Solving the economic lot scheduling problem with multiple identical facilities under the extended basic period approach

In this study, we solve the Economic Lot Scheduling Problem (ELSP) for a production system with parallel identical facilities. The ELSP with parallel identical facilities is concerned with the lot sizing, scheduling, and production assignment decision of n items so as to minimize the average total cost per unit time. Since the ELSP with parallel identical facilities has been proven as NP-hard, we propose two three-phase approaches based on the Genetic Algorithm (GA). In the first phase, we employ either Carreno's (1990) heuristic or a GA to determine the assignment of n items to the parallel identical facilities. Then, another GA utilizes the advantage of its multi-directional search ability to search for the candidate solutions (i.e., the replenishment cycles of the products) in the second phase. In the third phase, we use an efficient heuristic, namely, Proc FT, to test the feasibility of the candidate solutions and try to generate a feasible production schedule for each facility. Based on an example, we verify that our GA-based approaches efficiently solve the ELSP with parallel identical facilities within a reasonable run time, and it shall provide a useful decision-support tool for production managers.