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Bullet Holes in Bombers
Operations Research and Management Science Applied to Marketing
By
Jerry W. Thomas
Operations research achieved acclaim during World War II as a multidiscipline,
scientific approach to solve war-related operational problems. An operations
research team might be made up of a psychologist, a medical doctor, a mathematician,
and a historian, for example. Operations research investigations followed rigorous
scientific protocols and used mathematical concepts and methods. One famous
story of operations research success during the war involved an analysis of
Allied bombers returning from bombing missions over Europe. The military analyzed
the location of shrapnel damage and bullet holes in returning bombers, to identify
where to place additional armor on aircraft. Operations researchers were brought
in at the last minute to do a “confirmatory” analysis, but they
recommended that additional armor be placed on bombers everywhere except the
places with damage or bullet holes! The operations researchers realized that
analyzing damage to returning
bombers involved a sampling error. It was the bombers that did not return that
needed extra protection—and they needed it in the most vulnerable places
(the places not damaged on the returning bombers).
The power of this multidiscipline, scientific attack on problems was proven
again and again during the war. After the war, the promise and practice of operations
research moved into industry. Ford Motor Company hired 10 young U.S. Army Air
Force officers to bring advanced operations methods to Ford. This group, led
by Robert McNamara (later U.S. Secretary of Defense), soon earned the title
of “Whiz Kids” within Ford. This team transformed the managerial
systems and methods at Ford and helped publicize the benefits of operations
research and quantitative analysis. During the 1950s and 1960s operations research
(and management science, a synonymous term) methods spread rapidly throughout
U.S. industry, primarily in very large corporations. In the 1980s and 1990s
operations research and management science (OR/MS) continued to grow, fueled
by smaller, more powerful computers, the increasing availability of relatively
low-cost software, and the profusion of analytical methods and models.
However, despite the great promise of advanced quantitative methods, the ultimate
potential of OR/MS methods has never been fully realized. Corporate budget cutting
over the years, lack of senior management understanding and support, and corporate
emphasis on short-term tactical decisions over long-term optimal solutions are
some of the reasons. The utilization of OR/MS methods sinks to its nadir in
the marketing domain, despite the development in recent decades of a branch
of OR/MS devoted to marketing (i.e., marketing science).
Before exploring the application of OR/MS to marketing, some definition and
explanation might be useful. Most analysts define OR/MS to mean the application
of the scientific method and advanced analytics to the solution of business
problems. OR/MS almost always involves building a mathematical model of some
business process or system. There is an objective function; that is, a mathematical
definition of the object or thing to be optimized (to maximize profits or sales
revenue, or minimize costs, typically). Mathematical formulae are developed
to define the relationships among the variables. Algorithms and heuristics are
used to seek optimal solutions.There are probabilities and probability distributions
of relevant events. Stochastic processes (or random variations) are incorporated
into these models, and often constraints or limits are imposed on some variables
and/or solutions. Virtually all OR/MS methods can be characterized as optimization
techniques, and many involve simulation methods. The goal is to find optimal
solutions, given a set of variables, constraints, and probabilities. OR/MS offers
a varied and robust analytical toolkit. Some of the widely used OR/MS techniques
include linear programming, nonlinear programming, dynamic programming, integer
programming, Markov chain analyses, structural equation modeling, Monte Carlo
simulations, network flow models, transportation models, inventory models, decision
tree analyses, queuing theory, game theory, and Bayesian statistics. These models
and methods can answer profound marketing questions. Some examples:
- Optimal Restaurant Density. Let’s suppose
a restaurant chain (or some other type of retail chain) would like to know
“the number of units (retail stores) to build in a particular DMA (designated
marketing area) to maximize return on total investments within that DMA.”
At first this might seem like a simple, straightforward task, but an optimization
model would need to consider the following variables across DMAs:
- Warehousing, distribution, and supply chain costs
- Managerial efficiency, overhead, and related costs
- Operating costs (labor, utilities, taxes, etc.)
- Advertising efficiencies (the more restaurants, the bigger the ad budget)
- Media advertising costs
- Positioning, marketing strategy, and advertising themes and messages
- Promotion efficiencies (the more restaurants, the bigger the budget)
- The breadth and type of menu (wearout considerations)
- The size and seating capacity of each restaurant and unit sales
- DMA economic variables (employment, discretionary income, etc.)
- Competitive variables (number and mix of competitive restaurants)
- Demographic variables and trends
- Pricing power and price elasticity
- Real estate and construction costs
- Employee training and sharing efficiencies among the restaurants
- Liquor laws and liquor consumption
As the number of possible variables above suggests, deriving the maximum
return on investment (ROI) solution for a given DMA is complicated. The relevant
variables must be identified and quantified. All of the data must be organized
into a pristine analytical database, across multiple DMAs, with several years
of historical data. This data must be analyzed to derive formulae and build
algorithms, and then the ultimate model must be assembled, calibrated, tested,
and applied to determine the number of units that would maximize return on
total investment for each DMA.
In the example above, a nonlinear integer programming optimization model
with stochastic and dynamic components would most likely be recommended, but
many other quantitative approaches are available. Once implemented, such a
model could add millions of dollars to the bottom line of a major restaurant
chain (or other type of retail chain).
- Optimal Distribution System. Let’s suppose
a coffee company wants to create a distribution system that maximizes profitability
within given DMAs. The coffee company can deliver directly to the store (DSD,
direct store delivery) or ship coffee to the food retailers’ warehouses
that in turn move the product from warehouse to retail shelves (i.e., warehouse
distribution). What are the major variables to consider across DMAs?
- Out-of-stocks. What level of out-of-stocks is associated with
DSD versus warehouse distribution?
- What is the shelf space (number of facings) and shelf position implications
of DSD versus warehouse?
- What warehouses, trucks, employees, and infrastructure is required to
support DSD versus warehouse distribution, and what would be the comparative
costs?
- What is the tradeoff between spending more of the budget on media advertising
with warehouse distribution versus better in-store merchandising and control
with DSD?
- What is the relative cost of media advertising?
- Does DSD provide a product freshness (or product quality) advantage,
and is this advantage significant enough to positively affect market share?
- Does the same solution apply equally to all markets, or are some markets
better for DSD and some markets better for warehouse distribution?
- If DSD is the preferred distribution method, then what is the optimal
way to route trucks and service accounts?
As before, this is a complex set of questions. Time would be spent riding
trucks, visiting warehouses, and conducting depth interviews with warehouse
and store employees, DSD truck drivers, and executives at the coffee company
and their retail customers, to develop an understanding of the key variables
and the probable relationships among the variables. An analytical database
would be assembled and studied. The work would include product testing, measurement
of out-of-stocks, and brand share analyses. Transportation models, inventory
models, and advertising response models would be used to help derive the final
solutions.
- Optimal Product Line. Let’s suppose an
automotive manufacturer wants to create an optimal product line to help it
succeed over the next 20 years. What variables might be considered in creating an OR/MS optimization model?
- What is the range of market conditions (scenarios) the manufacturer
might face over the next 20 years?
- What are the probabilities of these market conditions or states?
- What are the longterm trends in fuel prices? Fuel types? Technological
probabilities?
- What are the boundaries of consumer acceptance, given extreme scenarios?
- How much variation in product line is permissible before brand image
begins to weaken? That is, what are the practical limits of brand elasticity?
- What is the optimal mix of cars, trucks, and other types of vehicles,
given different scenarios?
This project is challenging because it involves long-range forecasting
of the economy and future technologies. Econometric models would be part
of the solution, as would forecasts of demographic trends. Depth interviews
and surveys would be conducted among industry experts and executives to
identify new technologies and the future probabilities of each. Choice modeling
would be used to measure consumers’ “product line” preferences
and elasticities, given different market conditions. Lastly, all of this
would be pulled together in an integrated
model to identify optimal solutions.
- Optimal Positioning and Advertising Messaging.
What if an Internet dating service wants to optimize its television advertising?
Communicating in an optimal way with the target audience via a particular
media is a very complicated problem because the communication partially defines
the audience, and the audience partially defines the communication. An optimal
solution would involve some of the following variables:
- What is the architecture of target-audience possibilities?
Demographic? Attitudinal? Behavioral?
- What are the strategically viable positionings?
- What are viable themes, messages, and taglines?
- What imagery and colors correspond to the various positionings?
- What sounds and music best reinforce the advertising themes and messages?
- What characters and voices best support the messaging?
- What are the interaction effects among the variables?
- What contextual variables moderate the influence of particular positionings,
themes, and messages?
- What mix of advertising media optimizes profits?
In this example, some good old-fashioned qualitative research would be
used to help define the range of possibilities (positionings, themes, messages,
taglines, colors, imagery, etc.).
Survey research would be employed to provide a first approximation of target-audience
definition. The final optimization model would involve choice modeling experiments
among the broadly-defined target audience to identify a set of optimal solutions,
which would also precisely define corresponding optimal target audiences.
Other types of marketing applications for OR/MS methods include:
- Route or delivery system optimization
- Promotional optimization
- Package design optimization
- Product features optimization
- Pricing optimization
- Industry and category forecasting
- Inventory optimization
- Retail category optimization
- Store design optimization
The Team
The concept of a multidiscipline team in OR/MS has tended to fade away over
the years as the glitter of advanced quantitative techniques has garnered most
of the attention. Despite all of the mathematical advances and software improvements,
the multidiscipline team approach should not be forgotten. The value of different
educational and experiential backgrounds and different viewpoints in solving
complicated problems is time-tested and proven. Marketing research is a member
of the team and plays an important role in bringing new information and new
perspectives into the modeling process. Depth interviews, focus groups, ethnography,
and surveys can bring the experience and knowledge of customers, truck drivers,
shelf stockers, warehouse workers, store managers, and senior executives into
the analyses and modeling, and lead ultimately to much better and more accurate
OR/MS solutions.
The Challenge
The great challenge facing marketing executives at all levels is how to make
better decisions (i.e., decisions that maximize the long-term returns on marketing
investments). Rarely are these major decisions simple and obvious, even when
they appear to be. As the examples in this article suggest, many complex and
interacting variables must be understood and modeled to find the ultimate answer.
OR/MS methods, combined with marketing research, can be a valuable ally in the
search for long-term optimal solutions. So, strap on your parachute, put on
your goggles, and fly your business on the right course at the right altitude—with
armor in the right places.
Copyright © 2010 by Decision Analyst,
Inc.
This article may not be copied, published, or used in any way without written
permission of Decision Analyst.
About the Author
Jerry W. Thomas (jthomas@decisionanalyst.com)
is President/CEO of Dallas-Fort Worth based Decision Analyst. He may be reached
at 1-800-262-5974 or 1-817-640-6166.
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