Question

Problem 16-01 (Algorithmic)

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

Procurement Cost ($)	Probability	Labor Cost ($)	Probability	Transportation Cost ($)	Probability
10	0.35	20	0.2	3	0.72
11	0.25	23	0.25	5	0.28
13	0.4	24	0.35
		26	0.2

1. Compute profit per unit for the base-case, worst-case, and best-case.
   
   Profit per unit for the base-case: $  
   
   Profit per unit for the worst-case: $  
   
   Profit per unit for the best-case: $  
   
2. Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.
   
   Mean profit per unit = $  
   
3. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
4. Management believes the project may not be sustainable if the profit per unit is less than $4. Use simulation to estimate the probability the profit per unit will be less than $4. If required, round your answer to one decimal place.
   
   %

Answer 1

SOLUTION:

a).Base-case is the maximum probability case.
Profit per unit for base-case = selling price - procurement cost - labor cost - transportation cost

= 45 - 13 - 24 - 3 = $5

Profit per unit for the worst-case = 45-13-26-5 = $ 1

Profit per unit for the best-case = 45-10-20-3 = $ 12

b) Simulation model is following:

Procurement cost($)	Probability	RN Range
10	0.35	0.00
11	0.25	0.35
13	0.40	0.

Labor cost($)	Probability	RN Range
20	0.20	0.00
23	0.25	0.20
24	0.35	0.45
26	0.20	0.80

Rransportation cost($)	Probability	RN Range
3	0.72	0.00
5	0.28	0.72

SIMULATIOM:

Trial	Procurement cost	Labor cost	Transportation cost	Profit per unit
1	13	23	3	6
2	10	20	5	10
3	11	23	3	8
4	13	24	3	5
5	13	23	5	4
6	11	24	3	7
7	13	23	3	6
8	13	24	5	3
9	11	24	3	7
10	10	20	3	12
11	13	23	5	4
12	11	20	5	9
13	13	20	3	9
14	10	20	5	10
15	10	23	3	9

Mean profit per unit = 0.436

Probability that the mean profit per unit will be less than $ 4 = 0.136.

EXCEL formulas for simulation table:  

Trial	Procurement cost	Labor cost	Transportation cost	Profit per unit
1	LOOKUP(RAND(),$C$2:$C$4,$A$2:$A$4)	=LOOKUP(RAND(),$G$2:$G$5,$E$2:$E$5)	=LOOKUP(RAND(),$K$2:$K$3,$I$2:$I$3)	=$B$6-SUM(B10:D10)
2	LOOKUP(RAND(),$C$2:$C$4,$A$2:$A$4)	=LOOKUP(RAND(),$G$2:$G$5,$E$2:$E$5)	=LOOKUP(RAND(),$K$2:$K$3,$I$2:$I$3)	=$B$6-SUM(B11:D11)
3	LOOKUP(RAND(),$C$2:$C$4,$A$2:$A$4)	=LOOKUP(RAND(),$G$2:$G$5,$E$2:$E$5)	=LOOKUP(RAND(),$K$2:$K$3,$I$2:$I$3)	=$B$6-SUM(B12:D12)

Copy these formulas down SD 500 rows for 500 simulation trials.

Formula for mean profit (cell 110) =AVERAGE(E10:E509)
Formula for Probability that the mean profit per unit will be Is than $ 4 =COUNTIF(E10:E509," <"&4)/COUNT(E10:E509)

Mean profit per unit = $ 6.616

c)
Simulation approach is better than generating a variety of what-if scenarios, because there are 24 different possible combinations (3*4*2=24) of procurement, labor and transportation cost. So, 24 different what-if scenarios are required to generate all the possible profit. What-if scenarios do not account for the probability just as they happen in real life.
On the other hand, simulation does not require 24 different models, just one model is needed and it accounts for the probability, just it happens in real life. Hence simulation is better than generating a variety of what-if scenarios.
d)
Probability that the mean profit per unit will be less than $ 4 = 0.136
[the answers based on simulation will not match exactly with any answer key]

  

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