A Vehicle Routing Problem With Option for Outsourcing and Time-Dependent Travel Time

This paper studies the time-dependent vehicle routing problem with private fleet and common carriers (TDVRPPC), which provides an option to outsource the customer requests and considers real-world time-dependent travel times. The problem is commonly seen in the transportation and logistics industries as it considers the impact of changing traffic conditions on travel times, maximum working hour regulations as well as vehicle capacity constraints. The time-dependent travel time is modeled as a piecewise linear function, based on which a mixed integer programming model is proposed for the TDVRPPC. To solve this NP-hard problem, we customize a hybrid algorithm to harness an adaptive large neighborhood search algorithm for exploration and a tabu search for the exploitation of the search. Through constraint relaxation, dynamic and coordinated adjustment of diversification and intensification strengths of the hybridized procedures, as well as an effective segment-based evaluation method, the proposed algorithm performs well on newly generated test instances for the TDVRPPC and on benchmark instances for the simplified vehicle routing problem with private fleet and common carriers (VRPPC).