Question

Part II:InventoryManagement In the following, you need to manage the stock level of the company with respect to some costs that your team already estimated. The team report states that for one order made, the company should pay 20 AED as clerical costs and 30 AED as packing costs. It is stated also that the company spends 10 AED to produce one mask and that 80% of that corresponds to the cost of keeping one mask in stock for one year. With this information at hand you will manage to meet the annual demand for year 2021 and which corresponds to the demand forecast for period 15 = 30718.98

1- If the order quantity is 20% of the annual demand,Determine the ordering, holding, and total inventory costs for that order quantity.

2- If the order quantity is 50% of the annual demand,Determine the ordering, holding, and total inventory costs for that order quantity.

3- Can you tell if the order quantity, used in the previous question, is the optimal order quantity or not (that minimize the total inventory cost)? Explain why.

4- Using the EOQ model, Determine the optimal order quantity.

5- How many orders will be placed per year using the optimal order quantity.

6- Determine the ordering, holding, and total inventory costs for the optimal order quantity.
PLEASE ANSWER :(

Answer 1

Demand,D=30718.98

Ordering cost,Co=20+30=50

Unit cost of mask,Cu=10

Holding cost percentage i=80%=0.8

Question 1  If the order quantity is 20% of the annual demand ie 20% of 30718.98=6143.8

Then no: of orders=D/Ordering quantity=30718.98/6143.8=4.999=5 orders

Ordering cost=No: of orders*ordering cost per order

Ordering cost=5*50=250

Holding cost=(Average inventory/2)*i*Cu=(6143.8/2)*0.8*10=24575.2

Purchase cost=30718.98*10=307189.8

Total Inventory cost=Ordering cost+Holding cost+Purchase cost=250+24575.2+307189.8=332015

Question 2  If the order quantity is 50% of the annual demand ie 50% of 30718.98=15359.49

Then no: of orders=D/Ordering quantity=30718.98/15359.49=2 orders

Ordering cost=No: of orders*ordering cost per order

Ordering cost=2*50=100

Holding cost=(Average inventory/2)*i*Cu=(15359.49/2)*0.8*10=61437.96

Purchase cost=30718.98*10=307189.8

Total Inventory cost=Ordering cost+Holding cost+Purchase cost=100+61437.96+307189.8=368727.76

Question 3

Optimal Order Quantity,EOQ=

2DCO iCu

EOQ=$\sqrt{\frac{2*30718.98*50}{0.8*10}}$=619.66

For optimal quantity ,ordering costs and holding will be almost same. and also EOQ is 619.66,the order quantity used in question 2 is not the optimal order quantity

Question 4

Optimal Order Quantity,EOQ=

2DCO iCu

EOQ=$\sqrt{\frac{2*30718.98*50}{0.8*10}}$=619.66

Question 5

Annual Demand=30718.98

Optimal ordering quantity=619.66

No of orders with optimal ordering quantity is Annual Demand /Ordering quantity=30718.98/619.66=49.57 orders

Question 6  

If the order quantity is optimal order quanity which is 619.66

Then no: of orders=D/Ordering quantity=30718.98/619.66=49.57 orders

Ordering cost=No: of orders*ordering cost per order

Ordering cost=49.57*50=2478.5

Holding cost=(Average inventory/2)*i*Cu=(619.66/2)*0.8*10=2478.64

Purchase cost=30718.98*10=307189.8

Total Inventory cost=Ordering cost+Holding cost+Purchase cost=2478.5+2478.64+307189.8=312146.94