OPTIMAL JOB SCHEDULING FOR FLOWSHOPS

A review is given of the known formulations and solution methods of th e classical problem (Bellman-Johnson problem) in scheduling theory of the time sequencing of jobs in flowshops. The classification of optimi zation methods is presented. The following approaches and methods used to solve the problem are outlined: the combinatorial, permutation, an d algebraic approaches, approaches based on the study of critical path s in the matrix of flowshop processing times, methods relying on the s pecific features of the processing time matrix, and methods based on t he theory of infinite-valued logic. Information is provided on the app lication of the branch-and-bound method statistical modeling methods a nd mathematical programming method to the solution of the problem of j ob sequencing in flowshops. Preferable methods are defined by way of t heir comparison.