Discrete-Time Inventory Problems with Lead-Time and Order-Time Constraint

  • Lankere Benkherouf
  • Alain BensoussanEmail author
Part of the Systems & Control: Foundations & Applications book series (SCFA)


We consider a discrete-time inventory problem with infinite horizon, with a fixed lead time of several periods. When there is no restriction on the times of order, in particular when it is possible to make an order while some previous order is not yet delivered, then it is possible to reduce the problem to a standard one with no lead time (more precisely a lead time of one period) by considering the inventory position instead of the real inventory. This is a well-known result, which requires however the possibility of backlog. We consider here the same problem, this time imposing a constraint on the order times. It is not possible to make an order while some previous deliveries are pending. With this constraint, the problem cannot be reduced to a standard one for the inventory position.We solve the problem and show cases when the optimal policy is of (s, S) type.


Lead Time Inventory Model Bellman Equation Demand Process Infinite Horizon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Alain Bensoussan would like to acknowledge the support of WCU (World Class University) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (R31-20007).

The authors would also like to thank an anonymous referee for comments on an earlier version of the paper.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchKuwait UniversitySafatKuwait
  2. 2.International Center for Decision and Risk Analysis, School of ManagementUniversity of Texas at DallasRichardsonUSA
  3. 3.The Hong Kong Polytechnic UniversityKowloonHong Kong
  4. 4.Ajou UniversitySuwonKorea

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