Mathematical Decision Making

We offer mathematical consulting and software solutions (digital decision support systems and full decision automation with reporting) for a diverse set of business intelligence problems.

What sets us apart?

We are devoted mathematicians with a strong background in software development. We understand both, the mathematical optimization of business problems as well as the need for good software UI/UX for users to interact with complex tools. We build our problem solutions upon an expressive mathematical model giving flexibility for changes and customization wishes, as well as robust results – where commonly used (greedy) algorithms fail. Whereas already established software is mostly only tailored for very specific problems, but probably general within the problem setting, we intend to build solutions that can be trimmed to the specific customer and are furthermore adaptive to future business or legal requirements. Using optimization to maximize predefined objective functions, we are able to create solutions that really fit the customer’s needs.

Solutions

Scheduling Problems for Workforce Planning

Scheduling of the available workforce is a major success factor. We provide tools that support both your staff and planners in finding better schedules.

Staff Rostering

Generate optimal and fair allocation plans for a given set of shifts and staff. The focus lies in satisfying required tasks, while fulfilling given multiple constraints like for instance legal requirements.

Timetabling

Find feasible time slots for a given set of events (e.g. courses), where events depend on other resources (e.g. lecturer, class room, group of students).

Supply Chain Management and Logistics

We analyze and optimize decisions involving the supply chain as a whole (procurement, production, distribution and sales). Depending on the business this may include several of the solutions below in an integrated approach.

Warehouse Design

Strategic planning for the overall warehouse layout and flow considering a network of actions and nodes.

Warehouse Management & Order Processing

Handle orders as quickly as possible. Modern technology allows automation of many tasks (e.g. picking) aiming for high throughput using methods from combinatorial optimization. Calculate the optimal order timeline when processing multiple orders or deliveries, minimizing delivery time, costs and other resources.

Production Planning

Optimization of the production and packaging process by efficiently scheduling the available machines and resources (see also Staff Rostering) to gain more output with less effort.

Vehicle Routing

Optimal map-based routing for vehicles reaching different destinations while saving the drivers’ (idle) time.

Maintenance Planning

Find the right priorities when planning how much effort will be put into maintaining different resources, keeping your business alive while also reducing costs.

Cutting Stock Problems

Best way of cutting expensive material in order to reduce cutting time and waste.

Facility Location Problems

Plan facilities like factories, distributers and stores strategically, ensuring short paths for supply routes and optimal accessibility.

Evacuation Problems

Save lives in critical situations, when goods or support are limited and have to be distributed efficiently.

Financial Planning

Forecasting

Modelling and simulation of financial forecasts even based on many variables assuming uncertainty. Calculating robust estimators, while still considering the possible outcome of an unlikely event.

Portfolio Optimization

Select a best portfolio of assets with respect to a diverse set of possible constraints and an objective depending on your business needs.

Strategic Decisions

Negotiations

Making decisions in complex negotiations, not only based on instinctive feeling, but using objective strategies based on game theory. Depending on your business needs, we offer a mathematical analysis of your current position and possible strategies as a consulting option or a full-fledged digital negotiation support system.

Mechanism Design and Auctions

Rules and actions based on game theory for multiple involved parties, leading to a satisfying outcome depending on the current business case. One important type of mechanisms are fair auctions, where bidders’ needs and their true values of the asset is respected yet delivering a fair price for all parties involved. Depending on the current use-case, these mechanisms (auctions) can be either defined via public contracts (e.g. for auctions of oil drilling rights) or deployed via a software system used by all parties involved (e.g. ad auctions currently used by Google or Facebook).

Our Methodology

1. Current state evaluation
2. Problem definition
3. Data evaluation and generation
4. Prototyping
5. Development of a solution in work packages
6. Iterative deployment of work packages
7. Iteration and support

Tools = AI + Data Science + Big Data

• Mathematical modelling
• Machine learning
• Mathematical optimization
• Game theory
• Scalable data systems
• Statistics and reporting

Results

• Objective recommendations (classic mathematical consulting)
• Decision support system
• Decision automation system

Success Factors

• Solutions are robust and adaptive to changes caused by new regulations and changes in the problem environment
• Integration of stakeholders in the development process
• Handling the multi-objective nature of many problems
• Integration of optimization algorithms into a decision support system allows for a maximum of flexibility and freedom for the decision makers