The Job-Shop Problem and Immediate Selection

Abstract

In a job-shop scheduling problem we have n jobs J ₁,...,J _n to be processed on m different machines M _l,...,M _m . Each job J; consists of a number n _i of operations $\left( {i = 1,...,n;j,...,{n_i}} \right).$ which have to be processed in this order. Operations O _ij can be processed only by one machine μ _ij (i = 1,..., n; j _i = 1,..., n _i ). Denote by pi, the corresponding processing time. We assume that all processing times are integer numbers.