# Combinatorial Optimization

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We use combinatorial optimization for tackling the toughest Supply Chain Optimization problems in vehicle routing, integer and constraint programming. We help you to setup and maintain end-to-end optimization workflows to make better decisions.

## Combinatorial Optimization

### Which problems can be solved by combinatorial optimization?

Combinatorial optimization seeks to find the best solution to a problem out of a very large set of possible solutions. Here are some examples:

• Vehicle routing: Find optimal routes for vehicle fleets that pick up and deliver packages given constraints (e.g., “this truck can’t load more than 10 tons” or “all deliveries must be made within a one-hour time window”).
• Scheduling: find the optimal schedule for complex set of tasks, some of which need to be performed before others, on a fixed set of machines, or other resources.
• Bin packing: pack as many objects of various sizes as possible into a fixed number of bins with maximum capacitites.

In most cases, problems like these have a vast number of possible solutions—too many for a computer to search them all. To overcome this, we use state-of-the-art algorithms to narrow down the search set, in order to find an optimal (or close to optimal) solution.

## Combinatorial Optimization Technologies

Constraint Programming – A set of techniques for finding feasible solutions to a problem expressed as constraints (e.g., a machine can’t be used for two jobs simultaneously, or the distance to the warehouse must be less than the maximum warehouse distance, or no more than five customers can be assigned to a warehouse at once).

Linear and Mixed-Integer Programming – The linear optimizer finds the optimal value of a linear objective function, given a set of linear inequalities as constraints (e.g., assigning people to jobs, or finding the best allocation of a set of resources while minimizing cost).

Vehicle Routing – A specialized solver for identifying best vehicle routes given constraints.

Scheduling – Finding the optimal schedule for complex set of tasks, some of which need to be performed before others, on a fixed set of machines, or other resources.

Graph Algorithms – Algorithms for finding shortest paths, min-cost flows, max flows, and linear sum assignments.

Bin packing – is the problem of trying to find a set of objects to pack into containers (or bins). The objects have weights (or volumes), and each container has a capacity, which is the total weight (or volume) the container can hold.

## How does it work?

1. Define Project: Together, we define the project outcomes, deliverable, scope of the effort, business objectives and identify the data sets that are going to be used.
2. Data Integration: Data mining for Combinatorial Optimization prepares data from multiple sources for analysis.
3. Data Preparation: We inspect, clean and model data with the objective of discovering useful information. Also data enrichment belongs to this step.
4. Modelling: We select and configure the mathematical optimization engines needed for solving all problem specific requirements.
5. Scenario Comparison: Together, we define all relevant KPI’s to compare different scenarios with each other.
6. Visualization: We help you to build interactive dashboards for result visualization and evaluation. These dashboards can be shared with all relevant stakeholders within your organization.

### Find optimal solutions

Find the best solution to problems out of a very large set of possible solutions. In most cases, problems in Supply Chain Optimization have a vast number of possible solutions—too many for a computer to search them all.

### Reusable end-to-end workflows

If the data sources change, just reuse the existing workflows for recalculation. No manual effort needed. Setup schedules for recalculation to monitor and optimize, permanently.

### Flexibility

Your use case does not have to be adapted to the needs of a software software, we help you to configure the perfect solution for your planning problem.

### Data driven decisions

Make better decision based on data driven end-to-end optimization workflows.

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