Yoshiyuki Karuno

Approximate Scheduling Algorithms with Performance Guarantee for a Two-Machine Robotic Unit with an Intermediate Station

In this paper we consider the scheduling problem of minimizing the maximum completion time (i.e., the makespan) for a two-machine robotic unit of flowshop type, in which each of n jobs is processed on the first machine and later on the second machine. There is an intermediate station between the two machines for intermediate operations such as washing, chip disposal, cooling, drying and/or quenching. If only permutation schedules are allowed (i.e., sequences of jobs on the two machines have to be the same), the problem can be solved in polynomial time, although non-permutation problem (i.e., the original problem) is NP-hard in the strong sense. It is already known that, if the optimal permutation schedule is used as an approximate solution for the non-permutation problem, it gives a maximum completion time within twice the optimal. In this paper, we present a different approximate algorithm which is based on a relaxation to the single-machine problem with delivery times, and show that its non-permutation schedule also gives a maximum completion time within twice the optimal. Moreover, we examine its approximation performance by means of numerical experiments, comparing with the optimal permutation scheduling.

Optimal Scheduling for a Two-Machine Robotic Cell of Jobshop Type

In this paper we consider a scheduling problem for a two-machine robotic cell of jobshop type. The problem is an extension of the classical two-machine jobshop scheduling addressed by Jackson 6), but is NP-hard. We propose a greedy heuristic algorithm and test for its performance with numerical experiments.

Optimal Scheduling for a Three-Machine Robotic Cell with Finite Buffer

This paper discusses optimal flexible cyclic scheduling for a two-machine robotic cell with finite buffer for WIPs (work-in-process) such as FMCs (flexible manufacturing cells), where jobs are processed on two machines in the same order, and sent between machines by a transportation robot. Each cycle is allowed to have different types of jobs, and the objective is to find an optimal schedule that minimizes the cycle times. In this paper we propose a heuristic algorithm based on Gilmore-Gomory and Johnson methods for this problem, and show by numerical experiments that it gives good approximate schedules of about 2% or less relative errors for any size of buffer capacity in short computational time. Also, we numerically show how the system parameters affect the system efficiency, and conclude that one of the effective ways for improving the efficiency is to reduce the diversity of job processing times rather than to have large buffer and a fast transportation robot.