Mr. Beautiful, an organization that sells weight training sets, has an ordering
ID: 464982 • Letter: M
Question
Mr. Beautiful, an organization that sells weight training sets, has an ordering cost of
$45
for the BB-1 set (BB-1 stands for Body Beautiful Number 1). The carrying cost for BB-1 is
$20
per set per year. To meet demand, Mr. Beautiful orders large quantities of BB-1
7
times a year. The stockout cost for BB-1 is estimated to be
$45
per set. Over the past several years, Mr. Beautiful has observed the following demand during the lead time for BB-1:
Demand During Lead Time Probability
Value 1 10 0.1
Value 2 30 0.2
Value 3 50 0.2
Value 4 70 0.2
Value 5 90 0.2
Value 6 110 0.1
The reorder point for BB-1 is
50
sets. What level of safety stock should be maintained for BB-1?
The optimal quantity of safety stock which minimizes expected total cost is
nothing ______
sets (enter your response as a whole number).
Mr. Beautiful, an organization that sells weight training sets, has an ordering cost of dollar 45 for the BB-1 set (BB-1 stands for Body Beautiful Number 1). The carrying cost for BB-1 is dollar 20 per set per year. To meet demand, Mr. Beautiful orders large quantities of BB-1 7 times a year. The stockout cost for BB-1 is estimated to be dollar 45 per set. Over the past several years, Mr. Beautiful has observed the following demand during the lead time for BB-1: The reorder point for BB-1 is 50 sets. What level of safety stock should be maintained for BB-1? The optimal quantity of safety stock which minimizes expected total cost is nothing sets (enter your response as a whole number).Explanation / Answer
Carrying cost = $ 20 per set per year.
Number of orders per year = 7.
Stockout cost = $ 45 per set.
Reorder point = 50 sets.
Annual stockout cost = Sum of units short x Probability x Stockout cost per unit x Number of orders per year.
The purpose will be to find out level of safety stock that minimizes sum of additional inventory carrying cost and stockout cost.
Safety Stock
Additional Carrying Cost (in $)
Annual stockout Cost (in $)
Total Cost (in $)
60
60 x 20 = 1,200
0
1,200
50
50 x 20 = 1,000
10 x 0.1 x 45 x 7 = 315
1,000 + 315 = 1,315
40
40 x 20 = 800
20 x 0.1 x 45 x 7 = 630
800 + 630 = 1,430
30
30 x 20 = 600
30 x 0.1 x 45 x 7 + 10 x 0.2 x 45 x 7 = 1,575
600 + 1,575 = 2,175
20
20 x 20 = 400
40 x 0.1 x 45 x 7 + 20 x 0.2 x 45 x 7 = 2,520
400 + 2,520 = 2,920
10
10 x 20 = 200
50 x 0.1 x 45 x 7 + 30 x 0.2 x 45 x 7 +
10 x 0.2 x 45 x 7 = 4,095.
200 + 4,095 = 4,295
0
0
60 x 0.1 x 45 x 7 + 40 x 0.2 x 45 x 7 +
20 x 0.2 x 45 x 7 = 5,670.
5,670
The total cost is minimum when safety stock is 60 sets.
The level of safety stock that should be maintained for BB-I which minimizes expected total cost
= 60 sets.
Corresponding Reorder Point = 50 + 60 = 110 sets.
Safety Stock
Additional Carrying Cost (in $)
Annual stockout Cost (in $)
Total Cost (in $)
60
60 x 20 = 1,200
0
1,200
50
50 x 20 = 1,000
10 x 0.1 x 45 x 7 = 315
1,000 + 315 = 1,315
40
40 x 20 = 800
20 x 0.1 x 45 x 7 = 630
800 + 630 = 1,430
30
30 x 20 = 600
30 x 0.1 x 45 x 7 + 10 x 0.2 x 45 x 7 = 1,575
600 + 1,575 = 2,175
20
20 x 20 = 400
40 x 0.1 x 45 x 7 + 20 x 0.2 x 45 x 7 = 2,520
400 + 2,520 = 2,920
10
10 x 20 = 200
50 x 0.1 x 45 x 7 + 30 x 0.2 x 45 x 7 +
10 x 0.2 x 45 x 7 = 4,095.
200 + 4,095 = 4,295
0
0
60 x 0.1 x 45 x 7 + 40 x 0.2 x 45 x 7 +
20 x 0.2 x 45 x 7 = 5,670.
5,670
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