Analysis of a two-sided production policy with inventory-level-dependent production rates

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In this paper we analyse a stochastic production/inventory problem with compound Poisson demand and state (i.e. inventory level) dependent production rates. Customers arrive according to a Poisson process where the amount demanded by each customer is assumed to have a general distribution. When the inventory W (t) falls below a critical level m, production is started at a rate of r[W(t)], i.e. production rate dynamically changes as a function of the inventory level. Production continues until a level M (œ wm) is reached. Excess demand is assumed to be lost. We identify a dam content process X that is a dual for the inventory level W and develop the stationary distribution for the X process. To achieve this we use tools from renewal and level crossing theories. The two-sided (m, M) policy is optimized using the expected cost obtained from the stationary density of W and a conditional (on w) expected cost function for this process. For a special case, we obtain explicit results for all the relevant expressions. Numerical examples are provided for several test problems.

Original languageEnglish
Pages (from-to)221-237
Number of pages17
JournalApplied Stochastic Models and Data Analysis
Issue number4
StatePublished - Dec 1996


  • Level crossing
  • Optimization
  • Production system
  • Stationary distribution

ASJC Scopus subject areas

  • Modeling and Simulation
  • Management of Technology and Innovation


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