Question

Question 1

Khalil is the owner and manager of a hardware store. He sells on average 50 industrial hammers per month. He places an order to buy 50 hammers from a wholesaler at a cost of 20 OMR per unit at the end of each month. However, Khalil orders everything himself and finds that it takes a long time. He estimates that the value of his time spent placing each order is 75 OMR. a. What should be the unit handling cost for hammers in order for Khalil's current inventory management to be optimal according to the EOQ model?

b. What percentage of the unit purchase cost is the handling cost?

c. What is the optimal quantity if the unit handling cost is 20% of the cost of the unit?

d. What is the annual cost of the inventory management policy in this case (described in part

. What is the annual cost of the current inventory management policy (50 per month)?

f. Which policy is better? Justify your answer. g. The wholesaler generally delivers an order within 5 working days (25 working days per month), what is the reorder point according to the current policy (50 per month)

The wholesaler offered Khalil a discount of 2 OMR per unit if the quantity ordered exceeds 200 units and 5 OMR if the quantity is greater than 400 units. The handling cost per unit is 20% of the purchase cost. h. Calculate the optimal order quantity.

i. Calculate the annual cost of this inventory management policy.

Answer 1

Annual Quantity Demanded = Monthly Demand * 12 = 50*12= 600 units

Ordering Cost Per Order = 75 OMR

We have to calculate Holding Cost per unit per annum = Lets assume it as 'H'

Formula for calculating EOQ Level =

Square root of (2 * Annual Quantity Demanded * Ordering Cost Per Order / Holding Cost per unit per annum)

a.) What should be the unit handling cost for hammers in order for Khalil's current inventory management to be optimal according to the EOQ model?

Our Current Ordering Quantity is = 50, taking it as EOQ =50

Putting values in above formula -

50 = Square root of ( 2* 600* 75 / H )

Taking square both sides, we get-

2500 = 90000 / H

H = 36

Hence, our Holding Cost per unit per annum (H) is = 36 per unit per annum

b.) What percentage of the unit purchase cost is the handling cost?

Holding Cost per unit per annum is = 36 per unit per annum

Purchase cost per unit ( Given in Question ) = 20 OMR

Hence, percentage of the unit purchase cost is the handling cost is = 36/20*100 = 180%

c.) What is the optimal quantity if the unit handling cost is 20% of the cost of the unit?

Purchase cost per unit = 20 OMR

Handling cost = 20 * 20% = 4 OMR per unit per annum

EOQ= Square root of (2 * Annual Quantity Demanded * Ordering Cost Per Order / Holding Cost per unit per annum)

EOQ = Square root of (2 * 600* 75 / 4 )

= Square root of (22500)

= 150 units

d.) What is the annual cost of the inventory management policy in this case (described in part c). What is the annual cost of the current inventory management policy (50 per month)?

i.) Annual cost if EOQ level is 50 units-

Annual Cost = Annual Purchase cost + Annual Ordering Cost + Annual Holding Cost

Annual Purchase cost = Annual units Purchase * Purchase price per unit = 600 * 20 = 12000 OMR

Annual Ordering Cost = Number of Orders per annum * Ordering cost per order

Number of Orders per annum = Annual Quantity Purchase / EOQ = 600/50 = 12 Order

  Ordering cost per order = 75 OMR

Annual Ordering Cost = 12*75 = 900 OMR

Annual Holding Cost = Inventory /2 * Holding cost per unit

= 50 / 2 * 36 = 900 OMR

Hence, Annual Cost = Annual Purchase cost + Annual Ordering Cost + Annual Holding Cost

= 12000 + 900 +900 = 13,800 OMR

ii.) Annual cost if EOQ level is 150 units-

Annual Cost = Annual Purchase cost + Annual Ordering Cost + Annual Holding Cost

Annual Purchase cost = Annual units Purchase * Purchase price per unit = 600 * 20 = 12000 OMR

Annual Ordering Cost = Number of Orders per annum * Ordering cost per order

Number of Orders per annum = Annual Quantity Purchase / EOQ = 600/150 = 4 Order

  Ordering cost per order = 75 OMR

Annual Ordering Cost = 4*75 = 300 OMR

Annual Holding Cost = Inventory /2 * Holding cost per unit

= 150 / 2 * 4 = 300 OMR

Hence, Annual Cost = Annual Purchase cost + Annual Ordering Cost + Annual Holding Cost

= 12000 + 300 +300 = 12,600 OMR

f.) Which policy is better?

Existing Policy of ordering 50 units-

Annual Cost is = 13,800 OMR

New Policy at EOQ of 150 units-

Annual Cost is = 12,600 OMR

Hence, New Policy at EOQ of 150 units is better

g.) What is the reorder point according to the current policy (50 per month)

Average daily usage rate = Monthly usage / Number of working days per month = 50 /25 =2 units

Lead time = 5 Days

Reorder Point = (Average daily usage rate x Lead time)

Hence, Reorder Point = 2 * 5 = 10 units

h.) The wholesaler offered Khalil a discount of 2 OMR per unit if the quantity ordered exceeds 200 units and 5 OMR if the quantity is greater than 400 units. The handling cost per unit is 20% of the purchase cost. Calculate the optimal order quantity.

Particulars	Quantity ordered exceeds 200 units	Quantity ordered exceeds 400 units
Quantity Ordered	300	600
Purchase Price per unit	18	15
Handling Cost per unit	3.6	3.6
Ordering Cost Per Order	75	75
No. of Orders	2	1
EOQ (Round up to next unit)	159	159
i.) Annual Cost
Ordering Cost per annum	150	75
Holding Cost per annum	540	1080
Purchase Cost Per Annum	10800	9000
Annual Cost	11490	10155