We analyze a general model in which, at each echelon of the supply process, an arbitrary number of firms compete, offering one or multiple products to some or all of the firms at the next echelon, with firms at the most downstream echelon selling to the end consumer. At each echelon, the offered products are differentiated and the firms belonging to this echelon engage in price competition. The model assumes a general set of piece-wise linear consumer demand functions for all products (potentially) brought to the consumer market, where each product's demand volume may depend on the retail prices charged for all products; consumers' preferences over the various product/retailer combinations are general and asymmetric. Similarly the cost rates incurred by the firms at the most upstream echelon are general as well.We initially study a two-echelon sequential oligopoly with competing suppliers, each selling multiple products through a pool of multiple competing retailers. We characterize the equilibrium behavior under linear price-only contracts. In the second stage, given wholesale prices selected in the first stage, all retailers simultaneously decide on their retail prices to maximize their total profits among all products of all suppliers they choose to do business with. In the first stage, the suppliers anticipate the retailers' responses and all suppliers simultaneously maximize their total profits from all channels by selecting the wholesale prices. We show that in this two-stage competition model, a subgame perfect Nash equilibrium always exists. Multiple subgame perfect equilibria may arise but, if so, all equilibria are equivalent in the sense of generating unique demands and profits for all firms. We subsequently generalize our results to supply chain models with an arbitrary set of echelons, and show how all equilibrium performance measures can be computed with an efficient recursive scheme. Moreover, we establish how changes in the structure of the supply chain network, or changes in the model parameters, in particular, exogenous cost rates, or intercept values in the demand functions, impact on the system-wide equilibrium. These comparative statics results allow for the quantification of cost pass-through effects and the measurement and characterization of the brand value of different retailers and suppliers.

We analyze a general model in which, at each echelon of the supply process, an arbitrary number of firms compete, offering one or multiple products to some or all of the firms at the next or possibly subsequent echelons or directly to the end consumer. At each echelon, the offered products are differentiated and the firms belonging to this echelon engage in price competition. The model assumes a general set of piece-wise linear consumer demand functions for all products (potentially) brought to the consumer market, where each product's demand volume may depend on the retail prices charged for all products; consumers' preferences over the various product/retailer combinations are general and asymmetric. Similarly the cost rates incurred by the firms at the most upstream echelon are general as well. We initially study a two-echelon sequential oligopoly with competing suppliers, each selling multiple products indirectly through a pool of multiple competing retailers or directly to end consumers. In some cases, a supplier may choose to sell some or all of its products simultaneously via its direct sales channel and indirectly via some or all of the retailers. We characterize the equilibrium behavior under linear price-only contracts. In the second stage, given wholesale prices and prices of direct sales channels selected in the first stage, all retailers simultaneously decide on their retail prices to maximize their total profits among all products of all suppliers they choose to do business with. In the first stage, the suppliers anticipate the retailers' responses and all suppliers simultaneously maximize their total pro ts from all channels direct or indirect channels by selecting the wholesale prices and direct sales channel prices. We show that in this two-stage competition model, a subgame perfect Nash equilibrium always exists. Multiple subgame perfect equilibria may arise but, if so, all equilibria are equivalent in the sense of generating unique demands and profits for all firms. We subsequently generalize our results to supply chain models with an arbitrary set of echelons, and show how all equilibrium performance measures can be computed with an efficient recursive scheme. The model may, also be used to evaluate the impact of various structural changes in the supply chain network.

This book lays the foundations for quality modeling and analysis in the context of supply chains through a synthesis of the economics, operations management, as well as operations research/management science literature on quality. The reality of today's supply chain networks, given their global reach from sourcing locations to points of demand, is further challenged by such issues as the growth in outsourcing as well as the information asymmetry associated with what producers know about the quality of their products and what consumers know. Although much of the related literature has focused on the micro aspects of supply chain networks, considering two or three decision-makers, it is essential to capture the scale of supply chain networks in a holistic manner that occurs in practice in order to be able to evaluate and analyze the competition and the impacts on supply chain quality in a quantifiable manner. This volume provides an overview of the fundamental methodologies utilized in this book, including optimization theory, game theory, variational inequality theory, and projected dynamical systems theory. It then focuses on major issues in today's supply chains with respect to quality, beginning with information asymmetry, followed by product differentiation and branding, the outsourcing of production, from components to final products, to quality in freight service provision. The book is filled with numerous real-life examples in order to emphasize the generality and pragmatism of the models and tools. The novelty of the framework lies in a network economics perspective through which the authors identify the underlying network structure of the various supply chains, coupled with the behavior of the decision-makers, ranging from suppliers and manufacturers to freight service providers. What is meant by quality is rigorously defined and quantified. The authors explore the underlying dynamics associated with the competitive processes along with the equilibrium solutions. As appropriate, the supply chain decision-makers compete in terms of quantity and quality, or in price and quality. The relevance of the various models that are developed to specific industrial sectors, including pharmaceuticals and high technology products, is clearly made. Qualitative analyses are provided, along with effective, and, easy to implement, computational procedures. Finally, the impacts of policy interventions, in the form of minimum quality standards, and their ramifications, in terms of product prices, quality levels, as well as profits are explored. The book is filled with many network figures, graphs, and tables with data.

In this paper, we develop a supply chain network game theory model with product differentiation, possible outsourcing of production and distribution, and quality and price competition. The original firms compete with one another in terms of in-house quality levels and product flows, whereas the contractors, aiming at maximizing their own profits, engage in competition for the outsourced production and distribution in terms of prices that they charge and their quality levels. The solution of the model provides each original firm with its optimal in-house quality level as well as its optimal in-house and outsourced production and shipment quantities that minimize the total cost and the weighted cost of disrepute, associated with lower quality levels and the impact on a firm's reputation. The governing equilibrium conditions of the model are formulated as a variational inequality problem. An algorithm, which provides a discrete-time adjustment process and tracks the evolution of the product flows, quality levels, and prices over time, is proposed and convergence results given. Numerical examples are provided to illustrate how such a supply chain network game theory model can be applied in practice. The model is relevant to products ranging from pharmaceuticals to fast fashion to high technology products.

We address a generic price competition model in an industry with an arbitrary number of competitors, each offering all or a subset of a given line of N products. The products are substitutes in the sense that the demand volume of each product weakly increases whenever the price of another product increases. The cost structure is linear, with arbitrary cost rates.Our demand model is the unique regular extension of a set of demand functions that are affine in a limited polyhedral subset of the price space. A set of demand functions is regular if it satisfies the following conditions: under any given price vector, when some product is priced out of the market, i.e., has zero demand, any increase of its price has no impact on the demand volumes. Depending on the set of prices selected by the competing firms, a different product assortment is offered on the market.We characterize the equilibrium prices, product assortment and sales volumes in the price competition model, under this demand model. Under minimal conditions, we show that a pure Nash equilibrium always exists; while multiple price equilibria may arise, they are equivalent in the sense of generating an identical product assortment and sales volumes.

More than ever before the success of a company heavily depends on its supply chain and how efficient the network. A supply chain needs to be configured in such a manner as to minimize cost while still maintaining a good quality level to satisfy the end user and to be efficient, designing for the network and the whole chain is important. Including the cost of quality into the process of designing the network can be rewording and revealing. In this research the concept of cost of quality as a performance measure was integrated into the supply chain network designing process for a supply chain concerned with multi products multi components. This research discusses how this supply chain can be mathematically modeled, solutions for the resulted model and finally studied the effect of the inclusion of the quality as a parameter on the result of the deigning process. Nonlinear mixed integer mathematical model was developed for the problem and for solving the model two solutions based on Genetic algorithm and Tabu Search were developed and compared. The results and analysis show that the solution based on the Genetic algorithm outperforms the Tabu Search based solution especially in large size problems. In addition, the analysis showed that the inclusion of the cost of quality into the model effect the designing process and changes the resultant routes.