Corrections of costs to feasible solutions of economic lot scheduling problems

The paper considers the problem of choosing order quantities and a cyclic production pattern for several products that are produced in a common capacity constrained facility. The heuristic method from Segerstedt [Segerstedt, A. (1999). Lot sizes in a capacity constrained facility with available initial inventories. International Journal of Production Economics, 59, 469–475] is modified and improved. The method is compared with the heuristic technique according to Doll [Doll, C. L., & Whybark, D. C. (1973). An iterative procedure for the single-machine multi-product lot scheduling problem. Management Science, 20(1), 50–55; Goyal, S. K. (1975). Scheduling a single-machine multi-product system: A new approach. International Journal of Production Research, 13, 487–493]; the differences and similarities between the methods are illustrated in a common numerical example. It shows that feasible   solutions can be found, both with our method and others; where the production can be scheduled during a time interval, the initial inventory level is the same as the final and the schedule can be repeated in a cyclic pattern without shortages. (This definition of feasibility differs from traditional.) However, it shows that the common approximation for the inventory holding costs (qi2hi(1-di/pi)) does not fit. The real inventory holding cost becomes different compared to the approximated that is used in the calculations. The real inventory holding cost depends on the chosen scheduling, which makes it difficult to find an optimal solution. Different solutions and extensions are discussed.