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See detailAlgorithms for testing the collective consumption model
Talla Nobibon, Fabrice; Cherchye, Laurens; Crama, Yves ULg et al

Conference (2012, November 09)

In this talk, we discuss an extension of the strong axiom of revealed preferences to collective households. The question that we address is whether a set of observed consumption baskets can be decomposed ... [more ▼]

In this talk, we discuss an extension of the strong axiom of revealed preferences to collective households. The question that we address is whether a set of observed consumption baskets can be decomposed in such a way that each of the derived data sets reflects the choices of a “rational” (i.e., utility-maximizing) individual member of the household. Although testing revealed preference axioms on data generated by a single decisionmaker can be done in polynomial time, the extension to two-member households is NP-complete. We propose two algorithms for testing the collective consumption model on large data sets. The first one is an exact algorithm based on a new mixed-integer programming formulation, whereas the second one is a heuristic based on a simulated annealing procedure that solves a global optimization formulation of the problem. Computational experiments are performed on real-life data. [less ▲]

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See detailColoring Graphs Using Two Colors while Avoiding Monochromatic Cycles
Talla Nobibon, Fabrice ULg; Hurkens, Cor A. J.; Leus, Roel et al

in INFORMS Journal on Computing (2011)

We consider the problem of deciding whether a given directed graph can be vertex partitioned into two acyclic subgraphs. Applications of this problem include testing rationality of collective consumption ... [more ▼]

We consider the problem of deciding whether a given directed graph can be vertex partitioned into two acyclic subgraphs. Applications of this problem include testing rationality of collective consumption behavior, a subject in microeconomics. We prove that the problem is NP-complete even for oriented graphs and argue that the existence of a constant-factor approximation algorithm is unlikely for an optimization version that maximizes the number of vertices that can be colored using two colors while avoiding monochromatic cycles. We present three exact algorithms—namely, an integer-programming algorithm based on cycle identification, a backtracking algorithm, and a branch-and-check algorithm. We compare these three algorithms both on real-life instances and on randomly generated graphs. We find that for the latter set of graphs, every algorithm solves instances of considerable size within a few seconds; however, the CPU time of the integer-programming algorithm increases with the number of vertices in the graph more clearly than the CPU time of the two other procedures. For real-life instances, the integer-programming algorithm solves the largest instance in about a half hour, whereas the branch-and-check algorithm takes approximately 10 minutes and the backtracking algorithm less than 5 minutes. Finally, for every algorithm, we also study empirically the transition from a high to a low probability of a YES answer as a function of the number of arcs divided by the number of vertices. [less ▲]

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See detailProduction Planning in Automated Manufacturing
Crama, Yves ULg; Oerlemans, Alwin; Spieksma, Frits

Book published by Springer-Verlag - première édition (1994)

Detailed reference viewed: 65 (15 ULg)