# Pet Store (PS) sells a very popular blend of cat food at \$20 per pack. Average weekly demand of this cat food at PS is 500 packs per week. The owner of the store, John Snow, orders the packs of cat food from the Ice & Fire Co. (I&F) at \$15 per pack and have to pay a flat fee of \$100 per order for shipping and handling. PS uses a fixed order size as their inventory policy. Assume that the opportunity cost of capital and all other inventory cost is 15 percent annually and that there are 50 weeks in a year. (a) How many packs of food should PS order at a time? (b) What is PS’s total order cost for one year when John Snow orders the amount you found in part a above? (c) What is PS’s total holding cost for one year when John Snow orders the amount you found in part a above? (d) What is PS’s yearly inventory turns when John Snow orders the amount you found in part a above? (e) Determine the reorder level (on-hand inventory at time of reorder) if the replenishment lead time is three weeks. (f) Assume I&F is willing to give a 1 percent quantity discount if PS orders more than 5,000 or more packs at a time. If PS is interested in minimizing its total cost (i.e., purchase and inventory- related costs), should PS begin ordering 5,000 or more packs at a time?

Given are the following information :

Annual demand = D = 500 / week x 50 weeks = 25000 per annum

Ordering cost for John Snow of Pet store = Co = \$100 per order

Annual unit inventory holding cost = Ch = 15% of \$15 per pack = \$2.25 per pack

Number of packs of food should PS order at a time as per Economic Order Quantity ( EOQ ) model

= Square root ( 2 x Co x D /Ch)

= Square root ( 2 x 100 x 25000/2.25)

= 1490.71 ( 1491 )

PS should order 1491 PACKS AT A TIME

Total order cost for 1 year

= Ordering cost x Number of orders

= Co x Annual demand /EOQ

= \$100 x 25000/1491

= \$1677

Total holding cost for 1 year

= Annual unit inventory cost x Average inventory

= Ch x EOQ/ 2

= \$2.25 X 1491/2

= \$1677.37

Total ordering cost for 1 year = \$1677

Total holding cost for 1 year = \$1677.37

Average inventory in the system= EOQ/ 2 = 1491/2 = 745.5

PS’s yearly inventory turn = Annual demand/ Average inventory = 25000/ 745.5 = 33.53

Reorder level = Average weekly demand x Lead time ( weeks ) = 500 x 3 = 1500

YEARLY INVNETORY TURN = 33.53

REORDER LEVEL = 1500

At 1 percent quantity discount and order quantity of 5000 :

Revised annual unit inventory holding cost , Ch = 15% of ( 99% of \$15) = \$2.227

Revised annual inventory holding cost = Ch x Ordering quantity /2 = \$2.227 x 5000/2 = \$5567.5

Revised annual ordering cost = Co x Annual demand/Order quantity = \$100 x 25000/5000 = \$500

Total annual cost of inventory holding and annual ordering = \$5567.5 + \$500 = \$6067.5

Original annual ordering plus inventory holding cost = \$1677 + \$1677.37 = \$3354.37

Therefore , total cost of ordering plus inventory carrying for order quantity of 5000 increases by = \$6067.5 – \$3354.37 = \$2713.13

However annual savings in cost/ unit over 25000 units annually

= 1 % discount on \$15 per pack x 25000 packs

= \$0.15 x 25000

= \$3750

Therefore , savings in product cost ( \$3750) is more than increase in ordering and inventory holding cost of \$3354.37 resulting in a net savings of = \$3750 – \$3354.37 = \$395.63

Therefore , PS should begin ordering 5000 or more packs at a time

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