Mathematical Optimization

Here you will find information on the different topics of Mathematical Optimisation.

Optimal gate assignment in logistics facilities (e.g., of LTL-carriers)
Minimizing operational costs of internal processes (unloading, transfer, and loading)
The exact assignment of tours and transport relations to inbound and outbound gates
Modeling & Algorithms:
- Multicommodity flow models (with time slices)
- Column generation algorithms
- Scheduling-Heuristics

Efficient consolidation and routing of transport flows in logistics networks (rail and road freight traffic)
Optimization based on given network structures (customers, facilities, and hub locations)
Consideration of real world transport costs (e.g., based on trucks or trains) and handling costs in logistics facilities
Modeling & Algorithms:
- Multicommodity flow models (with time slices)
- Network design models
- Column generation algorithms
- Branch-and-price-and-cut algorithms
- Matheuristics

Staff requirement planning and staff planning in logistics facilities (e.g., distribution centers)
Crew scheduling and staff resource planning in the fields of transport, traffic, and waste management
Integration of hard and soft factors in planning (e.g., costs, satisfaction of staff members, legal and operational rules & restrictions)
Combination with planning or allocation of logistics resources (e.g., lift trucks, transport vehicles)
Modeling & Algorithms:
- Set partitioning & set covering models with additional constraints
- Column generation algorithms
- Lagrange relaxation and subgradient optimization
- Resource constrained shortest path algorithms

Optimization of given network structures in rail and road freight traffic
Planning of network structures („green field“) in rail freight traffic and road freight traffic
Multi-stage network planning considering different location types, hub functions and capacities
Consideration of real world transport costs (e.g., based on vehicles or trains) and handling costs in logistics facilities
Modeling & Algorithms:
- Mixed integer network design and flow models (e.g., hub location)
- Multi-allocation-models (individual routing for each transport relation) including real world transport costs based on required vehicles
- Branch & bound, branch & cut, and column generation algorithms
- Problem specific heuristics

Robust planning of groupage services via various pickup-and-delivery and vehicle routing problems
Consideration of stochastic influences (e.g., uncertain driving times and customer demands)
Minimization of required vehicles, operational costs, and arrival times
Strategic route planning based on different scenarios and target performance comparison
Modeling & Algorithms:
- Two-stage stochastic optimization models
- Savings-algorithms
- k-opt operators
- Scenario decomposition
- Evolutionary algorithms

Mixed integer multicommodity flow models (with time slices)
Mixed integer network design models
Multi-allocation-models (individual routing for each transport relation) including real world transport costs based on required vehicles
Two-stage stochastic optimization models
Set partitioning & set covering models with additional constraints
Lagrange relaxation & subgradient optimization
Column generation algorithms
Resource constrained shortest path algorithms
Branch-and-price-and-cut algorithms
Evolutionary algorithms
Problem specific heuristics / Matheuristics
Savings-algorithms & k-opt operators
Scenario decomposition

Selected projects of the Mathematical Optimization division