Tagungsband zum Doctoral Consortium der WI 2009

set, the required levels of safety stock can be determined to buffer against the given demand
uncertainties. The results in terms of the considered configuration parameters for the production
and distribution network provide the necessary basis for the cost analysis.
2. Solution approach
WI Doctoral Consortium 2009 27
This paper outlines the solution approaches for the subproblems 1) modelling aspects, 2) safety
stock allocation and 3) setting production planning parameters. For 1), a model of the product,
production and distribution system is defined. The safety stock allocation problem (2) is
computationally very complex and not solvable in reasonable time. Therefore, we develop a local
search heuristic that makes use of information about the network structure, demand uncertainty
information and demand patterns to guide the search for suitable stockpoints. Considering the fact
that the result of the optimisation serves as the basis for a cost analysis in the first place, the
guaranteed optimality of the solution is not a primary requirement and the use of heuristic
optimisation methods is reasonable. For the production planning parameter subproblem (3), a
mixed integer problem is formulated and solved with standard software.
2.1. Modelling product assortments as production and distribution networks
The first step is to define a formalism to describe assortment models as the basis for the entire
analysis. This formal model must capture all the relevant information required to perform a cost
assessment and also serves as the basis for the subsequent steps. It must capture all information
about the product and distribution structure to allow for the evaluation of inventory and setup cost
as well as the definition of assortment changes, both in product and in distribution structure.
This work deals with consumer goods supply chains, which implies several characteristics for the
organisation of the supply chain, the products it produces and the production processes involved. In
the supply chains considered, we distinguish four different types of actors (in the order found
upstream the supply chain):
• End customers: For consumer goods manufacturers, end customers are retailers and
wholesalers as well as professional users. Note that the term customer generally is not a
synonym for the consumers here.
• Local sales companies with distribution warehouses: End customers order at local sales
companies that ship the products from their distribution warehouses to the customers' stores
or warehouses.
• Production facilities: A number of specialised production facilities each produce a certain
product range and supply the local sales companies.
• Suppliers: External suppliers supply the production facilities with raw and packaging
material as well as selected semi finished components or finished products.
We define a model for a certain assortment with all its products, the customers who order these
products, the sales companies that sell them at different locations, the production facilities that
produce and ship them to the sales companies and the suppliers that deliver the raw materials and
components to the production facilities. We call this model a production and distribution network
(PDN). The network consists of all supply chain actors at their respective locations in which the
products, components and raw materials of a particular product assortment are procured, processed,
distributed and sold. The network may be limited upstream to a bounded number of supply stages.
Downstream, the network is bounded by the end customer stage. Let P be the set of all products
(raw, packaging, semi, finished) as identified by unique material numbers. N represents the existing
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