Avalanche Corporation Bayesian Analysis Case

Question 1. Determine the break-even volume for the two production options(bath and line)

Suppose the break-even volume should be x units total cost for batch flow production equals 475,000+ 75x total cost for line flow production equals 900,000+60x if 475,000+75x = 900,000+60x , we will have x= 28,334 units.

if more than 28,334 units are produced, the cost of batch flow production will be higher than that of line flow production, and the line production should be used; otherwise, when the volume is lower than 28,334 units, the batch flow production should be used.

Question 2. Determine the net income for each of the six demand and production options

2a. Draw an appropriate decision tree.
Please refer to the lower half of the decision-tree hardcopy handout. Thanks

2b. To maximize the expected value, what is the production decision .

There are three production levels: A. 15,000 units B. 30,000 units C. 40,000 units
From Question 1 we know that the break-even volume is 28,334 units. Therefore, for option A, batch flow production is adopted; while for option B and C, line production method is adopted.
And there are two sales forecast scenarios for Avalanche Racer: a) 35,000 units with probability of 0.6 b) 25,000 units with probability of 0.4.

Other factors include the selling price of Avalanche Racer is $125, and if and only if demand exceeds production, an outside vendor Snowcap is capable of producing for a cost of $ 75 per unit. Unsold units could be sold at $50 per unit.

Considering the net income of the six scenarios: 1) 35,000 units in demand and 15,000 units in supply, which means that 15,000 units will be produced by batch production and extra 20,000 units will be produced by outside vendor Snowcap.
Net Income = Total Income - Total Cost = 125*35,000 - (475,000+15,000*75+ 20,000*75) = $1,275,000

2) 35,000 units in demand and 30,000 units in supply, which means that 30,000 units will be produced by line production and extra 5,000 units will be produced by outside vendor Snowcap.
Net Income = Total Income - Total Cost = 125*35,000 - (900,000+30,000*60+ 5,000*75) =$ 1,300,00 3) 35,000 units in demand and 40,000 units in supply, which means that 35,000 units will be sold at $125 per unit while 5,000 units be sold at $50 per unit; and 40,000 units will all be produced by line production.
Net Income = Total Income - Total Cost = 125*35,000 + 5,000*50 - (900,000+40,000*60) = $1,325,000

4) 25,000 units in demand and 15,000 units in supply, which means 15,000 units will be produced by batch production while extra 10,000 units will be produced by outside vendor Snowcap
Net Income = Total Income - Total Cost = 25,000*125 - (475,000+ 15,000*75 + 10,000*75) =$ 775,000

5) 25,000 units in demand and 30,000 units in supply, which means 30,000 units will be produced by line production while 5,000 units of them will be sold at $ 50 per unit due to oversupply
Net Income = Total Income - Total Cost = 25,000*125 + 5,000*50 - (900,000 +30,000*60) = $675,000

6) 25,000 units in demand and 40,000 units in supply, which means 40,000 units will be produced by line production while 15,000 units of them will be sold at $50 per unit due to oversupply
Net Income = Total Income - Total Cost = 25,000*125 + 15,000*50 - (900,000 +40,000*60) = $575,000.

By applying the probabilities of two demand forecast conditions as 0.6 or 0.4, the calculation will result in EMVs for the three supply options A ,B and C.

Expected Monetary Values of the Six Scenarios of Demand and Supply Supply Options | Demand Forecasts | EMV | | 35,000 units | 25,000 units | | 15,000 units(A) | $1,275,000 | $775,000 | $1,075,000 | 30,000 units(B) | $1,300,000 | $675,000 | $1,050,000 | 40,000 units(C) | $1,325,000 | $575,000 | $ 1,025,000 | Probabilities (P) | 0.6 | 0.4 | |

Since the largest EMV (valued as $1,075,000)is from a scenario of 15,000 units in supply, the most appropriate production process should be batch production with 15,000 units.
The decision tree of production level is drawn by handwriting.

Question 3. How sensitive is the production given in 2b to the probabilities of selling 35,000 units Given the production volume in 2b equals 15,000, assuming that the probability of 35,000 units in demand is Y, while the probability of 25,000 units in demand is (1-Y) the EMV1 = 1,275,000Y + 775,000(1-Y)= 500,000Y+775,000
With production volume equals 30,000,EMV2= 1,300,000Y+ 675,000(1-Y) =625,000Y+675,000
With production volume equals 40,000, EMV3=1,325,000Y+575,000(1-Y) =750,000Y+575,000
Solve EMV1>EMV2, Y<0.8;
Solve EMV1>EMV3, Y<0.8;
As long as the probability is less than 0.8, the decision do not switch. Question 4. Calculation of Conditional Probabilities
As noted in the case, if we take selling 35,000 units for actual heavy snow condition and selling 25,000 units for actual light snow condition, then we have:
P (actual heavy) = 0.6 and P(actual light)= 0.4.

From Exhibit 2, more conditional probabilities are offered as:
P(predicted heavy/actual heavy)=0.9; P(predicted light/actual heavy)=0.1;
P(predicted heavy/actual light)=0.25; P(predicted light/actual light)=0.75.

According to Bayesian analysis, we can further infer other probabilities as following:
P(predicted heavy)= P(predicted heavy/actual heavy)*P(actual heavy)_+ P(predicted heavy/actual light)*P(actual light) = 0.9*0.6+0.25*0.4 = 0.64
Similarly, we have P(predicted light)= 0.1*0.6+0.75*0.4=0.36.

Now we can further calculate Probabilities for actual snowfall conditions.
P(Demand=35,000/predicted heavy)=P(predicted heavy/actual heavy)*P(actual heavy)/P(predicted heavy) = (0.9*0.6)/0.64=0.844;

P(Demand=25,000/predicted heavy) = 1-P(Demand=35,000/predicted heavy) =1- 0.84375 = 0.156;

P(Demand=25000/predicted light) =P(predicted light/actual light)*P(actual light)/P(predicted light) = (0.75*0.4)/0.36 = 0.833;

P(Demand=35,000/predicted light) = 1-P(Demand-=25,000/predicted light) = 1-0.833=0.167

Question 5 Should Jackson Hire the Consulting Firm for Further Information

Calculate the Expected Value with Perfect Information
Under perfect information, the Expected Value of Production = 1,325,000*0.6+775,000*0.4=$1,105,000;
The Expected Value of Perfect Information = 1,105,000-1,075,000=$30,000. The cost of hiring consulting firm is 20,000, less than the maximum value that Jack is willing to pay. So we need to look at the scenario with further discussion.
Please refer to the decision tree graph for detailed net income and EMVs.

Consider the cost of hiring Fantastic Forecaster is $20,000, for each of the previous six scenarios, the net income should be $20,000 less than without consulting.
By assigning net incomes of Three production options and the probabilities calculated in Question 4 into the decision tree, we can calculate new net income again in each scenario, the EMV of Hiring Fantastic Forecaster is $1,068,178, which is less than EMV of Not Hiring Fantastic Forecaster ($1,075,000). Therefore, by consulting with external information provider, the economic benefit of the production decision is not improved at all. Jackson should not hire the consulting firm for additional forecast.