On the stochastic inventory problem under order capacity constraints

Roberto Rossi*, Zhen Chen, S Armagan Tarim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.

Original languageEnglish
Pages (from-to)541-555
Number of pages15
JournalEuropean Journal of Operational Research
Issue number2
Early online date5 Jul 2023
Publication statusPublished - 16 Jan 2024

Keywords / Materials (for Non-textual outputs)

  • inventory
  • stochastic lot sizing
  • order capacity
  • modified multi-(s, S) policy


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