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.     

An assembly-type supply chain system controlled by kanbans under a just-in-time delivery policy

This research studies the assembly-type supply chain system controlled by kanban mechanism. First, a supply chain system is modeled as a mixed-integer nonlinear programming (MINLP) problem. A composite formulation of the assembly-type supply chain system is developed by appropriately aggregating the individual branch models as a whole system. The batch size, the number of batches, and the total quantity over one period in the mainline and each branch line are determined. The small size MINLP problems are solved optimally by a branch-and-bound method. For the large size MINLP problems, a heuristic is developed which divides the ATSCS into several small size problems, and then conquers them individually. Next, the kanban operation between two adjacent plants is developed to schedule the loading and unloading, and transportation. Coupled with plant-wide efforts for cost control and management commitment, a logistics system is built for controlling the production as well as the supply chain system, which results in minimizing the total cost of the supply chain system. Numerical examples are presented to illustrate the two heuristic procedures and a better solution is obtained for the ATSCS problem.     

A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand

We consider a time-based inventory control policy for a two-level supply chain with one warehouse and multiple retailers in this paper. Let the warehouse order in a fixed base replenishment interval. The retailers are required to order in intervals that are integer-ratio multiples of the base replenishment interval at the warehouse. The warehouse and the retailers each adopt an order-up-to policy, i.e. order the needed stock at a review point to raise the inventory position to a fixed order-up-to level. It is assumed that the retailers face independent Poisson demand processes and no transshipments between them are allowed. The contribution of the study is threefold. First, we assume that when facing a shortage the warehouse allocates the remaining stock to the retailers optimally to minimize system cost in the last minute before delivery and provide an approach to evaluate the exact system cost. Second, we characterize the structural properties and develop an exact optimal solution for the inventory control system. Finally, we demonstrate that the last minute optimal warehouse stock allocation rule we adopt dominates the virtual allocation rule in which warehouse stock is allocated to meet retailer demand on a first-come first-served basis with significant cost benefits. Moreover, the proposed time-based inventory control policy can perform equally well or better than the commonly used stock-based batch-ordering policy for distribution systems with multiple retailers.     

基于时变需求的集成多级供应链生产订货策略研究

考虑一个时变需求环境下集成多级供应链问题,在有限的规划时间内销售商以固定周期订货,而生产商以不同的周期生产,目的是寻找销售商最优的订货周期和生产商最佳的生产策略,从而使供应链系统的总运营成本最少.建立了该问题的混合整数非线性规划模型,求解该模型分为两步：先求对应一个订货周期的最佳生产策略,再求最优的订货周期,第一步用到了图论里求最短路方法.给出了两个步骤的算法和程序,实验证明它们是有效的.通过算例对模型进行了分析,研究了各参数对最优解及最小费用的影响.     

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 continuous resupply policy for deteriorating items with stock-dependent observable demand in a two-warehouse and two-echelon supply chain

This paper expands previous work on stock-dependent demand for a retailer with a two-warehouse (OW/RW) situation to the case of deteriorating items and where the retailer seeks to obtain the integrated optimal distribution policy from collaboration with a supplier. Motivated by practical applications and recent literature, a policy is considered whereby products in good order from the retailer’s back-room (RW) are frequently transferred to its capacitated main store OW. Because the demand depends on the stock of good products in the OW, the aim is to keep this stock at its full capacity with products in good condition, and this can be done for as long as the RW stock of good products is positive. A firm’s objective function is the Net Present Value (NPV) of the firm’s future cash-flows. The profit functions are developed for both this continuous resupply policy and the commonly used policy in the OW/RW literature. Numerical examples are included and have been solved with grid search methods. The examples illustrate the benefits of adopting the continuous resupply policy, and also collaboration between the retailer and the wholesaler. Moreover, it is shown how these benefits can be shared by small adjustments to the product’s unit price between the firms.     

Manufacturer’s return policy in a two-stage supply chain with two risk-averse retailers and random demand

This paper studies the manufacturer’s return policy and the retailers’ decisions in a supply chain consisting of one manufacturer and two risk-averse retailers under a single-period setting with price-sensitive random demand. We characterize each retailer’s risk-embedded objective via conditional value-at-risk, and construct manufacturer-Stackelberg games with and without horizontal price competition between the retailers. We explore, through numerical studies, the effects of the retailers’ aversion to risk and other parameters on the manufacturer’s return policy and profit and the retailers’ decisions. We further investigate the effect of distribution asymmetry by comparing the results with normal and lognormal demand.     

A coordination system for seasonal demand problems in the supply chain

This article considers a single product coordination system using a periodic review policy, participants of the system including a supplier and one or more heterogeneous buyers over a discrete time planning horizon in a manufacturing supply chain. In the coordination system, the demand of buyer in each period is deterministic, the supplier replenishes all the buyers, and all participants agree to plan replenishment to minimize total system costs. To achieve the objective of the coordination system, we make use of small lot sizing and frequent delivery policies (JIT philosophy) to transport inventory between supplier and buyers. Moreover, demand variations of buyers are allowed in the coordination system to suit real-world situations, especially for hi-tech industries. Furthermore, according to the mechanisms of minimizing the total relevant costs, the proposed method can obtain the optimal number of deliveries, shipping points and shipping quantities in each order for all participants in the coordination system.     

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.     

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.     

Optimal inventory policy with supply uncertainty and demand cancellation

We consider a periodic review model where the firm manages its inventory under supply uncertainty and demand cancellation. We show that because of supply uncertainty, the optimal inventory policy has the structure of re-order point type. That is, we order if the initial inventory falls below this re-order point, otherwise we do not order. This is in contrast to the work of Yuan and Cheung (2003) who prove the optimality of an order up to policy in the absence of supply uncertainty. We also investigate the impact of supply uncertainty and demand cancellation on the performance of the supply chain. Using our model, we are able to quantify the importance of reducing the variance of either the distribution of yield or the distribution of demand cancellation. The single, multiple periods and the infinite horizon models are studied.     

The coordinating contracts for a fuzzy supply chain with effort and price dependent demand

This paper investigates the coordination of a two-echelon supply chain with fuzzy demand that is dependent on both retail price and sales effort. In contrast with the centralized and decentralized decision models, two coordinating models based on symmetric information and asymmetric information about retailer’s scale parameter are developed by game theory, and the corresponding analytical solutions are obtained. Theoretical analysis and numerical examples yield the maximal supply chain profits in two coordination situations are equal to that in the centralized situation and greater than that in the decentralized situation. Furthermore, under asymmetric information contract, the maximal expected profit obtained by the low-scale-level retailer is higher than that under symmetric information contract.     

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.     

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.     

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.     

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.     

Manufacturing delivery performance for supply chain management

This paper considers single-stage make-to-order production systems. We focus on (1) modeling the appropriate expected costs under a variety of modeling assumptions and (2) characterizing the optimal policies. Our approach to solving the problem is to derive the distribution of actual completion times of the process for individual orders and to compare it to the corresponding quoted due dates in order to obtain the expected total costs. We then show the convexity of the objective cost function for determining the decision variable(s), the planned customer order leadtime.     

Coordination mechanism for the supply chain with leadtime consideration and price-dependent demand

We study a coordination contract for a supplier–retailer channel producing and selling a fashionable product exhibiting a stochastic price-dependent demand. The product’s selling season is short, and the supply chain faces great demand uncertainty. We consider a scenario where the supplier reserves production capacity for the retailer in advance, and permits the retailer to place an order not exceeding the reserved capacity after a demand information update during a leadtime. We formulate a two-stage optimization problem in which the supplier decides the amount of capacity reservation in the first stage, and the retailer determines the order quantity and the retail price after observing the demand information in the second stage. We propose a three-parameter risk and profit sharing contract that coordinates the supply chain. The proposed contract permits any agreed-upon division of the supply-chain profit between the channel members.