The traveling salesman problem with cumulative costs

Abstract

In this paper, we consider a special case of the time-dependent traveling salesman problem where the objective is to minimize the sum of all distances traveled from the origin to all other cities. Two exact algorithms, incorporating lower bounds provided by a Lagrangean relaxation of the problem, are presented. We also investigate a heuristic procedure derived from dynamic programming that is able to evaluate the distance from optimality of the produced solution. Computational results for a number of problems ranging from 15 to 60 cities are given. They show that problems up to 35 cities can be solved exactly and problems up to 60 cities can be solved within 3% from optimality.

Efficient GRASP+VND and GRASP+VNS metaheuristics for the traveling repairman problem

“…Like Simchi-Levi and Berman (1991) and Bianco et al (1993), we use the nearest neighbor heuristic to derive an upper bound for the TRP. The nearest neighborhood heuristic belongs to the family of greedy algorithms and constructs an initial solution by starting from the depot (v 0 ) and repeatedly adding the closest vertex to the last-added one until all vertices have been added.…”

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

“…The timedependent travelling salesman problem (TDTSP) is a generalization of the standard TSP in which the traversal cost of an arc depends on its position in the tour [34,48,61]. When the objective of the TDTSP is to minimize the sum of distances travelled from the depot to each node, the problem is known as the TSP with cumulative cost or cumulative TSP (CTSP) [14].…”

Cumulative Vehicle Routing Problems

“…When the objective of the TDTSP is to minimize the sum of distances traveled from the depot to all nodes, the problem is known as the Traveling Salesman Problem with Cumulative Cost or the Cumulative Traveling Salesman Problem (CTSP), as defined by Bianco et al(1993). The CTSP is exemplified by pizza delivery since the time it takes the pizza to reach the customer is determined by the total travel time from the depot.…”