Heuristic algorithms for visiting the customers in a rolling schedule environment

Abstract

In this study, we consider a scheduling problem of a company providing certain kind of services for its customers. In each period, customers call the company to request for the services. In a call j, the customer specifies a date d j and a time tolerance δ j . A profit can be realized if the service can be made within the period window d j ±δ j . The problem is to construct a schedule for each period so that the average profit of serving a subset of the customer calls is maximized in the long run. We consider the problem in a rolling schedule environment and propose several heuristics based on iterative customer assignment and iterative center-of-gravity scheme for solving it. Extensive computational experiments for problems with various sizes are generated and solved by these heuristics. For the small problem instances, the solutions obtained are compared against the upper bound obtained by solving the LP relaxation of the problem by a column generation scheme. The computational results show that the proposed heuristics all perform very well. For large problem instances, the solutions obtained are compared among the heuristics. The factors affecting the performance of the various heuristics are analyzed and discussed.