A Decomposition Algorithm for the Consistent Traveling Salesman Problem with Vehicle Idling

Abstract

The consistent traveling salesman problem aims to identify minimum-cost routes to be followed by a single vehicle so as to provide a set of customers with service that adheres to arrival-time consistency across the multiple time periods of a planning horizon. In this paper, we address this problem via a new, exact algorithm that decomposes the problem into a sequence of single-period traveling salesman problems with time windows within a branch-and-bound search procedure. The new algorithm is highly competitive, as it is able to solve to guaranteed optimality instances with up to 100 customers requiring service over a five-period horizon, effectively doubling the size of instances that were solvable by the previous state of the art. Furthermore, and in contrast to all previous approaches, the new algorithm accounts for route duration limits, whenever applicable, as well as incorporates the flexibility for the vehicle to idle before providing service to a customer. We in fact show that, for the benchmark instances we considered, the cost of implementing consistent routes can be reduced significantly if the vehicle is allowed to idle en route, further motivating the need for algorithmic schemes to incorporate this realistic option.

A scenario decomposition algorithm for strategic time window assignment vehicle routing problems

“…To the best of our knowledge, most of these approaches are heuristic in nature, and are based on the concept of generating a "template" routing plan that services only the most frequent customers; the daily routes are derived from the template by appropriately modifying it in a way that satisfies all service consistency requirements, in particular, driver and arrival-time consistency. With a focus on trying to address purely the requirement of arrival-time consistency, exact solution approaches for the ConTSP (the singlevehicle variant of the ConVRP) have been proposed in [34,35]. Given our result from later in this paper that establishes equivalence between the TWAVRP and arrival-time ConVRP, one can, in principle, adapt any of the aforementioned methods to obtain algorithms for the TWAVRP by ignoring aspects of driver consistency, whenever applicable.…”

“…Given our result from later in this paper that establishes equivalence between the TWAVRP and arrival-time ConVRP, one can, in principle, adapt any of the aforementioned methods to obtain algorithms for the TWAVRP by ignoring aspects of driver consistency, whenever applicable. We, however, shall choose the decomposition algorithm of [35] for this purpose, due to a number of reasons. First, because of its decomposition principle, it solves the original problem by breaking it down into period-specific routing problems with time windows.…”

“…The second consequence of the equivalence between the TWAVRP and the arrival-time ConVRP is that any algorithm developed for the latter can be used to obtain solutions for the former. In this paper, we adapt a decomposition algorithm proposed in [35] for the Consistent Traveling Salesman Problem (ConTSP), the single-vehicle variant of the ConVRP that focuses purely on the aspect of arrival-time consistency, to obtain a new algorithm for the TWAVRP. Our method can be viewed as a scenario decomposition algorithm in the language of stochastic programming, and is not based on branch(-price)-and-cut that has been the de facto approach for solving TWAVRP models.…”

Region Division in Logistics Distribution With a Two-Stage Optimization Algorithm

“…Considered the situation that time windows might be across periods for the same location, the multi periods MTSP with time window constraints was modeled by Yapicioglu [14]. Subramaniam and Gounaris extended the definition of the TSP with time windows to allow a waiting time at each customer location and to incorporate maximum route duration limits [15]. Then, the constraints on a minimal or maximum number of nodes that a traveler must visit are also common [16]- [18].…”

Exact and Heuristic Solution of the Consistent Vehicle-Routing Problem

“…Subramanyam and Gounaris (2016) present three mixedinteger, linear-programming (MILP) formulations and several classes of valid inequalities that are embedded in a branch-and-cut framework; they are able to solve all instances with up to five planning periods and 25 customers to guaranteed optimality and also some instances with up to 50 customers. Subramanyam and Gounaris (2017) decompose the problem into a sequence of single-period TSPs with time windows and solve the consistent TSP via branch and bound; they are able to solve instances with up to five planning periods and 100 customers, outperforming the results of Subramanyam and Gounaris (2016), but a few instances with 33 customers remain open.…”