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Online Advance Scheduling with Overtime: A Primal-Dual Approach

Author

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  • Esmaeil Keyvanshokooh

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

  • Cong Shi

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

  • Mark P. Van Oyen

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

Abstract

Problem definition : We study a fundamental online resource allocation problem in service operations in which a heterogeneous stream of arrivals that varies in service times and rewards makes service requests from a finite number of servers/providers. This is an online adversarial setting in which nothing more is known about the arrival process of customers. Each server has a finite regular capacity but can be expanded at the expense of overtime cost. Upon arrival of each customer, the system chooses both a server and a time for service over a scheduling horizon subject to capacity constraints. The system seeks easy-to-implement online policies that admit a competitive ratio (CR), guaranteeing the worst-case relative performance. Academic/practical relevance : On the academic side, we propose online algorithms with theoretical CRs for the problem described above. On the practical side, we investigate the real-world applicability of our methods and models on appointment-scheduling data from a partner health system. Methodology : We develop new online primal-dual approaches for making not only a server-date allocation decision for each arriving customer, but also an overtime decision for each server on each day within a horizon. We also derive a competitive analysis to prove a theoretical performance guarantee. Results : Our online policies are (i) robust to future information, (ii) easy-to-implement and extremely efficient to compute, and (iii) admitting a theoretical CR. Comparing our online policy with the optimal offline policy, we obtain a CR that guarantees the worst-case performance of our online policy. Managerial implications : We evaluate the performance of our online algorithms by using real appointment scheduling data from a partner health system. Our results show that the proposed online policies perform much better than their theoretical CR, and outperform the pervasive First-Come-First-Served (FCFS) and nested threshold policies (NTPO) by a large margin.

Suggested Citation

  • Esmaeil Keyvanshokooh & Cong Shi & Mark P. Van Oyen, 2021. "Online Advance Scheduling with Overtime: A Primal-Dual Approach," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 246-266, 1-2.
    • Handle: RePEc:inm:ormsom:v:23:y:2021:i:1:p:246-266
    DOI: 10.1287/msom.2019.0832
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    References listed on IDEAS

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    3. Esmaeil Keyvanshokooh & Pooyan Kazemian & Mohammad Fattahi & Mark P. Van Oyen, 2022. "Coordinated and Priority‐Based Surgical Care: An Integrated Distributionally Robust Stochastic Optimization Approach," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1510-1535, April.

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