Permutation Schedules Research Articles

2208 第2工程が複数台マシンを持つ2工程HFS(Hybrid Flowshop Scheduling)問題に対する最早開始時刻の連鎖割付の最適性の証明(OS9-1 システム最適化,OS9 システム最適化)

This research targets at the 2-stage HFS (Hybrid Flowshop Scheduling) Problem with multiple machines at the second stage. In order to make it possible that the algorithms for the problem is effectively searching the solution space, "Permutation Scheduling" for that problem, in which the jobs are assigned in the same starting order, is proposed. The proof that the optimal solution is included in the permutation scheduling is shown by using contradiction. In the proof, PERT (Project Evaluation Review Technique) diagram is used to compare the scheduling in and out of Permutation Schedule for the highlight of the difference between them.

Applying a hybrid simulated annealing and tabu search approach to non-permutation flowshop scheduling problems

Researchers have indicated that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion time-based criteria, such as makespan and total completion time. This study proposes a hybrid approach which draws on the advantages of simulated annealing and tabu search for the non-permutation flowshop scheduling problem, in which the objective function is the makespan of the schedule. To verify the effectiveness of the proposed hybrid approach, computational experiments are performed on a set of well-known non-permutation flowshop scheduling benchmark problems. The result shows that the performance of the hybrid approach is better than that of other approaches, including ant colony optimisation, simulated annealing, and tabu search. Further, the proposed approach found new upper bound values for all benchmark problems within a reasonable computational time.

Minimizing total completion time in two-machine flow shops with exact delays

We study the problem of minimizing total completion time in the two-machine flow shop with exact delay model. This problem is a generalization of the no-wait flow shop problem which is known to be strongly NP-hard. Our problem has many applications but little results are given in the literature so far. We focus on permutation schedules. We first prove that some simple algorithms can be used to find the optimal schedules for some special cases. Then for the general case, we design some heuristics as well as metaheuristics whose performance are shown to be effective by computational experiments.

A genetic algorithm and memetic algorithm to sequencing and scheduling of cellular manufacturing systems

This paper presents a group scheduling problem for manufacturing cells, in which parts may visit different cells. By addressing intra-cell scheduling, the sequence of parts within manufacturing cells is determined. In inter-cell scheduling however, the sequence of cells is obtained. Two evolutionary algorithms, namely a genetic algorithm (GA) and a memetic algorithm (MA), are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules. The performance of the proposed GA and MA is shown and evaluated on 15 test problems. The computational results reveal that the proposed MA outperforms the proposed GA and Lingo software in these test problems with respect to the average elapsed time to obtain the makespan and objective function value.

Metaheuristics for scheduling a non-permutation flowline manufacturing cell with sequence dependent family setup times

The broad applications of cellular manufacturing make flowline manufacturing cell scheduling problems with sequence dependent family setup times a core topic in the field of scheduling. Due to computational complexity, almost all published studies focus on using permutation schedules to deal with this problem. To explore the potential effectiveness of treating this argument using non-permutation schedules, three prominent types of metaheuristics—a simulated annealing, a genetic algorithm and a tabu search—are proposed and empirically evaluated. The experimental results demonstrate that in general, the improvement made by non-permutation schedules over permutation schedules for the due-date-based performance criteria were significantly better than that for the completion-time-based criteria. The results of this study will provide practitioners a guideline as to when to adopt a non-permutation schedule, which may exhibit better performance with additional computational efforts.

Multiple machine JIT scheduling: a tabu search approach

This paper presents an approach to solving the multiple machine, non-preemptive, earliness-tardiness scheduling problem with unequal due dates in a flow shop with machine tiers (FMT). In this variant of the flow shop problem, machines are arranged in tiers or groups, and the jobs must visit one machine in each tier. The processing times, machine assignments, and due dates are deterministic and known in advance. The objective is to find a permutation schedule that minimizes the total deviation of each job from its due date. A tabu search (TS) meta-heuristic combined with an LP evaluation function is applied to solve this problem and results are compared to optimal permutation solutions for small problems and the earliest due date schedule for large problems. Several neighborhood generation methods and two diversification strategies are examined to determine their effect on solution quality. Results show that the TS method works well for this problem. TS found the optimal solution in all but one of the small problem instances and improved the earliest due date solutions for larger instances where no optimal solutions could be found.

A note on two-stage hybrid flowshop scheduling with missing operations

The scheduling problem in a multi-stage hybrid flowshop has been the subject of considerable research. All the studies on this subject assume that each job has to be processed on all the stages, i.e., there are no missing operations for a job at any stage. However, missing operations usually exist in many real-life production systems, such as a system in a stainless steel factory investigated in this note. The studied production system in the factory is composed of two stages in series. The first stage contains only one machine while the second stage consists of two identical machines (namely a 1 × 2 hybrid flowshop). In the system, some jobs have to be processed on both stages, but others need only to be processed on the second stage. Accordingly, the addressed scheduling problem is a 1 × 2 hybrid flowshop with missing operations at the first stage. In this note, we develop a heuristic for the problem to generate a non-permutation schedule (NPS) from a given permutation schedule, with the objective of minimizing the makespan. Computational results demonstrate that the heuristic can efficiently generate better NPS solutions.

A performance evaluation of permutation vs. non-permutation schedules in a flowshop

It has been pointed out that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion-time based criteria, but there is a lack of comprehensive analyses. This paper presents an extensive computational investigation concerning the performance comparison between permutation and non-permutation schedules. The computational results indicate that in general, there is little improvement made by non-permutation schedules over permutation schedules with respect to completion-time based criteria. But the improvement is significant with respect to due-date based criteria, including total tardiness and total weighted tardiness. The results provide practitioners a guideline as to when to adopt a non-permutation schedule, which may exhibit better performance but require additional computational and control efforts.

Minimizing flow time in a flow-line manufacturing cell with family setup times

This paper considers the problem of scheduling part families and jobs within each part family in a flowline manufacturing cell with independent family setup times where parts (jobs) in each family are processed together. The objective is to minimize total flow time. A branch-and-bound algorithm capable of solving moderate sized problems is developed. Several heuristic algorithms are proposed and empirically evaluated as to their effectiveness and efficiency in finding optimal permutation schedules. These results show that several heuristic algorithms generate solutions that are better than those generated by an existing genetic algorithm.

Impact of permutation enforcement when minimizing total weighted tardiness in dynamic flowshops with uncertain processing times

This paper is motivated by the problem of meeting due dates in a flowshop production environment with jobs with different weights and uncertain processing times. Enforcement of a permutation schedule to varying degrees for dynamic flowshops is investigated with the goal of minimizing total weighted tardiness (TWT). The approaches studied are categorized as follows: (1) pure permutation scheduling (2) shift-based scheduling (3) pure dispatching (which leads to non-permutation sequences). A simulation-based experimental study was carried out to study the performance of the above methods with respect to minimizing TWT when new jobs arrive to the flowshop at every shift change. Results indicate significant gains in performance are possible when the permutation requirement is relaxed and shift-based scheduling is allowed. Shift-based scheduling yields competitive results with respect to the pure dispatching approach, even though dispatching has the advantage of a full relaxation of the permutation requirement.

Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups

This paper considers the problem of scheduling part families and jobs within each part family in a flowshop manufacturing cell with sequence dependent family setups times where it is desired to minimize the makespan while processing parts (jobs) in each family together. Two evolutionary algorithms-a Genetic Algorithm and a Memetic Algorithm with local search-are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules. The proposed algorithms use a compact representation for the solution and a hierarchically structured population where the number of possible neighborhoods is limited by dividing the population into clusters. In comparison to a Multi-Start procedure, solutions obtained by the proposed evolutionary algorithms were very close to the lower bounds for all problem instances. Moreover, the comparison against the previous best algorithm, a heuristic named CMD, indicated a considerable performance improvement.

On solving permutation scheduling problems with ant colony optimization

A new approach for solving permutation scheduling problems with ant colony optimization (ACO) is proposed in this paper. The approach assumes that no precedence constraints between the jobs have to be fulfilled. It is tested with an ACO algorithm for the single-machine total weighted deviation problem. In the new approach the ants allocate the places in the schedule not sequentially, as in the standard approach, but in random order. This leads to a better utilization of the pheromone information. It is shown by experiments that adequate combinations between the standard approach which can profit from list scheduling heuristics and the new approach perform particularly well.

Flow shop vs. permutation shop with time delays

This paper considers the evaluation of the worst-case performance ratio between the best solution of the flow shop problem and the permutation flow shop with time delays considerations. It is observed that, even in the restricted case of two machines and unit execution time operations, the two models may generate different optimal values for the makespan. More specifically, it is shown that, in the two-machine case, the performance ratio between the best permutation schedule and the best flow shop schedule is bounded by 2. When the operations of the n jobs are restricted to be unit execution time, this ratio is reduced to (2-(3/n+2)) for the two-machine case, and is m for the m-machine case.

Relative performance evaluation of permutation and non-permutation schedules in flowline-based manufacturing systems with flowtime objective

The flowline-based manufacturing system (FBMS) is a manufacturing environment wherein machines are arranged in the order in which jobs undergo operations, and jobs have an identical and uni-directional flow pattern. However, some or all jobs may not require processing on some machines. Scheduling of jobs in such a FBMS is considered in this paper with the focus on the development of non-permutation schedules. The significance of non-permutation schedules in improving the schedule performance measures, in the context of FBMS’s, is first brought out. A heuristic procedure to derive non-permutation schedules from a given permutation schedule is subsequently proposed. The minimization of total flowtime of jobs is considered as the objective in the first instance, followed by the consideration of the minimization of total weighted flowtime of jobs. An extensive computational experimentation has been performed to evaluate the effectiveness of the proposed heuristic in improving the performance measures. Further, the performance of the proposed heuristic in generating non-permutation schedules has been compared with that of the benchmark dispatching rules namely, the SPT and SWPT rules.

A Note on using Graphs in Regular Scheduling Problems

This paper deals with regular permutation scheduling on graphs. PeĹĄko and Czimmermann introduced this problem (in [3]) and it is generalisation of a matrix permutation problem. The goal is to minimise differences between row sums of a real matrix that represents a schedule, but external conditions don't allow moving matrix elements arbitrarily. The conditions can be represented by permutation obtained from a certain graph.

Decompositions, Network Flows, and a Precedence Constrained Single-Machine Scheduling Problem

We present an in-depth theoretical, algorithmic, and computational study of a linear programming (LP) relaxation to the precedence constrained single-machine scheduling problem 1|prec|ΣjwjCj to minimize a weighted sum of job completion times. On the theoretical side, we study the structure of tight parallel inequalities in the LP relaxation and show that every permutation schedule that is consistent with Sidney's decomposition has total cost no more than twice the optimum. On the algorithmic side, we provide a parametric extension to Sidney's decomposition and show that a finest decomposition can be obtained by essentially solving a parametric minimum-cut problem. Finally, we report results obtained by an algorithm based on these developments on randomly generated instances with up to 2,000 jobs.

Generating non-permutation schedules in flowline-based manufacturing sytems with sequence-dependent setup times of jobs: a heuristic approach

A flowline-based manufacturing system is a manufacturing environment where machines are arranged in accordance with the order of processing of jobs, with all jobs having an identical and unidirectional flow pattern through the machines; however, some or all jobs may have missing operations on some machines. In several practical situations the setup times of jobs are separable, significant and sequence-dependent. The problem of scheduling in such a flowline-based manufacturing system is considered with the focus on the development of non-permutation schedules. The deficiency of using the existing set of recursive equations in developing the timetable for permutation schedules is first highlighted, and a correct and modified set of recursive equations to take account of the missing operations properly is formulated. A simple heuristic procedure to derive non-permutation schedules from a given permutation sequence is proposed subsequently. Through extensive computational experimentation, it is shown that the proposed heuristic procedure yields solutions of good quality.

On ‘redundant’ constraints in Stafford's MILP model for the flowshop problem

This paper investigates a claim that the 1988 Stafford mixed-integer linear programming model for the flowshop with permutation schedules contained a set of redundant constraints that could be eliminated without loss of model feasibility. This claim is shown to be incorrect mathematically and through the use of a counterexample problem. Eight additional problems were solved to confirm these findings.

Performance enhancement by using non-permutation schedules in flowline-based manufacturing systems

A flowshop is a manufacturing environment with unidirectional flow of jobs through the various machines that are arranged in the order of job processing. A flowline-based manufacturing system (FBMS) is characterized by the flowline-based layout of machines with the machines arranged in the order of processing of jobs, but with the possibility of some or all jobs having missing operations on some machines. The significance of non-permutation schedules (NPS) and their effect on improving the schedule performance measures, in the context of FBMS, is highlighted in this paper. A simple heuristic procedure to derive NPS from a given permutation schedule is proposed. Results of the extensive computational experimentation, with makespan as the primary criterion and total flowtime as the secondary criterion, are presented. The results show that the proposed heuristic procedure for generating non-permutation schedule set is effective and improves the schedule performance measures with minimal computational effort.

Minimizing tardiness in a two-machine flow-shop

The two-machine flow-shop scheduling problem with the objective of minimizing total tardiness is considered in this paper. Dominance criteria are developed to establish the precedence constraints between jobs in an optimal schedule. A lower bound on the total tardiness of the problem is derived by constructing the sequence of jobs from front to back to simplify the bounding procedure. A branch-and-bound algorithm incorporating these properties is proposed to expedite the search for an optimal sequence. Computational experiments are conducted and the results demonstrate that the proposed algorithm surpasses an existing one in terms of both computation times and sizes of the problems solved. Scope and purpose An m-machine flow-shop requires all the n jobs to be processed following the same path from one to another on these m machines. For a two-machine flow-shop problem, however, one needs to consider only permutation schedules [1] on which both machines process the jobs in the same order. Besides the flow-shops that actually consist of two machines, there are many occasions in which a large complex facility can be viewed as though it performs two major operations. Even if a shop has several machines, two of them may be so restrictive and function as bottleneck ones. Total tardiness is a widely used scheduling performance measure in practical production environments for which there is no benefit for finishing jobs early, and the tardiness penalty is proportional to the delay over all jobs. The two-machine flow-shop problem with total tardiness as the scheduling criterion is NP-complete [2] and has been solved by branch-and-bound algorithms. However, more properties of the problem can be exploited and developed to enhance the computational efficiency of the algorithm.