# How Decision Optimization Can Help Solve Hard Business Problems

Original article was published by District Data Labs on Artificial Intelligence on Medium

By Andrew Pearson

Decision optimization is an analytics process that tries to find the best solution among various alternatives. Unlike an ordinary decision problem, which can be posed as a yes-no question, decision optimization problems consider a vast number of variables and provide the best possible solution available from a sea of many.

In general, decision optimization utilizes standard analytical modeling, and it can solve a whole host of business problems that occur naturally in many applications. Decision optimization is widely used in economics, game theory, and operations research, with some mechanical and engineering applications. Optimization problems arise naturally in many applications, and decision optimization can be used for the traveling salesman problem, dynamic pricing, vehicle routing, sales pricing strategies, best marketing model mixes, manufacturing strategies, and many others. Put simply, decision optimization tries to find the best solution for a given problem, utilizing what can be a vast set of data.

# What is Decision Optimization?

Decision optimization is a branch of mathematics that tries to maximize the output from a large set of input variables, each of which might exert a unique influence on the output.

Decision optimization is best explained by what’s known as the “traveling salesman problem,” which asks the following question, “Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?”

The complexity of decision optimization becomes apparent with the traveling salesman problem — with ten cities, there are more than 300,000 different roundtrips; however, with 15 cities, there are no less than 87 billion trips. The traveling salesman problem isn’t just about traveling salespeople. It has many other real-world applications, such as drilling holes in circuit boards, scheduling tasks on a computer, and ordering a genome’s features.

In Gartner’s Analytic Ascendancy Model, the analytics ladder starts with descriptive analytics (what happened?) and moves up to diagnostic analytics (why did it happen?), then onto predictive analytics (what could happen?), and finally to prescriptive analytics (what should happen?). Decision optimization belongs at the top.

Optimization is one of the most challenging things for a business to achieve because it requires data from so many different sources, an enormous amount of variables to be considered, and the mathematics involved can be bewilderingly complex. However, this is where analytics reaps its biggest reward and packs its most powerful ROI punch. With today’s highly sophisticated analytics software, decision optimization can solve problems that include millions of variables, countless constraints, and numerous trade-offs, as well as produce profits that make all the time invested well worthwhile.

# Optimizing Decisions with Scenario Modeling

An example that showcases the complexity and high-profit potential of decision optimization is one of a logistics and trucking company that owns 50 trucks and wants to figure out how to produce the highest operational profit. Obviously, keeping fully-loaded trucks on the road is the best option, but how is that done? Well, the following factors and equipment must be kept in mind:

• Trucks — including their type, age, ability, fuel capacity, certifiability, etc.
• Drivers — including salary, skills, licenses, and special driving skills (i.e., certifications to drive hazardous materials).
• Shipment orders — including type, size, weight, delivery, pickup schedule, and packing restrictions.

Of course, the trucking company wants to maximize truck and staff use (barring overtime) for the highest possible profits. Still, there are all kinds of restraints, including client schedules, availability of drivers and required trucks, hazardous materials requirements, fuel costs, insurance, maintenance costs, etc. The goal would be to have the trucks full, making timely pickups and deliveries, without the need for overtime, while avoiding late penalties.

A hundred things can go wrong, and a decision optimization model would attempt to proactively take these variables into account and produce a solution that delivers the highest profit according to all these factors. The output here would be a routing and shipping schedule that needs to be strictly followed during a given time period.

One variable that isn’t specifically mentioned is customer satisfaction and, while it is an unstated part of many other variables in the model, it is one of the most important ones. Decision optimization models the vast set of different scenarios available to the logistics company and then provides it with the schedule it believes will produce the highest profit, quickest routes, lowest cost, or whatever variable the logistics company is looking to focus on.

When Dell wanted to move into a new market (i.e., selling computers with fixed hardware configurations through indirect and non-customizable channels), they turned to their in-house analytics team to build forecasting models. The team created decision optimization models that looked at ways of improving their website design, which also helped increase customer conversion rates. Dell’s forecasting model considered the supply and demand variability and the impact of external demand factors, like prices and promotions. Dell’s model reduced markdown expenditures, improved online customer conversion rates, and enhanced customer satisfaction growth, which produced a margin impact of more than \$140 million.

One of the best examples of optimization on the revenue side is dynamic pricing, a revenue optimization process used by many types of businesses. Airlines use dynamic pricing to set prices according to supply and demand constraints, as do hotels and amusement parks.

For any dynamic pricing system, there must be three set conditions that have to be understood and managed:

1. Differences in customers
2. Variation in demand
3. Product perishability and a fixed production

If these three variables can be appropriately tweaked, an increase in revenue should follow, and sometimes the revenue increase can be substantial.

# Decision Optimization Methodology

The exponential nature of decision optimization means the number of variables and options can become overwhelming extremely quickly. However, working with a standard set of procedures can help ensure things don’t get too out of hand analytically.

The steps are as follows:

1. Understand the overall concept of your system — the traveling salesman problem is simple to understand, i.e., reduce the number of round trips required for a series of journeys. It’s a concept that also makes sense for manufacturers who want to ensure the shortest route is taken to keep costs to a minimum. Lay out your concept before anything else, understand the tasks involved, and the potential paths to get there.
2. Define the goal(s) — probably the most understandable and vital step of the process. Have clear and definable goals, even sub-goals along the way to keep you on track.
3. Identify variables (the things you can control) and the constraints (the things beyond your control). Analysts will decide what the independent and dependent variables should be and theorize what type of model best fits the problem.
4. Identify the controllable inputs and outputs — here, the analysts will ensure that the correct data sets will be utilized, and data cleanliness should be ensured. The standard modeler’s warning of ‘garbage in, garbage out’ is doubly important at this stage. Small data errors can reverberate through a decision optimization model and quickly produce nonsensical results.
5. Specify all quantities mathematically — theory becomes reality here. Every variable becomes a mathematical quantity that ensures all parameters of the problem are taken into account.
6. Run the model — here, the rubber meets the road. If all the data cleansing, data prep, and modeling work was done correctly, a model that accurately reflects the real-world problem should provide results to your original goal or goals.
7. Check model for completeness, cleanliness, and correctness — analysts can check the results to ensure nothing improper is happening under the hood and all the necessary modeling steps have been completed correctly.
8. Test, experiment, fine-tune, collect feedback, and continue perfecting the process. Models should be living things, adjusting and evolving with new variables, new constraints, new model results, etc., so this entire process should be seen as repeatable and ongoing work. Every model gets stale, and this fine-tuning can keep it fresh.

# Conclusion

It is almost impossible to list all the ways decision optimization modeling can help a business. As the examples above showed, decision optimization can help businesses optimize their operation, understand supply and demand constraints, manufacture products more inexpensively, increase customer conversion rates, and generate sales.

If the goal is to minimize cost in a production system, resources such as labor, raw materials, and technology can be looked at against production targets. For an airline, hotel, restaurant, or an amusement park, the goal would be to maximize their product, whether that is an airline seat, a hotel room, a restaurant table, or an amusement park ride. For advertisers, a marketing mix model would maximize profit by only targeting customers who are most likely to utilize the offers sent them. This can be one of the best ways to decrease marketing costs while increasing its effectiveness. For an IT department, the goal would be to maximize system performance with minimal resources, runtime, and cost.

When described to a layperson, a decision optimization solution can sound quite opaque — “Linear programming-based heuristic approaches solving two-sided matching problems that are multi-objective, under various constraints.” Undoubtedly, this description goes over the heads of most non-analysts, but don’t let the complicated jargon fool you. Substantial profit can be made when decision optimization is done right. Data is the most important element of decision optimization and, today, most companies are awash in data. Taking advantage of the extraordinary opportunity this technology holds should be an easy choice. Decision optimization can help companies understand their business on such a granular level that ROI is almost assured.