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  • 2108.03949v4

    Rights statement: This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, vol., issue, 2022 DOI: 10.1016/j.ejor.2022.08.019

    Accepted author manuscript, 704 KB, PDF document

    Embargo ends: 19/08/24

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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Distributionally Robust Resource Planning Under Binomial Demand Intakes

Research output: Contribution to Journal/MagazineJournal articlepeer-review

E-pub ahead of print
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<mark>Journal publication date</mark>19/08/2022
<mark>Journal</mark>European Journal of Operational Research
Publication StatusE-pub ahead of print
Early online date19/08/22
<mark>Original language</mark>English

Abstract

In this paper, we consider a distributionally robust resource planning model inspired by a real-world service industry problem. In this problem, there is a mixture of known demand and uncertain future demand. Prior to having full knowledge of the demand, we must decide upon how many jobs we will complete on each day of the plan. Any jobs that are not completed by the end of their due date incur a cost and become due the following day. We present two distributionally robust optimisation (DRO) models for this problem. The first is a non-parametric model with a phi-divergence based ambiguity set. The second is a parametric model, where we treat the number of uncertain jobs due on each day as a binomial random variable with an unknown success probability. We reformulate the parametric model as a mixed integer program and find that it scales poorly with the ambiguity and uncertainty sets. Hence, we make use of theoretical properties of the binomial distribution to derive fast heuristics based on dimension reduction. One is based on cutting surface algorithms commonly seen in the DRO literature. The other operates on a small subset of the uncertainty set for the future demand. We perform extensive computational experiments to establish the performance of our algorithms. Decisions from the parametric and non parametric models are compared, to assess the benefit of including the binomial information.

Bibliographic note

This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, vol., issue, 2022 DOI: 10.1016/j.ejor.2022.08.019