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.     

“Bricks vs. Clicks”: The impact of manufacturer encroachment with a dealer leasing and selling of durable goods

In durable goods markets, many brand name manufacturers, including IBM, HP, Epson, and Lenovo, have adopted dual-channel supply chains to market their products. There is scant literature, however, addressing the product durability and its impact on players’ optimal strategies in a dual-channel supply chain. To fill this void, we consider a two-period dual-channel model in which a manufacturer sells a durable product directly through both a manufacturer-owned e-channel and an independent dealer who adopts a mix of selling and leasing to consumers. Our results show that the manufacturer begins encroaching into the market in Period 1, but the dealer starts withdrawing from the retail channel in Period 2. Moreover, as the direct selling cost decreases, the equilibrium quantities and wholesale prices become quite angular and often nonmonotonic. Among other results, we find that both the dealer and the supply chain may benefit from the manufacturer’s encroachment. Our results also indicate that both the market structure and the nature of competition have an important impact on the player’s (dealer’s) optimal choice of leasing and selling.     

A supply chain model with direct and retail channels

We study a dual channel supply chain in which a manufacturer sells to a retailer as well as to consumers directly. Consumers choose the purchase channel based on price and service qualities. The manufacturer decides the price of the direct channel and the retailer decides both price and order quantity. We develop conditions under which the manufacturer and the retailer share the market in equilibrium. We show that the difference in marginal costs of the two channels plays an important role in determining the existence of dual channels in equilibrium. We also show that demand variability has a major influence on the equilibrium prices and on the manufacturer’s motivation for opening a direct channel. In the case that the manufacturer and the retailer coordinate and follow a centralized decision maker, we show that adding a direct channel will increase the overall profit. Our numerical results show that an increase in retailer’s service quality may increase the manufacturer’s profit in dual channel and a larger range of consumer service sensitivity may benefit both parties in the dual channel. Our results suggest that the manufacturer is likely to be better off in the dual channel than in the single channel when the retailer’s marginal cost is high and the wholesale price, consumer valuation and the demand variability are low.     

Price and lead time decisions in dual-channel supply chains

Manufacturers today are increasingly adopting a dual channel to sell their products, i.e., the traditional retail channel and an online direct channel. Empirical studies have shown that service quality (we focus on the delivery lead time of the direct channel) even goes beyond product price as one of the major factors influencing consumer acceptance of the direct channel. Delivery lead time has significant effects on demand, profit, and pricing strategy. However, there is scant literature addressing the decision on the promised delivery lead time of a direct channel and its impact on the manufacturer’s and retailer’s pricing decisions. To fill this gap, we examine the optimal decisions of delivery lead time and prices in a centralized and a decentralized dual-channel supply chain using the two-stage optimization technique and Stackelberg game, and analyze the impacts of delivery lead time and customer acceptance of a direct channel on the manufacturer’s and retailer’s pricing behaviours. We analytically show that delivery lead time strongly influences the manufacturer’s and the retailer’s pricing strategies and profits. Our numerical studies reveal that the difference between the demand transfer ratios in the two channels with respect to delivery lead time and direct sale price, customer acceptance of the direct channel, and product type have great effects on the lead time and pricing decisions.     

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.     

Outsourcing suppliers as downstream competitors: Biting the hand that feeds

In this paper, we highlight an aspect of supplier opportunism in the outsourcing paradox that has largely been ignored by extant research – the supplier as a direct competitor of the buyer firm. In light of this paradox, we offer a game-theoretic framework in which we identify conditions under which firms could alleviate or mitigate this outsourcing problem. Our results show that apart from transaction costs, firm-level capabilities (both ordinary and dynamic) play important roles in determining the make only, buy only, or make-and-buy options a firm could exercise in countering the threat of the supplier as a potential competitor in the downstream marketplace.     

Equilibrium analysis of supply chain structures under power imbalance

This paper investigates the implications of channel power on supply chain stability in a setting where multiple suppliers sell substitutable products through a common retailer. Such supply chains have been traditionally analyzed as one- or two-stage Stackelberg non-cooperative games with all suppliers sharing balanced (equal) decision-making power. In this paper, we relax this assumption and formulate game-theoretic models to examine scenarios where one supplier can act as the Stackelberg leader. Consequently, we analyze new supply chain structures and introduce the notion of structure dominance, a novel approach to analyze the performance of supply chains that has practical implications. Thus, a decision maker can employ the concepts of structure dominance to determine whether there exist supply chain scenarios that are more stable than others, i.e., less prone to power reconfigurations, at both agent and group level. We find that power imbalance causes significant declines in supply chain profits, and the more balanced the agents are the higher their profits when demand is linear, regardless of product competition. It develops that neither the Manufacturer Stackelberg nor the Retailer Stackelberg supply chains are stable structures in our generalized setting, but that structures where power is equally split between agents provide for best stability and performance.     

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.     

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.     

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.     

Revenue-sharing versus wholesale price mechanisms under different channel power structures

We consider a supply chain channel with two manufacturers and one retailer. Each manufacturer can choose either a wholesale price contract or a revenue-sharing contract with the retailer. We discuss and compare the results of two different types of contracts under different channel power structures, to check whether it is beneficial for manufacturers to use revenue-sharing contracts under different scenarios. Then we consider a supply chain channel with one manufacturer and two retailers. Each retailer can choose either a wholesale price contract or a revenue-sharing contract with the manufacturer. We analyze the likely outcomes under different scenarios to discover whether it is beneficial to use revenue-sharing contracts.     

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.     

Reverse bullwhip effect in pricing

Price variability is one of the major causes of the bullwhip effect. This paper analyzes the impact of procurement price variability in the upstream of a supply chain on the downstream retail prices. Procurement prices may fluctuate over time, for example, when the supply chain players deploy auction type procurement mechanisms, or if the prices are dictated in market exchanges. A game theory framework is used here to model a serial supply chain. Sequential price game scenarios are investigated to show that there is an increase in retail price variability and an amplified reverse bullwhip effect on prices (RBP) under certain demand conditions.     

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.     

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.     

On stability of collaborative supplier selection

This note discusses the possibility of fair gain sharing in cooperative situations where players optimally partition themselves across a number of alternative channels. An example is group purchasing among a set of buyers facing with a range of suppliers. We introduce channel selection games as a new class of cooperative games and give a representation of their cores. With two channels (suppliers), the game has a non-empty core if the gain functions across every individual channel is supermodular.     

Supply chain organization and e-commerce: a model to analyze store-picking, warehouse-picking and drop-shipping

Across many industries, e-commerce generates substantial modifications in supply chain structures. The aim of this article is to assess different forms of existing organizations when a store-based sales network coexists with a web site order network. Three main organizational models can be detected: “store-picking”, “dedicated warehouse-picking” and “drop-shipping”. We use a “newsboy” order policy model to compare the advantages of these different models and to note the impact of some parameters on inventory and flow management policies throughout the supply chain. Several effects are presented, particularly those linked to the size of the Internet market in relation to traditional market size and market demand hazards.      

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.     

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.