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     

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     

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     

Technical note: Reexamination of all‐or‐none inspection policies in a supply chain with endogenous product quality

This note studies the optimal inspection policies in a supply chain in which a manufacturer purchases components from a supplier but has no direct control of component quality. The manufacturer uses an inspection policy and a damage cost sharing contract to encourage the supplier to improve the component quality. We find that all‐or‐none inspection policies are optimal for the manufacturer if the supplier's share of the damage cost is larger than a threshold; otherwise, the manufacturer should inspect a fraction of a batch. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Specification vagueness and supply quality risk

Specifying quality requirement is integral to any sourcing relationship, but vague and ambiguous specifications can often be observed in practice, especially when a buyer is in the initial stage of sourcing a new product. In this research, we study a supplier's production incentives under vague or exact quality specifications. We prove that a vague specification may in fact motivate the supplier to increase its quantity provision, resulting in a higher delivery quality. Vague quality specification can therefore be advantageous for a buyer to screen potential suppliers with an initial test order, and then rely on the received quality level to set more concrete quality guidelines. There is a degree, though, to which vague quality specification can be effective, as too much vagueness may decrease the supplier's quantity provision and hence the expected delivery quality. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

General models for the supplier's all-unit quantity discount policy

The purpose of this article is to investigate some managerial insights related to using the all-unit quantity discount policies under various conditions. The models developed here are general treatments that deal with four major issues: (a) one buyer or multiple buyers, (b) constant or price-elastic demand, (c) the relationship between the supplier's production schedule or ordering policy and the buyers' ordering sizes, and (d) the supplier either purchasing or manufacturing the item. The models are developed with two objectives: the supplier's profit improvement or the supplier's increased profit share analysis. Algorithms are developed to find optimal decision policies. Our analysis provides the supplier with both the optimal all-unit quantity discount policy and the optimal production (or ordering) strategy. Numerical examples are provided. © 1993 John Wiley & Sons. Inc.     

Determination of suppliers' optimal quantity discount schedules with heterogeneous buyers

Although the quantity discount problem has been extensively studied in the realm of a single supplier and a single buyer, it is not well understood when a supplier has many different buyers. This paper presents an analysis of a supplier's quantity discount decision when there are many buyers with different demand and cost structures. A common discrete all‐unit quantity discount schedule with many break points is used. After formulating the model, we first analyze buyers' responses to a general discrete quantity discount schedule. This analysis establishes a framework for a supplier to formulate his quantity discount decision. Under this framework, the supplier's optimal quantity discount schedule can be formulated and solved by a simple non‐linear programming model. The applicability of the model is discussed with an application for a large U.S. distribution network. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 46–59, 2002; DOI 10.1002/nav.1052     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Quantity discount pricing policies for heterogeneous retailers with price sensitive demand

Although quantity discount policies have been extensively analyzed, they are not well understood when there are many different buyers. This is especially the case when buyers face price‐sensitive demand. In this paper we study a supplier's optimal quantity discount policy for a group of independent and heterogeneous retailers, when each retailer faces a demand that is a decreasing function of its retail price. The problem is analyzed as a Stackelberg game whereby the supplier acts as the leader and buyers act as followers. We show that a common quantity discount policy that is designed according to buyers' individual cost and demand structures and their rational economic behavior is able to significantly stimulate demand, improve channel efficiency, and substantially increase profits for both the supplier and buyers. Furthermore, we show that the selection of all‐units or incremental quantity discount policies has no effect on the benefits that can be obtained from quantity discounts. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Information disclosure with endogenous channel structure

This article investigates the firms' optimal quality information disclosure strategies in a supply chain, wherein the supplier may encroach into the retail channel to sell products directly to end consumers. We consider two disclosure formats, namely, retailer disclosure (R-C) and supplier disclosure (S-C), and examine the optimal disclosure format from each firm's perspective. We show that either firm prefers to delegate the disclosure option to its partner when the supplier cannot encroach. However, the threat of supplier encroachment dramatically alters the firm's preference of disclosure. The supplier may prefer the S-C format to the R-C format when the entry cost is low and the disclosure cost is high to achieve a higher quality information transparency. Meanwhile, the retailer may prefer the R-C format to the S-C format when the entry cost is intermediate to deter the possible encroachment of the supplier. In this sense, the firms' preferences of disclosure format can be aligned due to the threat of supplier encroachment. The consumer surplus is always higher under the S-C format while either disclosure format can lead to a higher social welfare. We also consider an alternative scenario under which the supplier encroaches after the product quality information is disclosed. An interesting observation appears that the supplier may encroach when the product quality is low but foregoes encroachment when the product quality gets higher.     

Revenue sharing contracts in a supply chain with uncontractible actions

We consider a supplier–customer relationship where the customer faces a typical Newsvendor problem of determining perishable capacity to meet uncertain demand. The customer outsources a critical, demand‐enhancing service to an outside supplier, who receives a fixed share of the revenue from the customer. Given such a linear sharing contract, the customer chooses capacity and the service supplier chooses service effort level before demand is realized. We consider the two cases when these decisions are made simultaneously (simultaneous game) or sequentially (sequential game). For each game, we analyze how the equilibrium solutions vary with the parameters of the problem. We show that in the equilibrium, it is possible that either the customer's capacity increases or the service supplier's effort level decreases when the supplier receives a larger share of the revenue. We also show that given the same sharing contract, the sequential game always induces a higher capacity and more effort. For the case of additive effort effect and uniform demand distribution, we consider the customer's problem of designing the optimal contract with or without a fixed payment in the contract, and obtain sensitivity results on how the optimal contract depends on the problem parameters. For the case of fixed payment, it is optimal to allocate more revenue to the supplier to induce more service effort when the profit margin is higher, the cost of effort is lower, effort is more effective in stimulating demand, the variability of demand is smaller or the supplier makes the first move in the sequential game. For the case of no fixed payment, however, it is optimal to allocate more revenue to the supplier when the variability of demand is larger or its mean is smaller. Numerical examples are analyzed to validate the sensitivity results for the case of normal demand distribution and to provide more managerial insights. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Dynamic inventory control with limited capital and short‐term financing

For most firms, especially the small‐ and medium‐sized ones, the operational decisions are affected by their internal capital and ability to obtain external capital. However, the majority of the literature on dynamic inventory control ignores the firm's financial status and financing issues. An important question that arises is: what are the optimal inventory and financing policies for firms with limited internal capital and limited access to external capital? In this article, we study a dynamic inventory control problem where a capital‐constrained firm periodically purchases a product from a supplier and sells it to a market with random demands. In each period, the firm can use its own capital and/or borrow a short‐term loan to purchase the product, with the interest rate being nondecreasing in the loan size. The objective is to maximize the firm's expected terminal wealth at the end of the planning horizon. We show that the optimal inventory policy in each period is an equity‐level‐dependent base‐stock policy, where the equity level is the sum of the firm's capital level and the value of its on‐hand inventory evaluated at the purchasing cost; and the structure of the optimal policy can be characterized by four intervals of the equity level. Our results shed light on the dynamic inventory control for firms with limited capital and short‐term financing capabilities.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 184–201, 2014     

Excess procurement strategies by a dominant buyer under constrained supply

Supply chains are often characterized by the presence of a dominant buyer purchasing from a supplier with limited capacity. We study such a situation where a single supplier sells capacity to an established and more powerful buyer and also to a relatively less powerful buyer. The more powerful buyer enjoys the first right to book her capacity requirements at supplier's end, and then the common supplier fulfills the requirement of the less powerful buyer. We find that when the supplier's capacity is either too low (below the lower threshold) or too high (above the higher threshold), there is no excess procurement as compared to the case when supplier has infinite capacity. When the supplier's capacity is between these two thresholds, the more powerful buyer purchases an excess amount in comparison to the infinite capacity case.     

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     

A three‐stage procurement optimization problem under uncertainty

This article examines a problem faced by a firm procuring a material input or good from a set of suppliers. The cost to procure the material from any given supplier is concave in the amount ordered from the supplier, up to a supplier‐specific capacity limit. This NP‐hard problem is further complicated by the observation that capacities are often uncertain in practice, due for instance to production shortages at the suppliers, or competition from other firms. We accommodate this uncertainty in a worst‐case (robust) fashion by modeling an adversarial entity (which we call the “follower”) with a limited procurement budget. The follower reduces supplier capacity to maximize the minimum cost required for our firm to procure its required goods. To guard against uncertainty, the firm can “protect” any supplier at a cost (e.g., by signing a contract with the supplier that guarantees supply availability, or investing in machine upgrades that guarantee the supplier's ability to produce goods at a desired level), ensuring that the anticipated capacity of that supplier will indeed be available. The problem we consider is thus a three‐stage game in which the firm first chooses which suppliers' capacities to protect, the follower acts next to reduce capacity from unprotected suppliers, and the firm then satisfies its demand using the remaining capacity. We formulate a three‐stage mixed‐integer program that is well‐suited to decomposition techniques and develop an effective cutting‐plane algorithm for its solution. The corresponding algorithmic approach solves a sequence of scaled and relaxed problem instances, which enables solving problems having much larger data values when compared to standard techniques. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

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     

Commitment decisions with partial information updating

In this paper, we extend the results of Ferguson M. Naval Research Logistics 8 . on an end‐product manufacturer's choice of when to commit to an order quantity from its parts supplier. During the supplier's lead‐time, information arrives about end‐product demand. This information reduces some of the forecast uncertainty. While the supplier must choose its production quantity of parts based on the original forecast, the manufacturer can wait to place its order from the supplier after observing the information update. We find that a manufacturer is sometimes better off with a contract requiring an early commitment to its order quantity, before the supplier commits resources. On the other hand, the supplier sometimes prefers a delayed commitment. The preferences depend upon the amount of demand uncertainty resolved by the information as well as which member of the supply chain sets the exchange price. We also show conditions where demand information updating is detrimental to both the manufacturer and the supplier. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

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     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

Maintaining systems with heterogeneous spare parts

We consider the problem of optimally maintaining a stochastically degrading, single‐unit system using heterogeneous spares of varying quality. The system's failures are unannounced; therefore, it is inspected periodically to determine its status (functioning or failed). The system continues in operation until it is either preventively or correctively maintained. The available maintenance options include perfect repair, which restores the system to an as‐good‐as‐new condition, and replacement with a randomly selected unit from the supply of heterogeneous spares. The objective is to minimize the total expected discounted maintenance costs over an infinite time horizon. We formulate the problem using a mixed observability Markov decision process (MOMDP) model in which the system's age is observable but its quality must be inferred. We show, under suitable conditions, the monotonicity of the optimal value function in the belief about the system quality and establish conditions under which finite preventive maintenance thresholds exist. A detailed computational study reveals that the optimal policy encourages exploration when the system's quality is uncertain; the policy is more exploitive when the quality is highly certain. The study also demonstrates that substantial cost savings are achieved by utilizing our MOMDP‐based method as compared to more naïve methods of accounting for heterogeneous spares.