Decomposition based heuristic algorithm for lot-sizing and scheduling problem treating time horizon as a continuum

In this paper, we deal with a new lot-sizing and scheduling problem (LSSP) that minimizes the sum of production cost, setup cost, and inventory cost. Incorporating the constraints of setup carry-over and overlapping as well as demand splitting, we develop a mixed integer programming (MIP) formulation. In the formulation, problem size does not increase as we enhance the precision level of a time period; for example, by dividing a time period into a number of microtime periods. Accordingly, in the proposed model, we treat the time horizon as a continuum not as a collection of discrete time periods. Since the problem is theoretically intractable, we develop a simple but efficient heuristic algorithm by devising a decomposition scheme coupled with a local search procedure. Even if in theory the heuristic may not guarantee finding a feasible solution, computational results demonstrate that the proposed algorithm is a viable choice in practice for finding good quality feasible solutions within acceptable time limit.