Production/clearing models under continuous and sporadic reviews

Oded Berman, Mahmut Parlar, David Perry, M. J.M. Posner

Research output: Contribution to journalArticlepeer-review


We consider production/clearing models where random demand for a product is generated by customers (e.g., retailers) who arrive according to a compound Poisson process. The product is produced uniformly and continuously and added to the buffer to meet future demands. Allowing to operate the system without a clearing policy may result in high inventory holding costs. Thus, in order to minimize the average cost for the system we introduce two different clearing policies (continuous and sporadic review) and consider two different issuing policies ("all-or-some" and "all-or-none") giving rise to four distinct production/clearing models. We use tools from level crossing theory and establish integral equations representing the stationary distribution of the buffer's content level. We solve the integral equations to obtain the stationary distributions and develop the average cost objective functions involving holding, shortage and clearing costs for each model. We then compute the optimal value of the decision variables that minimize the objective functions. We present numerical examples for each of the four models and compare the behaviour of different solutions.

Original languageEnglish
Pages (from-to)203-224
Number of pages22
JournalMethodology and Computing in Applied Probability
Issue number2
StatePublished - Jun 2005

Bibliographical note

Funding Information:
Research supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).


  • Clearing policies
  • Optimization
  • Stationary distributions

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics


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