《1994 A branch and bound algorithm for the job-shop scheduling problem》.pdfVIP

DISCRETE APPLIED MATHEMATICS ELSEVIER Discrete Applied Mathematics 49 (1994) 107-127 A branch and bound algorithm for the job-shop scheduling problem* Peter Brucker**, Bernd Jurisch, Bernd Sievers FB 6 Mathematik, Universitiit Osnabriick, D-49069 Osnabriick. Germany Received 28 January 1991; revised 7 January 1992 Abstract A fast branch and bound algorithm for the job-shop scheduling problem has been developed. Among other hard problems it solves the 10 x 10 benchmark problem which has been open for more than 20 years. We will give a complete description of this algorithm and will present computational results. Key words: Job-shop scheduling; branch and bound method 1. Introduction The job-shop scheduling problem may be formulated as follows. Consider n jobs J 1,. . . , J, and m different machines Ml, . . . , M,. Each job Ji consists of a number ni of operations Oil, . . . , Oini which have to be processed in this order. Furthermore, assume that operation Oik can be processed only by one machine ,k (i = 1, . . . , n; k= l,..., ai). Denote by Pik the corresponding processing time. There is only one machine of each type which can only process one operation at a time. Such an operation