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

S. K. Bar‐Lev, M. Parlar and D. Perry

Applied Stochastic Models and Data Analysis, 1996, vol. 12, issue 4, 221-237

Abstract: 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 w m) 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. © 1996 John Wiley & Sons, Ltd.

Date: 1996
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https://doi.org/10.1002/(SICI)1099-0747(199612)12:43.0.CO;2-B

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmda:v:12:y:1996:i:4:p:221-237

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