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.     

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.     

Transshipment incentive contracts in a multi-level supply chain

Transshipments within a supply chain can be difficult to implement as the costs and benefits are often incurred by different parties. This difficulty becomes even more problematic when the costs and benefits are not completely known by all parties. The primary purpose of this paper is to introduce the role of asymmetric information into the design of supply chain transshipment contracts. Using a representative supply chain from within the soft drink industry as an example, a multi-level contracting framework is developed that aligns incentives to encourage transshipments and improve performance in the absence of all parties having full information. Analysis of the proposed framework suggests that, even if a transshipment is likely to be unprofitable to the transshipping dyad, it may still be best for the entire supply chain. Moreover, overall supply chain inventories with transshipments do not necessarily increase relative to the no-transshipment case.     

Coordination mechanisms of supply chain systems

Supply chain management (SCM) has become an important management paradigm. As supply chain members are often separate and independent economic entities, a key issue in SCM is to develop mechanisms that can align their objectives and coordinate their activities so as to optimize system performance. In this paper, we provide a review of coordination mechanisms of supply chain systems in a framework that is based on supply chain decision structure and nature of demand. This framework highlights the behavioral aspects and information need in the coordination of a supply chain. The identification of these issues points out several directions of future research in this area.     

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.     

Coordination of supply chains by option contracts: A cooperative game theory approach

Manufacturer–retailer supply chains commonly adopt a wholesale price mechanism. This mechanism, however, has often led manufacturers and retailers to situations of conflicts of interest. For example, due to uncertain market demand, retailers prefer to order flexibly from manufacturers so as to avoid incurring inventory costs and to be able to respond flexibly to market changes. Manufacturers, on the other hand, prefer retailers to place full orders as early as possible so that they can hedge against the risks of over- and under-production. Such conflicts between retailers and manufacturers can result in an inefficient supply chain. Motivated by this problem, we take a cooperative game approach in this paper to consider the coordination issue in a manufacturer–retailer supply chain using option contracts. Using the wholesale price mechanism as a benchmark, we develop an option contract model. Our study demonstrates that, compared with the benchmark based on the wholesale price mechanism, option contracts can coordinate the supply chain and achieve Pareto-improvement. We also discuss scenarios in which option contracts are selected according to individual supply chain members’ risk preferences and negotiating powers.     

Coordination mechanism for a deteriorating item in a two-level supply chain system

The subject of the coordination between the suppliers and the buyers in multi-echelon inventory-distribution systems has been studied by many researchers. This paper considers a supply chain including a manufacturer and several buyers and assumes that the inventory items deteriorate over time and its inventory level decreases. In order to determine the order policies, coordination over the supply chain is achieved by scheduling the buyers’ delivery days and their coordination with the manufacturer’s production cycle. A mathematical model is developed and analyzed. To test the efficiency of the proposed model, two other models with the supposition of lot-sizing policies with common order cycle and independent deciding are also developed. In comparison to the other two models, the numerical results show that the synchronizing model of production and delivery cycles works better and has less total cost. In addition, in order to encourage the buyers in cooperation, a model on profit sharing is proposed that equitably shares the total savings with all the parties.     

On the role of revenue-sharing contracts in supply chains

The supply chain coordinating role of revenue-sharing has, to date, been examined only in static models. With downstream competition, the central conclusion in these models is negative: revenue-sharing cannot, except in degenerate form, achieve coordination. Incorporating dynamics, by allowing inventory carryover in discrete time, this paper establishes a foundation for revenue-sharing contracts in aligning incentives.     

Mesoscopic supply chain simulation

This paper reviews and compares existing approaches for supply chain modeling and simulation and applies the mesoscopic modeling and simulation approach using the simulation software MesoSim, an own development. A simplified real-world supply chain example is modeled with discrete event, mesoscopic and system dynamics simulation. The objective of the study is to compare the process of model creation and its validity using each approach. The study examines advantages of the mesoscopic approach for the simulation. Major benefits of the mesoscopic approach are that modeling efforts are balanced with the necessary level of detail and facilitate quick and simple model creation and simulation.     

On a cooperative advertising model for a supply chain with one manufacturer and one retailer

, , ,  and  recently studied a game-theoretic model for cooperative advertising in a supply chain consisting of one manufacturer and one retailer. However, the sales-volume (demand) function considered in this model can become negative for some values of the decision variables, and in fact, this does happen for the proposed Stackelberg and Nash equilibrium solutions. Yue et al. (2006) acknowledge the negativity problem and suggest two constraints to fix it; however, they do not incorporate these constraints into their mathematical analysis. In this paper, we show that the results obtained by analyzing the advertising model under the constraints suggested by Yue et al. can differ significantly from those obtained in the previous papers.     

Coordination of supply chains with bidirectional option contracts

In this paper we develop a supply contract for a two-echelon manufacturer–retailer supply chain with a bidirectional option, which may be exercised as either a call option or a put option. Under the bidirectional option contract, we derive closed-form expressions for the retailer’s optimal order strategies, including the initial order strategy and the option purchasing strategy, with a general demand distribution. We also analytically examine the feedback effects of the bidirectional option on the retailer’s initial order strategy. In addition, taking a chain-wide perspective, we explore how the bidirectional option contract should be set to attain supply chain coordination.     

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.     

Existence of equilibria in a decentralized two-level supply chain

In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.     

Pareto analysis of supply chain contracts under satisficing objectives

Supply chain coordination has become critical to firms as increased pressure is placed on them to improve performance. We evaluate the performance of Push, Pull, and Advance-purchase discount (APD) contracts in a manufacturer-retailer supply chain where one or both firms have a satisficing objective of maximizing the probability of achieving a target profit. We identify the resulting operational modes of the supply chain and potential conflicts over the preferred contracts under the Push, Pull, and APD contracts. When both firms are satisficing, conflict over the preferred contract arises when the manufacturer has an ambitious profit target or the retailer has a low profit target. We show that the Push contract can result in a large decrease in the expected profit of a risk-neutral manufacturer when the retailer maximizes the probability of achieving her maximum expected profit. We find that a modified buy-back and profit guarantee contracts can provide significant Pareto improvement over Push or APD contracts when the manufacturer is risk-neutral and the retailer is satisficing, while revenue-sharing contracts cannot. In contrast, revenue sharing and modified buy-back contracts are Pareto dominant under certain conditions when the manufacturer is satisficing and the retailer is risk-neutral.     

Wholesale-price contract of supply chain with information gathering

This paper investigates a wholesale-price contract of supply chain under the endogenous information structure. This supply chain consists of one supplier and one retailer during the selling season. The retailer does not know his selling cost but can spend resources to acquire information. The supplier offers a contract, which induces the retailer to gather information and generate more production orders with beta costs. We find that there exists an upper bound of the information gathering cost such that the supplier induces the retailer to gather information. The increasing cost of information gathering may decrease the order quantity and wholesale price. Moreover, the cost beta has an impact on the expected profits of the two parties. With the increasing cost of information gathering, the supplier’s expected profit is reduced, while that of the retailer becomes ambiguous in terms of the distribution function and the interval of selling cost information. Finally, a numerical example is presented to explain the main results.     

Single-supplier/multiple-buyer supply chain coordination: Incorporating buyers’ expectations under vertical information sharing

We address the coordination problem in a single-supplier/multiple-buyer supply chain. The supplier wishes to coordinate the supply chain by offering quantity discounts. To obtain their complete cost information, the supplier exchanges his own cost parameters with buyers leading to vertical information sharing. The supplier thinks that the buyers, as they have access to supplier’s setup and holding cost information, may demand a portion of the anticipated coordination savings based on the partial information they hold about the cost structure of the entire supply chain. We model each buyer’s expectations based on her limited view of the entire supply chain which consists of herself and the supplier only. These expectations are then incorporated into the modeling of the supply chain, which results in a generalization of the traditional Stackelberg type models. We discuss alternative efficiency sharing mechanisms, and propose methods to design the associated discount schemes that take buyers’ expectations into account. In designing the discount schemes, we consider both price discriminatory and non-price discriminatory approaches. The study adds to the existing body of work by incorporating buyers’ expectations into a constrained Stackelberg structure, and by achieving coordination without forcing buyers to explicitly comply with the supplier’s replenishment period in choosing their order quantities. The numerical analysis of the coordination efficiency and allocation of the net savings of the proposed discount schemes shows that the supplier is still able to coordinate the supply chain with high efficiency levels, and retain a significant portion of the net savings.     

A multi-objective approach to supply chain visibility and risk

This paper investigates the twin effects of supply chain visibility (SCV) and supply chain risk (SCR) on supply chain performance. Operationally, SCV has been linked to the capability of sharing timely and accurate information on exogenous demand, quantity and location of inventory, transport related cost, and other logistics activities throughout an entire supply chain. Similarly, SCR can be viewed as the likelihood that an adverse event has occurred during a certain epoch within a supply chain and the associated consequences of that event which affects supply chain performance. Given the multi-faceted attributes of the decision making process which involves many stages, objectives, and stakeholders, it beckons research into this aspect of the supply chain to utilize a fuzzy multi-objective decision making approach to model SCV and SCR from an operational perspective. Hence, our model incorporates the objectives of SCV maximization, SCR minimization, and cost minimization under the constraints of budget, customer demand, production capacity, and supply availability. A numerical example is used to demonstrate the applicability of the model. Our results suggest that decision makers tend to mitigate SCR first then enhance SCV.     

Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand

Several leading manufacturers recently combined the traditional retail channel with a direct online channel to reach a wider range of customers. We examine such a dual-channel supply chain under price and delivery-time dependent stochastic customer demand. We consider five decision variables, the price and order quantity for both the retail and the online channels and the delivery time for the online channel. Uncertainty frequently arises in both retail and online channels and so additional inventory management is required to control shortage or overstock and that has an effect on the optimal order quantity, price, and lead time. We developed mathematical models with the profit maximization motive. We analyze both centralized and decentralized systems for unknown distribution function of the random variables through a distribution-free approach and also for known distribution function. We examine the effect of delivery lead time and customers’ channel preference on the optimal operation. For supply chain coordination a hybrid all-unit quantity discount along a franchise fee contract is used. Moreover, we use the generalized asymmetric Nash bargaining for surplus profit distribution. A numerical example illustrates the findings of the model and the managerial insights are summarized for centralized, decentralized, and coordinated scenarios.     

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.     

The use of a premium-payment scheme in a supply chain involving capacity acquisition

We study a practice whereby a downstream firm makes to his supplier a premium-payment for a certain quantity of products. We show that the adoption of this practice can induce the supplier to build bigger capacity. The higher capacity level enables the supplier to satisfy a larger portion of demands from the downstream firm, and this leads to higher payoffs for both parties in the supply chain. With the assistance of an under-capacity penalty imposed on the supplier, this premium-payment scheme can help lure the parties into taking the channel-optimal actions. Our numerical examples help reveal various features of the scheme.