Job Flow Time Research Articles

Single-machine scheduling with flexible and periodic maintenance

This paper deals with the problem of scheduling a single machine with periodic maintenance, where the machine is assumed to be stopped periodically to be maintained or to be reset for a constant time w during the scheduling period. Meanwhile, the maintenance period [u, v] is assumed to have been arranged previously, and the time w would not be longer than the maintenance period [u, v] (ie w⩽u−v). The time u (v) is the earliest (latest) time at which the machine starts (stops) its maintenance. The objective is to minimize the mean flow time of jobs. Four mixed binary integer programming models are developed to optimally solve this problem. Also, an efficient heuristic is proposed for solving large-sized problems.

Generating efficient schedules for identical parallel machines involving flow-time and tardy jobs

This paper considers the problem of generating a set of efficient (non-dominated) schedules on identical parallel machines involving total flow-time and total number of tardy jobs. In view of the NP-hard nature of this problem, heuristic algorithms are proposed for its solution. Two evaluation methods that provide a scheme by which multiple non-dominated sets can be compared are described and used to compare the performance of the proposed algorithms. Results of several experiments demonstrate the capability of the proposed algorithms and evaluation methodologies to address the problem at hand.

A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs

In this paper, we consider the problem of permutation flowshop scheduling with the objectives of minimizing the makespan and total flowtime of jobs, and present a Multi-Objective Simulated-annealing Algorithm (MOSA). Two initial sequences are obtained by using simple and fast existing heuristics, supplemented by the implementation of three improvement schemes. Each of the two resultant sequences corresponds to a possible non-dominated solution containing the minimum value of one objective function. These sequences, taken one at a time, are given as the starting sequences to the MOSA. The MOSA seeks to obtain non-dominated solutions through the implementation of a simple probability function that attempts to generate solutions on the Pareto-optimal front. The probability function selects probabilistically a particular objective function, considering which the algorithm uncovers non-dominated solutions. Moreover, the probability function is varied in such a way that the entire objective-function space is covered uniformly so as to obtain as many non-dominated and well-dispersed solutions as possible. The parameters in the proposed MOSA are determined after conducting a pilot study. Two variants of the proposed algorithm, called MOSA-I and MOSA-II, with different parameter settings with respect to the temperature and epoch length, are considered in the performance evaluation of algorithms. In order to evaluate MOSA-I and MOSA-II, we have made use of 90 benchmark problems provided by Taillard [Eur. J. Operation. Res. 64 (1993) 278]. After an extensive literature survey, the following flowshop multi-objective scheduling algorithms have been identified as benchmark procedures: (a) MOGLS (Multi-Objective Genetic Local Search) by Ishibuchi and Murata [IEEE Trans. Syst., Man, Cybernet. C: Appl. Rev. 28 (1998) 392]; (b) Elitist Non-dominated sorting Genetic Algorithm (ENGA) by Bagchi [Multi-Objective Scheduling by Genetic Algorithms, Kluwer Academic Publishers, 1999]; (c) GPW (Gradual Priority Weighting) approach by Chang, Hsieh and Lin [Int. J. Prod. Econ. 79 (2002) 171]; and (d) a posteriori approach based heuristic by Framinan, Leisten and Ruiz-Usano [Eur. J. Operation. Res. 141 (2002) 559]. The non-dominated sets obtained from each of the existing benchmark algorithms and the proposed MOSA-I and MOSA-II are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by MOSA-I and MOSA-II. In addition, it is noteworthy that both MOSA-I and MOSA-II require less computational effort than the MOGLS, ENGA and GPW.

An application of the neural network energy function to machine sequencing

We apply a neural network approach for solving a one-machine sequencing problem to minimize either single- or multi-objectives, namely the total tardiness, total flowtime, maximimum tardiness, maximum flowtime, and number of tardy jobs. We formulate correspondingly nonlinear integer models, for each of which we derive a quadratic energy function, a neural network, and a system of differential equations. Simulation results based on solving the nonlinear differential equations demonstrate that our approach can effectively solve the sequencing problems to optimality in most cases and near optimality in a few cases. The neural network approach can also be implemented on a parallel computing network, resulting in significant runtime savings over the optimization approach.

Scheduling in dynamic assembly job-shops to minimize the sum of weighted earliness, weighted tardiness and weighted flowtime of jobs

In many manufacturing systems, jobs that are completed early are held as finished-goods inventory until their due-dates, and hence we incur earliness costs. Similarly, jobs that are completed after their due-dates incur penalty. The objective in such situations would, therefore, be to meet the due-dates of the respective jobs as closely as possible, and consequently minimize the sum of earliness and tardiness of jobs because earliness and tardiness of jobs greatly influence the performance of a schedule with respect to cost. In addition, a job incurs holding cost from the time of its arrival until its completion. Most studies on scheduling in such manufacturing systems assume unit earliness cost, unit tardiness cost and unit holding cost of a job. However, in reality such an assumption need not always hold and it is quite possible that there exist different costs of earliness, tardiness and holding for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (i.e. shops that manufacture multi-level jobs) with the consideration of jobs having different earliness, tardiness and holding costs. An attempt is made in this paper to present dispatching rules by incorporating the relative costs of earliness, tardiness and holding of jobs in the form of scalar weights. In the first phase of the study, relative costs (or weights for) earliness and tardiness of jobs are considered, and the dispatching rules are presented in order to minimize the sum of weighted earliness and weighted tardiness of jobs. In the second phase of the study, the objective considered is the minimization of the sum of weighted earliness, weighted tardiness and weighted flowtime of jobs, and the dispatching rules are presented by incorporating the relative costs of earliness, tardiness and flowtime of jobs. Simulation studies have been conducted separately for both phases of the current study, the performance of the scheduling rules have been observed independently, and the results of the simulation study have been reported. The proposed rules are found to be effective in minimizing the mean and maximum values of the measures of performance.

Pareto archived simulated annealing for job shop scheduling with multiple objectives

In this paper, the job shop scheduling problem is studied with the objectives of minimizing the makespan and the mean flow time of jobs. The simultaneous consideration of these objectives is the multi-objective optimization problem under study. A metaheuristic procedure based on the simulated annealing algorithm called Pareto archived simulated annealing (PASA) is proposed to discover non-dominated solution sets for the job shop scheduling problems. The seed solution is generated randomly. A new perturbation mechanism called segment-random insertion (SRI) scheme is used to generate a set of neighbourhood solutions to the current solution. The PASA searches for the non-dominated set of solutions based on the Pareto dominance or through the implementation of a simple probability function. The performance of the proposed algorithm is evaluated by solving benchmark job shop scheduling problem instances provided by the OR-library. The results obtained are evaluated in terms of the number of non-dominated schedules generated by the algorithm and the proximity of the obtained non-dominated front to the Pareto front.

Empirical Bayes forecasting methods for job flow times

We consider the problem of forecasting multi-class job flow times in a resource-sharing environment. We assume the deviation of flow times in each class from the class nominal value follows an exponential distribution with its parameter following a gamma distribution. A large simulation experiment is conducted to assess and compare the performance of the Bayes and empirical Bayes forecasting methods under differing model assumptions. Simulation results show that non-parametric empirical Bayes methods are more efficient and robust relative to the parametric empirical Bayes.

Bid construction scheme for job flow time reduction in auction-based fully-distributed manufacturing systems

This study presents a novel bid construction scheme for an auction-based fully-distributed manufacturing system. The scheme is applied to the planning and control of manufacturing activities. A set of independent machining resources in the system, each with several ongoing set-up dependent jobs, compete for an upcoming job. The manner in which a resource constructs a bid determines job allocation and resource utilization and, consequently, job flow times. Resources that employ simple heuristic methods (e.g., based on a first-come-first-served scheme) to construct bids, often neglecting setup considerations, limit their applicability and performance quality. Here, the bid construction problem of a resource is formulated as a setup-sequencing (SS) problem. The optimal sequencing theory is then applied to develop a dynamic programming (DP)-based bid construction algorithm. The proposed algorithm has a computational complexity lower than that of the best-known algorithm for the SS problem. Additionally, parallel and distributed computing technology is utilized to model and implement this auction-based manufacturing control system in order to gain further insights into the effectiveness of the proposed DP-based bid construction scheme. Experimental results demonstrate that the proposed bid construction scheme performs well, and its contribution becomes obvious in the case of larger setup times and lot sizes.

Two ant-colony algorithms for minimizing total flowtime in permutation flowshops

The problem of scheduling in flowshops with the objective of minimizing total flowtime is studied. For solving the problem two ant-colony algorithms are proposed and analyzed. The first algorithm refers to some extent to ideas by Stuetzle [Stuetzle, T. (1998). An ant approach for the flow shop problem. In: Proceedings of the sixth European Congress on intelligent techniques and soft computing (EUFIT '98) (Vol. 3) (pp. 1560-1564). Aachen: Verlag Mainz] and Merkle and Middendorf [Merkle, D., & Middendorf, M. (2000). An ant algorithm with a new pheromone evaluation rule for total tardiness problems. In: Proceedings of the EvoWorkshops 2000, lecture notes in computer science 1803 (pp. 287-296). Berlin: Springer]. The second algorithm is newly developed. The proposed ant-colony algorithms have been applied to 90 benchmark problems taken from Taillard [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278-285]. A comparison of the solutions yielded by the ant-colony algorithms with the best heuristic solutions known for the benchmark problems up to now, as published in extensive studies by Liu and Reeves [Liu, J., & Reeves, C.R. (2001). Constructive and composite heuristic solutions to the P//ΣCi scheduling problem. European Journal of Operational Research, 132,439-452, and Rajendran and Ziegler [Rajendran, C., & Ziegler, H. (2004). Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research, 155, 426-438], shows that the presented ant-colony algorithms are better, on an average, than the heuristics analyzed by Liu and Reeves and Rajendran and Ziegler.

A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs

In this paper the problem of permutation flow shop scheduling with the objectives of minimizing the makespan and total flow time of jobs is considered. A Pareto-ranking based multi-objective genetic algorithm, called a Pareto genetic algorithm (GA) with an archive of non-dominated solutions subjected to a local search (PGA-ALS) is proposed. The proposed algorithm makes use of the principle of non-dominated sorting, coupled with the use of a metric for crowding distance being used as a secondary criterion. This approach is intended to alleviate the problem of genetic drift in GA methodology. In addition, the proposed genetic algorithm maintains an archive of non-dominated solutions that are being updated and improved through the implementation of local search techniques at the end of every generation. A relative evaluation of the proposed genetic algorithm and the existing best multi-objective algorithms for flow shop scheduling is carried by considering the benchmark flow shop scheduling problems. The non-dominated sets obtained from each of the existing algorithms and the proposed PGA-ALS algorithm are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by the proposed PGA-ALS.

Mathematical modelling of multi-objective job shop scheduling with dependent setups and re-entrant operations

For the last thirty years, in job shop scheduling, the setup times of operations have been either ignored or combined with their corresponding processing times, independent setups, to simplify the work of model construction. However, in practice, the setup times of an operation are usually considered be sequence-dependent. Moreover, the performance of a scheduling system is not evaluated to satisfy a single objective, but to obtain a trade-off solution regarding multiple objectives. Therefore, this paper investigates job shop scheduling problems with re-entrant operations where the setup times, which vary according to the preceding operation which is processed on the same machine, and which can be separated from their corresponding processing times, cannot be omitted. Three practical performance measures – minimum total job flow time, minimum total job tardiness and minimum machine idle time – are considered. An integer programming model is first developed to optimise each single objective and an acceptable trade-off schedule, which makes use of a multiple-decision-making technique, the global criterion method, is obtained by evaluating three objectives simultaneously .

Modelling and heuristics of FMS scheduling with multiple objectives

The performance of a scheduling system, in practice, is not evaluated to satisfy a single objective, but to obtain a trade-off schedule regarding multiple objectives. Therefore, in this research, we make use of one of the multiple objective decision-making methods, a global criterion approach, to develop a multi-objective model for solving FMS scheduling problems with consideration of three performance measures, namely minimum mean job flow time, mean job tardiness, and minimum mean machine idle time, simultaneously. In addition, hybrid heuristics, which are a combination of two common local search methods, simulated annealing and tabu search, are also proposed for solving the addressed FMS scheduling problems. The feasibility and adaptability of the proposed heuristics are investigated through experimental results.

Distributed production planning using a graph-based negotiation protocol

A distributed model for allocating a single job to be processed through multiple machines and alternative routings so that the job flow time is experimentally shown to reach its minimum is presented. Issues are addressed pertaining to dynamic and fully distributed decision-making for determining the job flow time in a cooperative manner between system agents (i.e. machines and a job), and for selecting a good routing (i.e. a short flow time) for a job when alternative routings are available. Two cases with confirmed jobs and without confirmed jobs are examined. The proposed protocols can deal with job shop scheduling with multiple product types in a sequential manner. The model is developed on the basis of a distributed shortest path algorithm using asynchronous job-initiated protocols. These protocols are examined using object-oriented simulation models and it is shown how the agents converge to the optimal path in a finite time.

Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs

The problem of scheduling in permutation flowshops is considered with the objective of minimizing the makespan, followed by the consideration of minimization of total flowtime of jobs. Two ant-colony optimization algorithms are proposed and analyzed for solving the permutation flowshop scheduling problem. The first algorithm extends the ideas of the ant-colony algorithm by Stuetzle [Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT ’98), vol. 3, Verlag Mainz, Aachen, Germany, 1998, p. 1560], called max–min ant system (MMAS), by incorporating the summation rule suggested by Merkle and Middendorf [Proceedings of the EvoWorkshops 2000, Lecture Notes in Computer Science No. 1803, Springer-Verlag, Berlin, 2000, p. 287] and a newly proposed local search technique. The second ant-colony algorithm is newly developed. The proposed ant-colony algorithms have been applied to 90 benchmark problems taken from Taillard [European Journal of Operational Research 64 (1993) 278]. First, a comparison of the solutions yielded by the MMAS and the two ant-colony algorithms developed in this paper, with the heuristic solutions given by Taillard [European Journal of Operational Research 64 (1993) 278] is undertaken with respect to the minimization of makespan. The comparison shows that the two proposed ant-colony algorithms perform better, on an average, than the MMAS. Subsequently, by considering the objective of minimizing the total flowtime of jobs, a comparison of solutions yielded by the proposed ant-colony algorithms with the best heuristic solutions known for the benchmark problems, as published in an extensive study by Liu and Reeves [European Journal of Operational Research 132 (2001) 439], is carried out. The comparison shows that the proposed ant-colony algorithms are clearly superior to the heuristics analyzed by Liu and Reeves. For 83 out of 90 problems considered, better solutions have been found by the two proposed ant-colony algorithms, as compared to the solutions reported by Liu and Reeves.

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.

Dynamic Scheduling for Minimal Flow Time and Maximum Reliability

This paper presents a scheduling algorithm applied to a circular manufacture assembly with redundant facilities. The task is to switch on and off facilities in a manner that minimizes job failure cost and job flow time for a given job production order. The dynamic nature of the scheduling problem is dictated by the aging of the facilities. An example is given to show how our scheduling algorithm results in different system reliability, failure cost and job flow time under differently weighed cost functionals.

Using genetic algorithms for single-machine bicriteria scheduling problems

We consider two bicriteria scheduling problems on a single machine: minimizing flowtime and number of tardy jobs, and minimizing flowtime and maximum earliness. Both problems are known to be NP-hard. For the first problem, we developed a heuristic that produces an approximately efficient solution (AES) for each possible value the number of tardy jobs can take over the set of efficient solutions. We developed a genetic algorithm (GA) that further improves the AESs. We then adapted the GA for the second problem by exploiting its special structure. We present computational experiments that show that the GAs perform well. Many aspects of the developed GAs are quite general and can be adapted to other multiple criteria scheduling problems.

Exploratory analysis of flexible workday policies in a job shop

The degree to which simple policies for varying the length of each workday can affect job shop performance was investigated. The performance of a job shop operating on a fixed 8-hour day schedule was compared with a job shop that had some flexibility to vary an employee's workday by compensating hours in excess of an 8-hour day with an equivalent amount of time off. Thus, each flexible workday policy maintains an average workday of 8 hours/day for each employee. We simulated a hypothetical job shop to assess the effects of various environmental factors and workday policies on measures of interest to management and labour. We found significant improvement in job flow time with overtime (and time off) as little as an average of 24 min for every 8 hours of work.

Minimizing total flowtime and maximum job lateness in the twomachine flowshop system: a computerized algorithm

This paper is an improvement to an extension of a previously published paper which considered the dual criteria of minimizing flowtime and maximum lateness of jobs in the two-machine flowshop system. We discover the conditions that determine which of the pairs of adjacent jobs in a sequence should precede the other to minimize either of the two objective functions. We also present a Branch-and-Bound procedure to arrive at and optimal solution, along with a computerized example problem.

Operation-based flowtime estimation in a dynamic job shop

In the scheduling literature, estimation of job flowtimes has been an important issue since the late 1960s. The previous studies focus on the problem in the context of due date assignment and develop methods using aggregate information in the estimation process. In this study, we propose a new flowtime estimation method that utilizes the detailed job, shop and route information for operations of jobs as well as the machine imbalance information. This type of information is now available in computer-integrated manufacturing systems. The performance of the proposed method is measured by computer simulation under various experimental conditions. It is compared with the existing flowtime estimation methods for a wide variety of performance measures. The results indicate that the proposed method outperforms all the other flowtime estimation methods. Moreover, it is quite robust to changing shop conditions (i.e., machine breakdowns, arrival rate and processing time variations, etc.). A comprehensive bibliography is also provided in the paper.