Minimum cost path problem for Plug-in Hybrid Electric Vehicles

• We introduce minimum cost path problem for PHEVs and show that it is NP-complete.
• We present an MIQCP formulation as an exact solution methodology.
• We also present a dynamic programming based and a shortest path based heuristic.
• Our study is the first that addresses the battery degradation cost in MCPP context.
• We provide significant insights on the economics of PHEVs.

We introduce a practically important and theoretically challenging problem: finding the minimum cost path for PHEVs in a road network with refueling and charging stations. We show that this problem is NP-complete and present a mixed integer quadratically constrained formulation, a discrete approximation dynamic programming heuristic, and a shortest path heuristic as solution methodologies. Practical applications of the problem in transportation and logistics, considering specifically the long-distance trips, are discussed in detail. Through extensive computational experiments, significant insights are provided. In addition to the charging infrastructure availability, a driver’s stopping tolerance arises as another critical factor affecting the transportation costs.