Vehicle routing problem with time windows having stochastic customers demands and stochastic service times: Modelling and solution

Abstract

On-time and foolproof demand satisfaction has gained attention in today’s transportation and logistics industries due to their direct impact on business success. However, the uncertainty in customer’s demand, travel times or service times make it difficult to achieve 100% accuracy of these objectives. In the present study, one such issue has been considered as vehicle routing problem with time windows having stochastic demands and stochastic service times. To address this problem, a mathematical model has been developed which tries to maximize customer’s satisfaction and at the same time minimize total transportation cost. A modified ant colony system is proposed to solve the developed mathematical model. Numerical results on suitably modified datasets of Solomon benchmarks show that the proposed approach provides low cost solutions while maximizing the number of customers served and minimizing the penalties imposed due to late deliveries with little increase in total travelled distance. Certain penalties formulations provide several managerial insights to decision makers in the transportation industry.