Topology: Powerful and Versatile Tool to Improve OR Systems

Topology is a powerful tool that can be used to solve a wide range of operations research problems. By using topology, operations researchers can design more efficient and reliable networks, schedules, routes, and facility locations.

Operations research (OR) is a field of applied mathematics that uses mathematical models to solve problems in business and other fields. Topology is a branch of mathematics that studies the properties of shapes and spaces that are preserved under continuous deformations.

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OR and topology are related in a number of ways. For example, OR can be used to solve problems in network design and optimization, which are often topological problems. Additionally, OR can be used to develop models of complex systems, such as transportation networks and manufacturing systems, which can be represented as topological networks.

• Airline scheduling: Topology can be used to schedule flights in a way that minimizes the total time it takes for passengers to reach their destinations. For example, topology can be used to create a schedule that minimizes the number of layovers that passengers have to make.