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

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

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.

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

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

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

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

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

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 Server is the conversion rate of a simple description of a Biz-Café machine

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 Hour is the conversion rate of a simple description of a Biz-Café machine

We have seen that both inputs 1) Number of Servers, S, as an Input and 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

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

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

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

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, H Cups Sold, Q = (Q/H) x H Expand the ‘Cups per hour’ machine to make the number of servers explicit, S

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

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

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)

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)

Three Factor Machine Input Factor: HNumber of Hours Conversion factor #2, S/HServers per Hour Conversion factor #1, Q/SCups Sold per Server Output: QNumber of Cups Sold 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.

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)

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

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 Revenue Revenue, R = (dollar sales per server) x (servers per hour) x number of hours R = (R/S) x (S/R) x H 3) Output: Dollars of Gross Profit Gross Profit, G = (gross profit per server) x (servers per hour) x (number of hours, H) G = (G/S) x (S/H) x H

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.

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