Optimal location-multi-allocation-routing in capacitated transportation networks under population-dependent travel times

Abstract

A capacitated location-multi-allocation-routing model is presented for a transportation network with travel times between the nodes represented by links on the network. The concept of multi-allocation arises from the possibility of allocating the population in a demand node to more than one server node. In normal conditions, travel time between two nodes is a fixed value. However, since the flow of population in a link can affect the travel time, here the impact of the population flow on link time is considered to be simultaneous. This way, distribution of the population over the network has a direct influence on the travel link times. It is assumed that all links are two-way and capacities of the server nodes and arcs for accepting population are limited. Our aim is to find optimal locations of server node(s), optimal allocation of the population in demand nodes to the server(s) and optimal allocation of the population of the nodes to different routes to reach the assigned servers so that total transportation time is minimised. First, the proposed problem is formulated as a mixed-integer non-linear programming model, followed by its suitable transformation into a mixed-integer linear programming problem. Then, a standard genetic algorithm (GA) and a heuristic algorithm combining genetic algorithm and local search (GALS) are presented to solve large instances of the problem. Finally, three sets of numerical experiments are made to compare the results obtained by CPLEX, standard GA and GALS. Numerical results show outperformance of GALS over CPLEX and the standard GA.