How do you know if your stochastic programming solution is reliable?

1 What is stochastic programming?

Stochastic programming is a form of mathematical optimization that deals with problems where some of the parameters or variables are uncertain or random. For example, you may want to optimize your production plan, but you don't know the exact demand, costs, or availability of resources. Stochastic programming allows you to incorporate these uncertainties into your model and find the best solution that minimizes your expected costs, risks, or losses.

2 What are the challenges of stochastic programming?

Stochastic programming is not easy, as it involves solving complex and large-scale problems that often have multiple sources of uncertainty and nonlinear relationships. Moreover, stochastic programming solutions are not unique, as they depend on the assumptions and scenarios that you use to represent the uncertainty. Therefore, you need to be careful and critical when interpreting and implementing your solution, and check whether it is consistent, feasible, and stable.

3 How do you measure the quality of your solution?

One way to measure the quality of your solution is to use the optimality gap, which is the difference between the value of your solution and the value of the best possible solution. The optimality gap tells you how far you are from the optimal solution, and how much room there is for improvement. However, the optimality gap is not always easy to compute or estimate, especially for stochastic programming problems. Therefore, you may need to use other methods, such as sensitivity analysis, simulation, or statistical tests, to evaluate your solution.

4 How do you perform sensitivity analysis?

Sensitivity analysis is a method to examine how your solution changes when you vary some of the parameters or variables in your model. For example, you may want to see how your solution reacts to different levels of demand, costs, or resources. Sensitivity analysis can help you identify the most critical and influential factors that affect your solution, and how robust your solution is to changes in these factors. Sensitivity analysis can also help you validate your assumptions and scenarios, and test whether they are realistic and reasonable.

5 How do you use simulation?

Simulation is a method to generate and analyze random outcomes based on your model and solution. For example, you may want to simulate the demand, costs, and resources that you will face in the future, and see how your solution performs under these outcomes. Simulation can help you estimate the expected value and variability of your solution, and how likely it is to meet your objectives and constraints. Simulation can also help you compare different solutions and select the best one according to your preferences and criteria.

6 How do you apply statistical tests?

Statistical tests are methods to infer and draw conclusions from your data and results. For example, you may want to test whether your solution is significantly better than a benchmark or a competitor's solution, or whether your solution is consistent across different samples or scenarios. Statistical tests can help you confirm or reject your hypotheses and claims, and provide evidence and confidence for your solution. Statistical tests can also help you detect and correct errors and biases in your model and 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?