Restricted job completion time variance minimisation on identical parallel machines

This paper is concerned with scheduling a number of jobs on multiple identical parallel machines to minimise job Completion Time Variance (CTV), which is a performance measure that emphasises providing uniform service to jobs. CTV minimisation is closely related to common due date problems, service stability and the Just-in-Time (JIT) philosophy. This paper focuses on the restricted aspect of the problem, i.e., no idle times are allowed to insert before machines start to process jobs. By exploring the properties of optimal schedules, we develop a computationally efficient heuristic algorithm named Balanced Assignment, Verified Schedule (BAVS) to reduce job CTV. This paper takes into account the deterministic case in which the processing times of jobs are known in advance. Numerical results show that the BAVS algorithm is near-optimal for small-sized problem instances and outperforms some existing algorithms for large-sized problem instances. [Submitted 01 February 2008; Revised 02 July 2008; Accepted 21 October 2008]