Hybrid flow-shop with adjustment

The subject of this paper is a flow-shop based on a case study aimed at the optimisation of ordering production jobs in mechanical engineering, in order to minimize the overall processing time, the makespan. The production jobs are processed by machines, and each job is assigned to a certain machine for technological reasons. Before processing a job, the machine has to be adjusted; there is only one adjuster who adjusts all of the machines. This problem is treated as a hybrid two-stage flow-shop: the first stage of the job processing is represented by the machine adjustment for the respective job, and the second stage by the processing of the job itself on the adjusted machine. In other words, the job-processing consists of two tasks, where the first task is the machine adjustment for the job, and the second task is the job processing itself. A mathematical model is proposed, a heuristic method is formulated, and the NP hardness of the problem, called a “hybrid flow-shop with adjustment,” is proved.