Quantity Discount‐Based Inventory Coordination: Effectiveness and Critical Environmental Factors

It is understood that quantity discounts provide a practical foundation for coordinating inventory decisions in supply chains. The primary objective of this research is to test, under a variety of environmental conditions, the effectiveness of quantity discounts as an inventory coordination mechanism between a buyer and a supplier. A comprehensive simulation experiment with anova has been designed to investigate the impacts of (1) choice of quantity discount‐based inventory coordination policies, (2) magnitude of demand variation, (3) buyer's and supplier's relative inventory cost structure, and (4) buyer's economic time‐between‐orders on the effectiveness of supply chain inventory coordination. The analytical results confirm that the quantity discount policies have managerial properties as a mediator for inventory coordination. The results also show that the performance of quantity discount‐based inventory coordination policies is influenced significantly by environmental factors, such as the magnitude of demand variation, the buyer's and the supplier's inventory cost structure, and the buyer's economic time‐between‐orders.     

Optimal Quantity Discount Design with Limited Information Sharing*

In this article we address the optimal quantity discount design problem of a supplier in a two‐stage supply chain where the supplier and the buyer share annual demand information only. The supply chain faces a constant deterministic demand that is not price sensitive and operates with fixed setup costs in both stages. We show that the supplier can actually moderate a cost‐minimizing buyer to order in quantities different than the buyer's optimal order quantity in the traditional setting and develop a multi‐breakpoint quantity discount scheme that maximizes supplier's expected net savings. The proposed multi‐breakpoint discount scheme can be easily computed from the available information and, while also maximizing the supplier's net savings, is very effective in achieving high levels of supply chain coordination efficiency in the presence of limited information.     

Pay‐Back‐Revenue‐Sharing Contract in Coordinating Supply Chains with Random Yield

We consider coordination issues in supply chains where supplier's production process is subject to random yield losses. For a simple supply chain with a single supplier and retailer facing deterministic demand, a pay back contract which has the retailer paying a discount price for the supplier's excess units can provide the right incentive for the supplier to increase his production size and achieve coordination. Building upon this result, we consider coordination issues for two other supply chains: one with competing retailers, the other with stochastic demand. When retailers compete for both demand and supply, they tend to over‐order. We show that a combination of a pay back and revenue sharing mechanism can coordinate the supply chain, with the pay back mechanism correcting the supplier's under‐producing problem and the revenue sharing mechanism correcting the retailers' over‐ordering problem. When demand is stochastic, we consider a modified pay‐back‐revenue‐sharing contract under which the retailer agrees to not only purchase the supplier's excess output (beyond the retailer's order), but also share with the supplier a portion of the revenue made from the sales of the excess output. We show that this contract, by giving the supplier additional incentives in the form of revenue share, can achieve coordination.     

Competition and Coordination in a Two‐Channel Supply Chain

We study competition and coordination in a supply chain in which a single supplier both operates a direct channel and sells its product through multiple differentiated retailers. We study analytically the supply chain with symmetric retailers and find that the supplier prefers to have as many retailers as possible in the market, even if the retailers' equilibrium retail price is lower than that of the supplier, and even if the number of retailers and their cost or market advantage prevent sales through the direct channel. We find that the two‐channel supply chain may be subject to inefficiencies not present in the single‐channel supply chain. We show that several contracts known to coordinate a single‐channel supply chain do not coordinate the two‐channel supply chain; thus we propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the two‐channel supply chain with symmetric retailers. We provide some analytical results for the supply chain with asymmetric retailers and propose an efficient solution approach for finding the equilibrium. We find numerically that the supplier still benefits from having more retailers in the market and that linear quantity discount contracts can mitigate supply chain inefficiency, though they no longer achieve perfect coordination.     

需求和零售商购买成本同时扰动的供应链应急协调

供应链的契约协调机制是供应链管理的重要内容,突发事件下的供应链协调机制是近年来的研究热点。 研究了在单制造商单零售商组成的供应链中,假设生产成本是其生产数量的凸函数下,当市场需求为零售价格的非线性函数,突发事件造成需求和零售商购买成本同时发生扰动时,集权、分权供应链应对突发事件的最优策略。 首先证明了稳定环境下的数量折扣契约可以实现该供应链的协调,在集权式决策下,供应链的原有生产计划对突发事件具有一定的鲁棒性,但是当突发事件造成的扰动超过一定幅度时,供应链的协调将会被打破,供应链系统必须改变生产计划才能实现其利润最大化。 在分权式决策下,供应链的原数量折扣契约不能使扰动后的供应链达到协调,因此,设计了新的数量折扣契约来使扰动后的供应链达到协调。最后给出一个算例验证了相关结论。     

Quantity Flexibility Contract in the Presence of Discount Incentive

We design a new contract, which we refer to as the QFi contract, that combines the quantity flexibility (QF) mechanism and the price‐only discount incentive. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity and extra buffer inventory. In contrast, the price‐only discount contract places full inventory burden on the buyer. We show that the proposed QFi contract effectively balances the inventory risk for both the buyer and the supplier considering both the QF and discount mechanisms. We also show that the QFi contract is able to achieve supply chain coordination. More importantly, the QFi contract's coordinating price scheme does not require knowledge of demand distribution. We identify areas where the buyer and supplier may both benefit from implementing the QFi contract as opposed to the extant QF or price‐only (wholesale) discount contractual decisions in a decentralized supply chain. We also specify the conditions under which supply chain coordination can be achieved in a win‐win manner. We conclude with managerial implications and provide directions for future research.     

Coordinating Sales and Raw Material Discounts in a Global Supply Chain

In this paper, the supplier of a key component to a global manufacturer offers a one‐time price discount; we study the firm's optimal response to the discount under two different strategies. In the first strategy, the firm does not pass along the discount to its customers (sales subsidiaries); the firm simply coordinates purchasing and production among the different factories to take advantage of this one‐time price discount. In the second strategy, the firm offers price discounts for its most profitable products in different sales subsidiaries to increase their demand. We carried out experiments for the two strategies based on a mathematical programming model, built around Toshiba's global notebook supply chain. Model constraints include, among others, material constraints, bill‐of‐materials, capacity and transportation constraints, minimum lot size constraints, and a constraint on minimum fill rate (service level constraint). Unlike most models of this type in the literature, which define variables in terms of single arc flows, we employ path variables, which allow for direct identification and manipulation of profitable and non‐profitable products.     

基于数量折扣的改良品供应链协调策略

本文以改良品供应链为研究对象,采用数量折扣作为激励机制,研究了一个供应商和一个零售商构成的改良品二级供应链在批量对批量供应模式假设下的协调问题,以达到协调改良品供应链的目的。通过算例分析,发现基于数量折扣的改良品供应链协调策略有效地实现了改良品供应链的协调。最后对改良品供应链的改良率和市场需求率进行了敏感性分析,研究了它们对供应链的影响。     

PRICE‐DEPENDENT INVENTORY MODELS WITH DISCOUNT OFFERS AT RANDOM TIMES*

We consider an inventory model with a supplier offering discounts to a reseller at random epochs. The offer is accepted when the inventory position is lower than a threshold level. We compare three different pricing policies in which demand is induced by the resellers price variation. Policy 1 is the EOQ policy without discount offers. Policy 2 is a uniform price, stock‐independent policy. Policy 3 is a stock level‐dependent, discriminated price policy. Assuming constant demand rates, expressions are obtained for the optimal order quantities, prices, and profits. The numerical experiments show that if it is better to accept a suppliers discount, then it benefits the reseller to transfer the discount to downstream customers.     

A Stochastic Inventory Model With Fast‐Ship Commitments

We present a multiperiod model of a retail supply chain, consisting of a single supplier and a single retailer, in which regular replenishment occurs periodically but players have the option to support fast delivery when customers experience a stockout during a replenishment period. Because expedited shipments increase the supplier's transportation cost, and possibly production/inventory costs, the supplier typically charges a markup over and above the prevailing wholesale price for fast‐shipped items. When fast shipping is not supported, items are backordered if customers are willing to wait until the start of the next replenishment period. We characterize the retailers and the supplier's optimal stocking and production policies and then utilize our analytical framework to study how the two players respond to changes in supply chain parameters. We identify a sufficient condition such that the centralized supply chain is better off with the fast‐ship option. We find a range of markups for fast‐ship orders such that the fast‐ship option is preferred by both the supplier and the retailer in a decentralized chain. However, a markup that is a win–win for both players may not exist even when offering fast‐ship option is better for the centralized chain. Our analysis also shows that depending on how the markup is determined, greater customer participation in fast‐ship orders does not necessarily imply more profits for the two players. For some predetermined markups, the retailer's profit with the fast‐ship option is higher when more customers are willing to wait. However, the retailer may not be able to benefit from the fast‐ship option because the supplier may choose not to support the fast‐ship option when fast‐ship participation increases due to the fact that the fast‐ship participation rate adversely affects the initial order size.     

Impacts of buyers' order batching on the supplier's demand correlation and capacity utilization in a branching supply chain

There are several ways for a manufacturer to cope with demand uncertainty, e.g. inventories, capacity and cash. Among these, this study focuses on the second one, the capacity, especially on the problem of investing in flexible facilities and enhancing their utilization via demand management. In a supply chain, demands that an upstream firm (supplier) faces are the purchase orders from the downstream members (buyers). We analyse the impacts of buyers' order batching on the supplier's demand correlation and capacity utilization in a simple branching supply chain, where a supplier does business with two buyers whose market demands are correlated. Our results show that: (i) a supplier whofacesa smaller demand correlation coefficient (i.e. closer to-1) would invest more in flexible facilities; (ii) an increase in order lot size mitigates the correlation of purchase orders; and (iii) a supplier whose facilities are flexible would prefer frequent orders with smaller lots only when market demands are highly negatively correlated. This means that even suppliers whose facilities are flexible would rather prefer infrequent orders with larger lots in the presence of positively correlated demands. Additionally, some managerial implications are discussed.     

Coordinating Supply Chains via Advance‐Order Discounts,Minimum Order Quantities,and Delegations

To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier's production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre‐established price, we examine whether the supplier should offer advance‐order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance‐order discount contract is Pareto‐improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre‐specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance‐order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first‐best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto‐improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one‐supplier‐one‐manufacturer case continue to hold when we have two manufacturers.     

Channel Strategies and Stocking Policies in Uncapacitated and Capacitated Supply Chains*

A supply chain consisting of a single supplier distributing two independent products through multiple retailers is analyzed in this paper. The supplier needs to incentivize its retailers to adopt stocking policies that are mutually advantageous and that result in the optimal level of market coverage. The focus is on determining the optimal stocking policies for retailers and the resulting distribution strategy given that the supplier has either unlimited or limited capacity. The results provide insights on the optimal distribution strategy and stocking policies for the supply chain. In general, the paper shows that it is optimal for the supplier to use an intensive distribution strategy (i.e., the products are stocked by all retailers). Selective or exclusive strategies are optimal only when retailers are risk averse, stocking synergies exist, and there are differences in demand or supply uncertainties across products. The analysis also shows that retailers hold larger stocks of a product which generates higher supplier margins but only when the supplier has unlimited capacity. If the supplier has limited capacity, then their margins have no effect on retailers' stocking decisions. Contrary to conventional wisdom, retailers hold larger stocks of a product that has less demand uncertainty as compared to one that has more demand uncertainty.     

Price promotions,operations cost,and profit in a two-stage supply chain

The phenomenon in which demand variability increases as one moves upstream in the supply chain has been often observed in practice. This so-called “bullwhip effect” often increases upstream operations costs, including inventory holding and transportation costs. Price variations are considered to be one of the primary causes of the bullwhip effect, and thus everyday low price (EDLP) strategies are commonly recommended to counter the negative impacts of the bullwhip effect. However, trade promotions continue to play an important role in the U.S. supermarket industry as well as other industries. This paper investigates this apparent inconsistency between the literature and practice by employing a deterministic, two-stage supply chain model composed of a single supplier and a single retailer. We demonstrate that even though the use of trade promotions can indeed increase a retailer's and supplier's operations costs, these costs may be more than offset by increased revenues, even in the absence of explicit coordination. That is, if the supplier judiciously applies a trade promotion strategy and the retailer passes some of this discount to its customers, then under certain conditions, the resulting supply chain profit can exceed that under an EDLP strategy. We provide a broad set of computational results that validate this conclusion and discuss the resulting managerial insights.     

Drivers and Enablers That Foster Environmental Management Capabilities in Small‐ and Medium‐Sized Suppliers in Supply Chains

The limited capabilities and resources available within many small‐ and medium‐sized enterprises frequently hamper an effective response to environmental pressures, which in turn hurts large buying firms (i.e., customers). Using a case study method with multiple suppliers of two large buying firms, we mapped factors that initiated and improved environmental capabilities in small‐ and medium‐sized enterprises over time. Through several specific mechanisms, buyers' green supply chain management initiated and then enabled the improvement of suppliers' environmental capabilities. Independent of buyers, internal championing of environmental concerns also provided an impetus for small‐ and medium‐sized enterprise suppliers to acquire resources outside the supply chain. Thus, synergistic linkages emerged in supportive buyer‐supplier relationships, resource acquisition, and capability development. When these findings are combined with earlier research on larger suppliers, an integrative framework emerges that provides direction for suppliers, buyers, and public agencies seeking to improve environmental performance.     

Impact of secondary market on consumer return policies and supply chain coordination

In this paper, we develop a unified model to study the inventory management problem of a product and the coordination of the associated supply chain consisting of a single supplier and considerably many retailers in the presence of a secondary market. Specifically, consumer returns are allowed in the initial sales. Then, we introduce a secondary market to salvage the returns and the leftovers from the initial sales. In this secondary market, a discount price will be offered to the consumers but no returns are accepted. Moreover, between the primary and the secondary market, there is an internal market where retailers can trade among themselves so that they are able to adjust their inventory levels to prepare for the sales in the secondary market. We study the retailers' and the supply chain's inventory decision in this case and highlight the impact of the secondary market on the sales as well as on the supply chain coordination contracts. We conclude that the secondary market helps us to increase the total wholesale volume. Numerical examples show that the total sales profit is also increased. However, the secondary market aggravates the incentive conflict between the retailers and the supply chain on deciding the optimal inventory levels and hence requires the supplier to offer more generous buyback or sales rebate contracts for coordination of the supply chain. Finally, we extend our analysis to more general cases and also show that our results are robust to some of the modeling assumptions.     

The Impact of Information Sharing and Advance Order Information on a Supply Chain with Balanced Ordering

This paper considers a supply chain with one supplier and multiple retailers that face exogenous heterogeneous end‐customer demands, where all parties utilize base‐stock policies. Each retailer is restricted to order once in every order cycle and their orders are replenished in a balanced manner within the cycle. Our study investigates the impact of information sharing and advance order information (AOI) on the supply chain. We find that the supplier benefits from the two mechanisms via two important factors, the information about observed end‐customer demands and the decision on re‐establishing the replenishment sequence. We derive the supplier's optimal sequence for stochastically comparable end‐customer demands with AOI and propose a sequencing rule for the setting with information sharing. Our numerical study examines the cost impacts of two proposed mechanisms on the entire supply chain.     

Balancing Inventory and Stockout Risk in Retail Supply Chains Using Fast‐Ship

In this study, we consider a two‐retailer, one‐supplier supply chain in which retailers satisfy excess demand by offering to directly ship out‐of‐stock items on an expedited basis at no extra cost to customers. This practice is referred to as the fast‐ship option. We consider two scenarios along with the fast‐ship option. In the first scenario, retailers transship when out of stock, whereas in the second scenario, they do not. If they do not transship, some customers may perform the search on their own. In each scenario, the wholesale prices are either exogenous, or chosen endogenously by the supplier. For both cases, we determine the supplier's and the retailers’ optimal decisions. The key research question we ask and answer is the following: which of the two scenarios is preferred by either player when all decisions are made optimally? We show that when fewer customers are willing to search on their own and wholesale prices are exogenous, both the supplier and the retailers prefer to transship. In addition, the decision maker in a centralized chain will have the exact same preference as that of players in a decentralized setting when the retailers’ and the supplier's preferences coincide and wholesale prices are exogenous. This preference concordance does not hold if wholesale prices are endogenous.     

The Impact of External Demand Information on Parallel Supply Chains with Interacting Demand

This paper considers two parallel supply chains with interacting demand streams. Each supply chain consists of one supplier and one retailer. The two demand streams are jointly described with a vector autoregressive time‐series process in which they interact and their respective innovation errors correlate contemporaneously. For each supply chain, we develop insights into when and how much the supplier and the retailer can improve on their forecasting accuracy if the external demand history of the other supply chain is utilized. When this external demand history is not available or made available after a time lag, we develop a partial process and a delayed process to characterize the demand structure that the retailer can recover from the available demand histories. Our results show that the external demand history of the other supply chain always helps the retailer make better forecasts when demand streams interact; however, the enhanced information alters the retailer's order process, which may produce larger forecasting errors for the supplier. Conditions are established for the supplier to benefit from the external demand history of the other supply chain.     

货栈容量有限且库存量影响需求的供应链协调模型

本文研究了由一个供应商和一个零售商构成的供应链系统运作协调问题,在考虑零售商面临的市场需求依赖于库存水平、产品的零售价格与其存储时间有关、货栈容量有限且不允许缺货的情形下,首先给出了在分散式系统下供需双方的最优决策;其次,讨论了作为Stackelberg主导方的供应商如何设计批量折扣计划,使其自身利润最大化同时也实现供应链系统完美协调。理论分析结果和数值实验结果都表明该折扣模型对于改善供需双方绩效和供应链运作协调是十分有效的。