The secure time-dependent vehicle routing problem with uncertain demands

This paper addresses the transportation of valuable goods in which security carriers are interested to optimize the operating costs and the vehicle routes’ security. In real operations, route planning and scheduling are normally performed manually based on individual experience. Hereupon, an optimizing approach should be developed to target the robbery risk reduction and the distribution network’ operational costs. Facing the dangerous nature of operations, some considerations play an important role, including demand fluctuations and traffic congestion of the urban environment. To handle these issues, we respectively benefit from the robust optimization theory and considering time-dependent travel speeds with satisfying the “first-in-first-out” property. This paper proposes a rich vehicle routing problem denoted by the secure time-dependent vehicle routing problem with time windows including pickup and delivery with uncertain demands (S-TD-VRPTWPD-UD). A mathematical formulation and an efficient solution approach combining the greedy randomized adaptive search procedure (GRASP) and the iterated local search (ILS) are developed to minimize the predictability of route plans using an integrated risk index, besides the travel costs. Extensive computational experiments on this problem are performed to analyze the impact of the demand uncertainty and the speed time-dependency and to show the efficiency of the GRASP×ILS implementation. The results show the significant improvements due to the time-dependency as well as the extra cost of protecting the model against the worst-case scenario of demand requests by deriving the robust counterpart of the S-TD-VRPTWPD-UD.