Quantity Flexibility Contract Research Articles

Contracting for On-Time Delivery in the U.S. Influenza Vaccine Supply Chain

Although influenza vaccine shortage is often attributed to low supply, it has been observed that even with abundant supply, a major shortage can still occur due to late delivery. In this paper, motivated by the influenza vaccine industry, we study a supply chain contracting problem in the presence of uncertainties surrounding design, delivery, and demand of influenza vaccine. In this supply chain, a manufacturer has insufficient incentive to initiate at-risk early production prior to the design freeze because it is a retailer who reaps the most benefits from selling more vaccines delivered on time. Anticipating that late delivery will lead to potential loss in demand, the retailer tends to reduce the order size, which further discourages the manufacturer from making an effort to improve its delivery performance. To break this negative feedback loop, a supply contract needs to achieve two objectives: incentivize at-risk early production and eliminate double marginalization. We find that two commonly observed supply contracts in practice, the Delivery-time-dependent Quantity Flexibility (D-QF) contract and the Late-Rebate (LR) contract, may fail to coordinate the supply chain because of the tension between these two objectives. To resolve such a tension, we construct a Buyback-and-Late-Rebate (BLR) contract and show that a properly designed BLR contract can not only coordinate the supply chain but also can provide full flexibility of profit division between members of the supply chain. Numerical experiments further demonstrate that the BLR contract significantly improves supply chain efficiency compared to the contracts used in the industry.

A Quantity Flexibility Contract in a Supply Chain with Price Dependent Demand

We consider a quantity flexibility contract in a supply chain, under price dependent demand. The demand is random and follows a multiplicative model. We show that the retail price that maximizes expected retailer profits, is higher than the price that would maximize profits if there was no demand uncertainty. We then show that if the wholesale price lies in a certain range, there is a positive buyback fraction that the manufacturer would prefer. This preference is in comparison to not entering into a quantity flexibility contract at all. Finally, through numerical work we find that the contract results in a win-win situation for both the manufacturer and the retailer in the case of price dependent demand.

Purchasing decisions under stochastic prices: Approximate solutions for order time, order quantity and supplier selection

This paper analyzes purchasing strategies for retailers regarding the best timing and amount of purchases when operating under combined timing and quantity flexibility contracts in an environment of uncertain prices. To decrease the computational complexity and make the procedure adaptable to the case of multiple suppliers, we introduce, analyze, and compare a “time strategy” and a “target strategy” and then develop a hybrid “adaptive target strategy” to facilitate and improve the purchasing decision for the case of option contracts with generally rising prices. The adaptive target strategy is simpler and more intuitive than the traditional binomial lattice method, while the risk of failing to meet a target profit can also easily be calculated. We then extend the solution procedure to maximize expected profits in an environment of selecting among multiple suppliers with potentially different price processes, and we further provide risk analysis to help determine a good estimate for the number of option contracts from different suppliers to generate in order to create adequate risk protection. Numerical analysis demonstrates how the number of candidate suppliers impacts the expected profit and the risk. Monte Carlo simulation results demonstrate that the developed solution procedures provide satisfying outcomes and that the calculation is fast, even for multiple-dimension and multiple-supplier cases.

Mitigating bankruptcy propagation through contractual incentive schemes

With the increasing interdependence among supply chain members on material, information and capital, interactions and decisions characterized by operational parameters are important causes of bankruptcy propagation in supply chain. This paper investigates the methods for mitigating bankruptcy propagation through supply chain coordination. Based on a two-stage supply chain network that consists of multiple upstream manufacturers and multiple downstream retailers, the effectiveness of some typical contractual incentive schemes, including revenue sharing, price discount and quantity flexibility contracts, in mitigating bankruptcy propagation among supply chain members is examined. Through agent-based simulation experiments, it has been revealed that: 1) the three typical supply chain contracts with properly designed contract parameters are effective in mitigating bankruptcy propagation, but their effectiveness depends on operational parameters of the supply chain; 2) horizontal competition among retailers is an important factor in determining the effectiveness of these contracts; 3) revenue sharing contract turns out to be more effective in mitigating bankruptcy propagation than the other two contracts. By comparing the optimal contract parameters with and without considering bankruptcy risks, it has also been found that, a set of contract parameters that can maximize the profit of the supply chain may increase the occurrence of bankruptcy in supply chain, leading to the phenomenon of a risk–profit tradeoff.

Contract analysis: A performance measures and profit evaluation within two-echelon supply chains

Coordination is regarded as key in managing dependencies between distinctive members of a supply chain through the benefits of coordination mechanisms. Such coordination mechanisms are contracts, implemented to increase total supply chain profit, reduce costs and share risk among supply chain members. However, by contract implementation the retailer is constrained in his purchase by bearing the entire risk of holding the inventory (wholesale price contract) or by limited risk allocated to the supplier (buyback, revenue sharing and quantity flexibility contracts). By implementing an advanced purchase system the risk of inventory is fairly divided between the supplier and the retailer. In order to observe inventory implications on the supply chain bottom line, this article is directed towards the evaluation of performance measures and supply chain profit behavior under buyback, revenue sharing, quantity flexibility and advanced purchase discount contracts versus no coordination and wholesale price systems.

A Optimization Model of Incentive Mechanism between Manufacturer and Dealer in Supply Chain

According to the idea of existing quantity flexibility contract , aiming at the particularity of buyers' market's timeliness product, through introducing buyback contract method, a optimization model of supply chain flexibility contract is put forward which can incent dealer and make up the deficiency of single flexibility contract. An example is given to calculate the contented factors of wholesale price and rebate proportion to take the incentive mechanism effect, and to illustrate that manufacturer and dealer share the risk in the supply chain.

A composite contract based on buy back and quantity flexibility contracts

We introduce a composite (CP) contract for a two-stage supply chain by organically combining two component contracts: a buy back (BB) contract and a quantity flexibility (QF) contract. The CP contract is shown to have advantages over both component contracts in terms of supply chain coordination, profit allocation, and risk allocation. In particular, we obtain the following results: (a) as long as one of the component contracts is able to coordinate the supply chain, so is the CP contract. Moreover, when contract parameters are constrained, we find situations where the CP contract coordinates the supply chain when neither of the component contracts coordinates. (b) When contract parameters are constrained, the CP contract is more flexible in terms of profit allocation among supply chain members than the component contracts. (c) The CP contract is more flexible in terms of risk allocation than the component contracts.

Channel incentives in sharing new product demand information and robust contracts

Demand for a new product is often highly uncertain. As the developer of a new product, the manufacturer may reduce the uncertainty of the product’s demand through observing progress in his product development process or receiving demand signals directly from customers. This paper first shows that a centralized channel always benefits from improved demand information. Yet, to realize this benefit in a decentralized manufacturer–retailer channel, the manufacturer needs to disclose his private demand information to the retailer. We show that the manufacturer’s incentive to share his improved demand information depends on the supply contract signed with the retailer. Furthermore, mandating the manufacturer to disclose his improved demand information can actually reduce the total channel profit. We provide managerial insights by analyzing three widely used contract forms. We investigate whether these contracts are robust under an unanticipated demand information update observed by the manufacturer. We show that the quantity flexibility contract with a high return rate is not robust. The buyback contract, however, is robust and always achieves information sharing while preserving channel performance.

Flexibility or Cost Saving? Sourcing Decisions with Two Suppliers

ABSTRACTThis article studies a decentralized supply chain in which there are two suppliers and a single buyer. One supplier offers the quantity flexibility (QF) contract to the buyer, while the other offers the cheaper price. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity with additional buffer inventory. On the other hand, the price‐only contract places full inventory burden on the buyer, but with a cheaper price. We study this problem from the buyer's perspective and solve for the buyer's optimal procurement and forecasting decisions. We identify areas where flexibility and cheaper price have an advantage, one over the other. Our results indicate that the buyer significantly benefits from having multiple sources of supply. We also find that, from the system's standpoint, a multisupplier system may outperform a single‐supplier supply chain under certain conditions. Interestingly, we observe that providing too much flexibility may benefit the low‐price supplier rather than benefiting the QF supplier. We discuss the managerial implications and provide directions for future research opportunities.

A coordination theoretic model for three level supply chains using contracts

Typically, supply chain members are dependent on each other to manage various resources and information. The conflicting objectives and lack of coordination between supply chain members may often cause uncertainties in supply and demand. The basic elements of coordination theory like interdependency, coherency and mutuality may help in effective flow of information and material between the dependent supply chain members. Supply chain contract can be an effective coordination mechanism to motivate all the members to be a part of the entire supply chain. There are different types of supply chain contracts such as buy back and quantity flexibility contracts. Supply chain performance may be substantially improved by properly designing the contracts to share risks and rewards. The objective of this paper is to explore the applicability of coordination elements through an analytical model in three-level (Manufacturer-distributor-retailer) serial supply chains using contracts. The model evaluates the impact of supply chain contracts on various performance measures. The impact of some contract may be on some specific performance measure only, which helps managers to choose the type of contract if there is an objective of improving certain performance measure before hand. In three-level supply chains, the contracts are designed at two distinct interfaces: Manufacturer-distributor and distributor-retailer. The model demonstrates the complexity in evaluating the decision variables of three level supply chains. The proposed model is a novel approach to apply coordination theory at various levels of supply chain. The model also presents how the coordination elements are related to each other in various coordination cases.

Utilizing contract theory to reduce double marginalization for pre-recorded music products within the retail supply chain – A case study

The purpose of this case study is to analyze the effectiveness of three types of supply chain contracts within the pre-recorded music products supply chain. This article will analyze buyback contracts, revenue-sharing contracts and quantity flexibility contracts. The article will explain why managers in the pre-recorded music industry should adopt these supply chain contract approaches to increase revenues. The models described in the case study could be seamlessly utilized by music distributors and major consumer electronic retailers to maximize their revenues and profits within this highly competitive industry.

SUPPLY CHAIN COORDINATION WITH CVaR CRITERION

We study the coordination of supply chains with a risk-neutral supplier and a risk-averse retailer. Different from the downside risk setting, in a conditional value-at-risk (CVaR) framework, we show that the supply chain can be coordinated with the revenue-sharing, buy-back, two-part tariff and quantity flexibility contracts. Furthermore the revenue-sharing contracts are still equivalent to the buy-back contracts when the retail price is fixed. At the same time, it is shown that the risk-averse retailer of the coordinated supply chain can increase its profit by raising its risk-averse degree under mild conditions.

Pareto quantity flexibility contracts for a supply chain under multiple objectives

We analyse a decentralized supply chain consisting of a supplier and a retailer. The terms of trade between the two agents are specified by a quantity flexibility (QF) contract. We first identify the Pareto QF contracts for the supply chain where each agent adopts a satisficing objective, that is, to maximize the probability of achieving his/her predetermined target profit. It is shown that to coordinate such a supply chain, QF contracts have to degenerate into wholesale price (WP) contracts. This provides an additional justification for the popularity of WP contracts besides their simplicities and lower administration costs. Next, we consider the supply chain where each agent adopts multiple objectives, namely the satisficing objective and the objective of expected profit maximization (EPM). It is shown that there always exist QF contracts that coordinate the supply chain under the objective of EPM and are simultaneously Pareto optimal for the satisficing objective.

Implications of Renegotiation for Optimal Contract Flexibility and Investment

In a stylized model of biopharmaceutical contract manufacturing, this paper shows how the potential for renegotiation influences the optimal structure of supply contracts, investments in innovation and capacity, the way scarce capacity is allocated, and firms' resulting profits. Two buyers contract for capacity with a common manufacturer. Then, the buyers invest in innovation (product development and marketing) and the manufacturer builds capacity. Finally, the firms may renegotiate to allow a buyer facing poor market conditions to purchase less than the contractual commitment and a buyer facing favorable conditions to purchase more. We show that renegotiation can greatly increase the firms' investments and profits, provided that the contracts are designed correctly. Failing to anticipate renegotiation leads to contracts that allow too much flexibility in the buyer's order quantity, and perform poorly relative to contracts designed to anticipate renegotiation. We provide clear conditions under which quantity flexibility contracts with renegotiation coordinate the system. Where quantity flexibility contracts fail, employing tradable options improves performance.

Relating the multiple supply problem to quantity flexibility contracts

We consider two classes of problems in the supply chain management literature: the multiple supply problem and quantity flexibility contracts. We identify the similarities between these two problems and show that for both the total operating cost of the manufacturer is convex with respect to its arguments under mild conditions.

Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations

Under a revenue-sharing contract, a retailer pays a supplier a wholesale price for each unit purchased, plus a percentage of the revenue the retailer generates. Such contracts have become more prevalent in the videocassette rental industry relative to the more conventional wholesale price contract. This paper studies revenue-sharing contracts in a general supply chain model with revenues determined by each retailer's purchase quantity and price. Demand can be deterministic or stochastic and revenue is generated either from rentals or outright sales. Our model includes the case of a supplier selling to a classical fixed-price newsvendor or a price-setting newsvendor. We demonstrate that revenue sharing coordinates a supply chain with a single retailer (i.e., the retailer chooses optimal price and quantity) and arbitrarily allocates the supply chain's profit. We compare revenue sharing to a number of other supply chain contracts (e.g., buy-back contracts, price-discount contracts, quantity-flexibility contracts, sales-rebate contracts, franchise contracts, and quantity discounts). We find that revenue sharing is equivalent to buybacks in the newsvendor case and equivalent to price discounts in the price-setting newsvendor case. Revenue sharing also coordinates a supply chain with retailers competing in quantities, e.g., Cournot competitors or competing newsvendors with fixed prices. Despite its numerous merits, we identify several limitations of revenue sharing to (at least partially) explain why it is not prevalent in all industries. In particular, we characterize cases in which revenue sharing provides only a small improvement over the administratively cheaper wholesale price contract. Additionally, revenue sharing does not coordinate a supply chain with demand that depends on costly retail effort. We develop a variation on revenue sharing for this setting.

Quantity Flexibility Contracts: Optimal Decisions with Information Updates*

ABSTRACTWe study single and multiperiod quantity flexibility contracts involving one demand forecast update in each period and a spot market. We obtain the optimal order quantity at the beginning of a period and order quantities on contract and from the spot market at the then prevailing price after the forecast revision and before the demand materialization. The amount that can be purchased on contract is bounded by a given flexibility limit. We discuss the impact of the forecast quality and the level of flexibility on the optimal decisions and managerial insights behind the results.

Implications of Renegotiation for Optimal Contract Flexibility and Investment

After entering into supply contracts, firms often later renegotiate the terms of those contracts. For example, firms that obtain market demand information after signing supply contracts may benefit by renegotiating the contracts to allow buyers facing poor market conditions to purchase less than their contractual commitment and allowing buyers facing favorable conditions to purchase more. Consider a setting in which two buyers invest in innovation (product development, marketing) and obtain supply from a single manufacturer through quantity flexibility contracts, which specify the minimum quantity the manufacturer must supply and the minimum quantity the buyer must purchase. The potential for renegotiation of the supply contracts has important implications for the firms' investments in innovation and capacity, the allocation of capacity, and the resulting profits. Renegotiation can greatly increase the firms' profits, provided that contract parameters are chosen correctly. Failing to anticipate renegotiation leads to contracts that contain far too much flexibility, and perform poorly relative to contracts designed to anticipate renegotiation. We provide clear conditions under which a quantity flexibility contracts with renegotiation coordinate the system. Where quantity flexibility contracts fail, we show that tradable options perform very well.

Quantity flexibility contracts under Bayesian updating

In this paper, we consider a decentralized supply chain consisting of two independent players—a manufacturer and a retailer. Under a quantity flexibility contract, the retailer first proposes an initial forecast as the production reference to the manufacturer. Then she uses Bayesian procedure to update demand information, and makes ultimate purchase commitment, which is constrained by the negotiated flexibility and the manufacturer's production. We model the incentives of both parties and investigate the effect of flexibility ω, transfer price c and number of Bayesian updates n on the performance of two parties. Our theoretical analysis and numerical results show that given other parameters fixed, more flexibility always benefits the retailer, while the manufacturer can only benefit from very small quantity flexibility. In addition, this contract allows them to share the benefits from information updating.

The Quantity Flexibility Contract and Supplier-Customer Incentives

Consider a supply chain consisting of two independent agents, a supplier (e.g., a manufacturer) and its customer (e.g., a retailer), the latter in turn serving an uncertain market demand. To reconcile manufacturing/procurement time lags with a need for timely response to the market, such supply chains often must commit resources to production quantities based on forecasted rather than realized demand. The customer typically provides a planning forecast of its intended purchase, which does not entail commitment. Benefiting from overproduction while not bearing the immediate costs, the customer has incentive to initially overforecast before eventually purchasing a lesser quantity. The supplier must in turn anticipate such behavior in its production quantity decision. This individually rational behavior results in an inefficient supply chain. This paper models the incentives of the two parties, identifying causes of inefficiency and suggesting remedies. Particular attention is given to the Quantity Flexibility (QF) contract, which couples the customer's commitment to purchase no less than a certain percentage below the forecast with the supplier's guarantee to deliver up to a certain percentage above. Under certain conditions, this method can allocate the costs of market demand uncertainty so as to lead the individually motivated supplier and customer to the systemwide optimal outcome. We characterize the implications of QF contracts for the behavior and performance of both parties, and the supply chain as a whole.