Vehicle Routing Problems with Fuel Consumption and Stochastic Travel Speeds

Table 1

A comparison of existing vehicle routing models.

	Reference	Stochastic travel speed	Stochastic service time	Stochastic demand	Objective function	Weight	Time window	Independent decision variables	Solution approach
Uncertain VRP	Figliozzi [36]	No	Yes	No	Vehicle cost; travel time	No	Yes	Routes; service time	New metaheuristic
	Errico et al. [37]	No	Yes	No	Cost	No	Yes	Routes; service time	Column generation; branch-price-and-cut algorithms
	Marinaki and Marinakis [38]	No	No	Yes	Expected length	Yes	No	Route	Glowworm swarm optimization
	Sarasola et al. [39]	No	No	Yes	Total distance; lateness penalty	No	No	Route	Variable neighborhood search
	Zhang et al. [19]	No	No	Yes	Travel time; earliness penalty; lateness penalty	No	Yes	Route	Dynamic programming
Green VRP	Bektaş and Laporte [34]	No	No	No	Driver cost; operational cost; emissions cost	Yes	Yes	Route; start time	CPLEX solver
	Jabali et al. [40];	No	Yes	No	Driver cost; fuel cost; emissions cost	No	Yes	Routes; speed; route start time	Tabu search
	Xiao et al. [35]; Kuo [31]	No	No	No	Fuel consumption	Yes	No	Routes	Simulated annealing
	Franceschetti et al. [41]	No	Only two fixed periods	No	Emissions cost; driver wage	Yes	Yes	Routes; speed; departure time	MIP & DSOP algorithm
	Xiao and Abdullah [42]	No (time-dependent speed)	No	No	CO2 emissions; travel time; travel distance	Yes	Yes	Routes; travel distance in each period; time	Dynamic programming
	This paper	Yes	No	No	Fuel consumption; vehicle cost	Yes	No	Routes; vehicle load on each arc	MIP & improved simulated annealing