Problem 3 [22 points] Trojan Plastic (TP) produces various high quality BPA-free
ID: 340287 • Letter: P
Question
Problem 3 [22 points]
Trojan Plastic (TP) produces various high quality BPA-free plastic toys. The production process requires a special industrial chemical. Currently, annual demand for this chemical is normally distributed with mean 2000 pound and standard deviation 80. The cost per pound from supplier is $10. Shipping and handling cost is $100 per order. It takes 4 weeks to receive the chemical from the supplier after placing an order. TP also pays for special storage at 15% of the purchasing cost. The annual interest rate is 10% and TP maintains a service level of 97.5%. There are 52 weeks in every year.
a) (5 points) How many pounds of this chemical should TP order each time?
b) (4 points) At what level of on-hand inventory should TP place an order for this chemical?
c) (4.5 points) What is the average inventory of this special chemical in TP? What are the corresponding inventory turns? About how many orders would TP need to place in a year?
d) (4 points) What is the annual inventory related cost for Trojan Plastics (setup plus holding)?
e) (4.5 points) After a detailed study, TP found that during the production process, 5% this chemical is lost. In other words, process has a yield of 95%, i. e., 100 pounds of input will result in only 95 pounds of output. Should TP increase or decrease the EOQ calculated in part a) to account for this loss? What about the ROP and Safety Stock? Explain. (No need to run calculations.)
(i) EOQ will (Circle one)
Increase Decrease Remain the same
Explain:
(ii) ROP will (Circle one)
Increase Decrease Remain the same
Explain:
(iii) Safety Stock will (Circle one)
Increase Decrease Remain the same
Explain:
Explanation / Answer
Following data are provided :
Average Annual demand of chemicals = D = 2000 pounds
Cost of chemical including storage cost = 1.15 x $10 = $11.5 per Pound
Annual interest rate = 10%
Therefore , annual unit inventory holding cost = Ch = 10% of $11.5 per pound = $1.15 per Pound
Shipping and handling cost = Co = $100 per order
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 100 x 2000 / 1.15)
= 589.76 ( 590 rounded to nearest whole number )
Corresponding z value = NORMSINV ( 0.975) = 1.96
Standard deviation of demand during 52 weeks ( 1 year ) = 80
Lead time ( time to receive material after placing an order ) = 4 weeks
Therefore , Standard deviation of demand during lead time
= 80 x Square root ( 4 / 52 )
= 80 x 0.2773
= 22.184
Therefore , required safety stock
= Z value x standard deviation of demand during lead time
= 1.96 x 22.184
= 43.480 ( 44 rounded to next higher whole number )
On hand inventory level at which order should be placed is the reorder point
Reorder point
= Average weekly demand x Lead time ( weeks ) + safety stock
= ( 2000/52 ) x 4 + 44
= 153.84 + 44
= 197.84 ( 198 rounded to nearest whole number )
ON HAND INVENTORY LEVEL AT WHICH ORDER SHOULD BE PLACED = 198
Average inventory
= Economic order quantity / 2 + Safety stock
= 590/2 +44
= 295 + 44
= 339
Inventory turn = Annual demand / average inventory = 2000/339 = 5.90
Number of orders TP needs to place in a year
= Annual demand / EOQ
= 2000 / 590
= 3.389
= Annual unit inventory cost x average inventory
= $1.15 x 339
=$389.85
Annual ordering cost
= Shipping and handling cost per order x Number of orders
=$100 x 3.389
= $338.9
Annual inventory related cost
= Annual inventory holding cost + Annual ordering cost
= $389.85 + $338.9
= $728.75
The required quantity of input to meet annual demand of 2000 = 2000/0.95 = 2105.26
We have seen that order quantity ( EOQ ) is proportional to square root or annual demand
Since annual demand will now increase from 2000 to 2105.26, order quantity will accordingly increase.
Safety stock will not change because we have seen that safety stock is function of standard deviation of annual demand and not mean annual demand
Since reorder point is dependent on average weekly demand and average weekly demand will now increase because of increase in annual demand , reorder point will increase
EOQ WILL INCREASE
SAFETY STOCK WILL REMAIN SAME
REORDER POINT WILL INCREASE
ON HAND INVENTORY LEVEL AT WHICH ORDER SHOULD BE PLACED = 198
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