A branch-and-bound algorithm for solving the static rebalancing problem in bicycle-sharing systems
Résumé
We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T 1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.