A time-dependent green location-routing problem with variable speed of vehicles

Recently Green Location-Routing Problem (GLRP) has been considered by many researchers. The GLRP includes location for depots and routing the vehicles simultaneously by considering environmental aspects. In this work an extension of GLRP in the presence of traffic congestion and based on variable speed is presented. The speed of vehicles (and hence the travel time), fuel consumption and environmental effects are not only dependent on the distance traveled but also they are dependent on the traffic congestion at a different time of the day, as well considered in this paper. For the addressed problem, a nonlinear mixed-integer programming formulation is delivered and then a set of preprocessing rules to linearize the formulation is done. The objective of the proposed model is to minimize the fixed cost of operating depots, delayed and early servicing penalties as well as the costs of the CO2 emissions and the fuel consumption. The amount of fuel consumption and emissions are measured by a widely used comprehensive modal emission model. In the end, a heuristic algorithm based on the PSO algorithm is proposed to solve generated test instances. Computational results over test instances confirm the proposed algorithm can find optimal or near-optimal solutions.