This paper proposes environmental impact assessment indices to evaluate the environmental effects of link capacity degradation in transportation (road) networks. The indices are applicable in the case of either user-optimizing or system-optimizing behavior. We also construct environmental link importance indicators that allow for the ranking of links in transportation networks in terms of their environmental importance, should they be removed/destroyed. Numerical transportation network examples illustrate the proposed quantitative environmental indicators and further substantiate that system-optimizing behavior does not necessarily lead to reduced emissions.

In this paper we develop a rigorous modeling and analytical framework for the design of sustainable supply chain networks. We consider a firm that is engaged in determining the capacities of its various supply chain activities, that is, the manufacturing, storage, and distribution of the product to the demand locations. The firm is faced with both capital costs associated with constructing the link capacities as well as the links' operational costs. Moreover, the firm is aware of the emissions generated associated with the alternative manufacturing plants, storage facilities, and modes of transportation/shipment, which may have different levels of emissions due, for example, to distinct technologies of, respectively, production, storage, and transportation. The firm is assumed to be a multicriteria decisionmaker who seeks to not only minimize the total costs associated with design/construction and operation, but also to minimize the emissions generated, with an appropriate weight, which reflects the price of the emissions, associated with the various supply chain network activities. We provide both the network optimization modeling framework and an algorithm, which is then applied to compute solutions to a spectrum of numerical sustainable supply chain design examples in order to illustrate our approach.

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The Braess Paradox is the counterintuitive phenomenon that can occur in a useroptimized network system, such as a transportation network, where adding an additional link to the network increases the cost (travel time) for every user. In electrical circuits, electrons, analogous to drivers in a transportation network, traverse the network so that no electron can unilaterally change its cost (voltage drop) from an origin to a destination. In this paper, we show that the Braess Paradox can occur in electrical circuits consisting of diodes and resistors. We report measurements confirming the occurrence of the Braess Paradox in two different circuits, one with highly nonlinear link cost functions (I-V characteristics). These measurements show that the voltage increases, rather than decreases, when a link is added to the circuit under constant demand (current). This discovery identifies novel circuits in which the voltage and current can be independently adjusted. It also yields insights into the Braess paradox and transportation networks through a new computational mechanism.

In this paper, we take up the timely topic of the modeling, analysis, and solution of refugee migration networks. We construct a general, multiclass, multipath model, determine the governing equilibrium conditions, and provide alternative variational inequality formulations in path flows and in link flows. We also demonstrate how governmental imposed regulations associated with refugees can be captured via constraints. We provide qualitative properties and then establish, via a supernetwork transformation, that the model(s) are isomorphic to traffic network equilibrium models with fixed demands. Illustrative examples are given, along with numerical examples, inspired by a refugee crisis from Mexico to the United States, which are solved using the Euler method embedded with exact equilibration. The work sets the foundation for the development of additional models and algorithms and also provides insights as to who wins and who loses under certain refugee regulations.

In this paper, we construct a novel game theory model for multiple humanitarian organizations engaged in disaster relief. Each organization is faced with a two-stage stochastic optimization problem associated with the purchase and storage of relief items pre-disaster, subject to a budget constraint, and, if need be, additional purchases and shipments post the disaster. The model integrates logistical and financial components, in that the humanitarian organizations compete for financial donations, as well as freight service provision, and each seeks to maximize its expected utility. The expected utility function of each humanitarian organization depends on its strategies and on those of the other organizations, and their feasible sets do, as well, since the organizations are subject to common lower and upper bound demand constraints. The governing concept is that of a stochastic generalized Nash equilibrium. We provide alternative variational inequality formulations of the model and propose an algorithmic scheme, which at each iteration yields closed form expressions for the product purchase/storage/shipment variables and the associated constraint Lagrange multipliers. Numerical examples illustrate the modeling and computational framework.

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