Reference no: EM131105071

Reconsider Prob. 19.3-3. Because of the popularity of the Power model computer, Tim Madsen has found that customers are willing to purchase a computer even when none are currently in stock as long as they can be assured that their order will be filled in a reasonable period of time. Therefore, Tim has decided to switch from the basic EOQ model to the EOQ model with planned shortages, using a shortage cost of $200 per computer short per year.

(a) Use the Solver version of the Excel template for the EOQ model with planned shortages (with constraints added in the Solver dialogue box that C10:C11 integer) to find the new optimal inventory policy and its total variable inventory cost per year (TVC). What is the reduction in the value of TVC found for Prob. 19.3-3 (and given in the back of the book) when planned shortages were not allowed? (b) Use this same spreadsheet to generate a table that shows how TVC and its components would change if the maximum shortage were kept the same as found in part (a) but the order quantity were changed to the following values: 15, 17, 19, . . . , 35.

(c) Use this same spreadsheet to generate a table that shows how TVC and its components would change if the order quantity were kept the same as found in part (a) but the maximum shortage were changed to the following values: 10, 12, 14, . . . , 30.

Prob. 19.3-3

Tim Madsen is the purchasing agent for Computer Center, a large discount computer store. He has recently added the hottest new computer, the Power model, to the store's stock of goods. Sales of this model now are running at about 13 per week. Tim purchases these customers directly from the manufacturer at a unit cost of $3,000, where each shipment takes half a week to arrive. Tim routinely uses the basic EOQ model to determine the store's inventory policy for each of its more important products. For this purpose, he estimates that the annual cost of holding items in inventory is 20 percent of their purchase cost. He also estimates that the administrative cost associated with placing each order is $75.

(a) Tim currently is using the policy of ordering 5 Power model computers at a time, where each order is timed to have the shipment arrive just about when the inventory of these computers is being depleted. Use the Solver version of the Excel template for the basic EOQ model to determine the various annual costs being incurred with this policy.

(b) Use this same spreadsheet to generate a table that shows how these costs would change if the order quantity were changed to the following values: 5, 7, 9, . . . , 25.

(c) Use the Solver to find the optimal order quantity.

(d) Now use the analytical version of the Excel template for the basic EOQ model (which applies the EOQ formula directly) to find the optimal quantity. Compare the results (including the various costs) with those obtained in part (c).

(e) Verify your answer for the optimal order quantity obtained in part (d) by applying the EOQ formula by hand.

(f) With the optimal order quantity obtained above, how frequently will orders need to be placed on the average? What should the approximate inventory level be when each order is placed?

(g) How much does the optimal inventory policy reduce the total variable inventory cost per year (holding costs plus administrative costs for placing orders) for Power model computers from that for the policy described in part (a)? What is the percentage reduction?