Coordinating a three-level supply chain with quantity discounts

Numerous examples exist that illustrate how companies enjoying a strong position in a supply chain unilaterally dictate terms to their suppliers and/or their customers. This paper suggests a mechanism by which a company can coordinate its purchasing and production functions and create an integrated plan that dictates order and production quantities throughout a three-firm channel. Specifically, we model a company that attempts to dictate channel lot sizes by obtaining a quantity discount from its supplier while offering perhaps a different one to its customer. Previous quantity discount research has examined supply chains consisting of only two levels, a seller and a buyer. This paper considers a three-level chain (supplier–manufacturer–retailer) and explores the benefits of using quantity discounts on both ends of the supply chain to decrease costs. We show that incorporating quantity discounts into both ends of the supply chain can significantly decrease costs compared to concentrating only on the lower end. Furthermore, the results of the decentralized procedure described here are robust vis-à-vis a centralized decision-making procedure.     

Improving Profitability with Quantity Discounts under Fixed Demand

Quantity discount schedules have been studied, in the past, from the retailer's, and not the supplier's, point of view. These studies address the problem of determining the economic order quantities for the retailer, given a quantity discount schedule set by the supplier. In this paper, this problem is addressed from the supplier's point of view, assuming that the retailer always uses his optimal order quantity. It is shown that under certain circumstances, quantity discounts could be of benefit to the supplier (and obviously to the retailer), even when retailer's demand is insensitive to price changes. An algorithm is developed to determine the optimal pricing policy for a linear quantity discount schedule. Numerical examples are provided, and sufficient conditions when no quantity discount should be offered are derived.     

Quantity discounts in single-period supply contracts with asymmetric demand information

We investigate how a supplier can use a quantity discount schedule to influence the stocking decisions of a downstream buyer that faces a single period of stochastic demand. In contrast to much of the work that has been done on single-period supply contracts, we assume that there are no interactions between the supplier and the buyer after demand information is revealed and that the buyer has better information about the distribution of demand than does the supplier. We characterize the structure of the optimal discount schedule for both all-unit and incremental discounts and show that the supplier can earn larger profits with an all-unit discount.     

Coordinated replenishment systems with discount opportunities

In many practical situations, coordination of replenishment orders for a family of items can lead to considerable cost savings. A well-known class of strategies for the case where cost savings are due to reduced joint ordering costs is the class of can-order strategies. However, these strategies, which are simple to implement in practice, do not take discount possibilities into account. We propose a method to incorporate discounts in the framework of can-order strategies. A continuous review multi-item inventory system is considered with independent compound Poisson demand processes for each of the individual items. Discounts are offered by the supplier as a percentage of the total dollar value whenever this value exceeds a given threshold. Starting from the can-order strategy as a basic decision rule, we develop a simple heuristic to evaluate these discount opportunities. The performance of the can-order strategy with discount evaluation is compared with that of another class of discount evaluation rules as proposed by Miltenburg and Silver.     

Quantity discount coordination for allocation of purchase orders in supply chains with multiple suppliers

Studies about supply chain coordination have emphasised maximising the profit of the overall supply chain, but the profit changes of individual members in the supply chain have often been overlooked. It has been shown that profit increment of the whole supply chain may not be beneficial for every individual member. Therefore, the use of quantity discounts to achieve the coordination of a supply chain is discussed in this article. A two-echelon selling system with a single buyer and multiple suppliers is considered to enhance profitability for both sides at the same time. An acceptable quantity discount condition for both the buyer and the suppliers to determine an appropriate order quantity allocation to produce more profits in the supply chain is proposed. Furthermore, the profit distribution between the buyer and each supplier is studied. Finally, the results of the numerical application show that the buyer should focus on managing the procurement costs to decrease the acquiring costs, and the suppliers should focus on the fixed costs of management to reduce the production costs in machine operations.     

Multiple price breaks and alternative purchase lot-sizing procedures in material requirements planning systems

The paper reports the results of several simulation experiments that compare alternative procedures for determining purchase quantities in MRP systems when multiple discounts are available. The procedures are the modified least unit cost (LUCm), the modified MeLaren's order moment (MOMm) and a ‘traditional’ procedure (DOQ) that is commonly used when evaluating quantity discounts. For this work, three purchased parts with two levels of discount attractiveness, two price break offerings, requirement lumpiness and requirement uncertainty were used to evaluate each lot-sizing procedures. A simulation model was used to test 810 observations. This research indicates that the LUCm and MOMm procedures outperform the traditional procedure when multiple discounts are available. In addition, for high discount attractiveness between the price breaks, the LCCm and MOMm procedures are more than five per cent better than the traditional procedure. When the discount attractiveness between the price breaks is low, there is very little difference in the performance of the alternative procedures. Moreover, the LUCm procedure requires 13 45 per cent fewer units of inventory than the MOMm procedure and 66.35 per cent fewer units than the traditional procedure. LUCm emerges as the procedure of choice for the multiple discount lot-sizing problem in material requirements planning (MRP) systems. The LUCm procedure is easily understood; it takes advantage of multiple discounts; it uses considerably less safety stock and places fewer orders.     

A stochastic lot-sizing model with multi-supplier and quantity discounts

This research considers a stochastic lot-sizing problem with multi-supplier and quantity discounts. The objectives are to minimise total costs, where the costs include ordering cost, holding cost, purchase cost and shortage cost, and to maximise service level of the system. In this paper, we first formulate the stochastic lot-sizing problem as a multi-objective programming (MOP) model. We then transform the model into a mixed integer programming (MIP) model. Finally, an efficient heuristic dynamic programming (HDP) model is constructed for solving large-scale stochastic lot-sizing problems. An illustrative example with two cases for a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that the proposed two models are effective and accurate tools for determining the replenishment of touch panels from multiple suppliers for multi-periods.     

Improving a supplier's quantity discount gain from many different buyers

We consider the pricing and inventory decisions of a vendor who supplies a single product to multiple heterogeneous buyers. The problem is analyzed as a Stackelberg game in which the vendor acts as the leader by announcing its pricing policy to all the buyers in advance and the buyers act as followers by choosing their order quantity and the sassociated purchasing price independently under the vendors' pricing scheme. We propose in this paper a pricing policy for the vendor that offers price discounts based on the percentage increase from a buyers' order quantity before discount. The proposed policy is defined as a discrete all-unit quantity discount schedule with many break points. We show that: (i) the proposed policy offers a higher price discount to a buyer ordering a larger quantity and hence complies with general fair trade laws; (ii) an explicit solution is obtained for the vendors' optimal decision; and (iii) although suppliers in reality normally offer price discounts based on a buyers' unit increase in order quantity, the proposed policy is superior for the vendor when there are many different buyers. Other benefits of the proposed pricing policy are demonstrated by numerical examples.     

DISCOUNTING DECISIONS IN A SUPPLIER-BUYER RELATIONSHIP WITH A LINEAR BUYER'S DEMAND

In this paper, we analyze discounting decisions for a supplier with a group of homogeneous customers. We focus on two aspects: the gaming nature of the discount problem and the demand consideration in the process. We use a general quantity discount schedule and start with the Stackelberg equilibrium of the problem. It is shown that, for the seller to gain from quantity discount, he has to set up his quantity discount schedule such that the buyer will order more than his EOQ. Both the seller and the buyer can gain significantly from quantity discount. The incentive for discount is twofold: reducing inventory related cost and attracting more demand from the customers. In addition, quantity discount schedule can be very efficient in obtaining the maximum gain the seller and the buyer can possibly obtain together.     

The joint replenishment problem with quantity discounts under constant demand

In many practical situations quantity discounts on basic purchase price exist, and taking advantage of these can result in substantial savings. Quantity discounts have been considered in many production and inventory models. But unlike other research areas, there have been no studies to quantity discounts in the joint replenishment problem. The purpose of this paper is to develop efficient algorithms for solving this problem. Firstly, we suggest useful propositions to develop efficient heuristic algorithms. Secondly, we develop two algorithms using these propositions. Numerical examples are shown to illustrate the procedures of these algorithms. Extensive computational experiments are performed to analyze the effectiveness of the heuristics.The authors are grateful to the editor and two anonymous referees for their valuable comments on earlier versions of this paper. This work was supported by “Research Center for Logistics Information Technology (LIT)” hosted by the Ministry of Education and Human Resources Development in Korea.