Some scheduling problems in job-shop type manufacturing processes with technological precedence constraints

The paper is devoted to some scheduling problems in job-shop type manufacturing processes. It was assumed that job processing times may vary over the ranges of durations bounded by the normal and crash values. Precedence constraints between jobs may be also given. The problem is to find not only the order of jobs, satisfying given technological routes and precedence constraints, but also the allocation of locally and globally limited resources which minimize maximum completion time. Practical examples of manufacturing systems describing the problem under consideration are given. They describe some technological processes in soaking pits and forge shop departments in steel plants and copper electrorefining process in copper industry. It is shown that the problem is NP-hard even for some single machine cases. Some polynomially solved cases are also given. For the general case some exact algorithm is outlined, which is branch and bound type. It exploits some very effective elimination properties of the problem. Some computational results with 100 operation examples are also presented.