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

✍ Scribed by Bar-Lev, S. K. ;Parlar, M. ;Perry, D.

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 775 KB
• Volume: 12
• Category: Article
• ISSN: 8755-0024
• DOI: 10.1002/(sici)1099-0747(199612)12:4<221::aid-asm285>3.0.co;2-b

✦ Synopsis

In this paper we analyse a stochastic production/inventory problem with compound Poisson demand and state (i.e. inventory level) dependent production rates. Customers amve according to a Poisson process where the amount demanded by each customer is assumed to have a general distribution. When the inventory W ( f ) 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 (oe 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.