An Integer L-Shaped Algorithm for Time-Constrained Traveling Salesman Problem With Stochastic Travel and Service Times

Abstract

The time-constrained traveling salesman problem (TCTSP) is a variant of the classical traveling salesman problem, where only a subset of the customers can be visited due to the time limit constraint. In this paper, we consider the TCTSP with stochastic travel and service times. Given the normal working hours T and a tolerance time ΔT, the total travel and service times of a route can exceed T as long as it is within T+ΔT, though a penalty proportional to the amount in excess of T will be imposed. The problem consists of optimally selecting and sequencing a subset of customers to visit in the presence of random travel and service times to maximize the expected profit while satisfying the time limit constraint. We formulate the problem as a two-stage stochastic program with recourse, and propose an integer L-shaped solution method for solving it. Computational results show that the algorithm can solve problems with moderate size to optimality within reasonable time.

Runtime reduction techniques for the probabilistic traveling salesman problem with deadlines

“…These papers consider time constraints in the context of stochastic travel times. Teng et al [36] apply the L-shaped algorithm to the time-constrained traveling salesman problem (TCTSP) with stochastic travel and service times. In the TCTSP, the time constraint is on the length of the tour, which contrasts with this paper where the time constraints control when individual customers can be visited.…”

Optimizing practical orienteering problems with stochastic time-dependent travel times: towards congestion free routes

“…Solution methods for the OPSW or relevant problems similar to the OPSW were discussed in [21,41,42,106,107,134,138]. Note that in most of these works the term weight is used for the travel time and capacity for the time budget or t max .…”

A maritime inventory routing problem with stochastic sailing and port times

“…The VRP with stochastic travel and service times was also studied by Kenyon and Morton [13], considering stochastic programming models that minimized the expected completion time or maximized the probability of completing the routes within a given deadline. An integer L-shaped algorithm was used by Teng et al [20] to solve a time-constrained traveling salesman problem with stochastic travel and service times with up to 35 nodes. Although these papers present stochastic programming models for routing problems with uncertain travel times and service times, they do not consider heterogeneous fleets, a variable number of visits, nor inventory constraints.…”

“…Constraints (16) ensure that the sum of delivered goods should not be less than the sum of the consumption over the entire horizon T. Constraints (17) ensure that if ship v (un)loads one product at visit (i, m), then w imv must be one. Constraints (18)- (20) are the non-negativity and integrality requirements.…”