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Andreas Bärmann(Andreas.Baermannmath.unierlangen.de) Abstract: We consider the clique problem with multiplechoice constraints (CPMC) and characterize a case where it is possible to give an efficient description of the convex hull of its feasible solutions. This new special case, which we call staircase compatibility, generalizes common properties in several applications and allows for a linear description of the integer feasible solutions to (CPMC) with a totally unimodular constraint matrix of polynomial size. We derive two such totally unimodular reformulations for the problem: one that is obtained by a strengthening of the compatibility constraints and one that is based on a representation as a dual network flow problem. Furthermore, we show a natural way to derive integral solutions from fractional solutions to the problem by determining integral extreme points generating this fractional solution. We also evaluate our reformulations from a computational point of viewby applying them to two different realworld problem settings. The first one is a problem in railway timetabling, where we try to adapt a given timetable slightly such that energy costs from operating the trains are reduced. The second one is the piecewise linearization of nonlinear network flow problems, illustrated at the example of gas networks. In both cases, we are able to reduce the solution times significantly by passing to the theoretically stronger formulations of the problem. Keywords: Clique Problem with MultipleChoice Constraints, Staircase Compatibility, Total Unimodularity, Scheduling, Piecewise Linearization Category 1: Combinatorial Optimization (Polyhedra ) Category 2: Applications  OR and Management Sciences (Scheduling ) Category 3: Integer Programming ((Mixed) Integer Linear Programming ) Citation: Download: [PDF] Entry Submitted: 01/26/2018 Modify/Update this entry  
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