Star enterprises is a seller of lamps. In this case consider the replenishment/s
ID: 369924 • Letter: S
Question
Star enterprises is a seller of lamps. In this case consider the replenishment/stocking decision for product named Lamp A. Star purchases Lamp A from a supplier and then sells them to customers. The mean monthly demand for Lamp A is normal. It has a mean and standard deviation of 150 and 50, respectively. The lead-time for Lamp A is also normally distributed with mean of 1 month and standard deviation of 15 days (Assuming there are 30 days in a month). Star purchases Lamp A from the supplier for $30 per unit and uses an annual holding/carrying cost rate of 12%. The fixed cost associated with placing an order of Lamp A to the supplier is $80. Assume that Star estimates a $100 cost associated with each stock-out (independent of the units backordered). It targets a fill rate of 98% for Lamp A. FInd the following -
a)What is Stars’s Economic Order Quantity (EOQ), Reorder point and the associated Average monthly total cost of the operation?
b) Is this replenishment operation a Pull or a Push system?
Explanation / Answer
A.
B.
The replenishment is push system, as the ordering cost is lower than holding cost.
Monthly demand 150 D Demand annually 1800 units Annually p Purchase cost 30 $ per unit K Ordering cost 80 $ per order h Holding cost 3.6 $ per unit LT Lead time 1 Weeks Working days 360 Weeks SDW Std Dev of monthly demand 50 LTD Lead time demand 150 Units SLTD Std Dev for lead time 50 units Sigma Std Dev of annual demand 173.2051 SQRT((Lead time std dev^2)*D/LTD) P value for 1 stock out, 98 Z Z value 2.33 R So reorder point 252.6874 (LTD+SLTD *Z) EOQ (Sqrt(2*k*D/h) 282.8427 SS Safety stock 102.6874 (R-LTD) AI Average inventory 267.7651 units (EOQ+R)/2 (AI*h) Holding cost 963.9543 $ No of orders 6.363961 times Toc Total ordering cost annualy 509.1169 $ Total orders/EOQ Thc Annual Holding cost 963.9543 $ Tpc Purchasing cost annual 54000 $ TC Total cost 55473.07 $ Length of order cycle 56.56854 (Toc+Thc+Tpc) 57 days (Total days/No of orders)Related Questions
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