Intro to Decomposition: Creating a Three-Factor Model (Cups/Server) (Servers/Hour) (Hours)

1. Intro to Decomposition:Creating a Three-Factor Model(Cups/Server) (Servers/Hour) (Hours) Ted Mitchell

2. We have used • Miles per gallon as part of a simple Two-Factor description of a car’s performance • Given the machine’s conversion rate:miles per gallon • What is the output for this machine? • What is the input for this machine? • Output, miles = (conversion rate, r) x Input, gallons • Output, miles = (miles per gallon) x Input, gallons

3. We have also used • Miles per Hour as part of a simple Two-Factor description of a car’s performance • Both descriptions have the same output (miles) • Very different and important inputs (gas and time) • When we explicitly use the miles per gallon model, we leave the number of hours constant and implicit. • When we explicitly use the miles per hour model, we leave the number of gallons constant and implicit.

4. We want • Both Inputs made explicit in the same description • To make the number of gallons and the number of hours explicit in the same description requires a Three-Factor description of the car • There are Two possible descriptions depending on which input (hours or gallons) is considered more strategic for the analysis

5. Possibility #1 Uses Number of Hours as the Strategic Input • A Three-Factor Model of car that has both the number of hours and the number of gallons would be • Output: Miles = (Factor 1) x (Factor 2) x (Factor 3) • Factor 1 = conversion of miles per gallon, mpg • Factor 2 = conversion of gallons per hour, gph • Factor 3 = input factor number of hours

6. Possibility #2 Uses Gallons of Fuel as the Strategic Input • A Three-Factor Model of car that has both the number of hours and the number of gallons would be • Output: Miles = (Factor 1) x (Factor 2) x (Factor 3) • Factor 1 = conversion of miles per hour, mph • Factor 2 = conversion of hours per gallon, hpg • Factor 3 = input factor number of gallons

7. Welcome to the Art of • Marketing Management • Which of the two possible Three Factor models is most appropriate for the current analysis? • #1) Miles = mpg x gallons per hour x hours • #2) Miles = mph x hours per gallon x gallons

8. The Art of Creating a Three Factor Model Of the Biz-Cafe Machine

9. Create A Three-Factor Model of Biz-Cafe • Cups Sold Per Server is the conversion rate of a simple description of a Biz-Café machine • What is the Output? • What is the Input? • Cups Sold Per Serveris the conversion rate of a simple description of a Biz-Café machine

10. Create A Three-Factor Model of Biz-Cafe • Cups Sold Per Hour is the conversion rate of a simple description of a Biz-Café machine • What is the Output? • What is the Input? • Cups Sold Per Houris the conversion rate of a simple description of a Biz-Café machine

11. We have seen that both inputs • 1) Number of Servers, S, as an Inputand • 2) Number of Café Hours, H, as an Input • Have meaningful impacts on the Outputs of the Biz-Café Machine • Popular Outputs Include: • 1) Number of Cups Sold, Q • 2) Dollar of Sales Revenue, R • 3) Dollars of Gross Profit, G

12. When we consider the • Two Factor Machine with the Explicit impact of Hours of Operation, H, we leave the number servers, S, implicit and constant • Sales = Sales per hour x number of hours, H • When we consider the Two-Factor Model with number of servers, S, we leave the number of hours implicit and constant • Sales = Sales per server x number of servers, S

13. We wish to have both made Explicit • 1) Number of Servers, S, and • 2) Number of Store Hours, H, • made explicit as factors in the same description of Biz-Cafe machine

14. Creating a Three Factor ModelFrom a Two-Factor Model • Is a Three Stage Process • 1) A process of expansion • 2) A process of aggregation • 3) A process of decomposition

15. Step 1 • Assume that the number of Hours of operation is the strategic input • Identify the Two Factor Model you wish to expand into a Three Factor Model and in which a previously implicit variable is to be made explicit • Cups sold, Q = Cups per hour x hours, HCups Sold, Q = (Q/H) x H • Expand the ‘Cups per hour’ machine to make the number of servers explicit, S

16. Step 2 • Introduce the variable to be made explicit as unity into the Two Factor model • 1 = (Number of Servers, S) /(Number of Servers, S) = Unity • S/S = 1 • Cups Sold, Q = (Q/H) x 1 x Hours, H • Cups Sold, Q = (Q/H) x (S/S) x Hours, H

17. Step 3 Aggregate the Expansion Factors • Cups sold, Q = (Q/H) x (S/S) x Hours open, H • Cups Sold, Q = [(QxS) / (HxS)] x Hours open, H • Aggregate conversion rate, r = [(QxS) / (HxS)] • Aggregate conversion rate, r = [Q(S) / H(S)] is an ugly and large conversion factor

18. Step 4 Decompose the Big Ugly Aggregated Conversion Factor • Into two conversion rates • [(QxS) / (HxS)] = (Q/S) x (S/H) • Three Factor Model • Cups Sold, Q = (Q/S) x (S/H) x (Input: Hours, H) • where • (Q/S) = Conversion Factor #1 = (cups sold per server) • (S/H) = Conversion Factor #2 = (number of servers per hour) • H = Input Factor #3 = (Number of Hours, H)

19. Three Factor Marketing Machine • Model that makes the number of servers, S, and the number of operating hours, H, explicit elements in the Marketing Machine • Cups sold = (cups per server) x (servers per hour) x (number of hours)

20. Three Factor Machine Note: The original rate of Cups per Hour is lost and has been replaced by two new rates: Servers per Hour and Cups per Server.

21. Many people think of this as decomposing the original rate • The Rate of (Cups per Hour) into • (Cups sold per Server) x (Servers per Hour) • Cups per hour = Cups per server x servers per hour • But this is inaccurate • Reorganize the 3-Factor Machine as an identity of rates • Q = (Q/S) x (S/H) x H • Divide both sides by H • (Q/H) = (Q/S) x (S/H) • Cups per hour = (cups per server) x (servers per hour)

22. Do NOT fall into the conceptual trap • Of assuming that process of creating a multi-factor machine is the simple decomposition of the original conversion rate into 2 or more new conversion rates • Mile per gallon = Miles per Hour x Hours per Gallon • Miles per hour = Miles per gallon x gallons per Hour • Cups per hour = Cups per server x servers per hour • Do NOT lose sight of the original input

23. The other Outputs of the Two-Factor Models can be expended as well • 1) We did the output as cups sold • 2) Output: Dollars of Sales RevenueRevenue, R = (dollar sales per server) x (servers per hour) x number of hoursR = (R/S) x (S/R) x H • 3) Output: Dollars of Gross ProfitGross Profit, G = (gross profit per server) x (servers per hour) x (number of hours, H)G = (G/S) x (S/H) x H

24. We assumed that the hours of operation, H, was the strategic input • Output: Cups sold = (cups per server) x(servers per hour) x (Input: Number of hours, H) • However we could assume that the number of servers, S, is the most important input • Cups sold = (Cups per hour) x (Hours per server) x (Input: Number of Servers, S) • You build the one that is most appropriate for the analysis at hand.

25. Any Questions on the Art of • Expanding, Aggregating and Decomposing a Two-Factor Marketing Machine into a Three-Factor Marketing Machine?