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Steps for drawing decision tree
 Identify which decision first?
 2nd option depend on scenario?
 At event node – compute cost
 After event node – always scenario
 After decision node – always options, then reject one


 E(X) E(Y) + COV (X, Y)
 COV (X, Y) = 0 if X and Y are independent

Variable rate, or slope of regression, =

Properties of estimated coefficients using least square regression
 Unbiased
 Efficient ( min. variance)

Evaluation of estimated cost function
 Economic plausibility(sign of coeff)
 Slope coeff (high tvalue)
 Goodness of fit(high adjusted r2, ie low standard error)
 Linearity, constant variance of residue, independence of residual (DW stat 1.12.9), normal distribution

R2 indicates…while standard error of regression indicates…
 Percentage of variation in y explained by x
 On average how large the residuals are

 tcal = estimated coeff / standard error
 if tcal > ttab, reject coeff = 0

…indicates a strong relation between cost driver and costs

estimated coeff + (critical tvalue at 5%significance level) * standard error

for multivariable regression, cost drivers should correlation < ….; otherwise, ….problem arises

Characteristics of good sample
 Many reliable data
 Values for cost driver spans a wide range

Problems that arises with wrong cost function is used
 Cost prediction, eg. CVP analysis
 Cost control: wrong benchmark
 Performance evaluation
 Decision making, eg. Product mix and pricing

Reasons for cost functions to be nonlinear
 Economies of scale
 Discounts on large purchase
 Learning effect
 Multiple relevant ranges

Cumulative average time learning: formula
 Y=px^q
 Y=average time per unit
 P=time for 1st unit
 X=total no of units produced
 Q=coeff of learning

Cumulative average time learning: what if q=0 and q=1

Learning percentage formula

Cumulative average time learning: total time for producing 5th7th units?

Incremental unittime learning model: m represents
Time to produce last unit in a sequence of x units

Incremental unittime learning model: total time for producing first 3 units

Steps to Cal coefficient range; meaning of the range
 1. Find the slope of the critical constraint
 2. Find the slope of objective function
 3. Change the numerator or denominator such that two slopes are equal;
 Within this range optimal production plan does not change; as one product become more profitable relative to the other, production emphasis change

When constraint is binding, slack equals

What should management do facing bottleneck?
 Do not overproduce at nonbottleneck
 Increase efficiency and capacity of bottleneck, eg. Elim. Idle time, reduce setup time, shift production from bottleneck

finding dual price
 add one more constraint>
 change RHSconstraint equation>
 find new optimal solution>
 find new total CM>
 dual price = new total CM  old total CM

Throughput margin
Revenue less direct material costs

slope of constraint/objective
coeff x/ coeff y

operating leverage
total CM/OI

