Effects of constrained supply and price contracts on agricultural cooperatives

Planning strategies depend in part on the supply flow structure of a supply chain. In food supply chains, many firms are constrained by raw material supply (e.g. vegetables and milk). This paper first examines the economic consequences of constrained supply in agricultural cooperatives. Secondly, it deals with the effects of adding price contracts to the current cooperative contract. This model combines an inventory policy approach and a Monte-Carlo simulation, to take into account price uncertainty. We illustrate our results using the case of a dairy cooperative.     

Price-only contracts with backup supply

This paper studies a supply chain in which a manufacturer holds backup supply with extra cost to satisfy demand unmet by a retailer. We provide a simple threshold condition for when the manufacturer should hold backup supply. We also study how the backup supply affects the supply chain performance.     

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.     

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.     

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.     

Flexible supply contracts under price uncertainty

This article develops supply contracts covering environments with changing prices. We investigate characterization properties of the price processes, while considering costs and discount factors. We determine expressions of the contract’s expected low price and its second moment for a given horizon. We then employ these expected price and second moment values to identify an expected optimum time before the contract expires at which the lowest price occurs. Simulation experiments verify our analysis, and they illustrate how the optimum purchase time decreases as the drift term increases.     

Analysis and design of returns policies from a supplier's perspective

This paper considers the problem of designing a returns policy in a supply chain from a supplier's perspective. The supply chain considered here is assumed to have one supplier and one retailer who serves a random demand of a product with a short life cycle. The retailer can return all the unsold products to the supplier with a partial refund. We found that if the retailer behaviour is rational, that is, ordering the optimal quantity to maximize its expected profit, then both retailer and supplier could benefit from the returns policy. Furthermore, we established that the optimal buyback price is independent of the mean of the random demand, but the variance of the demand has a significant impact on setting the optimal buyback price. The higher the variance the higher the optimal buyback price and the larger the profit gain of both parties. Numerical studies are employed to help understand the benefits of returns policies for the supplier, the retailer, and the whole supply chain.     

First- and second-price sealed-bid auctions applied to push and pull supply contracts

We investigate a newsvendor-type retailer sourcing problem under demand uncertainty who has the option to source from multiple suppliers. The suppliers’ manufacturing costs are private information. A widely used mechanism to find the least costly supplier under asymmetric information is to use a sealed-bid reverse auction. We compare the combinations of different simple auction formats (first- and second-price) and risk sharing supply contracts (push and pull) under full contract compliance, both for risk-neutral and risk-averse retailer and suppliers. We show the superiority of a first-price push auction for a risk-neutral retailer. However, only the pull contracts lead to supply chain coordination. If the retailer is sufficiently risk-averse, the pull is preferred over the push contract. If suppliers are risk-averse, the first-price push auction remains the choice for the retailer. Numerical examples illustrate the allocation of benefits between the retailer and the (winning) supplier for different number of bidders, demand uncertainty, cost uncertainty, and degree of risk-aversion.     

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.     

Game-theoretic analyses of decentralized assembly supply chains: Non-cooperative equilibria vs. coordination with cost-sharing contracts

This paper considers a multiple-supplier, single manufacturer assembly supply chain where the suppliers produce components of a short life-cycle product which is assembled by the manufacturer. In this single-period problem the suppliers determine their production quantities and the manufacturer chooses the retail price. We assume that the manufacturer faces a random price-dependent demand in either additive or multiplicative form. For each case, we analyze both simultaneous-move and leader–follower games to respectively determine the Nash and Stackelberg equilibria, and find the globally-optimal solution that maximizes the system-wide expected profit. Then, we introduce appropriate buy-back and lost-sales cost-sharing contracts to coordinate this assembly supply chain, so that when all the suppliers and the manufacturer adopt their equilibrium solutions, the system-wide expected profit is maximized.     

Side-payment contracts in two-person nonzero-sum supply chain games: Review,discussion and applications

This paper investigates supply chain coordination with side-payment contracts. We first summarize specific side-payment contracts and present our review on the literature that developed general side-payment schemes to coordinate supply chains. Following our review, we discuss two criteria that a proper side-payment contract must satisfy, and accordingly introduce a decision-dependent transfer payment function and a constant transfer term. We present the condition that the transfer function must satisfy, and use Nash arbitration scheme and Shapley value to compute the constant transfer term and derive its closed-form solution. Next, we provide a five-step procedure for the development of side-payment contract, and apply it to four supply chain games: Cournot and Bertrand games, a two-retailer supply chain game with substitutable products and a one-supplier, one-retailer supply chain. More specifically, for the Cournot game, we construct a linear transfer function and a constant side-payment to coordinate two producers. For the Bertrand game, we build a nonlinear transfer function which is equivalent to a revenue-sharing contract, and show that the constant term is zero and two firms in the game equally share the system-wide profit. For a supply chain with substitutable products, we present a side-payment contract to coordinate two retailers. For a two-echelon supply chain, we develop a proper side-payment scheme that can coordinate the supply chain and also help reduce the impact of forward buying on supply chain performance.     

Designing contracts for a closed-loop supply chain under information asymmetry

This paper studies the problem of designing contracts in a closed-loop supply chain when the cost of collection effort is the retailer’s private information. We investigate four cases: two contracts (a two-part nonlinear contract and a collection effort requirement contract), each under complete information and asymmetric information. We derive the manufacturer’s optimal contracts for all four cases and analyze the impact of information on the equilibrium results of supply chain members.     

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.     

Methodological analysis of supply chains management applications

Formal modelling may be used to express management operational plans to achieve the desired normative objectives of firms. The plans so formulated should be demonstrably optimal with regard to certain specific objectives assumed by top management and ought to provide accurate results, when enacted, with a given tolerance at a prespecified probability.     

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.     

Analysis of supply contracts with quantity flexibility

This paper explores a class of supply contracts under which a buyer receives discounts for committing to purchases in advance. The further in advance the commitment is made, the larger the discount. As time rolls forward, the buyer can increase the order quantities for future periods of the rolling horizon based on updated demand forecast information and inventory status. However, the buyer pays a higher per-unit cost for the incremental units. Such contracts are used by automobile and contract manufacturers, and are quite common in fuel oil and natural gas delivery markets. We develop a finite-horizon dynamic programming model to characterize the structure of the optimal replenishment strategy for the buyer. We present heuristic approaches to calculate the order volume in each period of the rolling horizon. Finally, we numerically evaluate the heuristic approaches and draw some managerial insights based on the findings.     

回收再制造与定价决策模型及供应链协调分析

假定负责废旧产品回收再制造的生产商为主导者.针对单生产商和单零售商组成的逆向供应链,分析了Stackelberg博弈(分散式控制)下和合作(集中式控制)下的零售价和回收再制造率决策,发现集中式供应链的利润较高,给出了协调供应链的利润共享合同.针对单生产商和n个竞争零售商组成的供应链,分析了一主多从Stackelberg博弈和联合决策,结果表明供应链合作可降低产品的零售价格、提高回收再制造率和供应链总利润,进而给出了协调单生产商和n个零售商决策的利润共享合同.最后的算例表明了模型的合理性和协调合同的有效性.     

Towards integration: a revenue-sharing contract in a supply chain

Email: zhaoqiong.qin{at}erau.edu Received on 31 May 2006. Accepted on 11 December 2006. This paper deals with the problem of a revenue-sharing contractadopted in a supply chain involving one supplier and one retailerwith short life-cycle products. Under this contract, the retailercan obtain the product from the supplier at a discounted pricewhile as a compensation, the retailer must share his revenuewith the supplier at a certain revenue-sharing rate, say r (0 r 1), where r represents the portion of the revenue to bekept by the retailer. We use a two-stage (Stackelberg) gameto model the problem, where one player is the game's leaderand the other the game's follower. Our ultimate objective isto maximize the overall supply chain's total profit, and toshow the effects of salvage revenue and the revenue-sharingrate on transfer cost rate, profit of the supplier and retailerand the overall supply chain's total profit while upholdingthe individual components’ incentives. Our analysis exhibitsthat the case in which salvage revenue is not shared is preferredand the computational results to explore the effects of therevenue-sharing rate lead to many managerial insights regardingthe leader of the game.     

Minimizing customer order lead-time in a two-stage assembly supply chain

Coordination across different process stages of the supply chain is becoming more common as the information needed for this coordination is easier to obtain and share. With the availability of this information, managers are beginning to recognize that there can be benefits to scheduling processes in a coordinated fashion. Thus, finding good schedules for the entire supply chain has added importance to today’s managers. Coordination of the material as it moves from one stage to the next should lead to improved customer order lead-time performance for the whole chain and thus better customer service overall. We look at a two-stage assembly supply chain with the objective of minimizing the average customer order lead-time. Minimizing lead-time is becoming increasingly important as customers demand quicker response. But beyond this better customer service objective, minimizing lead-time is consistent with keeping inventory costs low. We introduce a number of properties of optimal solutions, results for special problem cases, and a series of lower bounds. We also provide a number of intuitive heuristics for coordinated supply chain scheduling and test them to determine their effectiveness.