We study a single machine scheduling problem, where the machine is unavailable for processing for a pre-specified time period. We assume that job processing times are position-dependent. The objective functions considered are minimum makespan, minimum total completion time and minimum number of tardy jobs. All these problems are known to be NP-hard even without position-dependent processing times. For all three cases we introduce simple heuristics which are based on solving the classical assignment problem. Lower bounds, worst case analysis and asymptotic optimality are discussed. All heuristics are shown numerically to perform extremely well.
Bibliographical noteFunding Information:
This paper was supported in part by The Recanati Fund and The Charles Rosen Chair of Management, The Hebrew University, Jerusalem, Israel.
- Number of tardy jobs
- Single machine scheduling
- Total completion time
- Unavailability period