Optimal base-stock level of the stochastic economic lot scheduling problem

The stochastic economic lot scheduling problem (SELSP) considers the make-to-stock production of multiple standardized products on a single machine with limited capacity, possibly random set-up times under random demands, and possibly random processing times. The SELSP is an NP-hard inventory problem. The solution methods for solving the SELSP may be classified into two categories, analytic approaches and heuristic approaches. However, these approaches usually take much computation time to secure an optimal solution. In this work, we propose a method that combines the artificial bee colony (ABC) algorithm and ordinal optimization (OO) theory to find a good enough solution quickly of SELSP. The proposed method utilizes the advantages of multi-directional search in ABC algorithm and goal softening in OO theory. The SELSP is firstly formulated as a polling system with quantity-limited lot-sizing policy. Then, the proposed method is applied to find a good enough base-stock level of the polling system using limited computation time. Test results further demonstrate that the proposed method is promising in the aspects of solution quality and computational efficiency.