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  • Zachary Collier

Making Trade-offs When You Have Multiple Objectives

I remember the first decision model that I ever built. It was when I was a kid, and I had this racing video game for the Nintendo. In it, you could choose from among several different race cars. Each of the cars had different stats – some had higher top speeds, some had better acceleration, some had better handling, etc. The problem was that the faster cars tended to have poor handling, and the ones with good handling were slow to accelerate. No single car dominated in each of the criteria, so it wasn’t clear which car was best.


So I had an idea – since every car had a score for each of the dimensions of performance (I think they were given a 1 to 5 score, but my memory is a bit fuzzy on the details here), I would just add up the scores given to each car, and the one with the highest score was the best car for racing.


What I had done (without knowing it of course) was to build a simple decision model which accounted for the trade-offs associated with selecting the different cars.


As it turns out, there is an entire field of study dedicated to supporting decisions involving trade-offs between multiple, conflicting objectives. The field of multi-criteria decision analysis (sometimes abbreviated as MCDA) offers a suite of tools that help decision makers prioritize courses of action when there is more than one dimension of performance to consider, making it difficult to choose a winner automatically (1). MCDA methods are grounded in concepts from economics related to the modeling of preferences and utilities.


The general decision making process follows the same few general steps:


1. Identify an overall goal: There has to be a reason for the decision. The goal for the video game example might be something as simple as “choose the best race car”.


2. Identify criteria: Criteria represent the dimensions of performance that are important to the decision maker – your various objectives. They represent the things that you value, and can be nested in the form of a tree, with criteria and sub-criteria. They should be MECE (mutually exclusive and collectively exhaustive). In the video game example, my criteria were speed, acceleration, and handling (because those were the only attributes given to me, but in reality there may be many more).


3. Weight the criteria: This is the step where the trade-offs come in. Some criteria may be more important than others. Weights give an idea of what you would give up in terms of performance along one criterion to gain in performance along another criterion. In my example above, I didn’t assign any explicit weights, but by default this means that they were all weighted equally (which is okay).


4. Identify and score alternatives: Alternatives are the things you choose between. And each alternative performs differently across each of the identified criteria. So for each alternative under consideration, they must be assessed for their performance along each dimension of interest. For example, each car (my alternatives) was already scored on a convenient numerical scale.


5. Synthesize the information and make a selection: Given the weights and scores, the information can be synthesized to come up with a prioritization of alternatives. Some methods provide a ranking, while others group alternatives into High, Medium, and Low categories. At this stage, it is good to do a sensitivity analysis to see how the results might change with changes in inputs.


Of course, this is a simple overview, and there are many more technical details involved to do this the right way. But the main takeaway is that businesses often have multiple objectives, some of which may conflict. In situations like that, when it isn’t clear what course of action to pursue, consulting with a trained expert in decision making can help guide you through the process of choosing the best path forward.


Collier Research Systems has deep expertise in decision support – taking the elements of your decision problem and identifying the best course of action to help you meet your objectives. To learn more, visit www.collierresearchsystems.com.


References:

(1) Belton V, Stewart T (2002) Multiple criteria decision analysis: an integrated approach. Springer, Boston.

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