Journal
OPTIMIZATION LETTERS
Volume 16, Issue 9, Pages 2543-2556Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s11590-022-01875-9
Keywords
Production planning; Demand uncertainty; Robust optimization
Funding
- French NationalAgency for Research [caasc ANR-18-CE10-0012]
- National Science Centre, Poland [2017/25/B/ST6/00486]
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This paper examines a robust inventory problem with uncertain cumulative demands, where interval-budgeted uncertainty sets are used to model possible demand scenarios. The study demonstrates that for discrete budgeted uncertainty, the robust min-max problem can be solved in polynomial time. Conversely, for continuous budgeted uncertainty, the problem is weakly NP-hard but can still be solved in pseudopolynomial time, particularly for nonoverlapping cumulative demand intervals, using an FPTAS.
In this paper, a robust inventory problem with uncertain cumulative demands is considered. Interval-budgeted uncertainty sets are used to model possible cumulative demand scenarios. It is shown that under discrete budgeted uncertainty the robust min-max problem can be solved in polynomial time. On the other hand, for continuous budgeted uncertainty, the problem is weakly NP-hard. It can be solved in pseudopolynomial time and admits an FPTAS for nonoverlapping cumulative demand intervals.
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