Hiroshi Kise

A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times

We consider a class of n-job one-machine scheduling problems with ready time ri, processing time pi, and due time di for each job i. Preemption is not allowed, and precedence constraints among jobs are not assumed. For this problem we show that there is a 0n2-time algorithm to find a schedule that minimizes the number of tardy jobs, under the assumption that ri

Automated Two-machine Flowshop Scheduling: A Solvable Case

Abstract This paper considers new flowshop scheduling problems related to automated manufacturing systems in which n jobs are processed on two machines Ma and Mb in this order. The job transportation between two machines is done by a single automated guided vehicle (AGV), and is crucial because no machine has buffer storage for work-in-process (WIP) and hence a machine cannot release a finished job until the empty AGV becomes available at that machine, while the AGV cannot transfer an unfinished job to a machine until the machine is empty. O(n 3) algorithms are given in this paper to find optimal sequences of n jobs that minimize their maximum completion time (i.e., makespan). Some numerical results are also given to evaluate the effect of computing optimal sequences.

A branch-and-bound algorithm with fuzzy inference for a permutation flowshop scheduling problem

Abstract This paper considers an m-machine permutation flowshop scheduling problem of minimizing the makespan. This classical scheduling problem is still important in modern manufacturing systems, and is well known to be intractable (i.e., NP-hard). In fact branch-and-bound algorithms developed so far for this problem have not come to solve large scale problem instances with over a hundred jobs. In order to improve the performance of branch-and-bound algorithms this paper proposes a new dominance relation by which the search load could be reduced, and notices that it is based on a sufficient precondition. This suggests that the dominance relation holds with high possibility even if the precondition approximately holds, thus being more realistic. The branch-and-bound algorithm proposed here takes advantage of this possibility for obtaining an optimal solution as early as possible in the branch-and-bound search. For this purpose this paper utilizes membership functions in the context of the fuzzy inference. Extensive numerical experiments that were executed through Monte Carlo simulations and benchmark tests show that the developed branch-and-bound algorithm can solve 3-machine problem instances with up to 1000 jobs with probability of over 99%, and 4-machine ones with up to 900 jobs with over 97%.

Monotonicity in optimal policy of a flexible manufacturing cell feeding several production lines

Abstract This paper deals with an optimal part selection problem tominimize the expected cost, in an automated manufacturing system in which a flexible manufacturing cell produces different parts for several production lines. The optimal control problem is formulated as an undiscounted semi-Markov decision process. Properties of the optimal policy are analyzed. Moreover, sufficiency conditions are derived for the optimal policy to be of control iimit type.

Branch-and-bound algorithms using fuzzy heuristics for solving large-scale flow-shop scheduling problems

The flow-shop scheduling problem has a long history since Johnson’s seminal paper in 1954, and is still actively studied. The problem is strongly NP-hard when the number of machines is greater than 2. Thus we have to rely on implicit enumeration procedures, such as branch-and-bound, for exact solutions. One of the objectives for researchers in studying such intractable problems is to develop new methods which can solve larger-scale problems. We discuss branch-and-bound algorithms for finding a permutation schedule minimizing the makespan in an m-machine flow shop where the jobs may all be available before processing begins or may be dynamically released. A branch-and-bound algorithm’s performance is helped by sharper lower bounds, good search methods in the tree and more effective dominance relations. Dominance relations are only sufficient but not necessary conditions for optimality, which suggests that optimality may hold with high probability even if a dominance condition is not satisfied exactly, but only approximately. Our algorithms exploit this fact by using a fuzzy approximation of dominance relationships for tie breaking in the search tree and for building initial incumbent schedules. These fuzzy heuristics together with an adaptive branching technique and a generalized decomposition method proved to be very effective for solving large problems. We review the results of large-scale computational experiments for two- and three-machine problems and report on the algorithms’ performance for problems on up to ten machines. The algorithms have proved to be effective in solving a large number of problems with up to several hundred jobs. An interesting byproduct of our research is the rather surprising insight that the difficulty of the problems with release times seems to depend much more on the relative size of the release times than on the number of jobs involved.

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.

Scheduling for an automated three-machine flowshop manufacturing system

This paper considers a scheduling problem of minimizing the maximum completion time for an automated flowshop manufacturing system such as FMS which consists of 3 machining cells with sufficient buffers, an AGV (automated guided vehicle) and loading/unloading stations. For this problem we propose a heuristic algorithm based on a fuzzy approximation (called fuzzy scheduling), and a branch-and-bound algorithm with fuzzy inferences. Computational experiences show that the fuzzy scheduling can give optimal or near optimal solutions, and the branch-and-bound algorithm can efficiently give optimal solutions with up to 400 parts with high probability over 90%.

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.

Jobshop Scheduling by an Iterative Approximation.

This paper proposes an iterative approximation method for minimizing the maximum lateness for a jobshop in which n jobs with ready times and due dates are processed on m machines in different orders. The proposed method consists of two phases I and II. Phase I sequences m machines one by one successively to obtain a feasible schedule of the m-machine shop, repeats this procedure m times by changing the first machine to be sequenced, and selects the best one. Phase II locally reoptimizes each machine based on sequences of the remaining (m-1) machines that have been the best ones obtained thus far. This procedure is repented until no improvement is possible. Computer simulations show that the proposed method can give schedules comparable to the SBI method by Adams et al., and better ones than representative dispaching rules.