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.     

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.     

A two-stage supply chain coordination mechanism considering price sensitive demand and quantity discounts

This paper explores the coordination between a supplier and a buyer within a decentralized supply chain, through the use of quantity discounts in a game theoretic model. Within this model, the players face inventory and pricing decisions. We propose both cooperative and non-cooperative approaches considering that the product traded experiences a price sensitive demand. In the first case, we study the dynamics of the game from the supplier's side as the leader in the negotiation obtaining a Stackelberg equilibrium, and then show how the payoff of this player could still improve from this point. In the second case, a cooperative model is formulated, where decisions are taken simultaneously, emulating a centralized firm, showing the benefits of the cooperation between the players. We further formulate a pricing game, where the buyer is allowed to set different prices to the final customer as a reaction to the supplier's discount decisions. For the latter we investigate the difference between feasibility of implementing a retail discount given a current coordination mechanism and without it. Finally the implications of transportation costs are analyzed in the quantity discount schedule. Our findings are illustrated with a numerical example showing the difference in the players’ payoff in each case and the optimal strategies, comparing in each case our results with existing work.     

Coordinating order quantity decisions in the supply chain contract under random demand

In this paper, we are concerned with the coordinating quantity decision problem in a supply chain contract. The supply chain contract is composed of one manufacturer and one retailer to meet the random demand of a single product with a short lifecycle. Our analysis show that the retailer expects to obtain higher profit under proper ordering policies, which can also maximize the expected profit of the supply chain. The manufacturer may induce the retailer to order the coordinated quantity by adjusting the unit return price. As a result, the supply chain is expected to achieve the optimal expected profit.     

Combined pricing and supply chain operations under price-dependent stochastic demand

In this study, we determined product prices and designed an integrated supply chain operations plan that maximized a manufacturer’s expected profit. The computational results of this study revealed that as the variance of the demand distribution increases, a manufacturer will increase its inventory to levels that are greater than the anticipated demand to prevent the potential loss of sales and will simultaneously raise product prices to obtain a greater profit. In the cost minimization approach, the manufacturer may earn the highest possible profits, as determined by the profit optimization approach, only if this firm precisely forecasts the mean market demand for its products. Greater inaccuracies in this forecast will produce lower levels of expected profit.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

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.     

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.     

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.     

Multi-period modeling of two-way price commitment under price-dependent demand

This paper examines the use of price-commitment policies in dynamic contracting in multiple-period, finite-time horizons. Two specific forms of price commitment are considered: one on the part of the retailer through a retail-fixed-markup contract and one on the part of the manufacturer through a price-protection contract. Optimal policies for each form of price commitment are analytically derived, as are optimal policies for the traditional price-only and centralized supply chain scenarios that we use as comparisons. We prove that optimal retail price and order size solutions exist in each period under the assumption of non-increasing price-dependent demand. We show that the existence of retailer inventory between periods causes the optimal policies to differ from a static single-period model. Further, we show that a supplier offers a price-protection policy as a signal to the retailer to resolve the gaming that naturally occurs under price-only; this effectively decouples the multi-period dynamic contracting setting into repeated single-period scenarios. However, the resulting behavior can actually inhibit supply chain performance. On the retail commitment side, we find that retail-fixed-markup policies are quite effective in improving supply chain efficiency. We show that such policies can lead to Pareto-improvement over price-only contracts and can even coordinate the supply chain in some situations.     

The impact of partial information sharing in a two-echelon supply chain

We consider a simple two-echelon supply chain composed of a manufacturer and a retailer in which the demand process of the retailer is an AR(1) where the random component is a function of both sides’ information. We focus on partial information sharing under which each side informs the other of an interval in which the exact value of its own component of demand lies. These various levels of information sharing can reduce the supply chain costs.     

碳税政策下时变需求依赖库存与价格的供应链协调模型

研究由一个供应商和一个零售组成的二级供应链系统在碳税政策下的协调问题.对于市场需求率为时变函数且依赖于当前库存水平和销售价格的情形,建立分散式和集中式供应链决策模型.比较两种模型得出供应商和零售商合作能够提高供应链的整体利润但是也会产生更多的碳排放.分别利用批发价格契约和两部收费契约协调分散式决策模型得出供应链协调的条件.最后通过数值算例验证理论结果并分析碳税单价对供应链在两部收费契约下实现协调的影响.     

Coordination of cooperative cost-reduction efforts in a supply chain partnership

We study cooperative cost reduction in a decentralized supply chain with a single manufacturer and multiple suppliers. The manufacturer assembles components that are procured from the suppliers to produce a final product. Both the manufacturer and the suppliers invest in reducing the unit production costs of the components. We see that neither of the two well-known conventional contracts, the wholesale price contract and the cost-plus pricing contract, generally coordinates the supply chain, i.e., under both of these types of contract, the individual optimal cost-reduction efforts of players deviate from the centralized system-optimal solution. However, this result is not surprising because these contracts encourage either only the manufacturer or only the suppliers alone to invest in cost reduction.     

Managing the order pipeline to reduce supply chain volatility

The bullwhip effect in particular, and supply chain volatility in general, has been the subject of much analytical and empirical investigation by researchers. One goal of this work has been to determine supply chain designs and policies that minimize volatility. Using a system dynamics approach, we use three distinct supply chain volatility metrics to compare the ability of two alternative pipeline inventory management policies to respond to a demand shock. The results indicate that no one policy dominates on all three metrics of supply chain volatility. A simplistic static pipeline policy minimizes the bullwhip effect and lessens the likelihood of on-hand inventory oscillations, while a more sophisticated dynamic pipeline policy may converge more rapidly to the new equilibrium. In addition, simulation results suggest that the dynamic policy provides better customer service through fewer stockouts and backorders.     

Inventory systems with stochastic demand and supply: Properties and approximations

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.     

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.     

Channel coordination using product returns for a supply chain with stochastic salvage capacity

We examine returns policy in a Newsboy framework. Unlike the prior literature, however, we assume that both supplier and retailer have limited and stochastic salvage capacities. We first analyze the case of integrated supply chain in which the agents’ decisions are fully coordinated for the joint profits. The result prescribes a partial returns policy, in which the retailer returns a part of the leftovers to the supplier and liquidates the remainder through its clearance sale. In a decentralized system, the supplier should motivate the retailer to duplicate the outcome of the integrated system in choosing order and returns quantities. We propose three coordination contracts, of which each uses two benefit transfer schemes as an incentive to the retailer, instead of using a single benefit scheme as in the prior literature. All three effectively coordinate the supply chain. The supplier, as a Stakelberg leader, chooses the most profitable one since each contract yields the different shares of the agents’ profits.     

Coordination in a two-stage capacitated supply chain with multiple suppliers

The aim of this paper is to coordinate the inventory policies in a decentralized supply chain with stochastic demand by means of contracts. The system considered is a decentralized two-stage supply chain consisting of multiple independent suppliers and a manufacturer with limited production capacities. The suppliers operate on a make-to-stock basis and apply base stock policy to manage their inventories. On the other hand, the manufacturer employs a make-to-order strategy. Under the necessary assumptions, each supplier is modeled as an M/M/1 make-to-stock queue; and the manufacturer is modeled as a GI/M/1 queue after deriving an approximate distribution for the interarrival times of the manufacturer. Once the supply chain is modeled as a queuing system, centralized and decentralized models are developed. Comparison of the optimal solutions to these models reveals that the supply chain needs coordination. Three different transfer payment contracts are examined in this paper. These are the backorder and holding cost subsidy contracts, the transfer payment contract based on Pareto improvement, and the cost sharing contract. Each contract is evaluated according to its coordination ability and whether it is Pareto improving or not. The results indicate that all three contracts can coordinate the supply chain. However, when the Pareto improvement is taken into account, the cost sharing contract seems to be the one that will be preferred by all parties.     

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.