Combining Artificial Bee Colony With Ordinal Optimization for 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 and set-up costs under random demands, random set-up times, and random production times. The SELSP is an NP-hard inventory problem. Current solutions for the SELSP can be classified as analytic or heuristic. In both approaches, however, the computation time needed to obtain an optimal solution is still unsatisfactory. In this paper, the SELSP is first formulated as a fixed-sequence base-stock (FSBS) system with quantity-limited lot-sizing policy. An algorithm combining artificial bee colony (ABC) approach and ordinal optimization (OO) theory, abbreviated as ABCOO, is then proposed to find a good enough base-stock level of the FSBS system using reasonable computation time. The proposed algorithm combines the advantage of multidirectional search in ABC with the advantage of goal softening in OO. Finally, the ABCOO algorithm is used to solve an SELSP involving 12 products and three queuing models. Test results obtained by the ABCOO algorithm are compared with four lot-sizing policies and three meta-heuristic methods. The base-stock level obtained by the ABCOO algorithm is excellent in terms of solution quality and computational efficiency. Furthermore, a time series forecasting technique is used to predict the variant demand rates needed to resolve time-lag problems of the ABCOO algorithm. Tests of the forecasting technique confirm that it considerably improves the performance and enables the proposed algorithm real-time applications.