• Industrial Engineering and Management Systems
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• v.15 no.1
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• pp.32-40
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• 2016

This paper considers a special case of a three machine flow shop scheduling problem in which operation processing time of each job is ordered such that machine 1 has the longest processing time, whereas machine 3, the shortest processing time. The objective of the problem is the minimization of the total completion time. Although the problem is simple, its complexity is yet to be established to our best knowledge. This paper first introduces the problem and presents some optimal properties of the problem. Then, it establishes several special cases in which a polynomial-time optimal solution procedure can be found. In addition, the paper proves that the recognition version of the problem is at least binary NP-complete. The complexity of the problem has been open despite its simple structure and this paper finally establishes its complexity. Finally, a simple and intuitive heuristic is developed and the tight worst case bound on relative error of 6/5 is established.

• Management Science and Financial Engineering
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• v.15 no.2
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• pp.69-100
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• 2009

In this paper, we consider a relatively new two-machine flow shop scheduling problem where the unit time WIP cost increases as a job passes through various stages in the production process, and the objective is to minimize the total WIP (work-in-process) cost. Specifically, we study three special cases of the problem. First, we consider the problem where processing times on machine 1 are identical. Second, the problem with identical processing times on machine 2 is examined. The recognition version of the both problems is unary NP-complete (or NP-complete in strong sense). For each problem, we suggest two simple and intuitive heuristics and find the worst case bound on relative error. Third, we consider the problem where the processing time of a job on each machine is proportional to a base processing time. For this problem, we show that a known heuristic finds an optimal schedule.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.138-141
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• 2006

This paper considers a two-machine flow-shop scheduling problem for minimizing mean flow time. Each job has three non-preemptive operations, where the first and third operations must be Processed on the first and second machines, respectively, but the second operation can be processed on either machine. A lower bound based on SPT rule is derived, which is then used to develop a branch-and-bound algorithm. Also, an efficient simple heuristic algorithm is developed to generate a near-optimal schedule. Numerical experiments are performed to evaluate the performances of the proposed branch-and-bound and the heuristic algorithm

• Industrial Engineering and Management Systems
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• v.14 no.1
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• pp.22-31
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• 2015

In this paper, a two-stage hybrid flow shop problem is considered. Specifically, there exist identical parallel machines at stage 1 and two dedicated machines at stage 2, and the objective of the problem is to minimize makespan. After being processed by any machine at stage 1, a job must be processed by a specific machine at stage 2 depending on the job type, and one type of jobs can have different processing times on each machine. First, we introduce the problem and establish complexity of several variations of the problem. For some special cases, we develop optimal polynomial time solution procedures. Then, we establish some simple lower bounds for the problem. In order to solve this NP-hard problem, three heuristics based on simple rules such as the Johnson's rule and the LPT (Longest Processing Time first) rule are developed. For each of the heuristics, we provide some theoretical analysis and find some worst case bound on relative error. Finally, we empirically evaluate the heuristics.

• Industrial Engineering and Management Systems
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• v.15 no.1
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• pp.11-18
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• 2016

This paper considers a scheduling problem in a flexible job shop with a reconfigurable manufacturing cell. The flexible job shop has both operation and routing flexibilities, which can be represented in the form of a multiple process plan, i.e. each part can be processed through alternative operations, each of which can be processed on alternative machines. The scheduling problem has three decision variables: (a) selecting operation/machine pairs for each part; (b) sequencing of parts to be fed into the reconfigurable manufacturing cell; and (c) sequencing of the parts assigned to each machine. Due to the reconfigurable manufacturing cell's ability of adjusting the capacity, functionality and flexibility to the desired levels, the priority scheduling approach is proposed in which the three decisions are made at the same time by combining operation/machine selection rules, input sequencing rules and part sequencing rules. To show the performances of various rule combinations, simulation experiments were done on various instances generated randomly using the experiences of the manufacturing experts, and the results are reported for the objectives of minimizing makespan, mean flow time and mean tardiness, respectively.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.1
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• pp.139-157
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• 1993

This paper presents possibilistic job scheduling based on the membership function as an alternative to probabilistic job scheduling and illustrates a methodology for solving job sequencing problem which the opinions of experts greatly disagree in each processing time. Triangular fuzzy numbers are used to represent the processing times of experts. Here, the comparison method is based on the dominance property. The criteria for dominance are presented. By the dominance criteria, for each job, a mojor TFN and a minor TFN are selected and apessimistic sequence with mojor TFNs and an optimistic sequence with minor TFNs are computed. The three-machine flow shop problem is considered as an example to illustrate the approach.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1124-1132
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• 2006

This paper considers a flow shop scheduling problem where a different WIP (work-in-process) state has different weight on the duration time. The objective is to minimize the sum of the weighted WIP. For the two machine flow shop case, the recognition version is unary NP-Complete. The three simple and intuitive heuristics H0, H1, and H2 are presented for the problem. For each heuristic, we find an upper bound on relative error which is tight in limit. For heuristic H2, we show that H2 dominates the other two heuristics.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.310-313
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• 1996

Mathematical programming method for finding optimal solution of job shop scheduling is inadequate to real situation because fo too much computation time. In contrast, dispatching rule is helpful for reducing compuation time but is not guaranted to find optimal solution. The purpose of this paper is to develop a new dispatching rule and procedure to minimize mean flow time whose result is near the optimal solution for job shop scheduling. First step is to select machine which have shortest finishing operation time among the schedulable operations. Second step is to select operation with regard to estimated remaining operation time. The suggested rule is compared with nondelay and MWKR rule for three examples, and is confirmed to be most effective to minimize mean flow time.

• Journal of Korean Institute of Industrial Engineers
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• v.35 no.4
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• pp.257-265
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• 2009

This paper considers the hybrid flow shop scheduling problem for the objective of minimizing the number of tardy jobs. In hybrid flow shops, each job is processed through multiple production stages in series, each of which has multiple identical parallel machines. The problem is to determine the allocation of jobs to the parallel machines at each stage as well as the sequence of the jobs assigned to each machine. Due to the complexity of the problem, we suggest search heuristics, tabu search and simulated annealing algorithms with a new method to generate neighborhood solutions. In particular, to evaluate and select neighborhood solutions, three surrogate objectives are additionally suggested because not much difference in the number of tardy jobs can be found among the neighborhoods. To test the performances of the surrogate objective based search heuristics, computational experiments were performed on a number of test instances and the results show that the surrogate objective based search heuristics were better than the original ones. Also, they gave the optimal solutions for most small-size test instances.