What are the best ways to interpret and communicate linear programming solutions?

1 Why interpretation matters

Interpreting linear programming solutions means understanding the meaning and implications of the optimal values, the dual prices, the reduced costs, and the slack or surplus variables. These elements can reveal important insights about the trade-offs, the sensitivity, the feasibility, and the efficiency of your model and solution. By interpreting them correctly, you can answer questions such as: How much can you improve the objective value by changing a constraint or a coefficient? How much slack or surplus do you have in each constraint? Which variables are binding or non-binding? How robust is your solution to changes in the data?

2 How to use examples

One of the simplest ways to interpret and communicate linear programming solutions is to use examples that illustrate the optimal values and the constraints. For example, if you are solving a production planning problem, you can show how much of each product you should produce, how much raw material you need, and how much profit you make. You can also compare different scenarios, such as increasing or decreasing the demand, the price, or the capacity. Examples can help you explain the logic and the intuition behind your solution, as well as the impact of your decisions.

3 How to use graphs

Another way to interpret and communicate linear programming solutions is to use graphs that visualize the feasible region, the objective function, and the optimal solution. Graphs are especially useful for two-dimensional problems, where you can plot the constraints as lines and the objective function as a level curve. You can also use graphs to show the dual prices, the reduced costs, and the slack or surplus variables as slopes, intercepts, and distances. Graphs can help you demonstrate the geometry and the algebra of your solution, as well as the effects of changes in the parameters.

4 How to use sensitivity analysis

A third way to interpret and communicate linear programming solutions is to use sensitivity analysis, which measures how much the optimal solution changes when you vary the data within certain ranges. Sensitivity analysis can be performed using software tools, such as Excel Solver or Gurobi, that provide reports on the allowable increase and decrease of each coefficient and right-hand side value. You can also use sensitivity analysis to test the validity of your assumptions, such as linearity, proportionality, and additivity. Sensitivity analysis can help you assess the reliability and the flexibility of your solution, as well as the opportunities and the risks of your model.

5 How to use tables

A fourth way to interpret and communicate linear programming solutions is to use tables that summarize the key information and statistics of your solution. Tables can include the optimal values, the dual prices, the reduced costs, the slack or surplus variables, the objective value, and the status of your model and solution. You can also use tables to compare different solutions or scenarios, such as optimal, suboptimal, infeasible, or unbounded. Tables can help you organize and present the data and the results of your solution, as well as the recommendations and the actions based on your solution.

6 How to use narratives

A fifth way to interpret and communicate linear programming solutions is to use narratives that tell the story and the message of your solution. Narratives can combine the elements of examples, graphs, sensitivity analysis, and tables, and explain them in a clear and concise language. Narratives can also highlight the main findings, the implications, the limitations, and the suggestions of your solution. Narratives can help you engage and persuade your audience, as well as convey the value and the relevance of your solution.

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?