How can you scale your operations research models and algorithms?

1 Simplify your models

To scale your operations research models and algorithms, it's important to simplify them as much as possible without sacrificing accuracy or relevance of the results. This can be done by reducing the number of variables, constraints, and parameters. To simplify your models, you can use linear or convex approximations of nonlinear or nonconvex functions, eliminate redundant or irrelevant variables or constraints with preprocessing techniques or logical rules, aggregate or disaggregate variables or constraints with appropriate levels of detail or granularity, and use symmetry or structure to exploit the properties of your problem. Symmetry breaking, decomposition, and reformulation are all useful tools for this.

2 Choose your algorithms

When scaling your operations research models and algorithms, it's important to choose your algorithms wisely based on the characteristics of your problem and the available resources. This is because your choice of algorithm can affect the speed, quality, and reliability of your solutions. To make an informed decision, consider the type and complexity of your problem (e.g. linear, nonlinear, integer, mixed-integer, stochastic, or dynamic), the size and sparsity (e.g. number and density of variables, constraints, and parameters), accuracy and feasibility (e.g. tolerance and bounds for optimality and feasibility gaps), as well as time and memory requirements (e.g. computational and storage complexity, scalability, and parallelizability).

3 Use heuristics and metaheuristics

A third step to scale your operations research models and algorithms is to use heuristics and metaheuristics, especially when your problem is too large, complex, or difficult to solve exactly or efficiently. Heuristics and metaheuristics are methods that can find good or near-optimal solutions in a reasonable time, without guaranteeing optimality or feasibility. Greedy algorithms make locally optimal choices at each step without considering the global consequences, while local search algorithms start from an initial solution and iteratively improve it by making small changes in the neighborhood of the current solution. Additionally, population-based algorithms maintain a set of solutions and apply operators such as selection, crossover, and mutation to generate new solutions. Lastly, hybrid algorithms combine different heuristics and metaheuristics, or heuristics and metaheuristics with exact methods to exploit their strengths and compensate their weaknesses.

4 Adapt to uncertainty and dynamics

A fourth step to scale your operations research models and algorithms is to adapt to uncertainty and dynamics, which are common features of real-world problems. These features can affect the parameters, variables, constraints, and objectives of your problem, making it more challenging and unpredictable. To handle this complexity, you can use stochastic programming to incorporate uncertainty into your problem by using probability distributions or robustness measures. Dynamic programming divides your problem into stages and optimizes decisions at each stage based on the current state and future value function. Online optimization updates your problem and solution as new information arrives, while adaptive optimization learns from feedback or data to optimize decisions by using learning algorithms or policies.

5 Evaluate and validate your solutions

Evaluating and validating your solutions is an important fifth step to scale your operations research models and algorithms. This helps you assess the quality, performance, and robustness of your solutions, and identify potential sources of errors, limitations, or improvements. Sensitivity analysis measures how your solutions change with respect to changes in the parameters, variables, constraints, or objectives of your problem. Benchmarking compares your solutions with other solutions such as optimal solutions, heuristic solutions, or solutions from other methods or sources. Simulation tests your solutions under different scenarios, conditions, or environments to measure the outcomes or impacts of your solutions. Verification and validation checks whether your solutions satisfy the requirements and assumptions of your problem and whether your problem represents the reality and objectives of your situation.

6 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?