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On the stochastic inventory problem under order capacity constraints

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  • Rossi, Roberto
  • Chen, Zhen
  • Tarim, S. Armagan

Abstract

We consider the single-item single-stocking location stochastic inventory system under a fixed ordering cost component. A long-standing problem is that of determining the structure of the optimal control policy when this system is subject to order quantity capacity constraints; to date, only partial characterisations of the optimal policy have been discussed. An open question is whether a policy with a single continuous interval over which ordering is prescribed is optimal for this problem. Under the so-called “continuous order property” conjecture, we show that the optimal policy takes the modified multi-(s,S) form. Moreover, we provide a numerical counterexample in which the continuous order property is violated, and hence show that a modified multi-(s,S) policy is not optimal in general. However, in an extensive computational study, we show that instances violating the continuous order property do not surface, and that the plans generated by a modified multi-(s,S) policy can therefore be considered, from a practical standpoint, near-optimal. Finally, we show that a modified (s,S) policy also performs well in this empirical setting.

Suggested Citation

  • Rossi, Roberto & Chen, Zhen & Tarim, S. Armagan, 2024. "On the stochastic inventory problem under order capacity constraints," European Journal of Operational Research, Elsevier, vol. 312(2), pages 541-555.
    • Handle: RePEc:eee:ejores:v:312:y:2024:i:2:p:541-555
    DOI: 10.1016/j.ejor.2023.06.045
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    References listed on IDEAS

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