Supply chain network design under profit maximization and oligopolistic competition

In this paper, we model the supply chain network design problem with oligopolistic firms who are involved in the competitive production, storage, and distribution of a homogeneous product to multiple demand markets. The profit-maximizing firms select both the capacities associated with the various supply chain network activities as well as the product quantities. We formulate the governing Nash–Cournot equilibrium conditions as a variational inequality problem and identify several special cases of the model, notably, a generalization of a spatial oligopoly and a classical oligopoly problem to include design capacity variables. The proposed computational approach, which is based on projected dynamical systems, fully exploits the network structure of the problems and yields closed form solutions at each iteration. In order to illustrate the modeling framework and the algorithm, we also provide solutions to a spectrum of numerical supply chain network oligopoly design examples.This paper makes a contribution to game theoretic modeling of competitive supply chain network design problems in an oligopolistic setting.     

Dynamic supernetworks for the integration of social networks and supply chains with electronic commerce: modeling and analysis of buyer–seller relationships with computations

In this paper, we develop a dynamic supernetwork framework for the modeling and analysis of supply chains with electronic commerce that also includes the role that relationships play. Manufacturers are assumed to produce a homogeneous product and to sell it either through physical or electronic links to retailers and/or directly to consumers through electronic links. Retailers, in turn, can sell the product through physical links to consumers. Increasing relationship levels in our framework are assumed to reduce transaction costs as well as risk and to have some additional value for both sellers and buyers. Establishing those relationship levels incurs some costs that have to be borne by the decision-makers in the supernetwork, which is multilevel in structure and consists of the supply chain and the social network. The decision-makers, who are located at distinct tiers in the supernetwork, try to optimize their objective functions and are faced with multiple criteria including relationship-related ones and weight them according to their preferences. We establish the optimality conditions for the manufacturers, retailers, and consumers, derive the equilibrium conditions, and provide the variational inequality formulation. We then present the projected dynamical system, which describes the disequilibrium dynamics of the product transactions, relationship levels, and prices on the supernetwork, and whose set of stationary points coincides with the set of solutions of the variational inequality problem. We also illustrate the dynamic supernetwork model through several numerical examples, for which the explicit equilibrium patterns are computed.     

A system-optimization perspective for supply chain network integration: The horizontal merger case

In this paper, we present a new theoretical framework for the quantification of strategic advantages associated with horizontal mergers through the integration of supply chain networks. The framework is a system-optimization one in which each firm is represented as a network of economic activities associated with manufacturing, distribution, and storage and with explicit capacities imposed on the links. We present the models pre- and post-horizontal mergers and define a measure for the quantification of the gains, if any, associated with the mergers. We illustrate the framework with several numerical examples. For simple classes of mergers we derive formulae for the strategic advantages.     

Migration equilibrium and variational inequalities

"In this paper, an equilibrium model of human migration is presented which can handle many classes of migrants and locations, in addition to equalities and inequalities. The equilibrium conditions are stated and then formulated as a variational inequality problem. Qualitative properties and computational aspects are briefly discussed."     

Securing the Sustainability of Global Medical Nuclear Supply Chains Through Economic Cost Recovery,Risk Management,and Optimization

In this paper, we develop a new generalized network model for the optimization of the complex operations of medical nuclear supply chains in the case of the radioisotope molybdenum, with a focus on minimizing the total operational cost, the total waste cost, and the risk associated with this highly time-sensitive and perishable, but critical, product used in health-care diagnostics. Our model allows for the evaluation of transitioning the production and processing of the radioisotope from highly enriched uranium targets to low enriched uranium targets. A case study for North America demonstrates how our model and computational framework can be applied in practice.     

Dynamics and equilibria of ecological predator-prey networks as nature’s supply chains

In this paper, we develop a dynamic network model of ecological food webs and prove that the set of stationary points of the projected dynamical system coincides with the set of solutions of a variational inequality governing the equilibrium of predator-prey networks. We also establish the equivalence between the ecological models and supply chain network equilibrium models and highlight the connections to spatial price equilibrium problems. We propose an algorithmic scheme, provide convergence results, and apply it to a food web drawn from a fisheries application.This paper is a contribution to the interdisciplinary supply chain network literature.     

An algorithm for the single commodity spatial price equilibrium problem

This paper presents a serial decomposition algorithm for the solution of the static single commodity spatial price equilibrium problem. The computational performance of this algorithm on randomly generated examples suggests that this method is more efficient and requires no more computer storage than other algorithms previously suggested for this problem.     

Global supply chain network dynamics with multicriteria decision-making under risk and uncertainty

In this paper, we consider the dynamics of a global supply chain network economy in the presence of risk and uncertainty in which distinct speeds of adjustment are included. We assume three tiers of decision-makers: manufacturers, distributors, and retailers, who acquire the product in order to satisfy the demand at the demand markets. The manufacturers, distributors, and retailers may be based in the same or in different countries and may transact in different currencies. We allow for electronic transactions in the form of electronic commerce between the manufacturers and the retailers as well as between the distributors and the retailers since the retailers may be physical or virtual. In addition, supply-side risk and demand-side risk are handled in our formulation with the former being expressed as a multicriteria decision-making problem for each manufacturer and distributor (with distinct weights associated with the criteria) and the latter being handled with the use of uncertain demands. The proposed framework allows for the modeling and theoretical analysis of such global supply chain networks, which involve competition within a tier of decision-makers but cooperation between tiers. Numerical examples are provided for illustrative purposes.     

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.