New complexity results on scheduling problem in a robotic cell

This paper explores the coordinated scheduling problem between production and transportation in a two stage flow shop with dedicated machines. There are two dedicated machines at the first stage and one common machine at the second stage. Each job has to be processed on a specified machine at the stage 1 depending on job type. A transporter with limited capacity is available to transport the semi-finished jobs from stage 1 to stage 2 for further processing. The objective is to minimize the makespan, i.e. the maximum completion time of all the jobs. The main focus is on the case where the transporter capacity is equal to two. New complexity results related to this case are established. Due to the NP-hardness of the general problem, we develop approximative approach to tackle the problem. Computational results indicate that the obtained solutions within moderate CPU time are of high quality.