## Fachbereich Mathematik

### Refine

#### Year of publication

- 2003 (4) (remove)

#### Language

- English (4) (remove)

#### Has Fulltext

- yes (4)

#### Is part of the Bibliography

- no (4)

#### Keywords

- Lineare Algebra (2)
- Mathematikunterricht (2)
- Modellierung (2)
- linear algebra (2)
- mathematical education (2)
- modelling (2)
- praxisorientiert (2)
- Dynamic cut (1)
- Earliest arrival augmenting path (1)
- Label correcting algorithm (1)
- Label setting algorithm (1)
- Lineare Optimierung (1)
- Multiple criteria analysis (1)
- Network flows (1)
- Simplex (1)
- Stücklisten (1)
- bills of materials (1)
- linear optimization (1)
- praxis orientated (1)
- simplex (1)

#### Faculty / Organisational entity

In this paper we discuss an earliest arrival flow problem of a network having arc travel times and capacities that vary with time over a finite time horizon T. We also consider the possibility to wait (or park) at a node before departingon outgoing arc. This waiting is bounded by the value of maximum waiting time and the node capacity which also vary with time.

We generalize the classical shortest path problem in two ways. We consider two - in general contradicting - objective functions and introduce a time dependency of the cost which is caused by a traversal time on each arc. The resulting problem, called time-dependent bicriteria shortest path problem (TdBiSP) has several interesting practical applications, but has not attained much attention in the literature.

This publication tries to develop mathematical subjects for school from realistic problems. The center of this report are business planning and decision problems which occur in almost all companies. The main topics are: Calculation of raw material demand for given orders, consumption of existing stock and the lot sizing.

Linear Optimization is an important area from applied mathematics. A lot of practical problems can be modelled and solved with this technique. This publication shall help to introduce this topic to pupils. The process of modelling, the reduction of problems to their significant attributes shall be described. The linear programms will be solved by using the simplex method. Many examples illustrate the topic.