Star enterprises is a seller of lamps. In this case consider the replenishment/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) EOQ = SQRT(2*D*S/H) = SQRT(2*150*80/3.6) = 82 (approx)

b) ROP = Average Demand During Lead Time+Safety Stock

By thumb rule, 98% fill rates would lead to approximately 69% service level => z=0.5

Safety stock = Z *( LT × Davg+ D ×  L) = 0.5*(15*5+50*30) = 175

ROP = 150+175 = 325

Total monthly cost of operation = Purchase cost+Ordering cost+Holding cost+Stockout cost

Total cost = (150*30)+(150/82)*80+(82/2)*3.6+(0.31*150*100) = 4500+147+148+4650 = 9445 $

b) The replenishment operation system is Push based as the standard deviation of demand is high and the customer purchases the products from suppliers and then fulfills customer.

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