A branch-and-bound approach for a Vehicle Routing Problem with Customer Costs

Abstract

• A hard Vehicle Routing Problem with additional time-dependent customer costs. • A new partition and permutation model that allows a direct calculation of execution times. • Two appropriate branch-and-bound schemes based on the partition and permutation model. • New lower bounds for the time-dependent customer costs and application in branch-and-bound schemes. • Numerical comparison of lower bounds and branch-and-bound schemes. An important aspect in railway maintenance management is the scheduling of tamping actions in which two aspects need to be considered: first, the reduction of travel costs for crews and machinery; and second, the reduction of time-dependent costs caused by bad track condition. We model the corresponding planning problem as a Vehicle Routing Problem with additional customer costs. Due to the particular objective function, this kind of Vehicle Routing Problem is harder to solve with conventional methods. Therefore, we develop a branch-and-bound approach based on a partition and permutation model. We present two branching strategies, the first appends one job at the end of a route in each branching step and the second includes one job inside a route in each branching step; and analyze their pros and cons. Furthermore, different lower bounds for the customer costs and the travel costs are defined and compared. The performance of the branch-and-bound method is analyzed and compared with a commercial solver.