We consider single machine lot scheduling problems. A number of customer orders of different sizes may be processed in the same lot. Splitting orders between consecutive lots is allowed. Three scheduling measures are considered: makespan, total completion time and total weighted completion time. In all cases, the goal is minimizing the relevant scheduling measure, subject to an upper bound on the total permitted rejection cost. All three problems studied here are NP-hard. We introduce efficient pseudo-polynomial dynamic programming algorithms for all cases. Our numerical tests indicate that the proposed algorithms can solve efficiently large-size problems.
Bibliographical noteFunding Information:
The second author was supported by the Israel Science Foundation (grant No. 2505/19), by the Recanati Fund of The School of Business Administration, and by Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem, Israel.
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- Dynamic programming
- Lot scheduling
- Order rejection
- Single machine