Optimal May Not Be Ideal:

A Territory Alignment Case
Study

*April 28 – May 1, 2002 - Le
Meridien Hotel, New Orleans, LA - committee@pmsa.net*

* *

1. Introduction

To align a sales force, all
you’ve got to do is specify the objective function to minimize, say, the
variance of the workload of the reps. Run the optimization process and, you’ll
get an extremely well balanced alignment. That’s the winner! In actuality,
those alignments do not always live up to expectations. Oftentimes, they fare
poorly, especially considering their pedigree. How can that be? This article explains
this apparent paradox. At issue is our operations research heritage. Indeed, we tend to equate “ideal” with
“optimal” where optimal corresponds to a solution that minimizes the objective
function. The blunder is we forget the objective function may, in some cases,
be a crude approximation if not a misrepresentation of the problem at hand.

This article takes a fresh
look at the definition of optimality and underscores two problems: inadequacy
and incompleteness. Inadequacy refers to the fact that the objective function
may not lead to the intended objective. This can be corrected by spelling out a
better objective function. Incompleteness means the objective function cannot
capture all the subtleties and nuances, no matter what that objective function
may be. The article then focuses on situations that require the buy-in from
multiple parties. Each party is viewed as an embodiment of one objective
function. There is no right or wrong answer, simply different emphases on
different aspects of the problem. The implication is we need to soft pedal
optimality in favor of two more important properties: universality and
plurality. Universality captures the robustness of the solution vis-a-vis
changes in the objective function. Plurality refers to the ability of the
problem-solving process to generate multiple solutions. The article also
discusses the implementation of an automatic alignment system based on these
principles.

2. Inadequacy and
Incompleteness

The objective function
example mentioned in the introduction is inadequate for two reasons. First, it
does not recognize change is disruptive and needs to be kept at a minimum.
Going for the optimal alignment may involve expensive relocations, disruptions
in customer relationships, and frustrating reductions in the rep’s ability to
make money (wallet disruption) unless the comp plan is modified accordingly. To
paraphrase, we may be better off not to shoot for the optimal endpoint B from A
but rather to shoot for a sub-optimal B’ because of the lesser friction
involved.

Second, the objective
function has to capture the dynamics of what is involved. It has to understand
this is about physical bodies that move from one place to another and have
40-60 hours in a week. This is why concepts such as windshield time, face time,
and territory time size rightly take center stage. From that vantage point, it
is not surprising a few decent size
customers may have to be dropped (incurs too much traveling) while smaller
customers may be picked up (only a stone throw away from larger customers that
the rep will be covering anyway). Reps in high density areas, such as New York,
may have to forgo top national customers while reps in low density areas, such
as Wyoming, may have to visit customers that are well below the cut-off in the
national ranking.

Unlike inadequacy,
incompleteness is not reflective of the lack of maturity of the modeler.
However encompassing the objective function may be, there will always be
subtleties that will fall through the cracks. Here are two examples.

** Example 1.** Consider an alignment based
on a 50-50 sales-potential index. Although unlikely, this may lead to a pure
potential territory with no sales, suggesting the model is unsatisfactory.
Indeed, information has been lost in the process. One way to address this
problem is to use vector comparison (the first dimension is sales and the
second is potential) instead of the regular scalar comparison (blending of
sales and potential in one number).

** Example 2.** In team sports such as
soccer and basketball, players are deployed based on their strengths and
weaknesses. Why is it then that in alignment, sales reps are regarded as
interchangeable commodities good for 100 index points of workload? For
starters, some can accomplish the work of four. Some are VP material while
others have only retirement in mind. From a personality standpoint, some have
the skills to penetrate new accounts. Some others are great at attending to
existing business. Yet others have the energy level that will put the most
obstinate customers to shame. Expanding on the vector approach broached above,
the rep can be modeled along multiple dimensions: workload capacity,
sprinter/marathon score, hunter/skinner score, and so on. Likewise customers
can be defined along the same dimensions. Matching customers with reps then amounts to comparing vectors as
opposed to scalars.

One can keep on criticizing
the model. For instance, the model does not capture the fact that John Smith
may be unwilling to relocate because his girlfriend just secured a three-year
stint in a large bank although he is single and fresh out of college. Here is
another one: the model does not capture
the fact that Jane has been sexually harassed by a major customer and a male
rep in a nearby territory ought to cover that customer. Those criticisms can be
repeated…ad nauseam!

3. Universality and
Plurality

If there is an ideal
objective function, it may be impossible to articulate. What we can actually capture
is an ersatz function. Because we operate in a multi-party setting, there is
not one objective function at stake but many. Indeed, each person may be
regarded as embodying one objective function, suggesting an outstanding
alignment should satisfy not one but a host of objective functions. The crucial
attribute here is universality, which can alternatively be viewed as
robustness. Indeed, a universal alignment is robust in the sense that a change
in the objective function hardly degrades the quality of the alignment.

Unexpected changes in the
marketplace (e.g. product recall) or sales organization (e.g. sudden defection
of personnel) may render the best alignment irrelevant, suggesting the need for
a plan B. The best backup being a lot of backup plans, the key attribute of any
alignment design process is plurality, i.e., its ability to generate a large
number of solutions. Note plurality begets universality. As we all know, the
larger the solution pool, the better the quality of the top solution. Likewise,
the higher the plurality of the alignment design process, the higher the
universality of the alignments.

4. Implications on
Implementation

The key to achieving
universality and plurality is through a massively productive alignment design
process. Because of the theoretical complexity of the alignment process,
enumeration is simply impractical. Indeed, alignment optimization is a spatial
variation of the classic knapsack problem which is known to be NP-hard
(non-deterministic polynomial). Steepest descent or greedy algorithms are
efficient but get trapped in local minima, suggesting superior algorithms such
as simulated annealing. Incidentally, simulated annealing has the ability to
produce myriads of alignments. This stems from its very approach of building
new solutions by tweaking previous solutions.

For that reason, we chose
simulated annealing to power the Bayser Aligner, an automatic alignment tool we
developed to design ideal alignments for our clients. We started off by making
improvements to the classic Metropolis algorithm. First, we endowed memory to
the search process to boost its productivity. Second, we developed a gearbox
that automatically switches to macro-transitions trials when elementary
transitions prove fruitless. This acts like a turbo that takes the focus to a
different region of the search space, to identify better solutions.

5. Conclusion

This article articulated four points. First, make sure the objective function is adequate, i.e., captures the basic dynamics of the problem at hand. Second, do not be frustrated if your model does not capture all the nuances and subtleties the eye discerns. Incompleteness is inherent to modeling, not to your skills. Third, the attribute of an outstanding alignment is not optimality but universality, and one way to enhance universality is through plurality of the alignment design process. Fourth, simulated annealing equipped with the proper extensions is an excellent engine to deliver universal and plural alignments.