Price competition with integrated and decentralized supply chains

We consider price competition with a linear demand function and compare two cases. In the first case each distribution channel is vertically integrated, while in the second, decentralised, case the manufacturers and retailers act independently. We explore the effect of varying the level of price competition on the profits of the industry participants and demonstrate the important role played by the spread of underlying market shares. The coefficient of variation of these market shares determines whether decentralised supply chains can outperform integrated supply chains with an appropriate level of competition.     

Resale price maintenance in supply chains with general multiplicative demand

We analyze a supply chain with a Resale Price Maintenance (RPM) contract in which the manufacturer sets the retail price with a general multiplicative price–demand function and prove the existence/uniqueness of an equilibrium. We also compare the equilibrium prices and quantities, consumer surplus and total system welfare for the RPM and wholesale price contracts. We conclude that a manufacturer may capture a smaller share of the total supply chain profit despite her ability to set the retail price.     

An agent-based model of supply chains with dynamic structures

This paper proposes a common agent-based model for the simulation of MTS and MTO supply chains with dynamic structures. Based on the model, scholars can model supply chains easily. Basic characters of supply chains are proposed in the model. Agents, who are used to simulate the members of supply chains, produce appropriate products by intelligent choices. The relationships among agents are connected by their products. Different agents’ attributes are presented by their knowledge and actions of agents are introduced in the paper. Experiments are produced to show the availability of the agent-based model. The model should be available as a toolkit for the studying of dynamic supply chains.     

Consumer environmental awareness and competition in two-stage supply chains

This paper focuses on the impact of competition and consumers’ environmental awareness on key supply chain players. We consider both the production competition between partially substitutable products made by different manufacturers, and the competition between retail stores. We use two-stage Stackelberg game models to investigate the dynamics between the supply chain players given three supply chain network structures. We find that as consumers’ environmental awareness increases, retailers and manufacturers with superior eco-friendly operations will benefit; while the profitability of the inferior eco-friendly firm will tend to increase if the production competition level is low, and will tend to decrease if the production competition level is high. In addition, higher levels of retail competition may make manufacturers with inferior eco-friendly operations more likely to benefit from the increase of consumers’ environmental awareness. Moreover, as production competition intensifies, the profits of the retailers will always increase, while the profits of the manufacturers with inferior eco-friendly operations will always decrease. The profitability of the manufacturers with superior eco-friendly operations will also tend to decrease, unless consumers’ environmental awareness is high and the superior manufacturer has a significant cost advantage related to product environmental improvement.     

Retail price markup commitment in decentralized supply chains

We investigate the operational decisions and resulting profits for a supply chain facing price-dependent demand under a policy where there is an ex-ante commitment made on the retail price markup. We obtain closed-form solutions for this policy under the assumption of a multiplicative demand function and we analytically compare its performance with that of a traditional price-only policy. We compare these results to results obtained when demand follows a linear additive form. These formulations are shown to be qualitatively different as the manufacturer’s wholesale pricing decision is independent of the retail price markup commitment in the multiplicative case, but not when demand is linear additive. We demonstrate that the ex-ante commitment can lead to Pareto-improving solutions under linear additive demand, but not under the multiplicative demand function. We also consider the effect of pricing power in the supply chain by varying who determines the retail price markup.     

Trade credit competition between two retailers in a supply chain under credit-linked retail price and market demand

The paper considers a supply chain system in which the sole manufacturer supplies the same product to two retailers who compete in offering trade credit period to customers. Both the market demand and retail prices vary with the trade credit periods offered by the retailers. The manufacturer also provides a trade credit period to both the retailers to settle down their accounts. The net profit function of the supply chain is derived considering possible relationships among the trade credit periods offered by the manufacturer and the retailers and the time when each retailer receives the last payment from his customer. An algorithm is developed to find the optimal solution of the proposed model. From the numerical study, it is observed that a two-level trade credit financing can increase profits not only for the manufacturer and the retailers but also for the whole supply chain.     

Fair transfer price and inventory holding policies in two-enterprise supply chains

A key issue in supply chain optimisation involving multiple enterprises is the determination of policies that optimise the performance of the supply chain as a whole while ensuring adequate rewards for each participant.In this paper, we present a mathematical programming formulation for fair, optimised profit distribution between echelons in a general multi-enterprise supply chain. The proposed formulation is based on an approach applying the Nash bargaining solution for finding optimal multi-partner profit levels subject to given minimum echelon profit requirements.The overall problem is first formulated as a mixed integer non-linear programming (MINLP) model. A spatial and binary variable branch-and-bound algorithm is then applied to the above problem based on exact and approximate linearisations of the bilinear terms involved in the model, while at each node of the search tree, a mixed integer linear programming (MILP) problem is solved. The solution comprises inter-firm transfer prices, production and inventory levels, flows of products between echelons, and sales profiles.The applicability of the proposed approach is demonstrated by a number of illustrative examples based on industrial processes.     

Bilateral information sharing in two supply chains with complementary products

Information sharing has been regarded as a major way to promote collaboration or to optimize overall supply chain performance. Most of the literature has focused on unilateral information sharing in a supply chain with single or substitutable products. This paper investigates bilateral information sharing in two supply chains with complementary products, and formulates four decision models based on different information sharing patterns. Our results show that (i) information sharing always benefits the manufacturer, and benefits the retailer and the whole supply chain under certain conditions; (ii) information sharing increases/decreases the positive effect of the retailer’s/manufacturer’s forecast on the optimal pricing strategies in its own supply chain; however, its impact depends on the parameter conditions in the other complementary supply chain.     

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.     

Equilibrium price as a coincidence point of two mappings

The existence of an equilibrium price vector in a nonlinear market model is analyzed. In the model, the demand and supply functions are obtained by maximizing the producer utility and profit, respectively. Sufficient conditions for the existence of an equilibrium price vector and its stability with respect to small perturbations in the model are given. The results are consequences of theorems on the existence and stability of coincidence points in the theory of α-covering mappings.     

Asymmetric dynamic price competition with uncertainty

We consider a dynamic setting-price duopoly model in which a dominant (leader) firm moves first and a subordinate (follower) firm moves second. We suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We analyse the effect of the production costs uncertainty on the profits of the firms, for different values of the intercept demand parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Social responsibility allocation in two-echelon supply chains: Insights from wholesale price contracts

Corporate social responsibility (CSR) is considered in a two-echelon supply chain consisting of an upstream supplier and a downstream firm that are bound by a wholesale price contract. CSR performance (the outcome of CSR conduct) of the whole supply chain is gauged by a global variable and the associated cost of achieving this CSR performance is only incurred by the supplier with an expectation of being shared with the downstream firm via the wholesale price contract. As such, the key issue is to determine who should be allocated as the responsibility holder with the right of offering the contract and how this right should be appropriately restricted. Game-theoretical analyses are carried out on six games, resulting from different interaction schemes between the supplier and the firm, to derive their corresponding equilibriums. Comparative institutional analyses are then conducted to determine the optimal social responsibility allocation based on both economic and CSR performance criteria. Main results are furnished in a series of propositions and their implications to the real-world business practice are discussed. The key findings are threefold: under the current model settings: (1) the optimal allocation scheme is to assign the supplier as the responsibility holder with appropriate restrictions on the corresponding rights to determine the wholesale price; (2) inherent conflict exists between the economic and CSR performance criteria and, hence, the two maxima cannot be achieved simultaneously; and (3) although integrative channel profit is not attainable, the system-wide profit will be improved by implementing optimal social responsibility allocation schemes.     

Repeated price competition with increasing marginal costs

We consider a repeated price setting game with firms facing increasing marginal costs and positive fixed costs. Besides setting prices, firms may decide to be not active. Since it is well known that there is no Nash-equilibrium in pure strategies in the stage game, we look for pure strategy equilibria in the repeated game and give a full characterization of all stationary symmetric equilibrium outcomes, supported by optimal penal codes (in pure strategies). [JEL-classification: D43, L13]     

Dynamic price competition with discrete customer choices

For many years, dynamic pricing has proven to be an effective tool to increase revenue in the airline and other service industries. Most studies, however, focused on monopolistic models and ignored the fact that nowadays consumers can easily compare prices on the Internet. In this paper, we develop a game-theoretic model to describe real-time dynamic price competition between firms that sell substitutable products. By assuming the real-time inventory levels of all firms are public information, we show the existence of Nash equilibrium. We then discuss how a firm can adapt if it knows only the initial – but not the real-time – inventory levels of its competitors. We compare a firm’s expected revenue under different information structures through numerical experiments.     

A note on competitive supply chains with generalised supply costs

This note generalises models from two influential papers in the theory of supply chain outsourcing under competition: 9 and 1. The first paper studies the impact of competitive intensity on the outsourcing decision from the supplier’s point of view for linear supply cost; the second paper examines the impact of supply economies of scale from the retailer’s point of view when selling perfectly substitutable products. By considering competitive intensity and supply economies of scale simultaneously, we find that equilibrium channel structures are primarily determined by the competitive intensity, which is true even under supply diseconomies of scale; the key message in the second paper of scale economies driving retailer’s outsourcing supply decision is highly dependent on the assumption of perfect substitutes. Our finding has no qualitative difference when either the suppliers or the retailers are modeled as the channel leader and make the outsourcing decisions.     

Bargaining in competing supply chains with uncertainty

Substantial literature has been devoted to supply chain coordination. The majority of this literature ignores competition between supply chains. Moreover, a significant part of this literature focuses on coordination that induce the supply chain members to follow strategies that produce the equilibria chosen by a vertically integrated supply chain. This paper investigates the equilibrium behavior of two competing supply chains in the presence of demand uncertainty. We consider joint pricing and quantity decisions and competition under three possible supply chain strategies: Vertical Integration (VI), Manufacturer’s Stackelberg (MS), and Bargaining on the Wholesale price (BW(α), α is the bargaining parameter) over a single or infinitely many periods. We show that, in contrast to earlier literature, using VIVI (VI in both chains) is the unique Nash Equilibrium over one period decision, while using MSMS or BW(α)BW(α) may be Nash Equilibrium over infinitely many periods.     

On the equivalence of quantity competition and supply function competition with sunk costs

This paper considers competition in supply functions in a homogeneous goods market in the absence of cost or demand uncertainty. In order to commit to a supply schedule, firms are required to build sufficient capacity to produce any quantity that may be prescribed by that schedule. When the cost of extra capacity (given the level of sales) is strictly positive, any Nash equilibrium outcome of supply function competition is also a Nash equilibrium outcome of the corresponding Cournot game, and vice-versa. Conversely, when the cost-savings from reducing output (given the capacity level) are sufficiently small, any outcome of iterated elimination of weakly dominated strategies in the supply function game is also an outcome of the same process in Cournot, and vice-versa.     

Coordination of supply chains with bidirectional option contracts

In this paper we develop a supply contract for a two-echelon manufacturer–retailer supply chain with a bidirectional option, which may be exercised as either a call option or a put option. Under the bidirectional option contract, we derive closed-form expressions for the retailer’s optimal order strategies, including the initial order strategy and the option purchasing strategy, with a general demand distribution. We also analytically examine the feedback effects of the bidirectional option on the retailer’s initial order strategy. In addition, taking a chain-wide perspective, we explore how the bidirectional option contract should be set to attain supply chain coordination.     

On the efficiency of price competition

We study the efficiency of price competition among multi-product firms in differentiated oligopolies. Under a general affine demand model, we show that total surplus (sum of industry profit and consumers’ surplus) under competition is at least 75% of the maximum total surplus achievable by a centralized planner. We also show, in contrast to more stylized oligopoly models, that price collusion can increase total surplus and that competition does not, in general, yield a Pareto efficient trade-off between industry profit and consumers’ surplus. However, the maximum deviation of total surplus from Pareto optimality is less than 10%. These results have implications regarding the effectiveness of current anti-trust regulations.