A quantity discount lot size model with disposals

Two types of quantity discounts are treated in the literature, namely, 'all units' discounts and incremental quantity discounts. In the all units quantity discounts model, the discount applies to every unit purchased. As a result, the total purchase cost is a discontinuous function of the quantity ordered. In other words, the cost of purchasing a quantity below a quantity for which a discount applies may be higher than that of purchasing the larger discount-applicable quantity. An obvious remedy to the discontinuous total purchase cost is to be able to buy a large enough quantity to qualify for a certain discount and then dispose of the excess at some finite disposal cost. Moreover, the assumption of a finite unit disposal cost is more realistic than that of the infinite disposal cost, which rules out any disposal. This paper introduces a finite unit disposal cost in the lot size model with all units quantity discounts and develops a method of obtaining optimal lot sizes for an entire range of unit disposal costs.