Wanda\'s Wreaths has problems with its best-selling wreath—the All-Seasoner. Wan
ID: 380816 • Letter: W
Question
Wanda's Wreaths has problems with its best-selling wreath—the All-Seasoner. Wanda, the owner, tells you that she always seems to have too many or too few of the All-Seasoner. She has hired you to help determine how much and when to order. At the same time, the company is considering quotes from 2 different suppliers, and you will help compare suppliers. You estimated the following information from the detailed records that Wanda kept on the wreath. You calculated the standard deviation of daily demand to be able to estimate the variation of demand during lead time—useful for calculating the amount of extra wreaths to have on hand to minimize stockouts that plagued Wanda. Wanda wanted to have the All-Seasoner available no less than 95% of the time.
Requirements (annual forecast)
1,900
units
Average daily demand
5.21
units (365 days)
Standard deviation of daily demand
0.13
Order processing cost
$80
per order
Annual inventory holding cost factor
33%
per year
Description
Supplier 1
Supplier 2
Per unit price of wreath
35
40
Average lead time in days
3.00
2.00
Standard deviation of lead time days
0.56
0.84
Note, do the interim calculations first and then use this supporting data in the total cost calculations. For instance, use number of orders (rounded) to calculate order cost. Round all answers to the nearest whole number. Find all of the information for Supplier 2.
Interim calculations
Supplier 1
Supplier 2
EOQ
162
Number of orders
12
Number of units for safety stock
5
Reorder point with safety stock
21
Total Cost Calculations
Supplier 1
Supplier 2
Total purchasing cost
$ 66,500
$
Ordering cost
960
1st year cost of safety stock
175
Holding cost of safety stock
58
Holding cost of cycle stock
936
TOTAL COST
$ 68,629
$ 78,415
Requirements (annual forecast)
1,900
units
Average daily demand
5.21
units (365 days)
Standard deviation of daily demand
0.13
Order processing cost
$80
per order
Annual inventory holding cost factor
33%
per year
Explanation / Answer
Supplier 1 Supplier 2 Annual Demand D = 1,900 1,900 Daily Demand µD = 5.21 5.21 Standard Deviation of Daily Demand D = 0.13 0.13 Ordering Cost per Order S = 80 80 Annual Holding Cost factor i = 33% 33% Per unit price of wreath P = 35 40 Average lead time in days L = 3 2 Standard Deviation of Lead Time L = 0.56 0.84 Annual Holding Cost per Unit H = i*P 11.55 13.20 Service level SL = 98% 98% Z-value corresponding to Service Level Z = NORMSINV(SL) 2.05 2.05 EOQ Q* = (2SD/H) 162 152 Number of orders N = D/Q 12 13 Numbe of units of safety stock ss = Z(L*D2 + µD2*L2 ) 5 7 Reorder Point with safety stock R = µD*L + ss 21 17 Total cost calculations Total Purchasing cost A = D*P 66,500 76,000 Ordering cost B = N*S 960 1,040 1st year cost of safety stock C = ss*P 175 280 Holding cost of safety stock D = ss*H 58 92 Holding cost of cycle stock E = (Q/2)*H 936 1,003 Total Cost = A+B+C+D+E 68,628 78,416
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