INVENTORY SYSTEM In realistic inventory system there are three variables The number of units demanded per order or per time period. The time b/w demands. The lead time (Time b/w placing an order for stocking an inventory system and receipt of that order). In very simple mathematical models of inventory system demand is a constant over time, and lead time is zero or a constant. But in realistic cases the demand occurs randomly in time, the no:of units demanded is also random.
Lead time distribution can often be fitted fairly well by a Gamma distribution [Hadely & Whitin, 1963]. The Geometric, Poisson and Negative binomial provides a range of distribution shapes that satisfy a variety of demand patterns [Fishman,1973]. Negative binomial:-Demand data are characterized by a long tail ie: Always large demand will occur. Geometric:- A special case of negative binomial, has its mode at unity, given that at least one demand occurred
Poisson distribution:-Simple, extensively tabulated and is well known. The tail of a Poisson distribution is shorter than Negative binomial distribution ie: fewer large demand will occur (Assuming that both models have the same mean demand).
RELIABILITY AND MAINTAINABILITY Time to failure has been modeled using numerous distributions, including the exponential, gamma & Weibull. If only random failure occur, the time-to-failure distribution may be modeled as exponential. Gamma distribution arises from modeling standby redundancy each component has an exponential time to failure.
When there are a number of components and failure is due to the most serious of a large number of defects, or possible defects, the Weibull distribution seem to do particularly well as a model. In situations where most failures are due to wear, the normal distribution may very well be appropriate. Long normal is applicable in describing time to failure for some types of components.
LIMITED DATA In many instances the simulation begins before data collection has been completed. Three distributions uniform, triangular & beta distributions are used to represent incomplete data. uniform distribution can be used when inter arrival or service time is known to be random, but no information is available about the distribution. Triangular distribution is used when assumptions are made about the minimum maximum and model values of the random variable.
Beta distribution provides a variety of distributional forms on the unit interval, which with appropriate modification can be shifted to any desired interval. The uniform distribution is a special case of a beta distribution.