The heterogeneous fleet vehicle routing problem with light loads and overtime: Formulation and population variable neighbourhood search with adaptive memory

In this paper we consider a real life Vehicle Routing Problem inspired by the gas delivery industry in the United Kingdom. The problem is characterized by heterogeneous vehicle fleet, demand-dependent service times, maximum allowable overtime and a special light load requirement. A mathematical formulation of the problem is developed and optimal solutions for small sized instances are found. A new learning-based Population Variable Neighbourhood Search algorithm is designed to address this real life logistic problem. To the best of our knowledge Adaptive Memory has not been hybridized with a classical iterative memoryless method. In this paper we devise and analyse empirically a new and effective hybridization search that considers both memory extraction and exploitation. In terms of practical implications, we show that on a daily basis up to 8% cost savings on average can be achieved when overtime and light load requirements are considered in the decision making process. Moreover, accommodating for allowable overtime has shown to yield 12% better average utilization of the driver's working hours and 12.5% better average utilization of the vehicle load, without a significant increase in running costs. We also further discuss some managerial insights and trade-offs.