Mean Flow Time Criterion Research Articles

Deadlock analysis in FMS in the presence of flexible process plans - a simulation study

The increased use of FMS to provide customers with diversified products efficiently has created a significant set of operational challenges for managers. This technology presents a number of decision problems to be solved by researchers and practitioners. There have been a number of attempts to solve design and operational problems in FMS. A special attention has been given to batch scheduling when flexible process plans (FPPs) remain available on the shop floor. An extensive simulation study under two manufacturing environments is performed to study the system performance in the presence of FPPs. Several interesting conclusions have been drawn from deadlock, makespan and mean flow time criteria.

Mean flow time minimization with given bounds of processing times

We consider a job shop scheduling problem under uncertain processing times and fixed precedence and capacity constraints. Each of the random processing times can take any real value between given lower and upper bounds. The goal is to find a set of schedules which contains at least one optimal schedule (with mean flow time criterion) for any admissible realization of the random processing times. In order to compute such a set of schedules efficiently and keep it as small as possible, we develop several exact and heuristic algorithms and report computational experience based on randomly generated instances.

Scheduling multiprocessor tasks for mean flow time criterion

Multiprocessor tasks are executed by more than one processor at the same moment of time. This work considers the problem of scheduling unit execution-time and preemptable multiprocessor tasks on m parallel identical processors to minimize mean flow time and mean weighted flow time. We analyze complexity status of the problem. When tasks have unit execution time and the number of processors is arbitrary the problem is shown to be computationally hard. Constructing an optimal preemptive schedule is also computationally hard in general. Polynomial algorithms are presented for scheduling unit execution time tasks when the number of processors is fixed, or the numbers of simultaneously required processors are powers of 2. The case of preemptable tasks requiring either 1 or m processors simultaneously is solvable in low-order polynomial time. Scope and purpose Efficient use of scarce resources is of vital importance both in computer and production systems. Scheduling theory attempts to provide guidelines and algorithms for efficient assignment of the resources to the activities. For a long time the classical scheduling theory assumed that a task can be executed only by one processor at the given moment of time. This assumption is too restrictive in the case of parallel computer systems and modern production systems where tasks (e.g. programs) can be processed on several processors in parallel. Therefore, a new scheduling model of multiprocessor tasks has been proposed recently. Multiprocessor tasks may require more than one processor simultaneously. In this work a deterministic multiprocessor task scheduling problem is analyzed. Most of the earlier publications on this subject assumed schedule length (makespan) optimality criterion. Here we consider different optimality criteria which are the mean flow time and the mean weighted flow time. These are important for the user of the computer system rather than for the owner of the computing facility because they are very closely related to the average waiting time observed by the user.

Heuristics for scheduling in a flow shop with multiple processors

This study investigates the performance of scheduling heuristics in a flow shop with multiple processors. We investigated five better performing flow shop heuristics for their performances of makespan and mean flow time criteria in a flow shop with multiple processors. The study examined the effects of problem characteristics (number of jobs, number of machine stages and number of parallel processors at each stage) and the performance of heuristics using regression analysis. We found that although structural characteristics explain most of the variation in performance, heuristics also had an effect. The experimental results showed that flow shop heuristics developed by Nawaz, Enscore, and Ham and that of Ho were comparable in performance in a flow shop with multiple processors. However, the former was slightly more consistent in results for both criteria.

A study of scheduling rules of flexible manufacturing systems: A simulation approach

This study examines the effects of scheduling rules on the performance of flexible manufacturing systems (FMSs). Several machine and AGV scheduling rules are tested against the mean flowtime criterion. In general, scheduling rules are widely used in practice ranging from direct applications as a stand-alone scheduling scheme to indirect application as a part of complicated scheduling systems. In this paper, we compare the rules under various experimental conditions by using an FMS simulation model. Our objective is to measure sensitivity of the rules to changes in processing time distributions, various levels of breakdown rates, and types of AGV priority schemes. A comprehensive bibliography is also presented in the paper.

Flowshop sequencing with mean flowtime objective

This paper introduces a near-optimal heuristic based on sorting methods to minimize the total or mean flowtime (completion time) for the n-job, M-machine flowshop. The mean flowtime criterion is important, because many important cost measures, such as finished goods turn-over, depend on flowtime. A simulation study is conducted to test the effectiveness of the proposed heuristic by comparing it with those of Rajendran and Rajendran and Chaudhuri. The simulation results show that the proposed heuristic performs better than the two existing heuristics, especially when the number of jobs is large (⩾20). Further, the results show that the proposed heuristic averages to 0.16% above the optimum for 2000 small test problems, ranging from five to nine jobs and from three to ten machines.

PRODUCTION PLANNING DECISIONS IN FLEXIBLE MANUFACTURING SYSTEMS WITH RANDOM MATERIAL FLOWS

Abstract In this paper, we consider the FMS planning problem of determining optimal machine workload assignments in order to rninimize mean part flow time. We decompose this problem into the subproblems of first forming machine groups and next assigning operations to these groups. Three types of grouping configurations—no grouping, partial grouping and total grouping—are considered. In both no grouping and partial grouping, each machine is tooled differently. While each operation is assigned to only one machine in no grouping, partial grouping permits multiple operation assignments. On the other hand, total grouping partitions the machines into groups of identically-tooled machines; each machine within a group is capable of performing the same set of operations. Within this grouping framework, we consider three machine loading objectives—minimizing the total deviation from the optimal group utilization levels, minimizing part travel and maximizing routing flexibility, for generating a variety of system configurations. A queueing network model of an FMS is used to determine the optimal configurations and machine workload assignments for the no grouping and total grouping cases. It is shown that under total grouping, the configuration of M machines into G groups that minimizes flow time is one in which the sizes of the machine groups are maximally unbalanced and the workload per machine in the larger groups is higher. This extends previous results on the optimality of unbalancing both machine group sizes and machine workload to the mean flow time criterion. A simulation experiment is next conducted to evaluate the alternative machine configurations to understand how their relative performance depends upon the underlying system characteristics, such as system utilization level and variation among operation processing times. We also investigate the robustness of these configurations against disruptions, such as machine unreliability and variation in processing batch sizes. While different configurations minimize mean flow time under different parameter values, partial grouping with state-dependent part routing performs well across a wide range of these values. Experimental results also show that the impact of disruptions can be reduced by several means, such as aggregating operations of a part to be performed at the same machine, in addition to providing routing flexibility.

Comparative performance analysis of priority rules in a constrained flow shop with multiple processors environment

Scheduling in a flow shop with multiple processors (FSMP) involves the sequencing of n jobs in a flow shop, where two or more identical processors are allowable at a machine stage. The constrained flow shop with multiple processors problem (CFSMP) considered in this study is a special case of the FSMP problem, in which the total number of jobs that can concurrently exist in the system is bounded by a prespecified number. A simulation experiment was performed to investigate the performance of six priority rules in the CFSMP environment for three performance measures namely makespan, mean flow time, and maximum flow time. A dynamic simulation model of the constrained flow shop with multiple processors environment was developed in which the queuing priorities at each machine stage were established dynamically. The results of the simulation study indicated that the shortest processing time first dispatching procedure (SPT) yielded superior performance for the makespan and mean flow time criteria. However, for the maximum flow time criterion, clear superiority of a particular dispatching procedure was not established.

Scheduling with Sequencing Flexibility*

ABSTRACTThis study examines the effects of sequencing flexibility on the performance of rules used to schedule operations in manufacturing systems. The findings show that taking advantage of even low levels of sequencing flexibility in the set of operations required to do a job results in substantial improvement in the performance of scheduling rules with respect to mean flowtime. Differences in the mean flowtime measure for various rules also diminish significantly with increasing sequencing flexibility. Performance improvements additionally result for such due‐date related performance measures as mean tardiness and the proportion of jobs tardy. At high levels of sequencing flexibility, some nonparametric scheduling rules outperform the shortest processing time rule in terms of the mean flowtime criterion. Rules based on job due dates also outperform rules based on operation milestones in terms of tardiness related criteria at high levels of sequencing flexibility. The implications of these findings for the design of manufacturing systems and product design are noted.

Openshop scheduling with machine dependent processing times

This paper examines the openshop problem with machine dependent processing times. Two objectives are considered; minimizing the maximal completion (makespan), and minimizing the mean flow time. For this problem with the makespan criteria and the number of jobs greater or equal to the number of machines we present an O( mn) optimal algorithm and prove that the same problem with the number of jobs less than the number of machines but greater or equal three is NP-hard. We also present an O( n) optimal algorithm for this problem with mean flow time criteria but two machines only, and for a special case with m machines describe an optimal O( mn) algorithm. The three machine openshop problem with machine dependent processing times and mean flow time criteria remains open.

Experimental investigation of FMS machine and AGV scheduling rules against the mean flow-time criterion

Although a significant amount of research has been carried out in the scheduling of flexible manufacturing systems (FMSs), it has generally been focused on developing intelligent scheduling systems. Most of these systems use simple scheduling rules as a part of their decision process. While these scheduling rules have been investigated extensively for a job shop environment, there is little guidance in the literature as to their performance in an FMS environment. This paper attempts to investigate the performances of machine and AGV scheduling rules against the mean flow-time criterion. The scheduling rules are tested under a variety of experimental conditions by using an FMS simulation model.

A Mixed-Integer Goal-Programming Formulation of the Standard Flow-Shop Scheduling Problem

Until recently, the majority of models used to find an optimal sequence for the standard flow-shop problem were based on a single objective, typically makespan. In many applications, the practitioner may also want to consider other criteria simultaneously, such as mean flow-time or throughput time. As makespan and flow-time are equivalent criteria for optimizing machine idle-time and job idle-time, respectively, these additional criteria could be inherently considered as well. The effect of job idle-time, measuring in-process inventory, could be of particular importance.This paper presents an extension of an earlier model developed by the authors, formulating the generalized N job, M machine standard flow-shop problem as a mixed-integer goal-programming model. The formulation was empirically tested through a comparison of the generated optimal solutions to their mathematically derived counterparts. For this, a special flow-shop problem with certain permutation properties was selected. In addition, a randomly chosen problem was solved to show the general applicability of the derived formulation.The model allows the incorporation of the makespan as well as the mean flow-time criteria, instead of optimization being based on a single objective.

Ordered Flow Shop Problems with no In-Process Waiting: Further Results

The ordered flow shop sequencing problem with no in-processing waiting (OFSNW) is considered with respect to mean flow time criterion. It is shown that the sequence in which jobs are arranged according to the shortest processing time rule (SPT) represents an optimal sequence. Additional results for the makespan criterion are also discussed.