Supply Disruptions,Heterogeneous Beliefs,and Production Efficiencies

Recent years have witnessed the pervasive supply disruptions and their impacts on supply chain performance. In this study, we investigate the optimal procurement design with supply disruptions and heterogeneous beliefs between the buyer and the supplier. We examine the impact of information asymmetry on the supplier's belief, the control right of the backup production, and the verifiability of supply disruption. The belief heterogeneity creates speculative gains and losses because the buyer and the supplier hold different estimates of the disruption probability. We demonstrate that the buyer's incentive to exploit this belief heterogeneity leads to real production inefficiencies in different scenarios. The production efficiency is not necessarily improved with more transparent information. Moreover, a very pessimistic supplier may have no incentive to invest in improving the reliability even if this is costless, and the supplier may produce more when the expected production cost becomes higher. When the buyer sees some value in using the supplier's estimate to update his own belief, we find that the main results hold unless the buyer completely abandons his belief.     

Pay‐Back‐Revenue‐Sharing Contract in Coordinating Supply Chains with Random Yield

We consider coordination issues in supply chains where supplier's production process is subject to random yield losses. For a simple supply chain with a single supplier and retailer facing deterministic demand, a pay back contract which has the retailer paying a discount price for the supplier's excess units can provide the right incentive for the supplier to increase his production size and achieve coordination. Building upon this result, we consider coordination issues for two other supply chains: one with competing retailers, the other with stochastic demand. When retailers compete for both demand and supply, they tend to over‐order. We show that a combination of a pay back and revenue sharing mechanism can coordinate the supply chain, with the pay back mechanism correcting the supplier's under‐producing problem and the revenue sharing mechanism correcting the retailers' over‐ordering problem. When demand is stochastic, we consider a modified pay‐back‐revenue‐sharing contract under which the retailer agrees to not only purchase the supplier's excess output (beyond the retailer's order), but also share with the supplier a portion of the revenue made from the sales of the excess output. We show that this contract, by giving the supplier additional incentives in the form of revenue share, can achieve coordination.     

Contracting and Coordination under Asymmetric Production Cost Information

We analyze a supply chain consisting of a supplier and a retailer. The supplier's unit production cost, which characterizes his type, is only privately known to him. When trading with the retailer, the supplier demands a reservation profit that depends on his unit production cost. We model this problem as a game of adverse selection. In this model, the retailer offers a menu of contracts, each of which consists of two parameters: the ordering quantity and the supplier's share of the channel profit. We show that the optimal contract depends critically on a surrogate measure—the ratio of the types’ reservation profit differential to their production cost differential. An important implication from our analysis is that information asymmetry alone does not necessarily induce loss in channel efficiency. The optimal contract can coordinate the supply chain as long as the low‐cost supplier's cost efficiency is neither much overvalued nor much undervalued in the outside market. We further discuss the retailer's preference of the supplier's type under different market conditions, as well as evaluate the effects of the supplier's reservation profit, the retail price, and the demand uncertainty on the optimal contract.     

Value of Sharing Production Yield Information in a Serial Supply Chain

New developments in corporate information technology such as enterprise resource planning systems have significantly increased the flow of information among members of supply chains. However, the benefits of sharing information can vary depending on the supply chain structure and its operational characteristics. Most of the existing research has studied the impact of sharing downstream information (e.g., a manufacturer sharing information with its suppliers). We evaluate the benefits of sharing upstream yield information (e.g., a supplier sharing information with the manufacturer) in a two‐stage serial supply chain in which the supplier has multiple internal processes and is faced with uncertain output due to yield losses. We are interested in determining when the sharing of the supplier's information is most beneficial to the manufacturer. After proposing an order‐up‐to type heuristic policy, we perform a detailed computational study and observe that this information is most beneficial when the supplier's yield variance is high and when end‐customer demand variance is low. We also find that the manufacturer's backorder‐to‐holding cost ratio has little, if any, impact on the usefulness of information.     

Supply Chain Sourcing Under Asymmetric Information

We study a supply chain with two suppliers competing over a contract to supply components to a manufacturer. One of the suppliers is a big company for whom the manufacturer's business constitutes a small part of his business. The other supplier is a small company for whom the manufacturer's business constitutes a large portion of his business. We analyze the problem from the perspective of the big supplier and address the following questions: What is the optimal contracting strategy that the big supplier should follow? How does the information about the small supplier's production cost affect the profits and contracting decision? How does the existence of the small supplier affect profits? By studying various information scenarios regarding the small supplier's and the manufacturer's production cost, we show, for example, that the big supplier benefits when the small supplier keeps its production cost private. We quantify the value of information for the big supplier and the manufacturer. We also quantify the cost (value) of the alternative‐sourcing option for the big supplier (the manufacturer). We determine when an alternative‐sourcing option has more impact on profits than information. We conclude with extensions and numerical examples to shed light on how system parameters affect this supply chain.     

Supplier Encroachment as an Enhancement or a Hindrance to Nonlinear Pricing

The objective of this study was to extend existing understanding of supplier encroachment to contexts in which there is information asymmetry and the supplier can use nonlinear pricing. Prior research has shown that supplier encroachment can mitigate double marginalization and thus benefit both the supplier and the reseller. However, under symmetric information, this benefit disappears if the supplier can use nonlinear pricing. In our model, the reseller observes the true market size while the supplier knows only the prior distribution, that is, a seemingly ideal setting for implementing mechanism design through nonlinear pricing. We first show that, because encroachment capability enables the supplier to make an ex post output decision, it fundamentally alters the structure of the optimal nonlinear pricing policy. In addition to the usual downward distortion effect, where the reseller may purchase less than the efficient quantity, we also have the possibility for upward distortion. Thus, under asymmetric information and nonlinear pricing, supplier encroachment has two opposing effects. On one hand, the ability to shift sales to the direct channel allows the supplier to reduce information rents with less sacrifice of efficiency; but on the other hand, by introducing the possibility of her own opportunistic behavior, it can result in upward distortion of the quantities sold through the reselling channel, which is a new source of inefficiency. Depending upon the relative efficiency of the reselling channel and the demand distribution, either of these two effects may dominate and the supplier's ability to encroach may either benefit or hurt both the supplier and the reseller.     

Push and Pull Contracts in a Local Supply Chain with an Outside Market*

Wholesale price contracts are widely studied in a single supplier‐single retailer supply chain, but without considering an outside market where the supplier may sell if he gets a high enough price and the retailer may buy if the price is low enough. We fill this gap in the literature by studying push and pull contracts in a local supplier–retailer supply chain with the presence of an outside market. Taking the local supplier's maximum production capacity and the outside market barriers into account, we identify the Pareto set of the push and/or pull contracts and draw managerial implications. The main results include the following. First, the most inefficient point of the pull Pareto set cannot always be removed by considering both the push and pull contracts. Second, the supplier's production capacity plays a significant role in the presence of an outside market; it affects the supplier's negotiating power with the retailer and the coordination of the supply chain can be accomplished only with a large enough capacity. Third, the import and export barriers influence the supply chain significantly: (i) an export barrier in the local market and the supplier's production capacity influence the supplier's export strategy; (ii) a low import (resp., export) barrier in the local market can improve the local supply chain's efficiency by use of a push (resp., pull) contract; and (iii) a high import (resp., export) barrier in the local market encourages the supplier (resp., retailer) to bear more inventory risk.     

Optimal Quantity Discount Design with Limited Information Sharing*

In this article we address the optimal quantity discount design problem of a supplier in a two‐stage supply chain where the supplier and the buyer share annual demand information only. The supply chain faces a constant deterministic demand that is not price sensitive and operates with fixed setup costs in both stages. We show that the supplier can actually moderate a cost‐minimizing buyer to order in quantities different than the buyer's optimal order quantity in the traditional setting and develop a multi‐breakpoint quantity discount scheme that maximizes supplier's expected net savings. The proposed multi‐breakpoint discount scheme can be easily computed from the available information and, while also maximizing the supplier's net savings, is very effective in achieving high levels of supply chain coordination efficiency in the presence of limited information.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

Competing on Time: An Integrated Framework to Optimize Dynamic Time‐to‐Market and Production Decisions

This study develops a comprehensive framework to optimize new product introduction timing and subsequent production decisions faced by a component supplier. Prior to market entry, the supplier performs process design activities, which improve manufacturing yield and the chances of getting qualified for the customer's product. However, a long delay in market entry allows competitors to enter the market and pass the customer's qualification process before the supplier, reducing the supplier's share of the customer's business. After entering the market and if qualified, the supplier also needs to decide how much to produce for a finite planning horizon by considering several factors such as manufacturing yield and stochastic demand, both of which depend on the earlier time‐to‐market decision. To capture this dependency, we develop a sequential, nested, two‐stage decision framework to optimize the time‐to‐market and production decisions in relation to each other. We show that the supplier's optimal market entry and qualification timing decision need to be revised in real time based on the number of qualified competitors at the time of market‐entry decision. We establish the optimality of a threshold policy. Following this policy, at the beginning of each decision epoch, the supplier should optimally stop preparing for qualification and decide whether to enter the market if her order among qualified competitors exceeds a predetermined threshold. We also prove that the supplier's optimal production policy is a state‐dependent, base‐stock policy, which depends on the time‐to‐market and qualification decisions. The proposed framework also enables a firm to quantify how market conditions (such as price and competitor entry behavior) and operating conditions (such as the rate of learning and inventory/production‐related costs) affect time‐to‐market strategy and post‐entry production decisions.     

The Impact of Information Sharing and Advance Order Information on a Supply Chain with Balanced Ordering

This paper considers a supply chain with one supplier and multiple retailers that face exogenous heterogeneous end‐customer demands, where all parties utilize base‐stock policies. Each retailer is restricted to order once in every order cycle and their orders are replenished in a balanced manner within the cycle. Our study investigates the impact of information sharing and advance order information (AOI) on the supply chain. We find that the supplier benefits from the two mechanisms via two important factors, the information about observed end‐customer demands and the decision on re‐establishing the replenishment sequence. We derive the supplier's optimal sequence for stochastically comparable end‐customer demands with AOI and propose a sequencing rule for the setting with information sharing. Our numerical study examines the cost impacts of two proposed mechanisms on the entire supply chain.     

Procurement Contracts in the Presence of Endogenous Disruption Risk

We consider a manufacturer facing an unreliable supplier with high or low type on initial reliability. The private reliability can be enhanced through process improvement initiated by either manufacturer (manufacturer‐initiated improvement, MI) or supplier (supplier‐initiated improvement, SI). We derive optimal procurement contracts for both mechanisms and find that the moral hazard does not necessarily generate more profit for high‐type supplier. Furthermore, information asymmetry causes a greater possibility of not ordering from low type in SI than MI. For low type, when an upward effort distortion appears in both mechanisms, a decreased (increased) unit penalty should be imposed in MI (SI) compared with symmetric information case. Although possibly efficient effort from the supplier could yield greater channel profit in SI, several scenarios violate this expectation. However, the manufacturer's expected profit in MI is no less than that in SI. When MI is extended to MSI where both manufacturer and supplier can exert effort, the expected profits of two parties are equal to those in SI. We further extend SI to SID, where both process improvement and dual‐sourcing are available. The manufacturer considers the trade‐off between the benefit from diversification and the loss from dual information rent to decide to choose SID or MI. By comparing SID with pure dual‐sourcing, we find that supplier's process improvement could either accelerate or retard the exercise of dual‐sourcing.     

Sharing shipment quantity information in the supply chain

This paper evaluates the benefit of a strategy of sharing shipment information, where one stage in a supply chain shares shipment quantity information with its immediate downstream customers—a practice also known as advanced shipping notice. Under a periodic review inventory policy, one supply-chain member places an order on its supplier every period. However, due to supplier's imperfect service, the supplier cannot always exactly satisfy what the customer orders on time. In particular, shipment quantities arriving at the customer, after a given lead-time, may be less (possibly more) than what the customer expects—we define this phenomenon as shipment quantity uncertainty. Where shipment quantity information is not shared with customers, the only way to respond is through safety stock. However, if the supplier shares such information, i.e. customers are informed every period of the shipment quantity dispatched, the customer may have enough time to adapt and resolve this uncertainty by adjusting its future order decisions. Our results indicate that in most circumstances this strategy, enabled by information technologies, helps supply-chain members resolve shipment quantity uncertainty well. This study provides an approach to quantify the value of shared shipment information and to help supply-chain members evaluate the cost-benefit trade-off during information system construction. Numerical examples are provided to indicate the impact of demand/shipment parameters on strategy implementation. While previous studies mainly focus on the information receiver's perspective, we evaluate a more general three-tier linear supply chain model via simulation, studying how this strategy affects the whole supply chain: the information sender, the information receiver and the subsequent downstream tier.     

Information leakage and supply chain contracts

This paper investigates information leakage under different contract configurations in a supply chain. We consider two competing retailers, one of whom (incumbent) has private information about market demand while the other (entrant) has no access to acquire any market demand information. We assume that the supplier is the leader who may choose a wholesale price contract (WPC) or a revenue-sharing contract (RSC) with each retailer independently. We explore the effect of the supplier's and incumbent's incentives on non-leakage equilibrium and find out that there exists a non-leakage equilibrium only when the incumbent signs an RSC with the supplier under an appropriately given revenue-sharing rate in situations of high demand variation.     

Mechanisms to Induce Buyer Forecasting: Do Suppliers Always Benefit from Better Forecasting?

In this study, we consider a supplier's contract offerings to a buyer who may obtain improved forecasts for her demand over time. We investigate how the supplier can take advantage of the buyer's better forecasts and what kind of contracts he should offer to the buyer in order to maximize his profits. We model a natural forecast evolution where the buyer can obtain a more accurate forecast closer to the selling season. We assume there is information asymmetry between the buyer and the supplier at all times in that the buyer understands her demand better than the supplier. Three types of contracts that the supplier can offer are considered: (1) one where a contract is offered before the buyer has a chance to obtain improved forecasts, (2) one where a contract is offered after the buyer has obtained improved forecasts, and (3) a contingent (dynamic) contract which offers an initial contract to the buyer before she obtains improved forecasts, followed by a later contract (contingent on the initial contract) offered after improved forecasts have been obtained. We consider two scenarios: (1) where the supplier is certain that the buyer can obtain more accurate forecasts over time, and (2) where the supplier is uncertain about the buyer's forecasting capability (or forecasting cost). In the first scenario, we show that among the three types of contracts, the contingent contract is always the most profitable for the supplier. Furthermore, using the contingent contract, the supplier always benefits from higher accuracy of the buyer's demand forecasts. In the second scenario, we explicitly model the supplier's level of certainty about the buyer's capability of obtaining better forecasts, and explore how the supplier can design contracts to induce the buyer to obtain better forecasts when she is capable.     

A Stochastic Inventory Model With Fast‐Ship Commitments

We present a multiperiod model of a retail supply chain, consisting of a single supplier and a single retailer, in which regular replenishment occurs periodically but players have the option to support fast delivery when customers experience a stockout during a replenishment period. Because expedited shipments increase the supplier's transportation cost, and possibly production/inventory costs, the supplier typically charges a markup over and above the prevailing wholesale price for fast‐shipped items. When fast shipping is not supported, items are backordered if customers are willing to wait until the start of the next replenishment period. We characterize the retailers and the supplier's optimal stocking and production policies and then utilize our analytical framework to study how the two players respond to changes in supply chain parameters. We identify a sufficient condition such that the centralized supply chain is better off with the fast‐ship option. We find a range of markups for fast‐ship orders such that the fast‐ship option is preferred by both the supplier and the retailer in a decentralized chain. However, a markup that is a win–win for both players may not exist even when offering fast‐ship option is better for the centralized chain. Our analysis also shows that depending on how the markup is determined, greater customer participation in fast‐ship orders does not necessarily imply more profits for the two players. For some predetermined markups, the retailer's profit with the fast‐ship option is higher when more customers are willing to wait. However, the retailer may not be able to benefit from the fast‐ship option because the supplier may choose not to support the fast‐ship option when fast‐ship participation increases due to the fact that the fast‐ship participation rate adversely affects the initial order size.     

Optimal Procurement Design of an Assembly Supply Chain with Information Asymmetry

We study a decentralized assembly supply chain in which an assembler (she) assembles a set of n components, each produced by a different supplier (he), into a final product to satisfy an uncertain market demand. Each supplier holds private cost information to himself, for which the assembler only has a subjective estimate. Furthermore, the assembler believes that the suppliers' costs follow a joint discrete probability distribution. The assembler aims to design an optimal menu of contracts to maximize her own expected profit. The assembler's problem is a complex multi‐dimensional constrained optimization problem. We prove that there exists a unique optimal menu of contracts for the assembler, and we further develop an efficient algorithm with a complexity of O(n) to compute the optimal contract. In addition, we conduct a comprehensive sensitivity analysis to analyze how environmental parameters affect individual firm's performance and the value of information to the assembler, to each supplier, and to the supply chain. Our results suggest that each supplier's private cost information becomes more valuable to the assembler and each supplier when the average market demand increases or when the final product unit revenue increases. Surprisingly, when a supplier's cost volatility increases and its mean remains the same, the value of information to the assembler or to each supplier does not necessarily increase. Furthermore, we show that when the suppliers' cost distributions become more positively correlated, the suppliers are always worse off, but the assembler is better off. However, the value of information for the assembler might increase or decrease.     

Investing in a Shared Supplier in a Competitive Market: Stochastic Capacity Case

When firms invest in a shared supplier, one key concern is whether the invested capacity will be used for a competitor. In practice, this concern is addressed by restricting the use of the capacity. We consider what happens when two competing firms invest in a shared supplier. We consider two scenarios that differ in how capacity is used: exclusive capacity and first‐priority capacity. We model firms' investment and production decisions, and analyze the equilibrium outcomes in terms of the number of investing firms and capacity levels for each scenario; realized capacity is a stochastic function of investment levels. We also identify conditions under which the spillover effect occurs, where one firm taps into the other firm's invested capacity. Although the spillover supposedly intensifies competition, it actually discourages firms' investment. We also characterize the firms' and supplier's preference about the capacity type. While the non‐investing firm always prefers spillovers from the first‐priority capacity, the investing firm does not always want to shut off the other firm's access to its leftover capacity, especially when allowing spillover induces the other firm not to invest. The supplier's preference depends on the trade‐off between over‐investment and flexibility.     

Allocating Capacity with Demand Competition: Fixed Factor Allocation*

We consider a supply chain consisting of a supplier and two retailers. The supplier sells a single product to the retailers, who, in turn, retail the product to customers. The supplier has limited production capacity, and the retailers compete for the supplier's capacity and are duopolists engaged in Cournot competition for their customers. When the sum of the retailers' orders exceeds the supplier's capacity, the supplier allocates his capacity according to a preannounced allocation rule. We propose a new capacity allocation rule, fixed factor allocation, which incorporates the ideas of proportional and lexicographic allocations: it prioritizes retailers as in lexicographic allocation, but guarantees only a fixed proportion of the total available capacity to the prioritized retailer. We show that (1) the fixed factor allocation rule incorporates lexicographic and proportional allocations from the perspectives of the supplier and the supply chain; (2) under fixed factor allocation, the supply chain profit is not affected by the allocation factor when it is greater than a threshold; (3) the retailers share the supply chain profit with the supplier depending on the value of the allocation factor; and (4) the fixed factor allocation coordinates the supply chain when the market size is sufficiently large. We also compare fixed factor with proportional and lexicographic allocations, respectively. Furthermore, we demonstrate how the supplier can optimize his capacity level and wholesale price under fixed factor allocation.     

The Impact of Contracts and Competition on Upstream Innovation in a Supply Chain

We consider a supply chain with an upstream supplier who invests in innovation and a downstream manufacturer who sells to consumers. We study the impact of supply chain contracts with endogenous upstream innovation, focusing on three different contract scenarios: (i) a wholesale price contract, (ii) a quality‐dependent wholesale price contract, and (iii) a revenue‐sharing contract. We confirm that the revenue‐sharing contract can coordinate supply chain decisions including the innovation investment, whereas the other two contracts may result in underinvestment in innovation. However, the downstream manufacturer does not always prefer the revenue‐sharing contract; the manufacturer's profit can be higher with a quality‐dependent wholesale price contract than with a revenue‐sharing contract, specifically when the upstream supplier's innovation cost is low. We then extend our model to incorporate upstream competition between suppliers. By inviting upstream competition, with the wholesale price contract, the manufacturer can increase his profit substantially. Furthermore, under upstream competition, the revenue‐sharing contract coordinates the supply chain, and results in an optimal contract form for the manufacturer when suppliers are symmetric. We also analyze the case of complementary components suppliers, and show that most of our results are robust.