### Mathematical Optimization Solving, In Action

Complex real-world problems are all around usâ€”from moving goods across global networks and managing traffic in congested cities, to orchestrating patient flow in hospitals. These kinds of problems are extremely complex, with trillions of possible solutions. To find the very best (optimal) solution, you need a powerful decision intelligence technology.

That’s where Gurobi comes in. With Gurobi’s mathematical optimization solver, you can identify optimal solutions to extremely complex problems, often in just seconds.

But it can be hard to grasp what this means without seeing it all in action.

That’s why our team has created a variety of demos, designed to give you a sense of what it’s like to solve complex problems using a mathematical optimization application. Of course, in a real-world business environment, these applications would be much more sophisticatedâ€”but the demos are here to give you a taste of what a solver like Gurobi can do.

### Workforce Scheduling Demo

Workforce scheduling in the service industry is a complex puzzle, often requiring businesses like restaurants to juggle fluctuating demands and limited staffing resources. This demo leverages a mixed-integer programming (MIP) model to minimize the hiring of temporary workers and balance the workload among permanent staff. By applying mathematical optimization techniques to a hypothetical two-week planning scenario with eight permanent workers, the demo illustrates an optimal solution that meets daily resource requirements while ensuring fairness. In essence, it shows how a mathematical optimization application can be a powerful tool for businesses aiming to achieve cost-effective and equitable workforce planning. Try the Workforce Scheduling Demo

### The Traveling Salesman Problem Demo

The Traveling Salesman Problem (TSP) is a cornerstone in the world of combinatorial optimization, posing a seemingly simple question that’s computationally complex to solve. This demo showcases how Gurobi’s Python interface can be used to construct a mathematical model of the TSP, offering an optimal solution that can be visualized. While the TSP itself is a classic problemâ€”tracing its roots back to the 1800s and gaining prominence through the works of mathematicians and computer scientistsâ€”it serves as a foundational technique for various modern applications. These range from vehicle routing and circuit design to genome sequencing and machine scheduling. The demo focuses on solving small instances of the TSP, acknowledging that larger instances require more advanced methods, such as those in the Concorde TSP Solver. Try the Traveling SalesmanÂ  Problem Demo

### Resource Matching Demo

In industries like IT outsourcing, accounting, and legal services, labor is often the most significant expense. While machine learning has been employed to score the compatibility between available resources and job requirements, the final assignment is still done manually. This leads to inefficiencies such as poor demand fulfillment, high project costs, and low customer satisfaction. The demo presents an approach that integrates machine learning and mixed-integer programming (MIP) to solve the Resource Matching Optimization (RMO) problem effectively. One of the key advantages of this MIP approach is its adaptability to changing business conditions. By simply adding new variables and constraints to the model, the Gurobi Optimizer can quickly find an updated solution, proving the method’s superiority over traditional heuristics. Try the Resource Matching Demo

### Offshore Wind Farming Demo

Offshore wind farms offer the promise of abundant, clean energy, but they come with high installation and operational costs. One of the significant expenses is laying the underwater cables that transfer electricity from the turbines to the shore. This demo uses integer programming to tackle this challenge, aiming to minimize the cost of these crucial underwater cables. By implementing the problem in the Gurobi Python interface, the demo computes an optimal cable-laying plan that minimizes costs while ensuring each turbine is connected to the shore and each cable can handle the generated current. This approach not only offers a solution for wind farms but also has broader applications in planning communication and transportation networks. Try the Offshore Wind Farming Demo

### Facility Location Problem Demo

Deciding where to build warehouses is a critical decision for any large supermarket chain. This demo uses the Gurobi Python interface to solve a facility location problem, focusing on a supermarket chain expanding in Northern England. The objective is to find the optimal trade-off between the cost of building new warehouses and the cost of delivering goods to supermarkets. While the example is specific to supermarkets, the same mathematical optimization techniques can be applied broadly in supply chain, logistics, and transportation planning. Try the Facility Location Problem Demo

### Cutting Stock Problem Demo

The cutting stock problem is a classic issue in manufacturing, particularly in industries like paper mills that need to cut large master rolls into smaller final rolls for customers. This demo showcases how Gurobi’s Mixed Integer Programming (MIP) solver can be used to generate an optimal master roll-cutting plan that minimizes both cutting and procurement costs, while satisfying customer demand for various roll sizes. Unlike machine learning techniques, which are not well-suited for this type of combinatorial optimization, mathematical optimization provides a scalable, precise solution that can save significant time and resources. Try the Cutting Stock Problem Demo

### Cell Tower Coverage Demo

Telecommunications companies face the complex challenge of providing maximum coverage while adhering to budget constraints and environmental considerations. This demo uses the Gurobi Python interface to solve a simple yet crucial covering problem: where to build cell towers to provide signal coverage for the largest number of people. While the example focuses on telecommunications, the same mathematical optimization techniques can be applied in various other sectors, offering a versatile solution for diverse covering problems. Try the Cell Tower Coverage Demo

### Mathematical Optimization Success Stories

Continue learning how mathematical optimization makes an impact on the real world. Check out our customer case studies.

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