An adaptive large neighborhood search heuristic for the vehicle routing problem with time windows and synchronized visits

Highlights

• An adaptive large neighborhood search heuristic is designed for this proble.

• A vehicle routing problem with time windows and synchronized visits is studied.

• Efficient solution evaluation and cross synchronization check methods are proposed.

• Efficiency of the approach is tested on existing and new benchmarks.

Abstract

This paper addresses a special vehicle routing problem, which extends the classical problem by considering the time window and synchronized-services constraints. A time window is associated with each client service and some services require simultaneous visits from different vehicles to be accomplished. This problem has many practical applications such as caregiver scheduling problem encountered in the home health care industry. The synchronization constraints in this problem interconnect various vehicles’ routes, making the problem more challenging than standard vehicle routing problem with time windows, especially in designing neighborhood search-based methods. A mixed-integer programming model is proposed for the problem. Motivated by the challenge of computational time, an efficient Adaptive Large Neighborhood Search heuristic is proposed to solve the problem. The approach is evaluated on benchmark instances acquired from the literature and new large-scale test instances first generated in this paper. The numerical results indicate that our solution method is able to outperform existing approaches.

Introduction

The vehicle routing problem (VRP) is a practical and central issue in a broad range of application systems, including distribution, transportation, healthcare, and supply chains. The classical VRP can be simply defined as the problem of designing least-cost delivery routes from a depot to a set of geographically scattered customers, subject to side constraints. In practice several variants of the VRP exist because of the diversity of operating rules and constraints encountered in real-life applications. In this paper, we focus on a particular variant of the VRP, the vehicle routing problem with time windows and synchronized visits (VRPTWSyn). In this problem, many vehicles start from one depot and go to service a set of geographically scattered customers such that each customer is visited only once within a given time interval (time window). More importantly, differs from the classical VRP with time windows, some customers need synchronized services, which means such customers must be served by two or more vehicles simultaneously at the same start time. Such customer is called “synchronized services customer” in this paper. Clearly, the synchronized service interconnects the routes of the vehicles; it makes this special vehicle routing problem more challenging to be tackled.

The VRPTWSyn has many practical applications. For example, Home Health Care (HHC) is a fast-growing medical service industry, which provides medical and paramedical services for customers at their homes. Each day the HHC company schedules the caregivers to visit and serve customers who need HHC services. The service routes for caregivers to complete services is similar to the vehicle routes in the VRP. Note in some HHC services, for example, transferring a customer with a lift between the bed and the wheel chair, the operations require more than one caregiver to be accomplished. Therefore, in such case the HHC crew scheduling problem can be formulated as the VRPTWSyn.

Clearly, the VRPTWSyn can be seen as an extension of the VRP with time windows (VRPTW). Because the VRPTW is a famous NP-hard combinatorial optimization problem and only relatively small instances of the VRPTW can be solved optimally within short computing times (Desaulniers et al., 2008), we focus on devising a heuristic to address the VRPTWSyn. However, the synchronization constraints make the problem extremely difficult to solve using traditional neighbourhood search heuristics. As noted by Rousseau et al. (2013), if the insertion of a special customer into a route would delay a synchronized-services customer i, all later customers involved in the second route (who also visits customer i) will also be delayed. This high number of interconnections between routes means that to insert a customer one might have to recalculate the visit time of every customer already scheduled. Constraint programming-based heuristics have been designed to solve this problem because constraint programming provides an easy way to express the synchronization constraints (Rousseau et al., 2003, Rousseau et al., 2013). With the goal of obtaining a high quality solution in a short time, in this paper we design special methods to address the aforementioned difficulty. Then, based on these methods, we build an Adaptive Large Neighbourhood Search (ALNS) algorithm to efficiently address this VRPTWSyn problem. Numerical experiments show that the ALNS algorithm proposed in this paper can produce satisfactory solutions within an acceptable execution time.

The rest of this paper is organized as follows. Section 2 introduces the relevant literature. A mathematical programming formulation for the VRPTWSyn is developed in Section 3. Section 4 proposes an ALNS algorithm to solve the problem. Computational results are reported in Section 5. Finally, conclusions are presented in Section 6.