Uncertain Data Dependency Constraints in Matrix Models

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9075)

Abstract

Uncertain data due to imprecise measurements is commonly specified as bounded intervals in a constraint decision or optimization problem. Dependencies do exist among such data, e.g. upper bound on the sum of uncertain production rates per machine, sum of traffic distribution ratios from a router over several links. For tractability reasons existing approaches in constraint programming or robust optimization frameworks assume independence of the data. This assumption is safe, but can lead to large solution spaces, and a loss of problem structure. Thus it cannot be overlooked. In this paper we identify the context of matrix models and show how data dependency constraints over the columns of such matrices can be modeled and handled efficiently in relationship with the decision variables. Matrix models are linear models whereby the matrix cells specify for instance, the duration of production per item, the production rates, or the wage costs, in applications such as production planning, economics, inventory management. Data imprecision applies to the cells of the matrix and the output vector. Our approach contributes the following results: 1) the identification of the context of matrix models with data constraints, 2) an efficient modeling approach of such constraints that suits solvers from multiple paradigms. An illustration of the approach and its benefits are shown on a production planning problem.

Keywords

Data uncertainty Data constraints Interval reasoning Interval linear programs 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LISTIC, Laboratoire d’Informatique, Systèmes, Traitement de l’Information et de la ConnaissanceUniversité de SavoieAnnecy-Le-Vieux CedexFrance

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