Question

How can I solve this in Pom- QM? Please show how to solve it step by step.

1) Speedy Wheels is a wholesale distributor of bicycles for the western United States. Its Inventory Manager, Ricky Sapolo, is currently reviewing the inventory policy for one popular model — a small, one-speed girl's bicycle that is selling at the rate of 250 per month. The administrative cost for placing an order for this model from the manufacturer is $200 and the purchase price is $70 per bicycle. The annual cost of the capital tied up in inventory is 20 percent of the value of these bicycles. The additional cost of storing the bicycles — including leasing warehouse space, insurance, taxes, and so on — is $6 per bicycle per year.

a. Use the basic EOQ model to determine the optimal order quantity and the total variable inventory cost per year.

b. Speedy Wheel's customers (retail outlets) generally do not object to short delays in having their orders filled. Therefore, management has agreed to a new policy of having small planned shortages occasionally to reduce the variable inventory cost. After consultations with management, Ricky estimates that the annual shortage cost (including lost future business) would be $30 times the average number of bicycles short throughout the year. Use the EOQ model with planned shortages to determine the new optimal inventory policy.

c. Construct a table with table with the same rows and columns as in Table 18.1 to compare the results from parts a and b.

Table 18.1 Comparison of the Basic EOQ Model and the EOQ Model with Planned Shortages for the ACT Problem EOQ Model with Planned Shortages 716 257 459 -41 $964 S618 S346 Basic EOQ Model uantit Order quantity Maximum shortage Maximum inventory level Reorder point Annual setup cost Annual holding cost Annual shortage cost Total variable cost 573 0 573 216 S1,204 S1,204 $2,407 S1,928

Answer 1

a) Annual demand U=250 * 12= 3000

per year purchage price of bicycle.=$70

per bicycle ordering cost R= $200

Inventory carrying cost per unit =$6

per bicycle per year annual cost of the capital 20% of the value of the bicycle

Total inventory carrying cost,Ic=(0.2*70)$ +6$

=20$

By EOQ model Q= V((2RU)/Ic)=V((2*200*3000)/20)

=244.9~245 bicycle per order

Total variable inventory cost is TIC= U/Q*R+Ic*(Q/2)