Time Window Restrictions Research Articles

A LP-based heuristic for a time-constrained routing problem

In this paper we present a LP-based heuristic for the solution of a Time Constrained Routing problem arising from innovative services accessible via World Wide Web. The problem consists of scheduling the visit of a tourist to a given geographical area in order to maximize his satisfaction degree whilst respecting time windows restrictions. We refer to this problem as the Intelligent Tourist Problem (ITP). ITP is formulated as a Set Packing problem with side constraints. Due to the huge number of variables in the formulation, the LP-relaxation is solved by a “column-and-row generation” approach. Then we run a MIP solver over the active columns to get a feasible solution. Computational experience on real-world instances is reported showing the effectiveness of the proposed approach.

A polyhedral study of the asymmetric traveling salesman problem with time windows

The asymmetric travelling salesman problem with time windows (ATSP-TW) is a basic model for scheduling and routing applications. In this paper we present a formulation of the problem involving only 0/1-variables associated with the arcs of the underlying digraph. This has the advantage of avoiding additional variables as well as the associated (typically very ineffective) linking constraints. In the formulation, time window restrictions are modelled by means of ``infeasible path elimination'' constraints. We present the basic form of these constraints along with some possible strengthenings. Several other classes of valid inequalities derived from related asymmetric travelling salesman problems are also described, along with a lifting theorem. We also study the ATSP-TW polytope, $P_{TW}$, defined as the convex hull of the integer solutions of our model. We show that determining the dimension of $P_{TW}$ is strongly {\em NP}--complete problem, even if only one time window is present. In this latter case, we provide a minimal equation system for $P_{TW}$. Computational experiments on the new formulation are reported in a companion paper [1997] where we show that it outperforms alternative formulations on some classes of problem instances.

Vehicle-routeing with Time Windows and Time-varying Congestion

This paper discusses vehicle-routeing and scheduling problems subject to time window restriction and time-varying traffic congestion. Time-varying congestion increases the complications of the problems and, in fact, makes it challenging even to find feasible solutions. Numerous heuristics have been developed for problems with time windows only, but few for those with both time windows and time-varying congestion. We identify a simple yet robust monotonicity property of arrival times, which allows us to simplify the computation. This property enhances the performance of existing heuristics. The feasibility check routines built upon this property considerably reduce computational burden.

Vehicle-Routeing with Time Windows and Time-Varying Congestion

This paper discusses vehicle-routeing and scheduling problems subject to time window restriction and time-varying traffic congestion. Time-varying congestion increases the complications of the problems and, in fact, makes it challenging even to find feasible solutions. Numerous heuristics have been developed for problems with time windows only, but few for those with both time windows and time-varying congestion. We identify a simple yet robust monotonicity property of arrival times, which allows us to simplify the computation. This property enhances the performance of existing heuristics. The feasibility check routines built upon this property considerably reduce computational burden.

Vehicle-routeing with Time Windows and Time-varying Congestion

This paper discusses vehicle-routeing and scheduling problems subject to time window restriction and time-varying traffic congestion. Time-varying congestion increases the complications of the problems and, in fact, makes it challenging even to find feasible solutions. Numerous heuristics have been developed for problems with time windows only, but few for those with both time windows and time-varying congestion. We identify a simple yet robust monotonicity property of arrival times, which allows us to simplify the computation. This property enhances the performance of existing heuristics. The feasibility check routines built upon this property considerably reduce computational burden.