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Two-stage stochastic days-off scheduling of multi-skilled analysts with training options

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Abstract

Motivated by a cybersecurity application, this paper studies a two-stage, stochastic days-off scheduling problem with (1) many types of jobs that require specialized training, (2) many multi-skilled analysts, (3) the ability to shape analyst skill sets through training decisions, and (4) a large number of possible future demand scenarios. We provide an integer linear program for this problem and show it can be solved with a direct feed into Gurobi with as many as 50 employees, 6 job types, and 50 demand scenarios per day without any decomposition techniques. In addition, we develop a matheuristic—that is, an integer-programming-based local search heuristic—for instances that are too large for a straightforward feed into a commercial solver. Computational results show our matheuristic can, on average, produce solutions within 4–7% of an upper bound of the optimal objective value.

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Notes

  1. Matheuristic is a portmanteau combining mathematical programming and heuristics that is becoming an increasingly popular term for this technique (Boschetti et al. 2009).

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Acknowledgements

We would like to thank our MITRE co-worker Kael Stilp for his comments on an earlier draft of this manuscript, which have helped us improve the exposition and content of the paper. We would also like to thank comments from our anonymous reviewers, who we think helped improved the clarity and exposition of this paper and brought a few interesting studies to our attention.

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Authors and Affiliations

  1. Operations Research Department, The MITRE Corporation, McLean, VA, 20111, USA

    Douglas S. Altner & Les D. Servi

  2. ThirdLove, San Francisco, CA, 94107, USA

    Erica K. Mason

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  1. Douglas S. Altner
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  2. Erica K. Mason
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  3. Les D. Servi
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Correspondence to Douglas S. Altner.

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Altner, D.S., Mason, E.K. & Servi, L.D. Two-stage stochastic days-off scheduling of multi-skilled analysts with training options. J Comb Optim 38, 111–129 (2019). https://doi.org/10.1007/s10878-018-0368-5

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