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     

Supply contracts in manufacturer‐retailer interactions with manufacturer‐quality and retailer effort‐induced demand

We consider a decentralized distribution channel where demand depends on the manufacturer‐chosen quality of the product and the selling effort chosen by the retailer. The cost of selling effort is private information for the retailer. We consider three different types of supply contracts in this article: price‐only contract where the manufacturer sets a wholesale price; fixed‐fee contract where manufacturer sells at marginal cost but charges a fixed (transfer) fee; and, general franchise contract where manufacturer sets a wholesale price and charges a fixed fee as well. The fixed‐fee and general franchise contracts are referred to as two‐part tariff contracts. For each contract type, we study different contract forms including individual, menu, and pooling contracts. In the analysis of the different types and forms of contracts, we show that the price only contract is dominated by the general franchise menu contract. However, the manufacturer may prefer to offer the fixed‐fee individual contract as compared to the general franchise contract when the retailer's reservation utility and degree of information asymmetry in costs are high. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Impact of transfer pricing methods for tax purposes on supply chain performance under demand uncertainty

Transfer pricing refers to the pricing of an intermediate product or service within a firm. This product or service is transferred between two divisions of the firm. Thus, transfer pricing is closely related to the allocation of profits in a supply chain. Motivated by the significant impact of transfer pricing methods for tax purposes on operational decisions and the corresponding profits of a supply chain, in this article, we study a decentralized supply chain of a multinational firm consisting of two divisions: a manufacturing division and a retail division. These two divisions are located in different countries under demand uncertainty. The retail division orders an intermediate product from the upstream manufacturing division and sets the retail price under random customer demand. The manufacturing division accepts or rejects the retail division's order. We specifically consider two commonly used transfer pricing methods for tax purposes: the cost‐plus method and the resale‐price method. We compare the supply chain profits under these two methods. Based on the newsvendor framework, our analysis shows that the cost‐plus method tends to allocate a higher percentage of profit to the retail division, whereas the resale‐price method tends to achieve a higher firm‐wide profit. However, as the variability of demand increases, our numerical study suggests that the firm‐wide and divisional profits tend to be higher under the cost‐plus method than they are under the resale‐price method. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Resale price maintenance contracts with retailer sales effort: Effect of flexibility and competition

In Resale Price Maintenance (RPM) contracts, the manufacturer specifies the resale price that retailers must charge to consumers. We study the role of using a RPM contract in a market where demand is influenced by retailer sales effort. First, it is well known that RPM alone does not provide incentive for the retailer to use adequate sales effort and some form of quantity fixing may be needed to achieve channel coordination. However, when the market potential of the product is uncertain, RPM with quantity fixing is a rigid contract form. We propose and study a variety of RPM contracts with quantity fixing that offer different forms of flexibility including pricing flexibility and quantity flexibility. Second, we address a long‐time debate in both academia and practice on whether RPM is anti‐competitive in a market when two retailers compete on both price and sales effort. We show that depending on the relative intensity of price competition and sales effort competition, RPM may lead to higher or lower retail prices compared to a two‐part tariff contract, which specifies a wholesale price and a fixed fee. Further, the impact of RPM on price competition and sales effort competition is always opposite to each other. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Supply chain coordination with shelf‐space and retail price dependent demand and heterogeneous retailers

We consider supply chain coordination in which a manufacturer supplies some product to multiple heterogeneous retailers and wishes to coordinate the supply chain via wholesale price and holding cost subsidy. The retail price is either exogenous or endogenous. The market demand is described by the market share attraction model based on all retailers'shelf‐spaces and retail prices. We obtain optimal solutions for the centralized supply chain, where the optimal retail pricing is a modified version of the well‐known cost plus pricing strategy. We further get feasible contracts for the manufacturer to coordinate the hybrid and decentralized supply chains. The manufacturer can allocate the total profit free to himself and the retail market via the wholesale price when the retail price is exogenous, but otherwise he cannot. Finally, we point out that different characteristics of the retail market are due to different powers of the manufacturer, and the more power the manufacturer has, the simpler the contract to coordinate the chain will be. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales

This paper studies a periodic‐review pricing and inventory control problem for a retailer, which faces stochastic price‐sensitive demand, under quite general modeling assumptions. Any unsatisfied demand is lost, and any leftover inventory at the end of the finite selling horizon has a salvage value. The cost component for the retailer includes holding, shortage, and both variable and fixed ordering costs. The retailer's objective is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We show that, under a mild assumption on the additive demand function, at the beginning of each period an (s,S) policy is optimal for replenishment, and the value of the optimal price depends on the inventory level after the replenishment decision has been done. Our numerical study also suggests that for a sufficiently long selling horizon, the optimal policy is almost stationary. Furthermore, the fixed ordering cost (K) plays a significant role in our modeling framework. Specifically, any increase in K results in lower s and higher S. On the other hand, the profit impact of dynamically changing the retail price, contrasted with a single fixed price throughout the selling horizon, also increases with K. We demonstrate that using the optimal policy values from a model with backordering of unmet demands as approximations in our model might result in significant profit penalty. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Coordination of pricing and inventory control across products

We consider the joint pricing and inventory‐control problem for a retailer who orders, stocks, and sells two products. Cross‐price effects exist between the two products, which means that the demand of each product depends on the prices of both products. We derive the optimal pricing and inventory‐control policy and show that this policy differs from the base‐stock list‐price policy, which is optimal for the one‐product problem. We find that the retailer can significantly improve profits by managing the two products jointly as opposed to independently, especially when the cross‐price demand elasticity is high. We also find that the retailer can considerably improve profits by using dynamic pricing as opposed to static pricing, especially when the demand is nonstationary. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

The effects of customer rebates and retailer incentives on a manufacturer's profits and sales

In some industries such as automotive, production costs are largely fixed and therefore maximizing revenue is the main objective. Manufacturers use promotions directed to the end customers and/or retailers in their distribution channels to increase sales and market share. We study a game theoretical model to examine the impact of “retailer incentive” and “customer rebate” promotions on the manufacturer's pricing and the retailer's ordering/sales decisions. The main tradeoff is that customer rebates are given to every customer, while the use of retailer incentives is controlled by the retailer. We consider several models with different demand characteristics and information asymmetry between the manufacturer and a price discriminating retailer, and we determine which promotion would benefit the manufacturer under which market conditions. When demand is deterministic, we find that retailer incentives increase the manufacturer's profits (and sales) while customer rebates do not unless they lead to market expansion. When the uncertainty in demand (“market potential”) is high, a customer rebate can be more profitable than the retailer incentive for the manufacturer. With numerical examples, we provide additional insights on the profit gains by the right choice of promotion.© 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Spatial pricing and product allocation in online retailing

Spatial pricing means a retailer price discriminates its customers based on their geographic locations. In this article, we study how an online retailer should jointly allocate multiple products and facilitate spatial price discrimination to maximize profits. When deciding between a centralized product allocation ((i.e., different products are allocated to the same fulfillment center) and decentralized product allocation (ie, different products are allocated to different fulfillment centers), the retailer faces the tradeoff between shipment pooling (ie, shipping multiple products in one package), and demand localization (ie, stocking products to satisfy local demand) based on its understanding of customers' product valuations. In our basic model, we consider two widely used spatial pricing policies: free on board (FOB) pricing that charges each customer the exact amount of shipping cost, and uniform delivered (UD) pricing that provides free shipping. We propose a stylized model and find that centralized product allocation is preferred when demand localization effect is relatively low or shipment pooling benefit is relatively high under both spatial pricing policies. Moreover, centralized product allocation is more preferred under the FOB pricing which encourages the purchase of virtual bundles of multiple products. Furthermore, we respectively extend the UD and FOB pricing policies to flat rate shipping (ie, the firm charges a constant shipping fee for each purchase), and linear rate shipping (ie, the firm sets the shipping fee as a fixed proportion of firm's actual fulfillment costs). While similar observations from the basic model still hold, we find the firm can improve its profit by sharing the fulfillment cost with its customers via the flat rate or linear rate shipping fee structure.     

The effect of a temporary product distribution channel on supply chain performance

We analyze a supply chain of a manufacturer and two retailers, a permanent retailer who always stocks the manufacturer's product and an intermittent deal‐of‐the day retailer who sells the manufacturer's product online for a short time. We find that without a deal‐of‐the‐day (DOTD) retailer, it is suboptimal for the manufacturer to offer a quantity discount while it is optimal for the retailer to offer periodic price discounts to consumers. With the addition of a DOTD retailer, it is likely to be optimal for the manufacturer to offer a quantity discount. We show that even without market expansion, i.e., no exclusive DOTD retailer consumers, opening the intermittent channel can leave the permanent retailer no worse‐off while increasing the manufacturer's profit. We identify the regular and discounted wholesale prices and the threshold quantity at which the manufacturer should give the discount. We also identify the optimal retail prices. We find that opening the intermittent channel increases the profit of the manufacturer, is likely to decrease the average retail price and to increase sales, and may increase the permanent retailer's profit. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 505–528, 2016     

Allocation with demand competition: Uniform,proportional, and lexicographic mechanisms

We examine capacity allocation mechanisms in a supply chain comprising a monopolistic supplier and two competing retailers with asymmetric market powers. The supplier allocates limited capacity to retailers according to uniform, proportional, or lexicographic mechanism. We study the impact of these allocation mechanisms on supplier pricing decisions and retailer ordering behavior. With individual order size no greater than supplier capacity, we show that all three mechanisms guarantee equilibrium ordering. We provide precise structures of retailer ordering decisions in Nash and dominant equilibria. Further, we compare the mechanisms from the perspective of the supplier, the retailers, and the supply chain. We show that regardless of whether retailer market powers are symmetric, lexicographic allocation with any priority sequence of retailers is better than the other two mechanisms for the supplier. Further, under lexicographic allocation, the supplier gains more profit by granting higher priority to the retailer with greater market power. We also extend our study to the case with multiple retailers. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 85–107, 2017     

Trade credit contract in the presence of retailer investment opportunity

This paper presents a model for designing a trade credit contract between a supplier and a retailer that would coordinate a supply chain in the presence of investment opportunity for the retailer. Specifically, we study a newsvendor model where the supplier offers a trade credit contract to the retailer who, by delaying the payment, can invest the accounts payable amount and earn returns. We find that when the channel partners have symmetric information about the retailer's investment return, a conditionally concessional trade credit (CTC) contract, which includes a wholesale price, an interest‐free period, and a minimum order requirement, can achieve channel coordination. We then extend the model to the information asymmetry setting in which the retailer's investment return is unobservable by the supplier. We show that, although the CTC contract cannot achieve the coordination in this setting, it can effectively improve channel efficiency as well as profitability for individual partners.     

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.     

Dynamic inventory and pricing models for competing retailers

We address infinite‐horizon models for oligopolies with competing retailers under demand uncertainty. We characterize the equilibrium behavior which arises under simple wholesale pricing schemes. More specifically, we consider a periodic review, infinite‐horizon model for a two‐echelon system with a single supplier servicing a network of competing retailers. In every period, each retailer faces a random demand volume, the distribution of which depends on his own retail price as well as those charged by possibly all competing retailers. We also derive various comparative statics results regarding the impact several exogenous system parameters (e.g., cost or distributional parameters) have on the equilibrium decisions of the retailers as well as their expected profits. We show that certain monotonicity properties, engrained in folklore as well as in known inventory models for centralized systems, may break down in decentralized chains under retailer competition. Our results can be used to optimize the aggregate profits in the supply chain (i.e., those of the supplier and all retailers) by implementing a specific wholesale pricing scheme. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

On the effectiveness of returns policies in the price‐dependent newsvendor model

We study in this paper the price‐dependent (PD) newsvendor model in which a manufacturer sells a product to an independent retailer facing uncertain demand and the retail price is endogenously determined by the retailer. We prove that for a zero salvage value and some expected demand functions, in equilibrium, the manufacturer may elect not to introduce buybacks. On the other hand, if buybacks are introduced in equilibrium, their introduction has an insignificant effect on channel efficiency improvement, but, by contrast, may significantly shift profits from the retailer to the manufacturer. We further demonstrate that the introduction of buybacks increases the wholesale price, retail price, and inventory level, as compared to the wholesale price‐only contract, and that the corresponding vertically integrated firm offers the lowest retail price and highest inventory level. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Locational tying of complementary retail items

We study a selling practice that we refer to as locational tying (LT), which seems to be gaining wide popularity among retailers. Under this strategy, a retailer “locationally ties” two complementary items that we denote by “primary” and “secondary.” The retailer sells the primary item in an appropriate “department” of his or her store. To stimulate demand, the secondary item is offered in the primary item's department, where it is displayed in very close proximity to the primary item. We consider two variations of LT: In the multilocation tying strategy (LT‐M), the secondary item is offered in its appropriate department in addition to the primary item's department, whereas in the single‐location tying strategy (LT‐S), it is offered only in the primary item's location. We compare these LT strategies to the traditional independent components (IC) strategy, in which the two items are sold independently (each in its own department), but the pricing/inventory decisions can be centralized (IC‐C) or decentralized (IC‐D). Assuming ample inventory, we compare and provide a ranking of the optimal prices of the four strategies. The main insight from this comparison is that relative to IC‐D, LT decreases the price of the primary item and adjusts the price of the secondary item up or down depending on its popularity in the primary item's department. We also perform a comparative statics analysis on the effect of demand and cost parameters on the optimal prices of various strategies, and identify the conditions that favor one strategy over others in terms of profitability. Then we study inventory decisions in LT under exogenous pricing by developing a model that accounts for the effect of the primary item's stock‐outs on the secondary item's demand. We find that, relative to IC‐D, LT increases the inventory level of the primary item. We also link the profitability of different strategies to the trade‐off between the increase in demand volume of the secondary item as a result of LT and the potential increase in inventory costs due to decentralizing the inventory of the secondary item. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Coordinated pricing and inventory control problems with capacity constraints and fixed ordering cost

This article addresses a single‐item, finite‐horizon, periodic‐review coordinated decision model on pricing and inventory control with capacity constraints and fixed ordering cost. Demands in different periods are random and independent of each other, and their distributions depend on the price in the current period. Each period's stochastic demand function is the additive demand model. Pricing and ordering decisions are made at the beginning of each period, and all shortages are backlogged. The objective is to find an optimal policy that maximizes the total expected discounted profit. We show that the profit‐to‐go function is strongly CK‐concave, and the optimal policy has an (s,S,P) ‐like structure. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Assessing the value of demand sharing in supply chains

We consider the problem of assessing the value of demand sharing in a multistage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order‐up‐to policy. We demonstrate how a typical supply chain player can determine the extent of its available information in the presence of demand sharing by studying the properties of the moving average polynomials of adjacent supply chain players. The retailer's demand is driven by the random shocks appearing in the autoregressive moving average representation for its demand. Under the assumptions we will make in this article, to the retailer, knowing the shock information is equivalent to knowing the demand process (assuming that the model parameters are also known). Thus (in the event of sharing) the retailer's demand sequence and shock sequence would contain the same information to the retailer's supplier. We will show that, once we consider the dynamics of demand propagation further up the chain, it may be that a player's demand and shock sequences will contain different levels of information for an upstream player. Hence, we study how a player can determine its available information under demand sharing, and use this information to forecast leadtime demand. We characterize the value of demand sharing for a typical supply chain player. Furthermore, we show conditions under which (i) it is equivalent to no sharing, (ii) it is equivalent to full information shock sharing, and (iii) it is intermediate in value to the two previously described arrangements. Although it follows from existing literature that demand sharing is equivalent to full information shock sharing between a retailer and supplier, we demonstrate and characterize when this result does not generalize to upstream supply chain players. We then show that demand propagates through a supply chain where any player may share nothing, its demand, or its full information shocks (FIS) with an adjacent upstream player as quasi‐ARMA in—quasi‐ARMA out. We also provide a convenient form for the propagation of demand in a supply chain that will lend itself to future research applications. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 515–531, 2014     

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     

The impact of manufacturer rebates on supply chain profits

Manufacturer rebates are commonly used as price discount tools for attracting end customers. In this study, we consider a two‐stage supply chain with a manufacturer and a retailer, where a single seasonal product faces uncertain and price‐sensitive demand. We characterize the impact of a manufacturer rebate on the expected profits of both the manufacturer and the retailer. We show that unless all of the customers claim the rebate, the rebate always benefits the manufacturer. Our results thus imply that “mail‐in rebates,” where some customers end up not claiming the rebate, particularly when the size of the rebate is relatively small, always benefit the manufacturer. On the other hand, an “instant rebate,” such as the one offered in the automotive industry where every customer redeems the rebate on the spot when he/she purchases a car, does not necessarily benefit the manufacturer. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007