Vehicle Routing Problems with Fuel Consumption and Stochastic Travel Speeds

Abstract

Conventional vehicle routing problems (VRP) always assume that the vehicle travel speed is fixed or time-dependent on arcs. However, due to the uncertainty of weather, traffic conditions, and other random factors, it is not appropriate to set travel speeds to fixed constants in advance. Consequently, we propose a mathematic model for calculating expected fuel consumption and fixed vehicle cost where average speed is assumed to obey normal distribution on each arc which is more realistic than the existing model. For small-scaled problems, we make a linear transformation and solve them by existing solver CPLEX, while, for large-scaled problems, an improved simulated annealing (ISA) algorithm is constructed. Finally, instances from real road networks of England are performed with the ISA algorithm. Computational results show that our ISA algorithm performs well in a reasonable amount of time. We also find that when taking stochastic speeds into consideration, the fuel consumption is always larger than that with fixed speed model.

Vehicle Routing with Space- and Time-Correlated Stochastic Travel Times: Evaluating the Objective Function

“…As pointed out earlier, some papers build on the assumption that customer-to-customer speeds are independent, despite the fact that this cannot be the case in real-world road networks with sufficient traffic flow. Apart from this, we see that Tas et al (2013Tas et al ( , 2014, Feng et al (2017) use distribution functions (so not scenarios) that can be added along paths, and these approaches are distinctly using stochastic independence. In Huang et al (2017) and Han et al (2014), the scenarios of travel speeds are assumed given, whereas the scenarios are sampled from a truncated normal distribution in Lee et al (2012).…”

“…Note that there are papers that use the assumption of independent customer-pair travel times (Tas et al 2013, Feng et al 2017. This can of course be seen as an approximation of real-world travel times.…”

The role of operational research in green freight transportation

“…Feng et al [47] model average speed on arcs between customers through a normal distribution. The presented mathematical model is based on the CEM and minimizes expected total cost including expected fuel consumption.…”

Vehicle Routing Problem with Deadline and Stochastic Service Times: Case of the Ice Cream Industry in Santiago City of Chile

“…The main challenge of these metaheuristics is to solve large combinatorial optimization problems in an adequate time period. Different authors have used metaheuristic algorithms to solve VRP: local search [24], simulated annealing [25], greedy randomized adaptive search procedure (GRASP) [26], swarm intelligence [27], tabu search (TS) [28,29], genetic algorithms [30], colony optimization [31], reactive search [32], and maximum coverage [33].…”