A robust basic cyclic scheduling problem

Abstract

This paper addresses the Basic Cyclic Scheduling Problem where the processing times are affected by uncertainties. We formulate the problem as a two-stage robust optimization problem with a budgeted uncertainty set. More precisely, we consider the uncertainty set introduced by Bertsimas and Sim (Oper Res 52(1):35–53, 2004) where the activity durations are subject to interval uncertainty and the level of robustness is controlled by a parameter. We propose three exact algorithms for solving the problem. Two of them use a negative circuit detection algorithm as a subroutine, and the last one is a Howard’s algorithm adaptation. Results of numerical experiments on randomly generated instances show that the Howard’s algorithm adaptation yields efficient results and opens perspectives on more difficult robust cyclic scheduling problems.

Keywords

• 90-08
• 90B35
• 90B36