A multistage optimisation algorithm for the large vehicle routing problem with time windows and synchronised visits

Abstract

We propose a multistage algorithm for the vehicle routing problem with time windows and synchronised visits, which is capable of solving large problem instances arising in home health care applications. The algorithm is based on a constraint programming formulation of the daily home care scheduling and routing problem. It contains visits with hard time windows and pairwise synchronisation to be staffed by carers who have different skills and work custom shift patterns with contractual breaks. In a computational study, we first experiment with a benchmark set from the literature for the vehicle routing problem with time windows and synchronised visits. Our algorithm reproduced the majority of the best-known solutions, and strictly improved results for several other instances. Most importantly, we demonstrate that the algorithm can effectively solve real scheduling instances obtained from a UK home care provider. Their size significantly surpass similar scheduling problems considered in the literature. The multistage algorithm solved each of these instances in a matter of minutes, and outperformed human planners, scheduling more visits and significantly reducing total travel time.

Keywords:

• Vehicle routing
• scheduling
• constraint programming
• health services
• practice of OR

Acknowledgements

Among many who offered us their time and expertise during this project, we owe special gratitude to employees of Cordia Services LLP and Glasgow City Council. Furthermore, we are grateful to Professor Mikael Rönnqvist for kindly sharing the benchmark problems (Bredström & Rönnqvist, 2007). Finally, we would like to thank two anonymous referees, whose comments helped to improve the presentation of the paper.

Disclosure statement

The authors declare that they have no conflict of interest.

Additional information

Funding

This work was funded by The Data Lab through an Innovation Centre Grant [Grant Number 17357].