A branch-and-cut algorithm for a realistic dial-a-ride problem

• Introduced a more realistic variant of the dial-a-ride problem.
• Formulated the problem into two models.
• Proposed eight families of valid inequalities to strengthen the models.
• Devised a branch-and-cut algorithm to solve the problem.
• The branch-and-cut algorithm optimally solved instances with up to 22 requests.

In this paper we study a realistic dial-a-ride problem which simultaneously considers multiple trips, heterogeneous vehicles, multiple request types, configurable vehicle capacity and manpower planning. All of these features originate from practical applications in recent years. To formulate the problem, we propose two mathematical models that use different methods to deal with requests associated with the depot. To further strengthen the models, we propose eight families of valid inequalities, and based on them, we propose a branch-and-cut algorithm to solve the problem. The branch-and-cut algorithm was extensively tested on a set of instances generated according to the data of a real world application. The computational results showed that seven families of inequalities can improve the lower bounds substantially and the branch-and-cut algorithm can solve instances with up to 22 requests within 4 h.