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What are the most effective ways to interpret optimization results?

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Optimization is a powerful technique in operations research that can help you find the best solutions for complex problems involving multiple objectives, constraints, and variables. However, optimization results are not always easy to interpret, especially when you deal with nonlinear, stochastic, or multi-objective models. In this article, you will learn some of the most effective ways to interpret optimization results and gain insights from them.

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Anshul Saxena, PhD

Demystifying business through LLM and Quantum Machine Learning| LLM Psychologist | Author | Educator |…
Charles Rosa

Fellow, Operations Research at XPO Logistics, Inc.
Ahmet Kandakoglu

Senior Manager, Data Science and Advanced Analytics @ IATA | Researcher | Lecturer | Top Operations Research Voice on…

1 Check the model status

The first thing you should do when you get optimization results is to check the model status. This tells you whether the solver was able to find an optimal solution, a feasible solution, or no solution at all. The model status also indicates if there were any errors, warnings, or limitations in the optimization process. You can usually find the model status in the output or report of the solver you used, such as Excel Solver, Gurobi, or CPLEX. If the model status is not optimal or feasible, you should check your model formulation, data, parameters, and solver settings for any issues that might prevent the solver from finding a good solution.

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Charles Rosa

Fellow, Operations Research at XPO Logistics, Inc.
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Sometimes the model status may tell you that the problem has no solution, but, more particularly, is unbounded. Or that you've exceeded the time, iteration, or memory limit to find a solution. Or that you are "optimal" within a particular tolerance (e.g., mipgap). There are a lot of ways status' that a solver might conclude with.

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2 Analyze the objective value

The next thing you should do is to analyze the objective value, which is the value of the objective function at the optimal or feasible solution. The objective value reflects how well the solution meets your goal, whether it is to maximize profit, minimize cost, or achieve some other measure of performance. You should compare the objective value with your expectations, benchmarks, or targets, and see if the solution is satisfactory or if there is room for improvement. You should also check the sensitivity of the objective value to changes in the input data, parameters, or constraints, and see how robust the solution is to uncertainty or variation.

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3 Examine the decision variables

The third thing you should do is to examine the decision variables, which are the variables that you can control or adjust in the optimization model. The decision variables represent the choices or actions that you need to make or take to achieve the optimal or feasible solution. You should look at the values of the decision variables and see if they make sense, are realistic, and are consistent with your assumptions and constraints. You should also check the sensitivity of the decision variables to changes in the input data, parameters, or constraints, and see how flexible the solution is to different scenarios or preferences.

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Anshul Saxena, PhD

Demystifying business through LLM and Quantum Machine Learning| LLM Psychologist | Author | Educator | Inventor|Researcher
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When I'm working on an optimization model, the third step I focus on is examining the decision variables. These are the elements within my control, the levers I can pull to steer towards the best possible outcome. I scrutinize the values of these variables, ensuring they're sensible, realistic, and align with the assumptions and constraints of my model. Additionally, I assess how sensitive these decision variables are to variations in input data, parameters, or constraints. This helps me understand the flexibility of my solution under various scenarios and preferences, and whether it can adapt to changing conditions.

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4 Evaluate the constraints

The fourth thing you should do is to evaluate the constraints, which are the conditions or limitations that you need to satisfy or respect in the optimization model. The constraints reflect the physical, technical, legal, or ethical aspects of the problem that you cannot violate or ignore. You should look at the values of the constraints and see if they are met, violated, or binding at the optimal or feasible solution. You should also check the sensitivity of the constraints to changes in the input data, parameters, or objective function, and see how tight or slack the constraints are and how they affect the solution.

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5 Explore the trade-offs

The fifth thing you should do is to explore the trade-offs, which are the compromises or sacrifices that you need to make or accept in the optimization model. The trade-offs arise when you have multiple objectives, conflicting constraints, or competing interests that you need to balance or reconcile in the optimization model. You should look at the trade-offs and see how they influence the optimal or feasible solution and the objective value. You should also check the trade-offs to changes in the input data, parameters, or weights, and see how they alter the solution and the objective value.

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6 Visualize the results

The sixth thing you should do is to visualize the results, which is to use graphs, charts, tables, or other visual tools to display and communicate the optimization results. Visualizing the results can help you understand, explain, and present the optimization results in a clear, concise, and compelling way. You should choose the appropriate visual tools for the type, size, and complexity of the optimization results, and use them to highlight the key features, patterns, and trends of the optimization results. You should also use visual tools to compare and contrast different solutions, scenarios, or alternatives, and to illustrate the trade-offs, sensitivities, and uncertainties of the optimization results.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Ahmet Kandakoglu

Senior Manager, Data Science and Advanced Analytics @ IATA | Researcher | Lecturer | Top Operations Research Voice on LinkedIn
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In my opinion, the key point is to explain the contribution of the model clearly and shortly using business performance measures or objectives. You should also highlight how you solve the problem or improve the current situation in terms of labour, time, money, etc. Interpreting the model results in terms of status, objective value, decision variables, constraints, reduced costs, shadow prices, etc. are on the technical side which can be an input for detailed recommendations for the decision makers, executives.

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What are the most effective ways to interpret optimization results?

1

2

3

4

5

6

7

1 Check the model status

2 Analyze the objective value

3 Examine the decision variables

4 Evaluate the constraints

5 Explore the trade-offs

6 Visualize the results

7 Here’s what else to consider

Operations Research

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What are the most effective ways to interpret optimization results?

1

2

3

4

5

6

7

1 Check the model status

2 Analyze the objective value

3 Examine the decision variables

4 Evaluate the constraints

5 Explore the trade-offs

6 Visualize the results

7 Here’s what else to consider

Operations Research

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