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Technical Note—Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems

Author

Listed:
  • Xiting Gong

    (Department of Decision Sciences and Managerial Economics, CUHK Business School, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong)

  • Tong Wang

    (Department of Management Science, Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai, China 200030)

Abstract

In this paper, we establish two preservation results of additive convexity for a class of optimal transformation problems and a class of optimal disposal problems. For both classes of problems, there are multiple resources; our results show that if these resources have different priorities to be transformed/disposed under the optimal policy, then the additive convexity and bounded monotonicity of the objective function are preserved to the value function after optimization. A key observation is that an optimal transformation problem with prioritized optimal decisions is equivalent to a serial inventory problem with zero lead times. We demonstrate the applications of our results to several stochastic optimization problems in operations management.

Suggested Citation

  • Xiting Gong & Tong Wang, 2021. "Technical Note—Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems," Operations Research, INFORMS, vol. 69(4), pages 1015-1024, July.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:4:p:1015-1024
    DOI: 10.1287/opre.2020.2064
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