A supply chain network equilibrium model

Netnomics, 2002

In this paper, we develop a framework for the formulation, analysis, and computation of solutions to supply chain network problems in the presence of electronic commerce. Specifically, we consider manufacturers who are involved in the production of a homogeneous product and can now sell and have delivered the product not only to retailers but also directly to consumers. In addition, the manufacturers can transact with the retailers electronically. We assume that both the manufacturers and the retailers seek to maximize their profits, whereas the consumers take both the prices charged by the retailers and the manufacturers, along with the associated transaction costs, in making their consumption decisions. We identify the network structure of the problem, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We then utilize variational inequality theory to obtain qualitative properties of the equilibrium pattern. In addition, we propose a continuous time adjustment process for the study of the disequilibrium dynamics and establish that the set of stationary points of the resulting projected dynamical system coincides with the set of solutions of the variational inequality problem. Finally, we apply an algorithm for the determination of equilibrium prices and product shipments in several supply chain examples. This paper synthesizes Business-to-Consumer (B2C) and Business-to-Business (B2B) decision-making in a supply chain context within the same framework.

developed a three tiered supply chain net-work equilibrium model consisting of manufacturers, retailers, and consumers, who may compete within a tier but cooperate between tiers. Using a variational inequality formulation, the equilibrium production outputs, shipments, and consumption quantities, along with the prices of the product associated with the different tiers could then be determined with an iterative computational procedure. further extended the basic framework to incorporate electronic commerce whereas focused on the dynamics of supply chain networks. Subsequently, Dong, Zhang, and Nagurney developed a supply chain network equilibrium model with random demands associated with the product at different retail outlets and formulated and solved the model as a variational inequality problem. Our work is similar in spirit, although derived from an entirely different perspective and application setting, to that of , who constructed a general network model of production, along with its variational inequality formulation.

Journal of Revenue and Pricing Management, 2017

In a supply chain, the importance of information elicitation from the supply chain players is vital to design supply chain network. The rationality and self-centredness of these players causes the information asymmetry in the supply chain and thus situation of conflict and non-participation of the players in the network design process. The supply chain players' non-participation or reluctance to participate in supply chain contract is due to the dynamics of the system evolving with many competitive players in supply chain. In this paper, a game theoretical dynamic pricing model has been proposed to elicit the information from the players. With the objective of maximizing the social utility, efforts have been made to value behavioural issues of supply chain. On the other hand, the reluctance of player due to the information asymmetry is measured in the form of inertia experienced by the players due to anxiety and dynamics in the market. Distinguishing cases based on level of risk and variety of product are considered to show the effect of inertia on social utility and corresponding output for each echelon of supply chain. The paper provides supply chain managers an efficient decision making ability to achieve conflict-free outcome with the maximum utility.

Iranian Journal of Management Studies, 2017

This paper discusses a problem in which decentralized supply chains enter the market simultaneously with no existing rival chains, shape the supply chains’ networks, and set wholesale and retail prices in a noncooperative manner. All the chains produce either identical or highly substitutable products. Customer demand is elastic and price-dependent. A three-step algorithm is proposed to solve this problem. Step one considers the supply chains’ potential network structures. Step two is based on a finite-dimensional variational inequality formulation and is solved by a modified projection method to determine equilibrium prices. Step three selects the equilibrium locations to shape the chains’ equilibrium network structure with the help of the Wilson algorithm. Finally, this approach is applied to a real-world scenario, and the results are discussed. Moreover, sensitivity analyses are conducted.

2020

2002

This paper presents a theoretical framework for supply chain network modeling, analysis, and computation in the presence of competition, in which all the decision-makers, who are located at distinct tiers of the network, are multicriteria decision-makers. In particular, in this framework, transportation time and transportation cost are explicit criteria and these can depend on the service level provided. The optimality conditions of the different tiers of decision-makers, consisting of manufacturers, retailers, and consumers are derived, as well as the equilibrium conditions of the integrated model. The variational inequality formulation of the governing equilibrium conditions is then utilized to obtain qualitative properties as well as a computational procedure for the determination of the equilibrium product shipments between the tiers of the network, the prices, as well as the service levels.

2007

In this paper, we present a multitiered dynamic supply chain network equilibrium modeling framework in which the decision-makers have sufficient information about the future and seek to determine their optimal plans that maximize their profits over the multiperiod planning horizon. We construct the finite-dimensional variational inequality governing the equilibrium of the multiperiod competitive supply chain network. The model allows us to investigate the interplay of the heterogeneous decision-makers in the supply chain in a dynamic setting, and to compute the resultant equilibrium pattern of product outputs, transactions, inventories, and product prices. We then establish the supernetwork equivalence of the multiperiod supply chain model with a properly configured transportation network, which provides a new interpretation of the equilibrium conditions of the former in terms of paths and path flows. This framework offers great modeling flexibility so that, for example, transportation delay and/or perishable products can be easily handled, as we also demonstrate. Numerical examples are provided to illustrate how such multiperiod supply chain problems can be reformulated and solved as transportation network equilibrium problems in practice.

Environment and Planning B-planning & Design, 2002

In this paper, we propose a multilevel network perspective for the conceptualization of the dynamics underlying supply chains in the presence of competition. The multilevel network consists of: the logistical network, the informational network, and the financial network. We describe the behavior of the network decision-makers, which are spatially separated, and which consist of the manufacturers/producing firms, the retailers, and the consumers located at the demand markets. We propose a projected dynamical system, along with stability analysis results, that captures the adjustments of the commodity shipments and the prices over space and time. A discrete-time adjustment process is described and implemented in order to illustrate the evolution of the commodity shipments and prices to the equilibrium solution in several numerical examples.

Journal of Global Optimization, 2017

This paper develops a supply chain network game theory framework with multiple manufacturers/producers, with multiple manufacturing plants, who own distribution centers and distribute their products, which are distinguished by brands, to demand markets, while maximizing profits and competing noncooperatively. The manufacturers also may avail themselves of external distribution centers for storing their products and freight service provision. The manufacturers have capacities associated with their supply chain network links and the external distribution centers also have capacitated storage and distribution capacities for their links, which are shared among the manufacturers and competed for. We utilize a special case of the Generalized Nash Equilibrium problem, known as a variational equilibrium, in order to formulate and solve the problem. A case study on apple farmers in Massachusetts is provided with various scenarios, including a supply chain disruption, to illustrate the modeling and methodological framework as well as the potential benefits of outsourcing in this sector.

Omega, 2013

In this paper, a closed-loop supply chain network is investigated with decentralized decision-makers consisting of raw material suppliers, retail outlets, and the manufacturers that collect the recycled product directly from the demand market. We derive the optimality conditions of the various decisionmakers, and establish that the governing equilibrium conditions can be formulated as a finitedimensional variational inequality problem. We establish convergence of the proposed algorithm that can allow for the discussion of the effects of competition, distribution channel investment, yield and conversion rates, combined with uncertainties in demand, on equilibrium quantity transactions and prices. Numerical examples are provided for illustration.