Designing a quantity discount scheme for a newsvendor-type product with numerous heterogeneous retailers

This paper presents a practical approach for designing a quantity-discount (“qd”) scheme for a manufacturer who supplies a newsvendor-type product to a large number of heterogeneous retailers. The main components of our approach are: (i) an information structure for handling a large number of heterogeneous retailers with changing identities; and (ii) expected-profit expressions for any given qd scheme. We show that these expected-profit expressions can be easily optimized to produce attractive qd schemes; also, these schemes are shown to be quite robust against errors in parameter estimation.     

Impact of product pricing and timing of investment decisions on supply chain co-opetition

In supply chain co-opetition, firms simultaneously compete and co-operate in order to maximize their profits. We consider the nature of co-opetition between two firms: The product supplier invests in the technology to improve quality, and the purchasing firm (buyer) invests in selling effort to develop the market for the product before uncertainty in demand is resolved. We consider three different decision making structures and discuss the optimal configuration from each firm’s perspective. In case 1, the supplier invests in product quality and sets the wholesale price for the product. The buyer then exerts selling effort to develop the market and following demand potential realization, sets the resale price. In case 2, the supplier invests in product quality followed by the buyer’s investment in selling effort. Then, after demand potential is observed, the supplier sets the wholesale price and the buyer sets the resale price. Finally, in case 3, both firms simultaneously invest in product quality and selling effort, respectively. Subsequently, observing the demand potential, the supplier sets the wholesale price and the buyer sets the resale price. We compare all configuration options from both the perspective of the supplier and the buyer, and show that the level of investment by the firms depends on the nature of competition between them and the level of uncertainty in demand. Our analysis reveals that although configuration 1 results in the highest profits for the integrated channel, there is no clear dominating preference on system configuration from the perspective of both parties. The incentives of the co-opetition partners and the investment levels are mainly governed by the cost structure and the level of uncertainty in demand. We examine and discuss the relation between system parameters and the incentives in desiging the supply contract structure.     

Pricing policies for substitutable products in a supply chain with Internet and traditional channels

This study considers pricing policies in a supply chain with one manufacturer, who sells a product to an independent retailer and directly to consumers through an Internet channel. In addition to the manufacturer’s product, the retailer sells a substitute product produced by another manufacturer. Given the wholesale prices of the two substitute products, the manufacturer decides the retail price of the Internet channel, and the retailer decides the retail prices of the two substitute products. Both the manufacturer and the retailer choose their own decision variables to maximize their respective profits. This work formulates the price competition, using the settings of Nash and Stackelberg games, and derives the corresponding existence and uniqueness conditions for equilibrium solutions. A sensitivity analysis of an equilibrium solution is then conducted for the model parameters, and the profits are compared for two game settings. The findings show that improving brand loyalty is profitable for both of the manufacturer and retailer, and that an increased service value may alleviate the threat of the Internet channel for the retailer and increase the manufacturer’s profit. The study also derives some conditions under which the manufacturer and the retailer mutually prefer the Stackelberg game. Based on these results, this study proposes an appropriate cooperation strategy for the manufacturer and retailer.     

How a dominant retailer might design a purchase contract for a newsvendor-type product with price-sensitive demand

A dominant retailer will purchase a newsvendor-type product from a manufacturer, who incurs a unit manufacturing cost k. The expected retail demand is a function of the unit retail price p. How should the retailer design her purchase contract? For this increasingly prevalent but inadequately studied scenario, we propose plausible adaptations of several contract formats that have been widely studied in the dominant-manufacturer context. For both symmetric-k and asymmetric-k-knowledge situations, we present performance results of these contracts. Our results then reveal that the performance of these contract formats under our scenario differs considerably from what one would surmise from the well-known results published for closely related scenarios. For example, the widely studied buyback and revenue-sharing formats turn out to be largely ineffective when implemented by a dominant retailer. In contrast, the two-part tariff format performs well relative to the theoretically optimal “menu of contracts.” Our results highlight the need to study purchase contract formats designed specifically for dominant-retailer newsvendor-product channels.     

Strategic wholesale pricing in a supply chain with a potential entrant

This paper develops an adverse selection model for a two-stage supply chain with one supplier, one retailer, and a potential outside entrant supplier who makes a partially substitutable product. The work is different from most research on entry deterrence that only considers a single-stage model. Our main interest is to investigate how the incumbent supplier can strategically maximize her profit by a wholesale pricing policy when facing the potential entrant. We focus on a model where the entrant supplier will sell her product through the same incumbent retailer. We derive the optimal decisions for each player and study the comparative statics of the equilibrium. To investigate how the supply chain structure may affect the deterrence strategy of the incumbent supplier, we also consider three alternative models with different channel structures, when both suppliers sell their products directly, when the entrant has another independent retailer, and when the entrant sells her product directly. Through the comparison, we find that the existence of the common downstream retailer often enhances the deterring motivation of the incumbent supplier.     

Cooperation in assembly systems: The role of knowledge sharing networks

Process improvement plays a significant role in reducing production costs over the life cycle of a product. We consider the role of process improvement in a decentralized assembly system in which a buyer purchases components from several first-tier suppliers. These components are assembled into a finished product, which is sold to the downstream market. The assembler faces a deterministic demand/production rate and the suppliers incur variable inventory costs and fixed setup production costs. In the first stage of the game, which is modeled as a non-cooperative game among suppliers, suppliers make investments in process improvement activities to reduce the fixed production costs. Upon establishing a relationship with the suppliers, the assembler establishes a knowledge sharing network – this network is implemented as a series of meetings among suppliers and also mutual visits to their factories. These meetings facilitate the exchange of best practices among suppliers with the expectation that suppliers will achieve reductions in their production costs from the experiences learned through knowledge sharing. We model this knowledge exchange as a cooperative game among suppliers in which, as a result of cooperation, all suppliers achieve reductions in their fixed costs. In the non-cooperative game, the suppliers anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of knowledge sharing in their cost functions. Based on this model, we investigate the benefits and challenges associated with establishing a knowledge sharing network. We identify and compare various cost allocation mechanisms that are feasible in the cooperative game and show that the system optimal investment levels can be achieved only when the most efficient supplier receives the incremental benefits of the cost reduction achieved by other suppliers due to the knowledge transfer.     

Inventory competition and allocation in a multi-channel distribution system

Consider a supply chain involving one manufacturer and one independent retailer. The manufacturer distributes her product to the end consumer through the independent retailer as well as through her direct channel. Each of the two channels faces a stochastic demand. If one channel is out of stock, a fraction of the unsatisfied customers visit the other channel, which induces inventory competition between the channels. Under the scenario described above, will the manufacturer ever undercut the retailer’s order when the capacity is infinite? What are the equilibria of the game? How does a capacity constraint affect the equilibrium outcome? What is the optimal inventory allocation strategy for the manufacturer? Using a game theoretic model we seek answers to the above questions. Both the capacitated and the infinite capacity games are considered. We establish the necessary condition for a manufacturer to undercut a retailer’s order and show that a manufacturer may deny the retailer of inventory even when the capacity is ample. We show that there can be an equilibrium in the capacitated game where a manufacturer might not use the entire capacity and still deny a retailer inventory. We also show that a mild capacity constraint may make both parties better off and thereby increase the total supply chain profit. We develop a simple yet practical contract called the reverse revenue sharing contract and show that along with a fixed franchise fee this contract can coordinates our decentralized supply chain.     

On a cooperative advertising model for a supply chain with one manufacturer and one retailer

, , ,  and  recently studied a game-theoretic model for cooperative advertising in a supply chain consisting of one manufacturer and one retailer. However, the sales-volume (demand) function considered in this model can become negative for some values of the decision variables, and in fact, this does happen for the proposed Stackelberg and Nash equilibrium solutions. Yue et al. (2006) acknowledge the negativity problem and suggest two constraints to fix it; however, they do not incorporate these constraints into their mathematical analysis. In this paper, we show that the results obtained by analyzing the advertising model under the constraints suggested by Yue et al. can differ significantly from those obtained in the previous papers.     

Pricing decisions for substitutable products with a common retailer in fuzzy environments

The pricing problem of substitutable products in a fuzzy supply chain is analyzed by using game theory in this paper. There are two substitutable products produced by two competitive manufacturers respectively and then sold by one common retailer to the consumers. Both the manufacturing cost and the customer demand for each product are characterized as fuzzy variables. How the two manufacturers and the common retailer make their own pricing decisions about wholesale prices and retail prices are explored under four different scenarios, and the corresponding expected value models are developed in this paper. Finally, a numerical example is given to illustrate the effectiveness of the proposed supply chain models.     

Demand disruption and coordination of the supply chain with a dominant retailer

This paper develops two coordination models of a supply chain consisting of one manufacturer, one dominant retailer and multiple fringe retailers to investigate how to coordinate the supply chain after demand disruption. We consider two coordination schedules, linear quantity discount schedule and Groves wholesale price schedule. We find that, under the linear quantity discount schedule, the manufacturer only needs to adjust the maximum variable wholesale price after demand disruption. For each case of the disrupted amount of demand, the higher the market share of the dominant retailer, the lower its average wholesale price and the subsidy will be under the linear quantity discount schedule, while the higher its fraction of the supply chain’s profit will be under Groves wholesale price schedule. When the increased amount of demand is very large and production cost is sufficiently low, linear quantity discount schedule is better for the manufacturer. However, when the production cost is sufficiently large, Groves wholesale price schedule is always better. We also find that the disrupted amount of demand largely affects the allocation of the supply chain’s profit.     

Modeling cooperation on a class of distribution problems

In this paper we study models of cooperation between the nodes of a network that represents a distribution problem. The distribution problem we propose arises when, over a graph, a group of nodes offers certain commodity, some other nodes require it and a third group of nodes neither need this material nor offer it but they are strategically relevant to the distribution plan. The delivery of one unit of material to a demand node generates a fixed profit, and the shipping of the material through the arcs has an associated cost. We show that in such a framework cooperation is beneficial for the different parties. We prove that the cooperative situation arising from this distribution problem is totally balanced by finding a set of stable allocations (in the core of an associated cooperative game). In order to overcome certain fairness problems of these solutions, we introduce two new solution concepts and study their properties.     

Product variety and channel structure strategy for a retailer-Stackelberg supply chain

Motivated by the observations that the direct sales channel is increasingly used for customized products and that retailers wield leadership, we develop in this paper a retailer-Stackelberg pricing model to investigate the product variety and channel structure strategies of manufacturer in a circular spatial market. To avoid channel conflict, we consider the commonly observed case where the indirect channel sells standard products whereas the direct channel offers custom products. Our analytical results indicate that if the reservation price in the indirect channel is sufficiently low, adding the direct channel raises the unit wholesale price and retail price in the indirect channel due to customization in the direct channel. Despite the fact that dual channels for the retailer may dominate the single indirect channel, we find that the motivation for the manufacturer to use dual channels decreases with the unit production cost, while increases with (i) the marginal cost of variety, (ii) the retailer’s marginal selling cost, and (iii) the customer’s fit cost. Interestingly, our equilibrium analysis demonstrates that it is more likely for the manufacturer to use dual channels under the retailer Stackelberg channel leadership scenario than under the manufacturer Stackelberg scenario if offering a greater variety is very expensive. When offering a greater variety is inexpensive, the decentralization of the indirect channel may invert the manufacturer’s channel structure decision. Furthermore, endogenization of product variety will also invert the channel structure decision if the standard product’s reservation price is sufficiently low.     

On a multi-period supply chain system with supplementary order opportunity

This paper considers a supplementary supply–order system in a multi-period situation. In each period, the buyer first places an initial order based on the demand prediction; he has the opportunity to place a supplementary order with the supplier after the demand of that period is realized. The supplier maintains an inventory, and decides the quantity to be produced and the quantity to be provided for the supplementary order in each time period. We formulate the problem as a multi-period inventory game, and derive the optimal production and order policies for the supplier and buyer, respectively. The existence and uniqueness of Nash equilibrium is proved in the generalized multi-period setting, and the closed-form Nash equilibrium solution is obtained when the parameters are stationary. Numerical study is performed to reveal more managerial insights. We find that the supplementary supply–order mechanism, if designed properly, can effectively improve the multi-period supply chain performance.     

Ordering policy and coordination of a supply chain with two-period demand uncertainty

We develop a two-period game model of a one-manufacturer and one-retailer supply chain to investigate the optimal decisions of the players, where stock-out and holding costs are incorporated into the model. The demand at each period is stochastic and price sharply drops in mid-life. We assume the retailer has a single order opportunity, and decides how much inventory to keep in the middle of selling season. We show that both the price-protection mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme may achieve channel coordination and access a ‘win-win’ situation under some conditions. The larger the lowest expected profit of the retailer, the lower the possibility of ‘win-win’ situation will be. Combined with the analysis of feasible regions for coordination policies, we find that PME scheme is not always better than ME scheme from the perspective of implementable mechanism. Finally, we find that adopting the dispose-down-to (DDT) policy can bring a larger improvement of the expected channel profit in the centralized setting, and it is interesting that by using DDT policy, double marginalization occurs only at Period 1, and however, does not plague the retailer in Period 2.     

The use of a premium-payment scheme in a supply chain involving capacity acquisition

We study a practice whereby a downstream firm makes to his supplier a premium-payment for a certain quantity of products. We show that the adoption of this practice can induce the supplier to build bigger capacity. The higher capacity level enables the supplier to satisfy a larger portion of demands from the downstream firm, and this leads to higher payoffs for both parties in the supply chain. With the assistance of an under-capacity penalty imposed on the supplier, this premium-payment scheme can help lure the parties into taking the channel-optimal actions. Our numerical examples help reveal various features of the scheme.     

Conditions of reverse bullwhip effect in pricing for price-sensitive demand functions

Supply chain mechanisms that exacerbate price variation needs special attention, since price variation is one of the root causes of the bullwhip effect. In this study, we investigate conditions that create an amplification of price variation moving from the upstream suppliers to the downstream customers in a supply chain, which is referred as the “reverse bullwhip effect in pricing” (RBP). Considering initially a single-stage supply chain in which a retailer faces a random and price-sensitive demand, we derive conditions on a general demand function for which the retail price variation is higher than that of the wholesale price. The investigation is extended to a multi-stage supply chain in which the price at each stage is determined by a game theoretical framework. We illustrate the use of the conditions in identifying commonly used demand functions that induce RBP analytically and by means of several numerical examples.     

Improving reliability of a shared supplier with competition and spillovers

Supplier reliability is a key determinant of a manufacturer’s competitiveness. It reflects a supplier’s capability of order fulfillment, which can be measured by the percentage of order quantity delivered in a given time window. A perfectly reliable supplier delivers an amount equal to the order placed by its customer, while an unreliable supplier may deliver an amount less than the amount ordered. Therefore, when suppliers are unreliable, manufacturers often have incentives to help suppliers improve delivery reliability. Suppliers, however, often work with multiple manufacturers and the benefit of enhanced reliability may spill over to competing manufacturers. In this study, we explore how potential spillover influences manufacturers’ incentives to improve supplier’s reliability. We consider two manufacturers that compete with imperfectly substitutable products on Type I service level (i.e., in-stock probability). The manufacturers share a common supplier who, due to variations in production quality or yield, is unreliable. Manufacturers may exert efforts to improve the supplier’s reliability in the sense that the delivered quantity is stochastically larger after improvement. We develop a two-stage model that encompasses supplier improvement, uncertain supply and random demand in a competitive setting. In this complex model, we characterize the manufacturers’ equilibrium in-stock probability. Moreover, we characterize sufficient conditions for the existence of the equilibrium of the manufacturers’ improvement efforts. Finally, we numerically test the impact of market characteristics on the manufacturers’ equilibrium improvement efforts. We find that a manufacturer’s equilibrium improvement effort usually declines in market competition, market uncertainty or spillover effect, although its expected equilibrium profit typically increases in spillover effect.     

Stability and monotonicity in newsvendor situations

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers’ dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.