The inventory manager has typically ordered a quantity of 800 each time an order

Question

The inventory manager has typically ordered a quantity of 800 each time an order is needed for one of their popular tires to take advantage of the discount provided by the supplier and save the company money. The following discount schedule has just been received reflecting recent changes in some of the discount percentages. The manager still maintains that an order quantity of 800 will save the company the most money because of the quantity discount.

Last year, for an annual demand of 1600 tires and a lot size of 800 tires which resulted in an acquisition cost of $71.95, they had a total ordering cost of $380 and a total carrying cost of $14000. They forecast an annual demand of 1600 tires again for this year. Their unit carrying cost per dollar of inventory and their unit ordering cost per order for this year is assumed to be the same as last year.

Question 10. What is the optimal inventory policy that minimizes total cost for a periodic review system?

(A) A policy of ( 4 weeks , 125 ) for a total cost of $132783

(B) A policy of ( 6 months, 800 ) for a total cost of $119500

(C) A policy of ( 1 quarter , 400 ) for a total cost of $129669

(D) A policy of ( 2 quarters , 800 ) for a total cost of $129500

(E) none of the above

Order Quantity Discount Acquisition Cost 0-399 0% 79.95 400-799 5% 75.95 800 or more 10% 71.95

Explanation / Answer

The Annual Demand D= 1600 Units

Ordering Cost Co = 380

Total Holding Cost = 14000

Per unit Holding cost Ch = $14000/1600 units = $8.75

First We are calculating The Economic Order Quantity

The formula for Calculating Economic Order Quantity = Square root ( 2*D*Co/Ch) = Square root (2*1600*380/8.75)

= Square root (138971) = 372.788 Units

As per theory , Total Cost of Ordering and Holding = Square root (2*D*Co*Ch) = Square root (10,640,000) = $3261.90

And Total Cost = Total Ordering and Holding Cost + Total Inventory Cost

= $3261.90 + 1600*71.95 = 3261.90+115120 = $ 118381.90

But Practically

If you take EQO as 372 units , there will be 4,30 orders , which is not possible

Now we consider the above options One by One

The least cost is making two orders in an year

SO answer goes to option B

Quantity 0-399 400-799 800> Inventory Cost Price 79.95 75.95 71.95 Ordering Cost 380 Holding Cost 8.75 S.l.NO Yearly Demand Oredring Quantity Number of Orders in a year Inventory Holding Cost Ordering Cost Total inventory Holding and Ordering CostCost Inventory Cost Total Cost 1 1600 125 13 546.875 4940 5486.875 127920 133406.9 2 1600 800 2 3500 760 4260 115120 119380 3 1600 400 4 1750 1520 3270 121520 124790 4 1600 800 2 3500 760 4260 115120 119380

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