New Formulation for the Vehicle Routing Problem with Stochastic Demands

The main purpose of the Vehicle Routing Problem (VRP) is to minimize the total cost of delivery. When customer demand is not considered, the total cost is only travel cost. This is obtained by solving the Traveling Salesman Problem (TSP). However, when customers' demands are stochastic (Vehicle Routing Problem with Stochastic Demands, SVRP), the vehicle may thus be unable to load the customer's demand, even if the expected demand along the route does not exceed the vehicle capacity. This situation is referred to as a failure. Therefore, in SVRP, it is necessary to minimize the sum of the travel cost obtained by solving the TSP and the additional cost incurred when delivering along the route.In previous studies, it was common to use the lower bound instead of directly calculating the value of the additional cost. In this study, we focused on calculating additional costs directly without using lower bounds. The method used here considers additional costs of multiple edges: edges that pass through the depot and edges that do not pass through the depot, for all edges connecting the depot to the customer. The method provides a new solution to find the exact value.