In this paper we propose a time-indexed IP formulation for job-shop scheduling problems. We first introduce a model with variables associated to job scheduling patterns and constraints associated to machine capacities and to job assignments. The exponential number of variables calls for a column generation scheme which is carried out by a dynamic programming procedure. However, the column generation process is time-consuming. Therefore we derive an equivalent compact formulation of the model, whose dual is a flow problem with side constraints. This problem can be solved faster and fits easily into a branch-and-bound scheme

A compact optimization approach for jobshop problems

LANCIA, Giuseppe;RINALDI, Franca;SERAFINI, Paolo
2007

Abstract

In this paper we propose a time-indexed IP formulation for job-shop scheduling problems. We first introduce a model with variables associated to job scheduling patterns and constraints associated to machine capacities and to job assignments. The exponential number of variables calls for a column generation scheme which is carried out by a dynamic programming procedure. However, the column generation process is time-consuming. Therefore we derive an equivalent compact formulation of the model, whose dual is a flow problem with side constraints. This problem can be solved faster and fits easily into a branch-and-bound scheme
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/883059
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