Break-Even Volume between Batch and Line flow production: Let total unit produced = X unit From Exhibit-1, Total cost for Batch production of X unit = $(475,000+75X) Similarly, Total Cost for Line production of X unit = $(900,000+60X) Now, for break-even volume, $(475,000+75X) = $(900,000+60X) X = 28,333 units So, More than 28,333 units of volume, the cost of batch production would be higher than that of line production. Determination of the net incomes and expected value for each production level using a payoff matrix: There are three production strategies in hand: a. Producing 15,000 units (A) b. Producing 30,000 units (B) c. Producing 40,000 units (C) And two state-of-natures (sales forecast) are: a. Demand of 35,000 units with probability 0.6 (X) b. Demand of 25,000 units with probability 0.4 (Y) Now, for each production strategy and state-of-nature (demands) we would calculate the payoffs keeping in mind the below case-mentioned criteria. 1. If the Production volume > 28,333 units we would follow Line production, else follow Batch production 2. Price of Avalanche Racer $125/Unit. 3. Outside vendor ‘Snowcap Inc.’ can produce those units for Avalanche Corp. at the cost of $75/unit only if the market demand is greater than the production volume. 4. Unsold units were to be cleared at the clearance sale for $50/unit. So, before payoff calculation the payoff matrix would look like: Production Strategies 15,000 (Batch) (A) 30,000 (Line) (B) 40,000 (Line) (C) Probabilities
35,000 Units (X)
Demand (State of Nature) 25,000 Units (Y)
0.6
0.4
EMVs
So, Net Income for X-A combination of Demand & Production Strategy: Net Income = (Total revenue – Total Cost) = $(125*35,000) – $(475,000 + 15,000*75 + 20,000*75) = $1,275,000 Here the 15,000 units will be produced according to batch flow production and excess production of 20,000 units will be outsourced to Snowcap Inc. Similarly, Net Income for Y-A combination of Demand & Production Strategy: Net Income = (Total revenue – Total Cost) = $(125*25,000) – $(475,000 + 15,000*75 + 10,000*75) = $775,000 Here 15,000 units will be produced according to batch flow production and excess production of 10,000 units will be outsourced to Snowcap Inc. Net Income for X-B combination of Demand & Production Strategy: Net Income = (Total revenue – Total Cost) = $(125*35,000) – $(900,000 + 30,000*60 + 5,000*75) = $1,300,000 Here 30,000 units will be produced according to line flow production and excess production of 5,000 units will be outsourced to Snowcap Inc. Net Income for Y-B combination of Demand & Production Strategy: Net Income = (Total revenue – Total Cost) = $(125*25,000) + $(5,000*50) – $(900,000 + 30,000*60) = $675,000 Here 30,000 units will be produced according to line flow production and excess produced 5,000 units will be cleared in the clearance sale at $50/unit. Net Income for X-C combination of Demand & Production Strategy: Net Income = (Total revenue – Total Cost) = $(125*35,000) + $(5,000*50) – $(900,000 + 40,000*60) = $1,325,000
Here 40,000 units will be produced according to line flow production and excess produced 5,000 units will be cleared in the clearance sale at $50/unit. Net Income for Y-C combination of Demand & Production Strategy: Net Income = (Total revenue – Total Cost) = $(125*25,000) + $(15,000*50) – $(900,000 + 40,000*60) = $575,000 Here 40,000 units will be produced according to line flow production and excess produced 15,000 units will be cleared in the clearance sale at $50/unit. So, after determining the payoffs the payoff matrix would look like: Production Strategies 15,000 (Batch) (A) 30,000 (Line) (B) 40,000 (Line) (C) Probabilities
35,000 Units (X) $1,275,000 $1,300,000 $1,325,000 0.6
Demand (State of Nature) 25,000 Units (Y) $775,000 $675,000 $575,000 0.4
EMVs
Calculation of Expected Monetary Values (EMVs) for each strategy: Strategy A: ($1,275,000*0.6) + ($775,000*0.4) = $1,075,000 Strategy B: ($1,300,000*0.6) + ($675,000*0.4) = $1,050,000 Strategy C: ($1,325,000*0.6) + ($575,000*0.4) = $1,025,000 The Completed Payoff Matrix would now appear to be:
Production Strategies
Demand (State of Nature) 35,000 Units (X)
25,000 Units (Y)
EMVs
15,000 (Batch) (A)
$1,275,000
$775,000
$1,075,000
30,000 (Line) (B)
$1,300,000
$675,000
$1,050,000
40,000 (Line) (C)
$1,325,000
$575,000
$1,025,000
Probabilities
0.6
0.4
Identification of the optimal production level based on maximizing the expected value: Production Strategies
Demand (State of Nature) 35,000 Units (X)
25,000 Units (Y)
EMVs
15,000 (Batch) (A)
$1,275,000
$775,000
$1,075,000
30,000 (Line) (B)
$1,300,000
$675,000
$1,050,000
40,000 (Line) (C)
$1,325,000
$575,000
$1,025,000
Probabilities
0.6
0.4
Maximum EMV for Production Strategy-A and thus the optimal production level would be 15,000 units of Batch production. Determination of the maximum amount that Avalanche is willing to pay for perfect information: From the Payoff Matrix we have, Production Strategies
Demand (State of Nature) 35,000 Units (X)
25,000 Units (Y)
EMVs
15,000 (Batch) (A)
$1,275,000
$775,000
$1,075,000
30,000 (Line) (B)
$1,300,000
$675,000
$1,050,000
40,000 (Line) (C)
$1,325,000
$575,000
$1,025,000
With Perfect Information
$1,325,000
$1,325,000
$1,105,000
Probabilities
0.6
0.4
So, the Expected Value with Perfect Information (EVwPI): $1,105,000 The Best EMV is: $1,075,000 Now, The Expected Value of Perfect Information (EVPI): EVwPI – Best EMV ($1,105,000) – ($1,075,000) = $30,000 The Maximum amount Avalanche Corp. is willing to pay for perfect information would be $30,000.
Decision Tree: In the next page, we have portrayed the decision tree analysis of the case, depicting two distinct decision points and 10 State of Nature nodes. Payoffs are calculated considering the consulting fee of $20,000 by the Fantastic Forecaster firm.
Calculation of the updated probabilities given the initial probabilities and the consultant’s conditional probabilities using Bayesian analysis: Legend Descriptions: HSP = Denotes the event of Prediction of Heavy Snow by the consulting firm. LSp = Denotes the event of Prediction of Light Snow by the consulting firm. HSA = Denotes the event of Actual Heavy Snowfall. LSA = Denotes the event of Actual Light Snowfall. Assumptions: As there is no such information in the case explicitly mentioning the probabilities of Actual Heavy and Light Snowfalls, we assume that they are correlated to the probabilities of High and Low demand of the Avalanche Racer respectively. So, P(HSA) = 0.6 and P(LSA) = 0.4 Probability Analysis: From Exhibit-2 we gather, P(HSP|HSA) = 0.9 ; P(LSP|HSA) = 0.1 ; P(HSP|LSA) = 0.25 ; P(LSP|LSA) = 0.75 From the above mentioned information we can synthesize that, P(HSP) = P(HSP|HSA)*P(HSA) + P(HSP|LSA)*P(LSA) P(HSP) = (0.9*0.6) + (0.25*0.4) P(HSP) = 0.64 = Probability of Heavy Snow Prediction Similarly, P(LSP) = P(LSP|HSA)*P(HSA) + P(LSP|LSA)*P(LSA) P(LSP) = (0.1*0.6) + (0.75*0.4) P(LSP) = 0.36 = Probability of Light Snow Prediction Now, Probability of Actual heavy Snowfall given that the Consultant’s Prediction of Heavy Snow = P(HSA|HSP) = [P(HSP|HSA)*P(HSA)] / P(HSP) = (0.9*0.6)/0.64 = 0.84375 Probability of Actual Light Snowfall given that the Consultant’s Prediction of Heavy Snow = P(LSA|HSP) = 1 - P(HSA|HSP) = 0.15625 Probability of Actual Heavy Snowfall given that the Consultant’s Prediction of Light Snow =
P(HSA|LSP) = [P(LSP|HSA)*P(HSA)] / P(LSP) = (0.1*0.6)/0.36 = 0.16667 Probability of Actual Light Snowfall given that the Consultant’s Prediction of Light Snow = P(LSA|LSP) = 1 - P(HSA|LSP) = 0.83333
Worth Consulting or Not? From the Decision tree diagram portrayed above, we find that the Expected Monetary Value (EMV) of the State of Nature node-1, is turning out to be $1,062,005, if Avalanche Corp. is taking decision to seek consultant’s opinion. Otherwise, the EMV value is $1,075,000. As the EMV for NOT seeking consultant’s opinion is higher than consulting the consultant, Avalanche Corp. should not consult with Fantastic Forecaster firm expensing $20,000 as it would not be economically beneficial for the firm.
