Risk pooling strategy in a multi-echelon supply chain with price-sensitive demand

This paper studies a nonstationary inventory and pricing problem. We consider a two-echelon supply chain with one supplier and two retailers, in which the supplier carries all inventory to supply the retailers. Both the reserved and pooled inventory systems are analyzed. Results with normally distributed demands are compared. Assuming the random demand at each retailer is price-sensitive, we further consider the cases when the retailers have and do not have service level requirements. We start with analyzing inventory and pricing strategies for the supplier in a one-period scenario. Then we extend our analysis to both the backlogging and lost-sale scenarios in an infinite planning horizon. The first author’s research is sponsored by Grant No. 70502009 and No. 70432001 of the Chinese National Natural Science Foundation and the second author’s research is sponsored by Grant #W911NF-04-D-0003 of the US Army Research Office and Grant #DMI-0553310 of the US National Science Foundation.     

Coordinating a decentralized supply chain with customer returns and price-dependent stochastic demand using a buyback policy

We investigate a decentralized supply chain that consists of a manufacturer and a retailer where the retailer simultaneously determines the retail price and order quantity while experiencing customer returns and price dependent stochastic demand. We propose an agreement between the manufacturer and the retailer that includes two buyback prices, one for unsold inventory and a second for customer returns, and show that this type of easy-to-implement agreement can achieve perfect supply chain coordination and be a win-win for both manufacturer and retailer when a complementary profit-sharing agreement is included.     

The impact of sharing customer returns information in a supply chain with and without a buyback policy

In this paper, we examine a single period problem in a supply chain in which a Stackelberg manufacturer supplies a product to a retailer who faces customer returns and demand uncertainty. We show that the manufacturer incurs a significant profit loss with and without a buyback policy if it fails to account for customer returns in the wholesale price decision. Under the assumption that the retailer is better informed than the manufacturer on customer returns information, we show that without a buyback policy, the retailer prefers not to share if the manufacturer overestimates while it prefers to share customer returns information if the manufacturer underestimates this information. If the manufacturer offers a buyback policy, we have the opposite results. We also discuss incentives to share the customer returns information and some of the issues that are raised in sharing this information.     

Analysis of supply chain coordination under fuzzy demand in a two-stage supply chain

This paper considers a two-stage supply chain coordination problem and focuses on the fuzziness aspect of demand uncertainty. We use fuzzy numbers to depict customer demand, and investigate the optimization of the vertically integrated two-stage supply chain under perfect coordination and contrast with the non-coordination case. As in the traditional probabilistic analysis, we prove that the maximum expected supply chain profit in a coordination situation is greater than the total profit in a non-coordination situation.     

Long-term and penalty contracts in a two-stage supply chain with stochastic demand

Recent applications of game-theoretic analysis to supply chain efficiency have focused on constructs between a buyer (the retailer or manufacturer) and a seller (the supplier) in successive stages of a supply chain. If demand for the final product is stochastic then the supplier has an incentive to keep its capacity relatively low to avoid creating unneeded capacity. The manufacturer, on the other hand, prefers the supplier’s capacity to be high to ensure that the final demand is satisfied. The manufacturer therefore constructs a contract to induce the supplier to increase its production capacity. Most research examines contracting when final demand is realized after the manufacturer places its order to the supplier. However, if final demand is realized before the manufacturer places its order to the supplier, these types of contracts can be ineffective. This paper examines two contracts under the latter timing scenario: long-term contracts in which the business relationship is repeated, and penalty contracts in which the supplier is penalized for too little capacity. Results indicate long-term contracts increase the profit potential of the supply chain. Furthermore, the penalty contracts can ensure that the supplier chooses a capacity level such that the full profit potential is achieved.     

Coordinating a supply chain with effort and price dependent stochastic demand

This paper investigates the issue of channel coordination for a supply chain facing stochastic demand that is sensitive to both sales effort and retail price. In the standard newsvendor setting, the returns policy and the revenue sharing contract have been shown to be able to align incentives of the supply chain’s members so that the decentralized supply chain behaves as well as the integrated one. When the demand is influenced by both retail price and retailer sales effort, none of the above traditional contracts can coordinate the supply chain. To resolve this issue, we explore a variety of other contract types including joint return policy with revenue sharing contract, return policy with sales rebate and penalty (SRP) contract, and revenue sharing contract with SRP. We find that only the properly designed returns policy with SRP contract is able to achieve channel coordination and lead to a Pareto improving win–win situation for supply chain members. We then provide analytical method to determine the contract parameters and finally we use a numerical example to illustrate the findings and gain more insights.     

Ordering policy and coordination of a supply chain with two-period demand uncertainty

We develop a two-period game model of a one-manufacturer and one-retailer supply chain to investigate the optimal decisions of the players, where stock-out and holding costs are incorporated into the model. The demand at each period is stochastic and price sharply drops in mid-life. We assume the retailer has a single order opportunity, and decides how much inventory to keep in the middle of selling season. We show that both the price-protection mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme may achieve channel coordination and access a ‘win-win’ situation under some conditions. The larger the lowest expected profit of the retailer, the lower the possibility of ‘win-win’ situation will be. Combined with the analysis of feasible regions for coordination policies, we find that PME scheme is not always better than ME scheme from the perspective of implementable mechanism. Finally, we find that adopting the dispose-down-to (DDT) policy can bring a larger improvement of the expected channel profit in the centralized setting, and it is interesting that by using DDT policy, double marginalization occurs only at Period 1, and however, does not plague the retailer in Period 2.     

A two-echelon supply chain of a returnable product with fuzzy demand

This study investigates the effects of the manufacturer’s refund on retailer’s unsold products for the two-echelon decentralized and centralized supply chains of a short life and returnable product with trapezoidal fuzzy demand, in which retailer returns the unsold and the customer’s unsatisfactory products to the manufacturer. For each returnable chain, we obtain the closed-form solution of order quantity to maximize the total expected profit of the supply chain, and confirm that demand fuzziness does indeed affect the order quantity and the members’ expected profits. We provide a number of managerial insights by comparing both chains and show that each chain is more advantageous to the members depending on certain condition. Our models are appropriate for a supply chain with a returnable product that lacks information about the demand.     

Analysis of a two-stage telecommunication supply chain with technology dependent demand

We analyze a two-stage telecommunication supply chain consisting of one operator and one vendor under a multiple period setting. The operator faces a stochastic market demand which depends on technology investment level. The decision variables for the operator are the initial technology investment level and the capacity of the network for each period. The capacity that the operator installs in one period also remains available in subsequent periods. The operator can increase or decrease the available capacity at each period. For this model, an algorithm to find the centralized optimal solution is proposed. A profit sharing contract where firms share both the revenue and operating costs generated throughout the periods along with initial technology investment is suggested. Also a coordinating quantity discount contract where the discount on the price depends on the total installed capacity is designed. The case where the vendor decides on the technology investment level and the operator decides on the capacity of the network is also analyzed and it is shown that this game has a unique Nash equilibrium.     

Contracting with demand uncertainty under supply chain competition

We examine supply chain contracts for two competing supply chains selling a substitutable product, each consisting of one manufacturer and one retailer. Both manufacturers are Stackelberg leaders and the retailers are followers. Manufacturers in two competing supply chains may choose different contracts, either a wholesale price contract in which the retailer??s demand forecasting information is not shared, or a revenue-sharing contract in which the retailer??s demand forecasting information is shared. Under supply chain competition and demand uncertainty, we identify which contract is more advantageous for each supply chain, and under what circumstances.     

Ordering and pricing decisions in a two-echelon supply chain with asymmetric demand information

This article examines coordinated decisions in a decentralized supply chain that consists of one supplier and one retailer, and faces random demand of a single product with a short life cycle. We consider a setting where the retailer has accurate demand information while the supplier does not. Such a problem with asymmetric demand information can be viewed as an extension of the newsboy problem in which both the supplier and the retailer possess the same demand information. Combining the mechanism of sharing demand information and that of quantity discount and return policy enables us to develop three coordinated models in contrast with the basic and uncoordinated model. We are able to show the ordinal relationship among the retailer’s optimal order quantities in these four models under a general form of random demand, and compare the supply chain profits and conduct sensitivity analysis analytically in four models under uniform random demand. We also provide numerical results under normal random demand that bear a resemblance to those under uniform random demand.     

Capacitated location model with online demand pooling in a multi-channel supply chain

This paper presents a location model that assigns online demands to the capacitated regional warehouses currently serving in-store demands in a multi-channel supply chain. The model explicitly considers the trade-off between the risk pooling effect and the transportation cost in a two-echelon inventory/logistics system. Keeping the delivery network of the in-store demands unchanged, the model aims to minimize the transportation cost, inventory cost, and fixed handling cost in the system when assigning the online demands. We formulate the assignment problem as a non-linear integer programming model. Lagrangian relaxation based procedures are proposed to solve the model, both the general case and an important special case. Numerical experiments show the efficiency of our algorithms. Furthermore, we find that because of the pooling effect the variance of in-store demands currently served by a warehouse is an important parameter of the warehouse when it is considered as a candidate for supplying online demands. Highly uncertain in-store demands, as well as low transportation cost per unit, can make a warehouse appealing. We illustrate with numerical examples the trade-off between the pooling effect and the transportation cost in the assignment problem. We also evaluate the cost savings between the policy derived from the model, which integrates the transportation cost with the pooling effect, and the commonly used policy, which is based only on the transportation cost. Results show that the derived policy can reduce 1.5–7.5% cost in average and in many instances the percentage of cost savings is more than 10%.     

Capacity allocation,ordering, and pricing decisions in a supply chain with demand and supply uncertainties

This paper studies coordinated decisions in a decentralized supply chain that consists of one Original Equipment Manufacturer (OEM), one manufacturer, and one distributor, and possesses uncertainties at both demand and supply sides. These uncertainties emerge, respectively, from random demand the distributor faces and randomness of capacity with which the OEM processes the manufacturer’s outsourced quantity. Sharing supply and demand uncertainty information along the supply chain enables us to develop three models with different coordination efforts—the OEM and manufacturer coordination, the manufacturer and distributor coordination, and the OEM, manufacturer, and distributor coordination—and quantify the coordinated decisions in these three models. Our analysis of these coordination models suggests that coordinating with the OEM improves the manufacturer’s probability of meeting downstream demand and his expected profit, yet coordinating with the manufacturer is not necessarily beneficial to the OEM when downstream coordination is lacking.     

供应链中需求在线的库存问题研究

考虑一个生产商和两个零售商之间的数量折扣问题,针对顾客需求量不确定时,生产商采用数量折扣策略鼓励零售商提高单次订货量,从而降低库存成本的决策问题,从在线算法与竞争分析的角度出发,结合零售商的议价能力这一因素,分别考虑两个零售商之间合作与非合作时的情形,设计了相应的平衡策略,并证明该策略为最优策略.     

Capacitated procurement planning with price-sensitive demand and general concave-revenue functions

This paper develops effective solution methods for discrete-time, finite-horizon procurement planning problems with economies of scale in procurement, price-sensitive demand, and time-invariant procurement capacities. Our models consider general concave-revenue functions in each time period, and seek to maximize total revenue less procurement and inventory holding costs. We consider the case in which prices may vary dynamically, as well the important practical case in which a constant price is required during the planning horizon. Under mild conditions on the revenue function properties, we provide polynomial-time solution methods for this problem class. The structural properties of optimal solutions that lead to efficient solution methods also serve to sharpen intuition regarding optimal demand management strategies in complex planning situations.     

Operations policy for a supply chain system with fixed-interval delivery and linear demand

This research addresses a production-supply problem for a supply-chain system with fixed-interval delivery. A strategy that determines the optimal batch sizes, cycle times, numbers of orders of raw materials, and production start times is prescribed to minimize the total costs for a given finite planning horizon. The external demands are time-dependent following a life-cycle pattern and the shipment quantities follow the demand pattern. The shipment quantities to buyers follow various phases of the demand pattern in the planning horizon where demand is represented by piecewise linear model. The problem is formulated as an integer, non-linear programming problem. The model also incorporates the constraint of inventory capacity. The problem is represented using the network model where an optimal characteristic has been analysed. To obtain an optimal solution with N shipments in a planning horizon, an algorithm is proposed that runs with the complexity of Θ(N²) for problems with a single-phase demand and O(N³) for problems with multi-phase demand.     

The use of advance demand information in a project-based supply chain

In a project environment, a manufacturer is confronted with two types of demand: regular demand from many small orders and very irregular, lumpy demand from infrequent, large orders. Manufacturers who build to stock must carry large safety stocks to meet the lumpy demand. As part of the project engineering process, however, project engineers and implementers (e.g. installers) typically have developed information about material requirements well in advance of placement of orders. We analyze the inventory reduction that could be achieved if the installer were to communicate advance demand information (ADI) to the manufacturer. We look at it in particular when the bid is placed. We focus on the following characteristics of available ADI in project environments: First, ADI information is uncertain, because decisions on installer and manufacturer selection have not yet been finalized. Second, information is detailed, available at the item level. We show that ADI is particularly valuable when potential demand for large projects is irregular and when proposals for potential projects have a high probability of leading to orders.     

Coordinating a three-echelon supply chain under price and quality dependent demand with sub-supply chain and RFM strategies

The paper considers a three-echelon supply chain which consists of one supplier, one manufacturer and one retailer for trading a single product. The market demand at the retailer is influenced by the retail price and the quality of the product. The quality of the finished product at the manufacturer depends on the supplier’s raw material quality. We analyze the model for both deterministic and stochastic demand patterns. We first study the centralized and decentralized systems, and then the decentralized system with a sub-supply chain coordination strategy (where the manufacturer chooses to merge with either the supplier or the retailer and then acts as a single entity) and the two-level retail fixed mark-up (RFM) strategy. In the case of the two-level RFM strategy, the manufacturer and the retailer use fixed mark ups over the supplier’s wholesale price. The proposed models are demonstrated through numerical examples. It is observed from the numerical study that the two-level RFM strategy is superior to the sub-supply chain coordination strategy. Further, the two-level RFM strategy in the stochastic demand scenario is not as effective as in the deterministic demand scenario.