produced in different places in order to satisfy the demands in different markets. This becomes the multi-facilities ELSP problems. In ELSP problems, it is known that if more items types to be produced by the facility, the production frequency of each item type will increase because of the balancing of the production rate and the demand rate. Consequently, the number of set-up time and set-up cost increases accordingly. Thus, reallocating the common items, which can be produced in any facilities, to be produced only on certain facility can certainly reduce the number of production frequency, and lead to lower related costs. The objective of this paper is to propose an optimization methodology combining Integer Programming and Genetic Algorithm to solve multi-facility ELSP problems. This paper proposes to divide themain problem into amaster problem and sub-problems, which are solved by Integer Programming and Genetic Algorithm respectively. To demonstrate the significance of reallocating the common items and aggregating them to produce in certain facility, several models have been designed and tested. The comparison of the models demonstrates the reduction of the costs benefited by result of common items reallocation.