Problem 7-16 Michigan State Figurine Inc. (MSF) sells crystal figurines to Spart
ID: 339822 • Letter: P
Question
Problem 7-16 Michigan State Figurine Inc. (MSF) sells crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $31 per unit. They send orders electronically to the manufacturer, costing $56 per order and they experience an average lead time of six days for each order to arrive from the manufacturer. Their inventory carrying cost is 20 percent. The average daily demand for the figurines is two units per day. They are open for business 250 days a year. The supplier decides to offer a volume discount. They will sell the crystal figurines at $7 per unit for orders of 250 units or more. Answer the following questions a. How many units should the firm order each time? Assume there is no uncertainty at all about the demand or the lead time. (Round your answer to the nearest whole number.) Number of units b. How many orders will they place in a year? Number of orders per year c.What is the average inventory? Average inventory 125 units d. What is the annual ordering cost? nual ordering cost 112 e. What is the annual inventory carrying cost? Annual inventory carrying cost 175Explanation / Answer
Annual demand for figurine = D = 2 x 250 = 500
Ordering cost = Co = $56 per order
Annual unit holding cost = 20% of unit price
Annual unit holding cost ( for order qty less than 250 ) = Ch1 = 20% of $31 = $6.2
Annual unit holding cost ( for order quantity 250 units or more ) = Ch2 = 20% of $7 / unit = 1.4
Therefore, derived economic order quantity ( EOQ ) for order qty < 250 will be
= Square root ( 2 x Co x D / Ch1)
= Square root ( 2 x 56 x 500 / 6.2)
= 95.03 ( 95 rounded to nearest whole number )
Derived economic order quantity (EOQ) for order quantity > = 250 will be
= Square root ( 2 x Co x D / Ch2 )
= Square root ( 2 x 56 x 500 / 1.4)
= 200
However derived EOQ of 200 does not match with the quantity slab (order qty > = 250 ) it is supposed to belong to. Therefore , EOQ of 200 is rejected as possible Economic Order Quantity ( EOQ )
EOQ is the quantity which minimizes total annual ordering cost plus annual inventory holding cost.
However since there is a price discount available at next higher quantity slab, we will compare total costs for EOQ =95 and order quantity = 250 ( beginning of next slab)
Total cost for order quantity =95 :
Annual purchase cost = Price unit x annual demand = $31 x 500 = $15500
Annual ordering cost = Ordering cost x Number of orders = Co x Annual demand/ order quantity = $ 56 x 500 / 95 = $294.74
Annual inventory holding cost = annual unit holding cost x Average inventory = Ch1 x Order quantity / 2 = $6.2 x 95/2 = $294.50
Total annual cost = $15500 + $294.74 + $294.50 =$16089.24
Total cost for order quantity = 250 :
Annual purchasing cost = $ 7 x 500 = $3500
Annual ordering cost = Ordering cost x Number of orders = Co x Annual demand/ order quantity = $56 x 500/250 = $112
Annual inventory holding cost = Annual unit inventory holding cost x average inventory = Ch2 x Order quantity/ 2 = $1.4x 250/2 = $175
Total annual cost = $3500 + $112 + $175 = $3787
Since total annual cost is less for order quantity of 250, optimum order quantity should be 250 units
NUMBER OF UNITS = 250
Number of orders they will place in a year
= annual demand/ order quantity
= 500/ 250
= 2
NUMBER OF ORDERS IN A YEAR = 2
Average inventory = Order quantity / 2 = 250 /2 = 125
AVERAGE INVENTORY = 125
ANNUAL ORDERING COST = $112
ANNUAL INVENTORY HOLDING COST = $175
NUMBER OF UNITS = 250