Team orienteering problem with stochastic time-dependent travel time

Abstract

According to United Nations, human population living in urban areas is expected to increase in the coming years. This increase will have an effect on the traffic density in the urban areas. This motivates employees whose job is to visit customers during the day, such as logistics company employees, to consider the impact of traffic density on the travel times while visiting customers. This study aims to find prior optimal tours for more than one agent to visit customers and to maxi-mize total expected profit within a given time limit while taking the uncertainties in travel times caused by traffic congestion into account. Agents are not required to visit every customer and the tour of each agent starts and ends at a certain depot node. It is assumed that the travel time to go from a customer to another customer is random and depends on the departure. We use a time-dependent travel time model that has first-in-first-out property while calculating the travel times. We propose a two-stage stochastic mixed-integer program to formulate the problem and suggest Integer L-shaped method in order to solve large-scale problem instances. In our computational study, we analyze the benefit of using stochastic solutions, and observe that Integer L-shaped method is superior to CPLEX in terms of computational time.