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Conference Papers Year : 2011

## Robust Optimization Approaches To Minimum Cost Tools Selection Problems

Alexandre Dolgui
Sergey Kovalev
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#### Abstract

We study the following problem. Production line functioning implies a selection of tools which are able to execute a given set of operations, N = f1; : : : ;ng. Operation i 2 N must be performed by a single eligible tool of the set Ti = f(i;1); (i;2); : : : ; (i; ri)g, i = 1; : : : ;n. There are costs ci j associated with the tools (i; j), which are uncertain due to the market price fluctuations. The discrete and interval scenarios are proposed for modeling the cost uncertainty. In the discrete scenario case, the twodimensional cost structure c with entries ci j, i = 1; : : : ;n, j = 1; : : : ; ri, belongs to a given finite set : c 2 Sdsc. In the interval scenario case, each cost ci j of a cost structure c can take any value from a given interval [ai j;bi j] : c 2 Sint . The problem is to select n tools, one for each operation, so that the total cost is minimized. We suggest three robust optimization approaches for solving this problem, which are called minmax, min-max regret and min-max relative regret. The min-max solution minimizes the maximum total cost over all scenarios. The min-max (relative) regret solution minimizes maximum (relative) deviation of the selected tools cost from the minimum total cost over all scenarios. A recent survey of the min-max and min-max regret approaches to combinatorial optimization problems was given by Aissi et al. [1].

#### Domains

Modeling and Simulation

### Dates and versions

emse-00679631 , version 1 (16-03-2012)

### Identifiers

• HAL Id : emse-00679631 , version 1

### Cite

Alexandre Dolgui, Sergey Kovalev. Robust Optimization Approaches To Minimum Cost Tools Selection Problems. 12ème congrès de la société Française de Recherche Opérationnelle et d'Aide à la Décision (ROADEF 2011), Mar 2011, Saint Etienne, France. pp.submission 436. ⟨emse-00679631⟩

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