# What is Mathematical Optimization?

### Mathematical Optimization: Make Better Business Decisions

Mathematical Optimization, also known as mathematical programming, is an extremely powerful prescriptive analytics technology that enables companies to solve complex business problems and make better use of available resources and data. Mathematical programming allows you to capture the key features of a complex real-world problem as an optimization model. An optimization model is comprised of relevant objectives (business goals), variables (decisions in your control) and constraints (business rules) to recommend a solution that generates the best possible result. A math programming solver is the computational engine that reads the optimization model and then delivers an optimal feasible solution.

### Mathematical Optimization in Industry

Mathematical programming technologies are being used by leading companies, often resulting in tens or even hundreds of millions of dollars in cost savings and revenue.

The following are examples of industries and companies using mathematical optimization:

• Electrical power distribution: New York ISO uses optimization to choose the most cost-effective way to deliver electricity to customers.
• Finance: Betterment uses optimization to choose the optimal mix of assets, which maximize after-tax returns while minimizing risk.
• Government: The FCC used optimization to generate the first two-sided spectrum auction, generating $20 Billion in revenue. • Logistics: FedEx streamlines costs by optimizing the routing of packages through their shipping network. • Manufacturing: SAP uses optimization to efficiently schedule the production of goods in factories in order to meet customer orders. • Sports scheduling: The NFL uses optimization to compute the best possible league schedules. ### Efficient Use of Resources Mathematical Optimization can be implemented wherever critical resources are being utilized. Mathematical programming models can: • Capture the important decisions in your business process • Should I build this product? • Should I send this truck to Boston? • Should I buy this stock? • Capture the resources potentially consumed by these decisions • Building this product uses these machines. • Sending this truck consumes time, fuel, manpower. • Capture the potential conflicts between these activities • The total budget is$X.
• Building these two products requires the same machine.
• If I send this truck to Boston, I can’t deliver anything to New York.
• Suggest a plan of action that maximizes the overall efficiency of the process

You can specify what it means to maximize efficiency – maximizing profit, minimizing cost, minimizing delays, etc. Similarly, your resources can be anything – money, raw materials, machines, workers, etc. You can translate the often very tangible items that are part of a business process into the mathematical objects that are used and then represent them in the optimization model.

### Mathematical Optimization and Solvers

Math Programming Solvers are the primary tool used in mathematical optimization. Users can use a broad range of programming or modeling languages to build mathematical models, then call a solver, such as the Gurobi Optimizer, to automatically consider trillions or more possible combinations to find the best one. Mathematical Programming Solvers like the Gurobi Optimizer can be used as a decision-making assistant to help guide choices of a skilled expert, or as a fully automated tool to make decisions with no human intervention.