Algorithms

ORion-PI^® responds to the growing dynamics and flexibility of the markets with a new mathematical approach: the Quant-based Combinatorial Optimization. This in-house developed technology has been successfully employed in operative production planning for the past ten years.

In the optimization of logistics networks and the calculation of strategic supply chain scenarios (SCM) Axxom uses its own algorithms as well: The so-called Cost Scaling-Algorithm (CSA) exceeds the well-known linear programming approach, e.g. in that it also maps non-linear restrictions such as freight rates, fixed and complexity costs.

Conventional planning systems often are based on inflexible solution patterns. Our optimization technologies proopt5^® and proomm^® combine a number of different optimization methods and selects – depending on the task – the most adequate among all available algorithms. Exemplary approaches are:

• The Hungarian method
  This combinatorial approach is used for the assignment of quants – smallest disposition units – to the optimal resource at the right time.
  
• Evolution method
  Modeled on the example of nature this method not only considers isolated plans but the over-all evolutionary development of a system.
  
• Search tree
  The search tree method generally applies when algorithms are combined to meet very specific restrictions. The method shows: the more constraints, the closer one gets to the optimal solution.
  
• Heuristics
  All classical planning rules and heuristics are available in ORion-PI^®.
  
• Branch-and-bound method
  The branch-and-bound method generates with each iteration one solution which considers all constraints. The new control parameters then are adapted with the aid of evolutionary methods.