Multi-product lot scheduling with backordering and shelf-life constraints

In this paper, we revisit the economic lot scheduling problem (ELSP), where a family of products is produced on a single machine, or facility, on a continual basis. Our focus is on the determination of a feasible production schedule, including the manufacturing batch size of each item. We assume that total backordering is permissible and that each of the products has a limited post-production shelf life. Several studies examining this problem have suggested a rotational common cycle approach, where each item is produced exactly once every cycle. To ensure schedule feasibility, we resort to the technique of reducing individual production rates and allow the flexibility of producing any item more than once in every cycle, in conjunction with appropriate timing adjustments. In order to solve this more generalized model, which is NP hard, we suggest a two-stage heuristic algorithm. A numerical example demonstrates our solution approach.