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DGAP - The Dynamic Generalized Assignment Problem

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  • Konstantin Kogan
  • Avraham Shtub

Abstract

The Generalized Assignment Problem (GAP) is a well-known operations research model. Given a set of tasks to be assigned to a group of agents and the cost of performing each task by each agent, the model allocates tasks to agents to minimize the total cost subject to the availability of a single resource type. The single resource is consumed by the agents when performing these tasks. In this paper, we add the impact of time to the model assuming that each task has a due date, and inventory cost as well as shortage cost is incurred when a task is finished ahead or after its due date, respectively. We formulate the continuous-time op-timal control model of the problem where identical tasks are grouped into jobs (or batches), each job is performed by each agent with a fixed (production) rate, while due dates are transformed into demand. As a result, analytical properties of the optimal behavior of such a dynamic system are derived. Based on those properties, an efficient time-decomposition procedure is developed to solve the problem. Copyright Kluwer Academic Publishers 1997

Suggested Citation

  • Konstantin Kogan & Avraham Shtub, 1997. "DGAP - The Dynamic Generalized Assignment Problem," Annals of Operations Research, Springer, vol. 69(0), pages 227-239, January.
    • Handle: RePEc:spr:annopr:v:69:y:1997:i:0:p:227-239:10.1023/a:1018933012422
    DOI: 10.1023/A:1018933012422
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    Cited by:

    1. Range, Troels Martin & Kozlowski, Dawid & Petersen, Niels Chr., 2019. "Dynamic job assignment: A column generation approach with an application to surgery allocation," European Journal of Operational Research, Elsevier, vol. 272(1), pages 78-93.
    2. Range, Troels Martin & Kozlowski, Dawid & Petersen, Niels Chr., 2016. "Dynamic job assignment: A column generation approach with an application to surgery allocation," Discussion Papers on Economics 4/2016, University of Southern Denmark, Department of Economics.
    3. Shao, Kaining & Fan, Wenjuan & Lan, Shaowen & Kong, Min & Yang, Shanlin, 2023. "A column generation-based heuristic for brachytherapy patient scheduling with multiple treatment sessions considering radioactive source decay and time constraints," Omega, Elsevier, vol. 118(C).
    4. Dong, Su & Johar, Monica S. & Kumar, Ram L., 2023. "An optimization approach for hybrid workflows in platform-enabled private service marketplaces," European Journal of Operational Research, Elsevier, vol. 310(2), pages 874-890.

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