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Since the 1990’s, network reliability has been considered as a new index for evaluating transportation networks under uncertainty. A large number of studies have been revealed in the literature in this field, which are mostly dedicated to developing relevant measures that can be utilized for the evaluation of vulnerable networks under different sources of uncertainty, such as daily traffic flow fluctuations, natural disasters, weather conditions, and so fourth. This paper addresses the resource allocation problem in vulnerable transportation networks, in which multiple performance reliability measures should be met at their desired levels, while the overall cost of upgrading links’ performances should be minimized simultaneously. For this purpose, a new approach has been considered to formulate the two well-known performance measures, connectivity and capacity reliability, along with their application in a bi-objective nonlinear mixed integer goal programming model. In order to take into account the uncertain conditions of supply, links’ capacities have been assumed to be random variables and follow normal distribution functions. A computationally efficient method has been developed that allows calculating the network-wise performance indices simply by means of a set of functions of links’ performance reliabilities. Using this approach, as the performance reliability of links are themselves functions of the random links’ capacities, they can be simply calculated through numerical integration. To achieve desirable levels for both connectivity reliability and capacity reliability (as network-wise performance reliability measures) two distinct objectives have been considered. One of the objectives seeks to maximize each of the measures regardless of what is happening to the other objective function which minimizes the budget. Since optimization models with two conflicting objectives cannot be solved directly, the well-known goal attainment multi-objective decision-making (MODM) approach has been adapted to formulate the model as a single objective model. Then the resultant single objective model has been solved through the generalized gradient method, which is a straightforward solution algorithm coded in existing commercial software such as MATLAB programming software. To show the applicability of the proposed model, numerical results are provided for a simple network. Also, to show the sensitiveness of the model to decision maker’s direction weights, the results of sensitivity analysis are presented..

Keywords: Network design, Resource allocation, Multi-objective programming, Urban transportation networks, Connectivity reliability, Capacity reliability.

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