June Dong

A supply chain network equilibrium model

This paper develops an equilibrium model of a competitive supply chain network that can provide a benchmark for evaluating both price and product flows. This model is sufficiently general to capture both the independent behavior of various decision-makers (manufacturers, retailers and consumers) as well as the effect of their interactions. The network structure of the supply chain is identified and equilibrium conditions are derived. A finite-dimensional variational inequality formulation is established. The algorithm is applied to numerical examples to determine the equilibrium product flows and prices. Theoretical and empirical results demonstrate that solutions to supply chain network equilibrium problems with nonlinear and nonseparable functions can be computed using the modified projection method. The model provides the foundation for developing dynamic models for the study of the evolution of supply chains.

Supply Chain Networks, Electronic Commerce, and Supply Side and Demand Side Risk

In this paper, we develop a supply chain network model in which both physical and electronic transactions are allowed and in which supply side risk as well as demand side risk are included in the formulation. The model consists of three tiers of decision-makers: the manufacturers, the distributors, and the retailers, with the demands associated with the retail outlets being random. We model the optimizing behavior of the various decision-makers, with the manufacturers and the distributors being multicriteria decision-makers and concerned with both profit maximization and risk minimization. We derive the equilibrium conditions and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium pattern in terms of existence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. We illustrate the supply chain network model through several numerical examples for which the equilibrium prices and product shipments are computed. This is the first multitiered supply chain network equilibrium model with electronic commerce and with supply side and demand side risk for which modeling, qualitative analysis, and computational results have been obtained.

A supply chain network equilibrium model with random demands

Abstract In this paper, we develop a supply chain network model consisting of manufacturers and retailers in which the demands associated with the retail outlets are random. We model the optimizing behavior of the various decision-makers, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium pattern in terms of existence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. Finally, we illustrate the model through several numerical examples for which the equilibrium prices and product shipments are computed. This is the first supply chain network equilibrium model with random demands for which modeling, qualitative analysis, and computational results have been obtained.

A multiclass, multicriteria traffic network equilibrium model with elastic demand

In this paper, we develop a multiclass, multicriteria traffic network equilibrium model in which travelers of a class perceive their travel disutility or generalized cost on a route as a weighting of travel time and travel cost, each of which is flow-dependent. In addition, the weights are not only class-dependent but also link-dependent. The model is an elastic demand model and allows the demand function for each class and origin/destination (O/D) pair to depend, in general, upon the disutilities of all classes at all O/D pairs. The formulation of the governing equilibrium conditions, as well as the qualitative analysis, and the computational procedure, are based on finite-dimensional variational inequality theory. The model provides an alternative to existing multimodal and multicriteria traffic network equilibrium models and has location choice implications as well.

Supply Chain Networks and Electronic Commerce: A Theoretical Perspective

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.

Multitiered Supply Chain Networks: Multicriteria Decision—Making Under Uncertainty

In this paper, we present a supply chain network model with multiple tiers of decision-makers, consisting, respectively, of manufacturers, distributors, and retailers, who can compete within a tier but may cooperate between tiers. We consider multicriteria decision-making for both the manufacturers and the distributors whereas the retailers are subject to decision-making under uncertainty since the demands associated with the product are random. We derive the optimality conditions for the decision-makers, establish the equilibrium conditions, and derive the variational inequality formulation. We then utilize the variational inequality formulation to provide both qualitative properties of the equilibrium product shipment, service level, and price pattern and to propose a computational procedure, along with convergence results. This is the first supply chain network model to capture both multicriteria decision-making and decision-making under uncertainty in an integrated equilibrium framework.

The formulation and computation of general financial equilibrium

In this paper a model of competitive financial equilibrium is introduced, which yields the optimal composition of assets and liabilities in each sectors portfolio, as well as the market clearing prices for each instrument. The variational inequality formulation of the equilibrium conditions is then utilized to establish existence and uniqueness properties of the solution pattern. Finally, an algorithm is proposed for the computation of the equilibrium pattern; the algorithm resolves the problem into simple network subproblems which can then be solved in closed form. The algorithm is then applied to an example.

A projected dynamical systems model of general financial equilibrium with stability analysis

In this paper, we present a dynamic model of general financial equilibrium. The model assumes utility-maximizing sectors in the economy that take the prices of the financial instruments as given. The economy, in turn, determines prices of the instruments that balance the supplies and demands. The financial adjustment process is shown to satisfy a projected dynamical system. This methodology is then used to establish, under certain conditions on the utility functions, both the stability and the asymptotical stability of the equilibrium asset, liability, and price pattern. This approach unveils a dynamic approach to competitive equilibrium problems that have, heretofore, been studied, principally, in the static framework of finite-dimensional variational inequality theory.

Modeling of Supply Chain Risk under Disruptions with Performance Measurement and Robustness Analysis

In this chapter, we develop a new supply chain network model with multiple decision-makers associated at different tiers and with multiple transportation modes for shipment of the good between tiers. The model formulation captures supply-side risk as well as demand-side risk, along with uncertainty in transportation and other costs. The model also incorporates the individual attitudes towards disruption risks among the manufacturers and the retailers, with the demands for the product associated with the retailers being random. We present the behavior of the various decision-makers, derive the governing equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We also propose a weighted supply chain performance and robustness measure based on our recently derived network performance/efficiency measure and provide supply chain examples for which the equilibrium solutions are determined along with the robustness analyses. This chapter extends previous supply chain research by capturing supplyside disruption risks, transportation and other cost risks, and demand-side uncertainty within an integrated modeling and robustness analysis framework.

MULTICRITERIA NETWORK EQUILIBRIUM MODELING WITH VARIABLE WEIGHTS FOR DECISION-MAKING IN THE INFORMATION AGE WITH APPLICATIONS TO TELECOMMUTING AND TELESHOPPING

Abstract In this paper, we develop a multicriteria network equilibrium framework for modeling decision-making in the Information Age. We consider distinct classes of decision-makers, each of whom has a set of criteria associated with the decision along with weights which are variable and criterion-dependent. The decisions take place on a network in which links can be either physical, as in the case of transportation, or virtual, as in the case of telecommunications. We derive the equilibrium conditions and establish qualitative properties of the equilibrium pattern. The model enables the prediction of the number of decision-makers that will select particular choices, along with the incurred generalized costs. We then apply the modeling schema to telecommuting versus commuting and to teleshopping versus shopping decision-making.