Abstract
This study treats the probabilistic safety stock n-items inventory system having varying order cost and zero lead-time subject to two linear constraints. The expected total cost is composed of three components: the average purchase cost; the expected order cost and the expected holding cost. The policy variables in this model are the number of periods Nr* and the optimal maximum inventory level Qmr* and the minimum expected total cost. We can obtain the optimal values of these policy variables by using the geometric programming approach. A special case is deduced and an illustrative numerical example is added.
Highlights
In many situations demand is probabilistic since it is a random variable having a known probability distribution
The aim of this study is to investigate the probable safety stock multi-item, single source inventory model with zero lead-time and varying order cost under two constraints, one of them of the expected holding cost and the other on the expected cost of safety stock
CONCLUSIONWe draw the curves and min E (TC) against β, which indicate the values of N*r and β that give the minimum value of the expected total cost of our numerical example
Summary
In many situations demand is probabilistic since it is a random variable having a known probability distribution. All researchers have studied unconstrained probabilistic inventory models assuming the ordering cost to be constant and independent of the number of periods. Hariri and Abou-El-Ata[5] deduced the deterministic multi-item production lot size inventory model with a varying order cost under a restriction: a geometric programming approach. Abou-El-Ata, et al[1] studied the probabilistic multi-item inventory model with varying order cost under two restrictions: a geometric programming approach. The aim of this study is to investigate the probable safety stock multi-item, single source inventory model with zero lead-time and varying order cost under two constraints, one of them of the expected holding cost and the other on the expected cost of safety stock. The following form gives the expected holding cost per period: Fig. 1: Inventory system with safety stock. To find the optimal number of periods N*r , use the following relations due to Duffin and Peterson’s theorem[2] as follows:
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