Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost

•Addressed a VRP variant that considers stochastic demands and weight-related cost.•Adopted the a priori optimization solution concept to deal with the problem.•Proposed a novel and flexible recourse strategy.•Implemented three ALNS heuristics to solve the problem.•Generated test instances and benchmark results for future researchers of the problem. The vehicle routing problem (VRP) with stochastic demands and weight-related cost is an extension of the VRP. Although some researchers have studied the VRP with either stochastic demands or weight-related cost, the literature on this problem is quite limited. We adopt the a priori optimization to tackle this problem and propose a dynamic programming to compute the expected cost of each route. We develop the adaptive large neighborhood search heuristics equipped with several approximate methods for the problem. To evaluate our heuristics, we generate 84 test instances. Computational results demonstrate the performance of our heuristics and can serve as benchmarks for future researchers.