POLI 410 Lecture Notes - Lecture 7: Carrying Cost, Standard Deviation
15 Jun 2018
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Practice Question for Safety Stock Model
Practice Questions Set - Question 1 (Safety Stock)
A service station uses 1,200 cases of oil a year. Ordering cost is $40 per order and annual
carrying cost is $3 per case. The station owner has specified an annual service level of 99%.
What level of safety stock is appropriate if lead time demand is normally distributed with a mean
of 80 cases and a standard deviation of 5 cases?
Information
• The mean of the LTD is m = 80 cases.
• The standard deviation of the LTD is s = 5 cases.
• The annual demand is R = 1,200 cases per year.
• The cost is K= $40/order.
• The annual inventory holding cost is h = $3 per case.
• The ASL = 99%.
*In the safety stock, the order quantity is calculated with the EOQ.
The only difference is that the Safety Stock Model adds inventory (safety stock) to the ROP.
1. Calculate the Order Quantity.
EOQ = SquR of ([2 x R x K] / 2)
EOQ = 179 cases
2. Find E[z].
ASL = 1 - (E[z] x std)/EOQ
0.99 = 1 - (E[z] x 5)/179
E[z] = 0.361
3. Find the corresponding Z value for 0.361 in the E[z] table.
Z = 0.08
4. Find the ROP.
ROP = Mean of LTD + Safety Stock = 80 + 0.08 (5) = 80 + 0.4 = 80.4
Round up the value to 81.
5. Find the number of units of Safety Stock.
The average LTD is 80 cases.
Compared to the mean, the standard deviation of the LTD is quite long, we are only
carrying 1 additional unit to manage the variability in the system.
The safety stock is 1 case.
Practice Questions Set - Question 4 (Safety Stock)
A. What is the total annual (purchase + holding + ordering) cost for this particular item for
JSK Inc.?
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Document Summary
Practice questions set - question 1 (safety stock) A service station uses 1,200 cases of oil a year. Ordering cost is per order and annual carrying cost is per case. The station owner has specified an annual service level of 99%. *in the safety stock, the order quantity is calculated with the eoq. The only difference is that the safety stock model adds inventory (safety stock) to the rop: calculate the order quantity. Eoq = squr of ([2 x r x k] / 2) E[z] = 0. 361: find the corresponding z value for 0. 361 in the e[z] table. Rop = mean of ltd + safety stock = 80 + 0. 08 (5) = 80 + 0. 4 = 80. 4. Round up the value to 81: find the number of units of safety stock. Compared to the mean, the standard deviation of the ltd is quite long, we are only carrying 1 additional unit to manage the variability in the system.
