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Operations Management Formula Sheet
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Complete overview of all formulas and quantitative information given in the course on Operations Management and Product Management
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Meeting Topic Formulas1 Competitor Wilcox - Perceptual Maps
Analysis 1-25 N products, M perceptual attributes → N*M questions
Stress = i<j(d(hat)i,j - di,j)2
2 Customer Appendix 6A: Economic Value to the Customer (p 71)
Analysis 26-73 Difference in total cost or EVC = TCa - TCn
Appendix 6B: Latent Class Methods
Norisus - Cluster Analysis
Squared Euclidean Distance
3 Product Appendix 9B: Assessing Discrimination and Preference (p 145)
Development and %AAe = %At + ¼ (% neither t)
Testing 113-146 %BBe = %Bt + ¼ (% neither t)
% neither e = ½ (% neither t)
where
%AAe = expressed percentage who choose A both times
%At = True percentage who prefer A
% neither t = True percentage of subjects who cannot tell the difference
4 Forecasting 74- Sales and Marketing Management buying power index =
112 Bass Diffusion 0,2* (% of population of area compared to US) + 0,3* (% of retail sales of area of US total) + 0,5* (% of
Model disposable income of area of US total) = % of product sold in various regions
Sales Extrapolation Methods
Moving Average e.g. St = (St-1 + St + St+1)/3
Exponential Smoothing St+1 = aSt + (1 - a)St
Regression analysis Sales = a + b(time)
Nonlinear relations
Logarithmic function Sales = b0 + b1 (log advertising)
Multiplicative model Sales = b0X1b1X2b2 ; coefficients interpreted as elasticity’s
Share forcasts Share brand i = exp(BXi) all brands exp(BXj)
Bass Model (forcasting really new products)
Pt = p + [q/M]Y(t-1)
where
Pt = Probability of purchase given no previous purchase
Y(t-1) = Total # who have purchased product through period t-1
M = The market potential (saturation level)
q = Parameter representing rate of diffusion of product
reflecting influence of others (coefficient of immitation)
p = Initial probability of purchase (coefficient of innovation)
Sales in period t
S(t) = [M - Y(t-1)] Pt
Substituing Pt from Bass into Sales
S(t) = pM + [q-p] Y(t-1) - q/M[Y(t-1)] 2
Regression of the model
Sales = c0+ c1Y(t-1)+c2[Y(t-1)] 2
c0 = pM
c1 = [q-p]
c2 = -q/M
Note on Bass Diffusion Model
St = Pt * UMt formula for # of people that’ll adopt product or service in a given month,year, etc.
Pt = Adoption probability in period t
UMt = untapped market
UMt = M - Yt -1
Pt = p + q * Yt -1
, M
M = total # of consumers in adopting target segment
Yt -1 = cumulative # of people that have already adopted
product/service
p = coefficient of innovation → intrinsic tendency to adopt
new product
q = coefficient of imitation
5 Strategic Efficiency = Actual output x100%
Capacity Planning Effective capacity
& Decision Trees
148-177 Utilization = Actual output x100%
Design capacity
Total cost = FC + VC Total Revenue = R x Q Variable cost = Q x v Total revenue = R x Q
Break-even point = Volume of output where :
Total cost = Total revenue
Profit = Q(R - v) - FC
Contribution margin = Revenue per unit - variable cost per unit
Required volume Q = P + FC to generate specified profit
R-v
Q_BEP = FC
R-v
5 Decision Theory Maximin = alternative with best of worst possible payoffs
178-199 Maximax = alternative with best possible payoff
Laplace = alternative with best average payoff of any of
the alternatives (equally likely)
Minimax regret = alternative that has the least of worst
regrets
Expected Monetary Value (EMV) = determine payoff of each alternative & choose alternative that has best expected
payoff
eg. 0.3(10$) + 0.5(10$) + 0.2(10$) = 10$ …...for all
Expected Value of Perfect Information (VPI) =
Expected payoff under certainty - Expected payoff under risk
Lecture p252-283 _
6 Location Center of Gravity Method
Planning & x_bar = (Sum of xi) / n
Transportation y_bar = Sum of yi) / n
284-312 xi = x coordinate of destination i
yi = y coordinate for destination i
n = Number of destinations
If # of units to be shipped not the same
→ Weighted avergae
x_bar = (Sum of xi*Qi) / (Sum of *Qi)
y_bar = Sum of yi*Qi) / (Sum of *Qi)
Qi = Quantity to be shipped to destination i
6 The _
Transportation
Model 313 - 318
7 Project Deterministic Time Estimates
Management 564- ES & EF involve forward pass EF=ES+t
615 LS &LF involve backward pass LS=LF-t
Slack time: Slack=LS-ES or LF-EF
Probabilistic Time Estimatesnm,.
te=average or expected time of an activity
to=optimistic time
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