An Economic Lot-Sizing Problem with Perishable Inventory and Economies of Scale Costs: Approximation Solutions and Worst Case Analysis

The costs of many economic activities such as production, purchasing, distribution, and inventory exhibit economies of scale under which the average unit cost decreases as the total volume of the activity increases. In this paper, we consider an economic lot-sizing problem with general economies of scale cost functions. Our model is applicable to both non-perishable and perishable products. For perishable products, the deterioration rate and inventory carrying cost in each period depend on the age of the inventory. Realizing that the problem is NP-hard, we analyze the effectiveness of easily implementable policies. We show that the cost of the best Consecutive-Cover-Ordering (CCO) policy, which can be found in polynomial time, is guaranteed to be no more than (4 + 5)/7=1.52 times the optimal cost. In addition, if the ordering cost function does not change from period to period, the cost of the best CCO policy is no more than 1:5 times the optimal cost.