Total Flowtime Of Jobs Research Articles

A Two-Stage Multi-Objective Genetic Algorithm for a Flexible Job Shop Scheduling Problem with Lot Streaming

The work in this paper is motivated by a recently published article in which the authors developed an efficient two-stage genetic algorithm for a comprehensive model of a flexible job-shop scheduling problem (FJSP). In this paper, we extend the application of the algorithm to solve a lot streaming problem in FJSP while at the same time expanding the model to incorporate multiple objectives. The objective function terms included in our current work are the minimization of the (1) makespan, (2) maximum sublot flowtime, (3) total sublot flow time, (4) maximum job flowtime, (5) total job flow time, (6) maximum sublot finish-time separation, (7) total sublot finish-time separation, (8) maximum machine load, (9) total machine load, and (10) maximum machine load difference. Numerical examples are presented to illustrate the greater need for multi-objective optimization in larger problems, the interaction of the various objective function terms, and their relevance in providing better solution quality. The ability of the two-stage genetic algorithm to jointly optimize all the objective function terms is also investigated. The results show that the algorithm can generate initial solutions that are highly improved in all of the objective function terms. It also outperforms the regular genetic algorithm in convergence speed and final solution quality in solving the multi-objective FJSP lot streaming. We also demonstrate that high-performance parallel computation can further improve the performance of the two-stage genetic algorithm. Nevertheless, the sequential two-stage genetic algorithm with a single CPU outperforms the parallel regular genetic algorithm that uses many CPUs, asserting the superiority of the two-stage genetic algorithm in solving the proposed multi-objective FJSP lot streaming.

Bounding strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimising the total flowtime of jobs

Bounding strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimising the total flowtime of jobs

A Hybrid Algorithm for Multi-Objective Optimization of Minimizing Makespan and Total Flow Time in Permutation Flow Shop Scheduling Problems

This paper proposes, a multi-objective optimization of minimizing makespan and total flow time of jobs for permutation flow shop scheduling is considered. Bi-objective issues are comprehended by doling out uniform weight to every objective function in view of its preference or determining every competent solutions. In flow shop scheduling environment, many meta-heuristic algorithms have been used to find optimal or near-optimal solutions due to the computational cost of determining exact solutions. This work provides a hybridization of genetic algorithm and simulated annealing algorithm (HGASA) based multi-objective optimization algorithm for flow shop scheduling. HGASA could be a simple and proficient algorithm that is utilized to determine for every single and multi-objective problem in flow shop scheduling shop environment. This algorithm can works simply for realistic manufacturing system applications. The proposed hybrid algorithm searches the optimal solution for objectives by considering the makespan and total flow time. The performance of the proposed HGASA was tested on standard flow shop benchmark problems to calculate its performance. The test results show that the HGASA algorithm performed better in terms of searching quality and efficiency than other meta-heuristic algorithms.

Evolutionary Hybrid Particle Swarm Optimization Algorithm for Solving NP-Hard No-Wait Flow Shop Scheduling Problems

The no-wait flow shop is a flowshop in which the scheduling of jobs is continuous and simultaneous through all machines without waiting for any consecutive machines. The scheduling of a no-wait flow shop requires finding an appropriate sequence of jobs for scheduling, which in turn reduces total processing time. The classical brute force method for finding the probabilities of scheduling for improving the utilization of resources may become trapped in local optima, and this problem can hence be observed as a typical NP-hard combinatorial optimization problem that requires finding a near optimal solution with heuristic and metaheuristic techniques. This paper proposes an effective hybrid Particle Swarm Optimization (PSO) metaheuristic algorithm for solving no-wait flow shop scheduling problems with the objective of minimizing the total flow time of jobs. This Proposed Hybrid Particle Swarm Optimization (PHPSO) algorithm presents a solution by the random key representation rule for converting the continuous position information values of particles to a discrete job permutation. The proposed algorithm initializes population efficiently with the Nawaz-Enscore-Ham (NEH) heuristic technique and uses an evolutionary search guided by the mechanism of PSO, as well as simulated annealing based on a local neighborhood search to avoid getting stuck in local optima and to provide the appropriate balance of global exploration and local exploitation. Extensive computational experiments are carried out based on Taillard’s benchmark suite. Computational results and comparisons with existing metaheuristics show that the PHPSO algorithm outperforms the existing methods in terms of quality search and robustness for the problem considered. The improvement in solution quality is confirmed by statistical tests of significance.

Mitigating Service Variability in MapReduce Clusters via Task Cloning: A Competitive Analysis

Measurement traces from real-world production environment show that the execution time of tasks within a MapReduce job varies widely due to the variability in machine service capacity. This variability issue makes efficient job scheduling over large-scale MapReduce clusters extremely challenging. To tackle this problem, we adopt the task cloning approach to mitigate the effect of machine variability and design corresponding scheduling algorithms so as to minimize the overall job flowtime in different scenarios. For offline scheduling where all jobs arrive at the same time, we design an $O(1)$ -competitive algorithm, which gives priorities to jobs with small effective workload. We then extend this offline algorithm to yield the so-called Smallest Remaining Effective Workload based $\beta$ -fraction Sharing plus Cloning algorithm (SREW+C( $\beta$ )) for the online case. We also show that SREW+C( $\beta$ ) is $(1+ 2\beta + \epsilon)$ -speed $O(\frac{1}{\beta \epsilon })$ -competitive with respect to the sum of job flowtime within a cluster. We demonstrate via trace-driven simulations that SREW+C( $\beta$ ) can significantly reduce the overall job flowtime by cutting down the elapsed time of small jobs substantially. In particular, SREW+C( $\beta$ ) reduces the total job flowtime by 14, 10 and 11 percent respectively when comparing to Mantri, Dolly and Grass.

A NSGA-II based memetic algorithm for multiobjective parallel flowshop scheduling problem

In many real-world manufacturing applications, a number of parallel flowshops are often used to process the jobs. The scheduling problem in this parallel flowshop system has gained an increasing concern from the operational research community; however, multiple scheduling criteria are rarely considered simultaneously in the literature. In this paper, a special parallel flowshop scheduling (PFSS) problem that consists of two parallel non-identical shops, one with two consecutive machines and the other with only one machine, is investigated with two objective functions of minimizing the total flow time of jobs and the number of tardy jobs in the two-machine flowshop. A multiobjective evolutionary algorithm (MOEA) based memetic algorithm hybridizing the local search technique into the framework of NSGA-II, which is well known as the most popular MOEA, is proposed for addressing the investigated PFSS problem. A set of test instances are employed to examine the performance of the proposed algorithm in comparison with two peer MOEAs, which also adopt the similar algorithm mechanism of NSGA-II. Experimental results indicate the effectiveness and efficiency of the proposed NSGA-II based memetic algorithm in solving the multiobjective PFSS problem.

Parallel machine scheduling with batch deliveries to minimize total flow time and delivery cost

AbstractMotivated by the flow of products in the iron and steel industry, we study an identical and parallel machine scheduling problem with batch deliveries, where jobs finished on the parallel machines are delivered to customers in batches. Each delivery batch has a capacity and incurs a cost. The objective is to find a coordinated production and delivery schedule that minimizes the total flow time of jobs plus the total delivery cost. This problem is an extension of the problem considered by Hall and Potts, Ann Oper Res 135 (2005) 41–64, who studied a two‐machine problem with an unbounded number of transporters and unbounded delivery capacity. We first provide a dynamic programming algorithm to solve a special case with a given job assignment to the machines. A heuristic algorithm is then presented for the general problem, and its worst‐case performance ratio is analyzed. The computational results show that the heuristic algorithm can generate near‐optimal solutions. Finally, we offer a fully polynomial‐time approximation scheme for a fixed number of machines. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 492–502, 2016

A Hungarian penalty-based construction algorithm to minimize makespan and total flow time in no-wait flow shops

This paper presents a penalty-based construction algorithm for the no-wait flow shop scheduling problem with the objective of minimizing makespan and total flow time of jobs. The proposed method, derived from Hungarian penalty method originally used for the classic assignment problem is employed to generate an initial schedule of jobs, which is further improved by an insertion technique to obtain an optimal or near-optimal schedule. The results of computational experiments on a large number of test problems show that the proposed method performs significantly better than the state-of-the-art procedures while requiring comparable computational effort.

A NSGA-II and NSGA-III comparison for solving an open shop scheduling problem with resource constraints

This paper presents an open shop scheduling problem based on a real mechanical workshop made of m machines that process n jobs. It deals with different resource constraints related to the tools allocation and the multi-skills staff assignment. Resource skills and their availability are required to execute one process task. In this work, we expose a multi-objective problem where the idea is to minimize three objectives simultaneously. The first one considers the minimization of the total flow time of jobs in the production system, then the workload balancing concerning both, humans and machines is addressed. We propose and compare two multi-objective methods: NSGA-II and NSGA-III. Computational experiments are designed according to the literature, we expose the small and large sized instances to present the general performance of these algorithms using the hyper-volume metric to compare them.

Single-machine batch scheduling of linear deteriorating jobs

We consider the problem of scheduling jobs in batches on a single machine where the processing time of each job is a simple increasing linear function of its waiting time, i.e., the time between the starting time of processing the batch to which the job belongs and the starting time of processing of the job. The objective is to minimize the sum of the total job flow time and the batching cost. We first show that the case with a given number of batches is strongly NP-hard and we present a fully polynomial-time approximation scheme (FPTAS) for this case. We then show that the case with an arbitrary number of batches is also strongly NP-hard and there is no polynomial-time approximation algorithm with a constant upper bound for this case unless P=NP.

A Hybrid ILS-VND Based Hyper-heuristic for Permutation Flowshop Scheduling Problem

In this paper an iterated local search (ILS) is embedded with a variable neighborhood Descent (VND) hyper-heuristic. The proposed hyper-heuristic combines low-level heuristics. Several variants from the literature within the proposed ILS were implemented and tested. This article conducts an empirical study involving hard combinatorial optimization problems, permutation flowshop scheduling problem (PFSP) with the objectives of minimizing makespan and the total flowtime of jobs. The proposed ILS based hyper-heuristic proved its general and applicable across the studied problems.

A heuristic algorithm to minimise the total flowtime of jobs in permutation flowshops

A heuristic algorithm with six implementations (HA-I to HA-VI) is presented in this paper, and it is used to solve the permutation flowshop scheduling problem to minimise the total flowtime of jobs. These implementations have been evaluated by using the 90 benchmark flowshop scheduling problem instances, and the solutions yielded are compared with the solutions reported in the literature. The comparison shows that the implementations all together have produced better solutions for 28 problem instances and same solutions for 29 problem instances, out of 90 problem instances considered with respect to the solutions by Iterated Local Search algorithm proposed by Dong et al. (2009). They have also produced better solutions for 50 problem instances and the same solutions for 19 problem instances, out of 90 problem instances considered with respect to the solutions by PSOvns algorithm proposed by Tasgetiren et al. (2007), as reported in Dong et al. (2009).

A Pareto-Optimal Solution for a Multi-Objective Scheduling Problem with Periodic Maintenance Requirement

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.

Minimizing makespan and total flowtime in permutation flowshops by a bi-objective multi-start simulated-annealing algorithm

In this study, a bi-objective multi-start simulated-annealing algorithm (BMSA) is presented for permutation flowshop scheduling problems with the objectives of minimizing the makespan and total flowtime of jobs. To evaluate the performance of the BMSA, computational experiments were conducted on the well-known benchmark problem set provided by Taillard. The non-dominated sets obtained from each of the existing benchmark algorithms and the BMSA were compared, and then combined to form a net non-dominated front. The computational results show that more than 64% of the solutions in the net non-dominated front are contributed by the proposed BMSA. It is believed that these solutions can serve as new benchmarks for future research.

Efficient Heuristics for Flowshop Scheduling for Minimizing the Makespan and Total Flowtime of Jobs

The problem of scheduling in permutation flowshops has been extensively investigated by many researchers. Recently, attempts are being made to consider more than one objective simultaneously and develop algorithms to obtain a set of Pareto-optimal solutions. Varadharajan et al. (2005) presented a multi-objective simulated-annealing algorithm (MOSA) for the problem of permutation-flowshop scheduling with the objectives of minimizing the makespan and the total flowtime of jobs. The MOSA uses two initial sequences obtained using heuristics, and seeks to obtain non-dominated solutions through the implementation of a probability function, which probabilistically selects the objective of minimizing either the makespan or the total flowtime of jobs. In this paper, the same problem of heuristically developing non-dominated sequences is considered. We propose an effective heuristics based on simulated annealing (SA), in which the weighted sum of the makespan and the total flowtime is used. The essences of the heuristics are in selecting the initial sequence, setting the weight and generating a solution in the search process. Using a benchmark problem provided by Taillard (1993), which was used in the MOSA, these conditions are extracted in a large-scale experiment. The non-dominated sets obtained from the existing algorithms and the proposed heuristics are compared. It was found that the proposed heuristics drastically improved the performance of finding the non-dominated frontier.

Bi-criteria improved genetic algorithm for scheduling in flowshops to minimise makespan and total flowtime of jobs

Bi-criteria improved genetic algorithm (IGA) for flowshop scheduling problem is proposed in this paper. The primary concern of flowshop scheduling problem considered in this work is to obtain the best sequence, which minimises the makespan and total flow time of all jobs. The initial population of the genetic algorithm is created using popular NEH constructive heuristic (Nawaz et al. 1983). In IGA, multi-crossover operators and multi-mutation operators are applied randomly to subpopulations divided from the original population to enhance the exploring potential and to enrich the diversity of the crossover templates. The performance of the proposed algorithm is demonstrated by applying it to benchmark problems available in the OR-Library. Computation results based on some permutation flowshop scheduling benchmark problems (OR-Library) show that the IGA gives better solution when compared with the earlier reported results.

Fuzzy job shop scheduling with lot-sizing

This paper deals with a problem of determining lot-sizes of jobs in a real-world job shop-scheduling in the presence of uncertainty. The main issue discussed in this paper is lot-sizing of jobs. A fuzzy rule-based system is developed which determines the size of lots using the following premise variables: size of the job, the static slack of the job, workload on the shop floor, and the priority of the job. Both premise and conclusion variables are modelled as linguistic variables represented by using fuzzy sets (apart from the priority of the job which is a crisp value). The determined lots’ sizes are input to a fuzzy multi-objective genetic algorithm for job shop scheduling. Imprecise jobs’ processing times and due dates are modelled by using fuzzy sets. The objectives that are used to measure the quality of the generated schedules are average weighted tardiness of jobs, the number of tardy jobs, the total setup time, the total idle time of machines and the total flow time of jobs. The developed algorithm is analysed on real-world data obtained from a printing company.

A genetic algorithm for flowshop scheduling with multiple objectives

In this paper, we study the permutation flowshop scheduling problem with the objectives of minimizing the makespan and total flowtime of jobs. An attempt is made to solve the multi-objective problem by using the Proposed Genetic Algorithm (ProGA). In order to evaluate the ProGA, we have made use of benchmark flowshop scheduling problems, and the heuristically non-dominated solutions for these problems are obtained from each of the existing methodologies and the ProGA. These non-dominated solutions are combined to obtain a net heuristic non-dominated front for a given problem. It is found that most of the solutions on the net non-dominated front are yielded by the ProGA, bringing out the superiority of the proposed genetic algorithm.

A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem

In this paper, a particle swarm optimization algorithm (PSO) is presented to solve the permutation flowshop sequencing problem (PFSP) with the objectives of minimizing makespan and the total flowtime of jobs. For this purpose, a heuristic rule called the smallest position value (SPV) borrowed from the random key representation of Bean [J.C. Bean, Genetic algorithm and random keys for sequencing and optimization, ORSA Journal of Computing 6(2) (1994) 154–160] was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems. In addition, a very efficient local search, called variable neighborhood search (VNS), was embedded in the PSO algorithm to solve the well known benchmark suites in the literature. The PSO algorithm was applied to both the 90 benchmark instances provided by Taillard [E. Taillard, Benchmarks for basic scheduling problems, European Journal of Operational Research, 64 (1993) 278–285], and the 14,000 random, narrow random and structured benchmark instances provided by Watson et al. [J.P. Watson, L. Barbulescu, L.D. Whitley, A.E. Howe, Contrasting structured and random permutation flowshop scheduling problems: Search space topology and algorithm performance, ORSA Journal of Computing 14(2) (2002) 98–123]. For makespan criterion, the solution quality was evaluated according to the best known solutions provided either by Taillard, or Watson et al. The total flowtime criterion was evaluated with the best known solutions provided by Liu and Reeves [J. Liu, C.R. Reeves, Constructive and composite heuristic solutions to the P∥∑ C i scheduling problem, European Journal of Operational Research 132 (2001) 439–452], and Rajendran and Ziegler [C. Rajendran, H. Ziegler, Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs, European Journal of Operational Research, 155(2) (2004) 426–438]. For the total flowtime criterion, 57 out of the 90 best known solutions reported by Liu and Reeves, and Rajendran and Ziegler were improved whereas for the makespan criterion, 195 out of the 800 best known solutions for the random and narrow random problems reported by Watson et al. were improved by the VNS version of the PSO algorithm.

Dispatching in flowshops with bottleneck machines

This paper addresses the problem of dispatching in flowshops with bottleneck machines. The presence of bottleneck machines results in the restricted throughput in flowshops. The objective is to develop dispatching rules for scheduling by taking into account the presence of bottleneck machines. The measures of performance are the minimization of total flowtime of jobs, the minimization of the sum of earliness and tardiness of jobs, and the minimization of total tardiness of jobs, considered separately. Many existing conventional dispatching rules and the proposed dispatching rules have been extensively investigated for their performance by generating a large number of problems of various sizes and bottleneck conditions. The results of the experimental investigation show that the proposed dispatching rules emerge to be superior to the conventional dispatching rules.