Sebastian Velten

Dynamic supply chain design with inventory

In this paper, we deal with a facility location problem where we build new facilities or close down already existing facilities at two different distribution levels over a given time horizon. In addition, we allow to carry over stock in warehouses between consecutive periods. Our model intends to minimize the total costs, including transportation and inventory holding costs for products as well as fixed and operating costs for facilities. After formulating the problem, we propose a Lagrangian approach which relaxes the constraints connecting the distribution levels. A procedure is developed to solve the resulting, independent subproblems and, based on this solution, to construct a feasible solution for the original problem.

A flexible model and efficient solution strategies for discrete location problems

Flexible discrete location problems are a generalization of most classical discrete locations problems like p-median or p-center problems. They can be modeled by using so-called ordered median functions. These functions multiply a weight to the cost of fulfilling the demand of a customer, which depends on the position of that cost relative to the costs of fulfilling the demand of other customers. In this paper a covering type of model for the discrete ordered median problem is presented. For the solution of this model two sets of valid inequalities, which reduces the number of binary variables tremendously, and several variable fixing strategies are identified. Based on these concepts a specialized branch & cut procedure is proposed and extensive computational results are reported.

An extended covering model for flexible discrete and equity location problems

To model flexible objectives for discrete location problems, ordered median functions can be applied. These functions multiply a weight to the cost of fulfilling the demand of a customer which depends on the position of that cost relative to the costs of fulfilling the demand of the other customers. In this paper a reformulated and more compact version of a covering model for the discrete ordered median problem (DOMP) is considered. It is shown that by using this reformulation better solution times can be obtained. This is especially true for some objectives that are often employed in location theory. In addition, the covering model is extended so that ordered median functions with negative weights are feasible as well. This type of modeling weights has not been treated in the literature on the DOMP before. We show that several discrete location problems with equity objectives are particular cases of this model. As a result, a mixed-integer linear model for this type of problems is obtained for the first time.

Strategische Supply-Chain Entscheidungen in der Stahlindustrie - eine Fallstudie

Diese Arbeit befasst sich mit strategischen Entscheidungen im Bereich des Supply-Chain-Managements. Dabei wird ein allgemeines mathematisches Optimierungsmodell zur Standortplanung vorgestellt. Das Modell ist dynamisch und kapazitatsbeschrankt; es kann auf mehrere Produkte und Ebenen angewendet werden und berucksichtigt externe Materialbeschaffung, Produktions-, Vertriebs- und Lagerentscheidungen, Sicherheitsbestande, Budgetrestriktionen und Kapazitatsverlegungen. Um die Nachfrage moglichst kostenminimal zu decken, werden Kapazitatserweiterungen bzw.-reduzierungen betrachtet. Das formale Modell wird auf ein Beispiel aus der Stahlindustrie angewendet, wobei die Praxistauglichkeit des Modells analysiert wird. Alle Berechnungen erfolgen mit Hilfe des Optimierungstools XPressMP (Dash Optimization 2004).

Optimization problems with flexible objectives : A general modeling approach and applications

We study optimization problems extended by a flexible objective, namely the Ordered Median Function (OMF). The OMF incorporates a large number of objectives into one function. Concrete objectives are given by choosing values for a parameter vector. Using optimization problems extended by the OMF, only one model, solution algorithm and implementation is necessary to analyze many concrete objectives.

Optimal Control Strategies for Incoming Inspection

Acceptance sampling is one important part of logistic processes and production. Because of that, we developed a new model, named DMGI (Dynamic Mixed Goods Inspection) which uses past inspections in order to support companies deciding which delivery should be inspected in goods income.