Oligopolistic contracting: Channel coordination under competition

We study contracts between a single retailer and multiple suppliers of two substitutable products, where suppliers have fixed capacities and present the retailer cost contracts for their supplies. After observing the contracts, the retailer decides how much capacity to purchase from each supplier, to maximize profits from the purchased capacity from the suppliers plus his possessed inventory (endowment). This is modeled as a noncooperative, nonzero‐sum game, where suppliers, or principals, move simultaneously as leaders and the retailer, the common agent, is the sole follower. We are interested in the form of the contracts in equilibrium, their effect on the total supply chain profit, and how the profit is split between the suppliers and the retailer. Under mild assumptions, we characterize the set of all equilibrium contracts and discuss all‐unit and marginal‐unit quantity discounts as special cases. We also show that the supply chain is coordinated in equilibrium with a unique profit split between the retailer and the suppliers. Each supplier's profit is equal to the marginal contribution of her capacity to supply chain profits in equilibrium. The retailer's profit is equal to the total revenue collected from the market minus the payments to the suppliers and the associated sales costs.     

Strategic dynamic sourcing from competing suppliers with transferable capacity investment

We study the supplier relationship choice for a buyer that invests in transferable capacity operated by a supplier. With a long‐term relationship, the buyer commits to source from a supplier over a long period of time. With a short‐term relationship, the buyer leaves open the option of switching to a new supplier in the future. The buyer has incomplete information about a supplies efficiency, and thus uses auctions to select suppliers and determine the contracts. In addition, the buyer faces uncertain demand for the product. A long‐term relationship may be beneficial for the buyer because it motivates more aggressive bidding at the beginning, resulting a lower initial price. A short‐term relationship may be advantageous because it allows switching, with capacity transfer at some cost, to a more efficient supplier in the future. We find that there exists a critical level of the switching cost above which a long‐term relationship is better for the buyer than a short‐term relationship. In addition, this critical switching cost decreases with demand uncertainty, implying a long‐term relationship is more favorable for a buyer facing volatile demand. Finally, we find that in a long‐term relationship, capacity can be either higher or lower than in a short‐term relationship. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

An EOQ model with multiple suppliers and random capacity

We consider an EOQ model with multiple suppliers that have random capacities, which leads to uncertain yield in orders. A given order is fully received from a supplier if the order quantity is less than the supplier's capacity; otherwise, the quantity received is equal to the available capacity. The optimal order quantities for the suppliers can be obtained as the unique solution of an implicit set of equations in which the expected unsatisfied order is the same for each supplier. Further characterizations and properties are obtained for the uniform and exponential capacity cases with discussions on the issues related to diversification among suppliers. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Supplier certification and quality investment in supply chains

Global sourcing has made quality management a more challenging task, and supplier certification has emerged as a solution to overcome suppliers' informational advantage about their product quality. This article analyzes the impact of certification standards on the supplier's investment in quality, when a buyer outsources the production process. Based on our results, deterministic certification may lead to under‐investment in quality improvement technology for efficient suppliers, thereby leading to potential supply chain inefficiency. The introduction of noisy certification may alleviate this under‐investment problem, when the cost of information asymmetry is high. While allowing noisy certification always empowers the buyer to offer a menu to screen among heterogeneous suppliers, the buyer may optimally choose only a limited number of certification standards. Our analysis provides a clear‐cut prediction of the types of certifiers the buyer should use for heterogeneous suppliers, and we identify the conditions under which the supplier benefits from noisy certification. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Supplier‐buyer contracting: Asymmetric cost information and cutoff level policy for buyer participation

We consider the problem of designing a contract to maximize the supplier's profit in a one‐supplier–one‐buyer relationship for a short‐life‐cycle product. Demand for the finished product is stochastic and price‐sensitive, and only its probability distribution is known when the supply contract is written. When the supplier has complete information on the marginal cost of the buyer, we show that several simple contracts can induce the buyer to choose order quantity that attains the single firm profit maximizing solution, resulting in the maximum possible profit for the supplier. When the marginal cost of the buyer is private information, we show that it is no longer possible to achieve the single firm solution. In this case, the optimal order quantity is always smaller while the optimal sale price of the finished product is higher than the single firm solution. The supplier's profit is lowered while that of the buyer is improved. Moreover, a buyer who has a lower marginal cost will extract more profit from the supplier. Under the optimal contract, the supplier employs a cutoff level policy on the buyer's marginal cost to determine whether the buyer should be induced to sign the contract. We characterize the optimal cutoff level and show how it depends on the parameters of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 41–64, 2001     

Disruption‐management strategies for short life‐cycle products

Supplier diversification, contingent sourcing, and demand switching (whereby a firm shifts customers to a different product if their preferred product is unavailable), are key building blocks of a disruption‐management strategy for firms that sell multiple products over a single season. In this article, we evaluate 12 possible disruption‐management strategies (combinations of the basic building‐block tactics) in the context of a two‐product newsvendor. We investigate the influence of nine attributes of the firm, its supplier(s), and its products on the firs preference for the various strategies. These attributes include supplier reliability, supplier failure correlation, payment responsibility in the event of a supply failure, product contribution margin, product substitutability, demand uncertainties and correlation, and the decision makes risk aversion. Our results show that contingent sourcing is preferred to supplier diversification as the supply risk (failure probability) increases, but diversification is preferred to contingent sourcing as the demand risk (demand uncertainty) increases. We find that demand switching is not effective at managing supply risk if the products are sourced from the same set of suppliers. Demand switching is effective at managing demand risk and so can be preferred to the other tactics if supply risk is low. Risk aversion makes contingent sourcing preferable over a wider set of supply and demand‐risk combinations. We also find a two‐tactic strategy provides almost the same benefit as a three‐tactic strategy for most reasonable supply and demand‐risk combinations. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Allocation of quality improvement targets based on investments in learning

Purchased materials often account for more than 50% of a manufacturer's product nonconformance cost. A common strategy for reducing such costs is to allocate periodic quality improvement targets to suppliers of such materials. Improvement target allocations are often accomplished via ad hoc methods such as prescribing a fixed, across‐the‐board percentage improvement for all suppliers, which, however, may not be the most effective or efficient approach for allocating improvement targets. We propose a formal modeling and optimization approach for assessing quality improvement targets for suppliers, based on process variance reduction. In our models, a manufacturer has multiple product performance measures that are linear functions of a common set of design variables (factors), each of which is an output from an independent supplier's process. We assume that a manufacturer's quality improvement is a result of reductions in supplier process variances, obtained through learning and experience, which require appropriate investments by both the manufacturer and suppliers. Three learning investment (cost) models for achieving a given learning rate are used to determine the allocations that minimize expected costs for both the supplier and manufacturer and to assess the sensitivity of investment in learning on the allocation of quality improvement targets. Solutions for determining optimal learning rates, and concomitant quality improvement targets are derived for each learning investment function. We also account for the risk that a supplier may not achieve a targeted learning rate for quality improvements. An extensive computational study is conducted to investigate the differences between optimal variance allocations and a fixed percentage allocation. These differences are examined with respect to (i) variance improvement targets and (ii) total expected cost. For certain types of learning investment models, the results suggest that orders of magnitude differences in variance allocations and expected total costs occur between optimal allocations and those arrived at via the commonly used rule of fixed percentage allocations. However, for learning investments characterized by a quadratic function, there is surprisingly close agreement with an “across‐the‐board” allocation of 20% quality improvement targets. © John Wiley & Sons, Inc. Naval Research Logistics 48: 684–709, 2001     

Should firms conceal information when dealing with common suppliers?

A firm making quantity decision under uncertainty loses profit if its private information is leaked to competitors. Outsourcing increases this risk as a third party supplier may leak information for its own benefit. The firm may choose to conceal information from the competitors by entering in a confidentiality agreement with the supplier. This, however, diminishes the firm's ability to dampen competition by signaling a higher quantity commitment. We examine this trade‐off in a stylized supply chain in which two firms, endowed with private demand information, order sequentially from a common supplier, and engage in differentiated quantity competition. In our model, the supplier can set different wholesale prices for firms, and the second‐mover firm could be better informed. Contrary to what is expected, information concealment is not always beneficial to the first mover. We characterize conditions under which the first mover firm will not prefer concealing information. We show that this depends on the relative informativeness of the second mover and is moderated by competition intensity. We examine the supplier's incentive in participating in information concealment, and develop a contract that enables it for wider set of parameter values. We extend our analysis to examine firms' incentive to improve information. © 2014 Wiley Periodicals, Inc. 62:1–15, 2015     

Contracts and coordination: Supply chains with uncertain demand and supply

Considering a supply chain with a supplier subject to yield uncertainty selling to a retailer facing stochastic demand, we find that commonly studied classical coordination contracts fail to coordinate both the supplier's production and the retailer's procurement decisions and achieve efficient performance. First, we study the vendor managed inventory (VMI) partnership. We find that a consignment VMI partnership coupled with a production cost subsidy achieves perfect coordination and a win‐win outcome; it is simple to implement and arbitrarily allocates total channel profit. The production cost subsidy optimally chosen through Nash bargaining analysis depends on the bargaining power of the supplier and the retailer. Further, motivated by the practice that sometimes the retailer and the supplier can arrange a “late order,” we also analyze the behavior of an advance‐purchase discount (APD) contract. We find that an APD with a revenue sharing contract can efficiently coordinate the supply chain as well as achieve flexible profit allocation. Finally, we explore which coordination contract works better for the supplier vs. the retailer. It is interesting to observe that Nash bargaining solutions for the two coordination contracts are equivalent. We further provide recommendations on the applications of these contracts. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 305–319, 2016     

Collaborative procurement among competing buyers

Collaborative procurement emerged as one of the many initiatives for achieving improved inter‐firm coordination and collaboration. In this article, we adopt a game‐theoretical approach to study the interaction between two firms who procure jointly, but produce independently and remain competitors in a product market characterized by price‐sensitive demand. We study the underlying economics behind collaborative procurement, examine the effects of collaboration on buyer and supplier profitability, and derive conditions under which collaboration is beneficial to each participant. We find that a necessary and sufficient condition for a buyer to collaborate is to increase its sales. We identify the conditions that lead equal size buyers (i.e., consortia consisting of only large buyers or only small buyers) versus different size buyers to collaborate. We also determine the conditions that make collaboration profitable for the supplier, and show that rather than selling a large quantity to a single buyer, the supplier prefers to sell to multiple buyers in smaller quantities. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Information technology (IT) infrastructure relies on a globalized supply chain that is vulnerable to numerous risks from adversarial attacks. It is important to protect IT infrastructure from these dynamic, persistent risks by delaying adversarial exploits. In this paper, we propose max‐min interdiction models for critical infrastructure protection that prioritizes cost‐effective security mitigations to maximally delay adversarial attacks. We consider attacks originating from multiple adversaries, each of which aims to find a “critical path” through the attack surface to complete the corresponding attack as soon as possible. Decision‐makers can deploy mitigations to delay attack exploits, however, mitigation effectiveness is sometimes uncertain. We propose a stochastic model variant to address this uncertainty by incorporating random delay times. The proposed models can be reformulated as a nested max‐max problem using dualization. We propose a Lagrangian heuristic approach that decomposes the max‐max problem into a number of smaller subproblems, and updates upper and lower bounds to the original problem via subgradient optimization. We evaluate the perfect information solution value as an alternative method for updating the upper bound. Computational results demonstrate that the Lagrangian heuristic identifies near‐optimal solutions efficiently, which outperforms a general purpose mixed‐integer programming solver on medium and large instances.     

Models for production planning under power interruptions

We present a robust optimization model for production planning under the assumption that electricity supply is subject to uncertain interruptions caused by participation in interruptible load contracts (ILCs). The objective is to minimize the cost of electricity used for production while providing a robust production plan which ensures demand satisfaction under all possible interruption scenarios. The combinatorial size of the set of interruption scenarios makes this a challenging problem. Furthermore, we assume that no probabilistic information is known about the supply uncertainty: we only use the information given in the ILC to identify an uncertainty set that captures the possible scenarios. We construct a general robust framework to handle this uncertainty and present a heuristic to compute a good feasible solution of the robust model. We provide computational experiments on a real‐world example and compare the performance of an exact solver applied to the robust model with that of the heuristic procedure. Finally, we include the operational impact of interruptions such as “recovery modes” in the definition of the uncertainty set. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

A selective newsvendor approach to order management

Consider a supplier offering a product to several potential demand sources, each with a unique revenue, size, and probability that it will materialize. Given a long procurement lead time, the supplier must choose the orders to pursue and the total quantity to procure prior to the selling season. We model this as a selective newsvendor problem of maximizing profits where the total (random) demand is given by the set of pursued orders. Given that the dimensionality of a mixed‐integer linear programming formulation of the problem increases exponentially with the number of potential orders, we develop both a tailored exact algorithm based on the L‐shaped method for two‐stage stochastic programming as well as a heuristic method. We also extend our solution approach to account for piecewise‐linear cost and revenue functions as well as a multiperiod setting. Extensive experimentation indicates that our exact approach rapidly finds optimal solutions with three times as many orders as a state‐of‐the‐art commercial solver. In addition, our heuristic approach provides average gaps of less than 1% for the largest problems that can be solved exactly. Observing that the gaps decrease as problem size grows, we expect the heuristic approach to work well for large problem instances. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

The bottleneck problem with minimum quantity commitments

Given an edge‐distance graph of a set of suppliers and clients, the bottleneck problem is to assign each client to a selected supplier minimizing their maximum distance. We introduce minimum quantity commitments to balance workloads of suppliers, provide the best possible approximation algorithm, and study its generalizations and specializations. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Markets for surplus components with a strategic supplier

We study markets for surplus components, which allow manufacturers with excess component inventory to sell to firms with a shortage. Recent developments in internet commerce have the potential to greatly increase the efficiency of such markets. We develop a one‐period model in which a monopolist supplier sells to a number of independent manufacturers who are uncertain about demand for final goods. After uncertainty is resolved, the manufacturers have the opportunity to trade. Because uncertainty is over demand functions, the model allows us to endogenize both the price of final goods and the price of components in wholesale and surplus markets. We derive conditions on demand uncertainty that determine whether a surplus market will increase or decrease supplier profits. Increased costs of transacting on the surplus market may benefit manufacturers, because of the impact of these costs on the supplier's pricing power. The surplus market can decrease overall efficiency of the supply chain, since the benefit of better allocation of components may be outweighed by an increased double‐marginalization effect. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Optimal control policies for an inventory system with commitment lead time

We consider a firm which faces a Poisson customer demand and uses a base‐stock policy to replenish its inventories from an outside supplier with a fixed lead time. The firm can use a preorder strategy which allows the customers to place their orders before their actual need. The time from a customer's order until the date a product is actually needed is called commitment lead time. The firm pays a commitment cost which is strictly increasing and convex in the length of the commitment lead time. For such a system, we prove the optimality of bang‐bang and all‐or‐nothing policies for the commitment lead time and the base‐stock policy, respectively. We study the case where the commitment cost is linear in the length of the commitment lead time in detail. We show that there exists a unit commitment cost threshold which dictates the optimality of either a buy‐to‐order (BTO) or a buy‐to‐stock strategy. The unit commitment cost threshold is increasing in the unit holding and backordering costs and decreasing in the mean lead time demand. We determine the conditions on the unit commitment cost for profitability of the BTO strategy and study the case with a compound Poisson customer demand.     

Collaboration in contingent capacities with information asymmetry

We study the optimal contracting problem between two firms collaborating on capacity investment with information asymmetry. Without a contract, system efficiency is lost due to the profit‐margin differentials among the firms, demand uncertainty, and information asymmetry. With information asymmetry, we demonstrate that the optimal capacity level is characterized by a newsvendor formula with an upward‐adjusted capacity investment cost, and no first‐best solution can be achieved. Our analysis shows that system efficiency can always be improved by the optimal contract and the improvement in system efficience is due to two factors. While the optimal contract may bring the system's capacity level closer to the first‐best capacity level, it prevents the higher‐margin firm from overinvesting and aligns the capacity‐investment decisions of the two firms. Our analysis of a special case demonstrates that, under some circumstances, both firms can benefit from the principal having better information about the agent's costs. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 54:, 2007     

The incentive effect of acceptance sampling plans in a supply chain with endogenous product quality

This article studies a firm that procures a product from a supplier. The quality of each product unit is measured by a continuous variable that follows a normal distribution and is correlated within a batch. The firm conducts an inspection and pays the supplier only if the product batch passes the inspection. The inspection not only serves the purpose of preventing a bad batch from reaching customers but also offers the supplier an incentive to improve product quality. The firm determines the acceptance sampling plan, and the supplier determines the quality effort level in either a simultaneous game or a Stackelberg leadership game, in which both parties share inspection cost and recall loss caused by low product quality. In the simultaneous game, we identify the Nash equilibrium form, provide sufficient conditions that guarantee the existence of a pure strategy Nash equilibrium, and find parameter settings under which the decentralized and centralized supply chains achieve the same outcome. By numerical experiments, we show that the firm's acceptance sampling plan and the supplier's quality effort level are sensitive to both the recall loss sharing ratio and the game format (i.e., the precommitment assumption of the inspection policy). © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Evergreening and operational risk under price competition

“Evergreening” is a strategy wherein an innovative pharmaceutical firm introduces an upgrade of its current product when the patent on this product expires. The upgrade is introduced with a new patent and is designed to counter competition from generic manufacturers that seek to imitate the firm's existing product. However, this process is fraught with uncertainty because the upgrade is subject to stringent guidelines and faces approval risk. Thus, an incumbent firm has to make an upfront production capacity investment without clarity on whether the upgrade will reach the market. This uncertainty may also affect the capacity investment of a competing manufacturer who introduces a generic version of the incumbent's existing product but whose market demand depends on the success or failure of the upgrade. We analyze a game where capacity investment occurs before uncertainty resolution and firms compete on prices thereafter. Capacity considerations that arise due to demand uncertainty introduce new factors into the evergreening decision. Equilibrium analysis reveals that the upgrade's estimated approval probability needs to exceed a threshold for the incumbent to invest in evergreening. This threshold for evergreening increases as the intensity of competition in the generic market increases. If evergreening is optimal, the incumbent's capacity investment is either decreasing or nonmonotonic with respect to low end market competition depending on whether the level of product improvement in the upgrade is low or high. If the entrant faces a capacity constraint, then the probability threshold for evergreening is higher than the case where the entrant is not capacity constrained. Finally, by incorporating the risk‐return trade‐off that the incumbent faces in terms of the level of product improvement versus the upgrade success probability, we can characterize policy for a regulator. We show that the introduction of capacity considerations may maximize market coverage and/or social surplus at incremental levels of product improvement in the upgrade. This is contrary to the prevalent view of regulators who seek to curtail evergreening involving incremental product improvement. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 71–89, 2016