Minimum Cost Flow-Based Integrated Model for Electric Vehicle and Crew Scheduling

Table 1

A summary of the studies related to the integrated VCSP models and algorithms.

Type	Publication	Model	Approach
Include crew considerations in VSP	[16–18]	LP dual	Heuristic
	[19, 20]	SP & CSP constraints	Branch and price
	[7] (EVCSP)	SP & CSP constraints	Adaptive large neighborhood search
Schedule vehicles heuristically in CSP	[5]	SP	Matching heuristic
	[21–23]	SC	Heuristic
	[24]	SP	Branch and cut and price
	[14, 25]	SP & side constraints	Branch and price
	[4]	SP & side constraints	Lagrangian heuristic
Change vehicle schedule in CSP	[26]	TSF	Column generation
Complete integration	[26] (No changeovers ), [27]	SC	Heuristic
	[4, 28–33], [34] (EVCSP), [35]	QAF & SP	Lagrangian heuristic
	[36]	MCF & SP	Lagrangian heuristic
	[37–40]	MCF & SP/SC	Column generation & branch and bound/price
	[41] (considering delays)	MCF & SP	Column generation
	[42]	MCF & SP	Hybrid evolutionary
	[43]	MCF & SP	Bundle method
	[44]	MCF & SP	Splitting method
	[45] (no changeovers)	MCF & SP	Valid inequality & CPLEX
	[46]	MCF & SC	—
	[47, 48]	MCF & SC	Decomposition approach
	[6]	MCF & SP	Heuristic
	[2]	TSF & SP	Column generation & Lagrangian relaxation
	[49] (Considering delays), [50]	TSF & path-based formulations	Lagrangian heuristic
	[51]	TSF & SP	Branch and price
	[52]	TSF	Matheuristic
	[53]	CM	Simulated annealing
	[54]	CM	Greedy randomized adaptive search
	[55]	CM	Variable neighborhood search
	[3] (considering the crew’s reliability)	CM	Variable neighborhood search
	[56] (no changeovers)	MCM	Heuristic
	[57, 58]	MCM	Hybrid evolutionary
	[59]	RSP	Column generation-based approach

^aSC/SP: set covering/set partitioning. ^bTSF: time-space network flow. ^cMCF: multicommodity network flow. ^dQAF: quasi-assignment network flow. ^eMCM: maximum covering model. ^fCM: constraint-based model. ^gLP: linear programming. ^hRSP: resource-constrained shortest path.