Meets the Traveling Salesman


Creytn Crosby, Analyst at EP

While in college, an interesting yet classic data problem was presented to my class to demonstrate just how complicated problems can become when exact solutions are desired – The Traveling Salesman. The problem goes something like this:

Say that we have a Traveling Salesman who is assigned many different cities across the United States. His job is to travel to each of the cities, meet with prospective clients, sell his wares, and then move on to the next city. After finishing his tour across all the cities, the Traveling Salesman is to return home – hopefully to enjoy some well-earned rest.

Priding himself on his efficiency, our Salesman doesn’t want to visit any city twice, and he wants to find the route that will require him to travel the shortest total distance. Whether this resource in actuality is total distance, time or capital spent it doesn’t much matter, the problem remains essentially the same.

With just a few cities, say three to five, this problem seems straightforward. Simply trace out possible routes, add up the distances, and list them out to find the shortest route. These routes are called ‘Hamiltonian Cycles.’1 However, as this list of cities grows, the total possible routes from which to choose quickly becomes a number far too big for us to efficiently solve in a reasonable timeframe. In ONE EXAMPLE, a list of 304 cities across the country results in 2.3 x 10^624 combinations2! To put this number in slight better perspective, that is far more than the observable atoms in the universe… Even for a supercomputer, getting a total, complete, and for-sure answer to this problem is close to impossible, and definitely not efficient for a Salesman who needs to move and work quickly in his market. There are just too many options to justify completely solving the problem. Big Data scientists have loved and shared this problem many times, but even with their complex algorithms and processing powers, they have come to the same imperfect conclusion.

So why does the Salesman worry about this in the first place? Most all of us, whether salespeople, business owners, data scientists, students, or employees have strong desires to do the best and be the best we can, and we realize the power that big data has to magnify those efforts. Accurately gathered, analyzed, and interpreted data is indeed a world-changing resource, but in our data-saturated world, it is important that we remember the Traveling Salesman as we determine how to best make our decisions.


1 THE DATA POINTS THAT SERVE AS ‘STOPS’ ON OUR ROUTE TO THE BEST DECISION. Not all KPI’s are created equal, and as you continue to grow and expand your operations, it is important that data is funneled as it travels upward. Perhaps the color, id number, manufacture date, and shelf location of all items are vital pieces of data for the operations manager, but the factory or divisional manager will find this information as more of a detour than a destination. In SaaS-model companies, this might take the form of overly complex CRM pages, sales records, or historical data. In whatever case, we should consider what we really need to know.

2 THE OVERALL BENEFIT OF CONSIDERING THIS NEW DATA. We should ask ourselves, “If this company could perfectly tailor our product/service/offering to the customer based on this one piece of data, how much value would this create?” Working in business valuation, Economics Partners realizes that establishing this incremental value can be difficult, but as experts in your field, you can use that experience to determine what difference this information would or could make to your business model, your costs, or your customers. If this estimate of incremental or marginal value is significant, then it may qualify to join the ranks of the elite KPI’s present in most or all reports.

3 THE RESOURCES SPENT IN GATHERING, STRATIFYING, AND INTERPRETING THAT DATA. In their fervor to use big data to take over their respective corners of the world, many a starry-eyed entrepreneur has stared blankly through their glass-walled office window (resting their gaze somewhere around the coffee-maker) and has mumbled “wouldn’t it be great if we could track such-and-such? Yeah, that would be amazing…” without then examining the total costs associated with that decision. This data could require surveying consumers, programming new dashboards, training salespeople on new questions, adding new webpage requirements, entering the raw data into your system, and meeting with others to again transfix on the coffee-maker and now ask “So, what can we actually do with this data?” These all require actual resources, and so we must all be aware of the many different forms these costs can take and prepare to respond accordingly.


Reach out to an analyst to ask questions or to get started on your valuation.


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    Just as the Traveling Salesman will have to begin his route whether he has the best route or not, so we must all move forward with the best information we have. We cannot be held back by the fear of better routes, nor can we allow the constant nag for more information distract us from fully utilizing the amazing insights we have already gathered. Simply pack your suitcase, keep your papers in order, and hit the road.


    Economics Partners (EP) is among the most active transfer pricing and valuation firms in the country and has been ensuring the highest quality analysis on the market for over a decade. EP specializes in the application of microeconomics, financial analysis for tax, financial reporting, and strategic matters.

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