How do you solve complex network problems?

1 Network models

The first step to solve a network problem is to define a network model that represents the situation you want to analyze. A network model consists of a set of nodes, which are the entities or locations involved in the problem, and a set of links, which are the connections or relationships between the nodes. Each node and link can have attributes, such as costs, capacities, demands, or flows, that describe their characteristics or constraints. You also need to define an objective function, which is a mathematical expression that measures the performance or value of a network solution.

2 Network optimization

The second step is to find the best network solution that maximizes or minimizes the objective function, subject to the attributes and constraints of the nodes and links. This process is known as network optimization, and there are several methods available depending on the type and complexity of the problem. Linear programming (LP) is a technique that can solve network problems with linear objective functions and constraints, but may not capture some nonlinear or integer aspects. Integer programming (IP) can model more realistic and complex network problems, but is more difficult to solve than LP. Heuristics and metaheuristics are useful for problems that are too complex or large to solve with exact methods, such as LP or IP. Heuristics use logic or rules to generate or improve solutions, while metaheuristics use strategies or mechanisms to explore or exploit the solution space.

3 Network analysis

The third step is to evaluate and compare the network solutions obtained from the optimization methods, and to identify the trade-offs, sensitivities, or uncertainties involved in the problem. This process, known as network analysis, can be done with different tools such as sensitivity analysis, scenario analysis, and visualization. Sensitivity analysis measures how the network solution changes with respect to changes in parameters or inputs like costs, capacities, or demands. It can help to understand the impact of uncertainty, variability, or errors in the data and find critical or binding constraints of the problem. Scenario analysis compares different network solutions under different scenarios or assumptions such as demand growth, supply disruption, or policy change. It can help evaluate robustness, flexibility, or risk of the network solutions and find best or worst case scenarios of the problem. Visualization displays the network solution in a graphical or interactive way using maps, charts, or dashboards. This can aid communication, interpretation, or exploration of the network solution and uncover patterns, trends, or anomalies in the data.

4 Network software

The fourth step is to use network software that can help you implement the techniques and tools described above. Network software can be divided into two categories: general-purpose software, which can solve a variety of network issues using various methods and tools (such as Excel Solver, GAMS, CPLEX, or MATLAB), and special-purpose software, which can address specific types of network problems using tailored methods and tools (including TransCAD, ArcGIS Network Analyst, NetLogo, or NetworkX).

5 Network applications

In the fifth step, you can apply network models, optimization, analysis, and software to real-world problems or situations that require network solutions. For instance, network models can be used in logistics to plan and design supply chains or distribution networks while optimizing costs or service levels. They can also be used in transportation to analyze traffic flows and manage transportation modes while optimizing travel time or safety. Additionally, network models can be utilized in telecommunications to configure communication networks and optimize bandwidth or latency. Lastly, they can be applied in social sciences to study social networks and optimize influence or reach.

6 Network skills

The sixth and final step is to develop or enhance your network skills, which are the knowledge, abilities, or competencies that can help you solve complex network problems using operations research. To do this, you need to have a solid foundation in mathematics, especially in linear algebra, calculus, and discrete mathematics. Additionally, you must have a good command of programming languages, software tools, and data structures. You also need strong analytical skills to formulate, solve, and evaluate network problems using logical thinking, critical thinking, and problem-solving skills. Finally, you must have an effective way to present, explain, and discuss network solutions using verbal, written, and visual skills.

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?