(An) optimal price scheduling for quantity discount

Abstract

Most of the researches on quantity discount deal with the problem of determining the economic order quantities from the perspective of the buyer, assuming a quantity discount schedule is already given by the supplier. The purpose of this thesis is to analyze how the supplier can formulate the terms of a quantity discount pricing schedule, assuming that buyers always behave optimally. First, the effects of price and order size are analyzed on the inventory related cost of a single customer and the profit of a supplier. In this regard, three cases are formulated as follows; Case 1 : The supplier tries to maximize his profit without increasing the current inventory related cost of the customer. Case 2 : The customer tries to minimize his inventory related cost without decreasing the current profit of the supplier. Case 3 : Both the supplier and the customer tries to minimize a joint cost function under the condition that the gain induced by the changes of price and order size are split according to a predetermined ratio. The first two can be regarded as the special cases of the third. The above results are extended to the case where the supplier has to pay the freight cost which increases stepwise as the order size increases. And then, we discuss how the seller can determine parameters, i.e., discount rate and price break point, of some well-known quantity discount systems to reach intended levels of price and order size. Second, the problem of designing an optimal quantity discount schedule is analyzed for the case where the supplier deals with multiple customers and with a single price break. Both all-unit and incremental price discount systems are considered. We investigate the cases where both the discount coefficient and the price break point are unknown and either one of them is prescribed. An algorithm is developed which maximizes the supplier``s economic gain without causing any additional cost to the customers. Third, the problem of designing an optimal q...