Total Flow Time Research Articles

Hedge against total flow time uncertainty of the uniform parallel machine scheduling problem with interval data

We consider a total flow time minimisation problem of uniform parallel machine scheduling when job processing times are only known to be bounded within certain given intervals. A minmax regret model is proposed to identify a robust schedule that minimises the maximum deviation from the optimal total flow time over all possible realisations of the job processing times. To solve this problem, we first prove that the maximal regret for any schedule can be obtained in polynomial time. Then, we derive a mixed-integer linear programming (MILP) formulation of our problem by exploiting its structural properties. To reduce the computational time, we further transform our problem into a robust single-machine scheduling problem and derive another MILP formulation with fewer variables and constraints. Moreover, we prove that the optimal schedule under the midpoint scenario is a 2-approximation for our minmax regret problem. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.

Hepatic necro-inflammation and elevated liver enzymes: Evaluation with MRI perfusion imaging with gadoxetic acid in chronic hepatitis patients

To evaluate liver necro-inflammation and function by using gadoxetic acid-enhanced dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), with histological analysis as the reference standard. Seventy-nine subjects (21 healthy subjects; 58 chronic hepatitis patients) who received gadoxetic acid-enhanced DCE-MRI were divided into three subgroups: no (A0, n = 31), mild (A1, n = 27), and moderate-severe (A2-A3, n = 21) activities. Two DCE-MRI models were measured: (1) a dual-input single-compartment model to obtain absolute arterial, portal venous, and total blood flow, arterial fraction (ART), distribution volume, and mean transit time; (2) a curve analysis method to obtain peak, slope, and AUC (area under curve). The serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) levels also obtained. Statistical testing included Kruskal-Wallis tests for continuous data, Pearson's correlation tests, and multiple linear regression analyses. Hepatic necro-inflammatory activity grades were significantly correlated with fibrotic stages, serum ALT level, ART and AUC. ART was helpful to predict the mild activity (≤ A1 versus >A1; Az = 0.728), whereas AUC could differentiate no activity from any activity (A0 versus >A0; Az = 0.703). Peak, slope and AUC were all associated with AST and ALT (p < 0.05). Gadoxetic acid-enhanced DCE-MRI parameters may be used to evaluate the severity of hepatic necro-inflammation and function.

Solution algorithms for unrelated machines minmax regret scheduling problem with interval processing times and the total flow time criterion

An uncertain version of the task scheduling problem on unrelated machines to minimize the total flow time is considered. It is assumed that processing times are not known a priori, but they belong to intervals of known bounds. The absolute regret is applied to evaluate the uncertainty, and minmax regret task scheduling problem is solved. A simple 2-approximate middle intervals time efficient algorithm is proposed. More time consuming but better in terms of the quality of solutions scatter search based heuristic algorithm is described. Its usefulness is justified via computational experiments.

No-Wait Flow Shop Scheduling Based on Discrete Harmony Search Algorithm

This paper proposed a discrete harmony search algorithm, named DHS, for solving the no-wait flow shop scheduling problem with the objective to minimize total flowtime. Firstly, the total flowtime is shown. Secondly, a harmony is represented as a discrete job permutation and the well-known NEH method is proposed to initialize the harmony memory. Thirdly, Extensive computational experiments are carried out based on a set of well-known benchmark instances. Computational results show the effectiveness of the DHS algorithm in solving the no-wait flow shop scheduling problem.

Research on Virtual Cellular Manufacturing Scheduling Based on the Scale-Free Random Network Model

This paper studies the resource conflict resolution problem for virtual cellular manufacturing inter-cell scheduling. The existing literatures on resource conflict of inter-cell scheduling don't take account into delay within building a model. They try to resolve conflict according to coordination strategy, but it is always accompanied by delay. In view of this deficiency and new characteristics of virtual cellular inter-cell scheduling problem, we consider the tardiness of all products. A hybrid multi-objective particle swarm optimization algorithm is proposed, and considers task priority of shared resource. A new decoding method which simulates market mechanism solves resource conflict problem. The feasible task scheduling shortens total flow time and tardiness, improves the utilization of shared resource. Finally, an example is used to verify its feasibility and validity.

Decision Tree Based Scheduling for Flexible Job Shops with Multiple Process Plans

This paper suggests a decision tree based approach for flexible job shop scheduling with multiple process plans, i.e. each job can be processed through alternative operations, each of which can be processed on alternative machines. The main decision variables are: (a) selecting operation/machine pair; and (b) sequencing the jobs assigned to each machine. As an extension of the priority scheduling approach that selects the best priority rule combination after many simulation runs, this study suggests a decision tree based approach in which a decision tree is used to select a priority rule combination adequate for a specific system state and hence the burdens required for developing simulation models and carrying out simulation runs can be eliminated. The decision tree based scheduling approach consists of construction and scheduling modules. In the construction module, a decision tree is constructed using a four-stage algorithm, and in the scheduling module, a priority rule combination is selected using the decision tree. To show the performance of the decision tree based approach suggested in this study, a case study was done on a flexible job shop with reconfigurable manufacturing cells and a conventional job shop, and the results are reported by comparing it with individual priority rule combinations for the objectives of minimizing total flow time and total tardiness. Keywords—Flexible job shop scheduling, Decision tree, Priority rules, Case study.

Scheduling of Jobs on Identical Parallel Machines to Minimize Total Flow Time Subject to Optimal Makespan

Algorithms based on Simulated Annealing and Tabu search has been proposed and implemented on scheduling a problem of parallel machines. The identical parallel machine scheduling problem has been considered to minimize the total flow-time subject to optimal makespan. The proposed algorithms have two phases. In the first phase, an initial solution has been obtained using Longest Processing Time (LPT) dispatching rule and in the second phase, simulated annealing and tabu search have been applied to reach a near optimal solution. The performance of the both proposed algorithms have been evaluated by comparing their results for different number of jobs and processing times. The computational results indicate that the proposed Tabu Search algorithm is capable of obtaining better solutions for the given scheduling problem as compared to the Simulated Annealing algorithm. Although both of these algorithms provide the best solutions as compared to the other heuristic algorithms but in comparison of these two; Tabu Search provides the better solutions for the given problem.

The Resource Conflict Resolution Problem for Virtual Cellular Manufacturing Inter-Cell Scheduling under the Conditions of Resource Sharing

This paper studies the resource conflict resolution problem for virtual cellular manufacturing inter-cell scheduling. The existing literatures on resource conflict of inter-cell scheduling don't take account into delay within building a model.They try to resolve conflict according to coordination strategy, but it is always accompanied by delay. In view of this deficiency and new characteristics of virtual cellular inter-cell scheduling problem, we consider the tardiness of all products. A hybrid multi-objective particle swarm optimization algorithm is proposed, and considers task priority of shared resource. A new decoding method which simulates market mechanism solves resource conflict problem. The feasible task scheduling shortens total flow time and tardiness, improves the utilization of shared resource. Finally, an example is used to verify its feasibility and validity.

A Novel Variant of QGA with VNS for Flowshop Scheduling Problem

In this paper, scheduling problem of flowshop with the criterion of minimizing the total flow time has been considered. An effective hybrid Quantum Genetic Algorithm and Variable Neighborhood Search (QGA-VNS or QGA VNS ) has been proposed as solution of Flow Shop Scheduling Problem (FSSP). First, the QGA is considered for global search in optimal solution and then VNS has been integrated for enhancing the local search capability. An adaptive two-point crossover and quantum interference operator (QIC) has been used in quantum chromosomes, which is based on the probability learning and quality of solution at each iteration. Further, a Longest Common Sequence (LCS) method has been adopted to construct the neighborhood solutions for intensifying local search with VNS. The neighborhood solutions will be based on the common sequence similar to the longest common sequence in global solution in each iteration, represented as LCSg. After selection of individual, VNS will be applied further exploring the local search space based on LCS neighborhood solutions. Results and comparisons with different algorithms based on the famous benchmarks demonstrates the effectiveness of proposed QGA-VNS.

Solving tri-objective multistage hybrid flow shop scheduling problems using a discrete firefly algorithm

Hybrid flow shop (HFS) scheduling problems turn into a fascinating area of research for the past several decades. However, most of the researchers consider only single objective and makespan is the most vital objective function. The real industrial scheduling problems involve multiple conflicting objectives. The HFS scheduling problems were proved to be NP-hard (non-deterministic polynomial time hard) problems. In this paper, we present a discrete firefly algorithm (DFA) to minimise the makespan, total flow time and machine idle time in a multistage HFS environment consisting of n jobs and k stages with identical parallel machines. The performance of the proposed algorithm is tested with a real industrial case study data and random problem instances. Computational results proved the effectiveness of the proposed algorithm.

Robust Metaheuristics for Scheduling Cellular Flowshop with Family Sequence-Dependent Setup Times

In manufacturing systems, minimization of the total flow time has a great impact on the production time, the productivity and the profitability of a firm. This paper considers a cellular flowshop scheduling problem with family sequence setup time to minimize the total flow time. Two metaheuristic algorithms based on Genetic algorithm (GA) and particle swarm optimization (PSO) are proposed to solve the proposed problem. As it is customarily accepted, the performance of the proposed algorithms is evaluated using Design of Experiments (DOE) to study the robustness of the proposed metaheuristics based on the Relative Percentage Deviation (RPD) from the lower bounds. The results of the DOE evaluation of the proposed algorithms show that PSO-based metaheuristic is better than GA for solving scheduling problems in cellular flow shop, which aims to minimize the total flow time.

Multi-objective flow shop scheduling problem with stochastic parameters: fuzzy goal programming approach

Flow shop scheduling problem with stochastic parameters is dealt with in this paper. A multi-objective mixed integer linear programming model is proposed in this concern which can generate non-permutation schedules. To provide a more realistic model, process time and release time are considered stochastic variables with normal distribution. The objective functions are minimising three performance measures including maximum completion time (Makespan), total flow time and total tardiness. Chance constrained programming (CCP) approach and fuzzy goal programming (FGP) are applied to deal with the stochastic parameters and multi-objective function. Due to the complexity of the problem, we have implemented an adapted genetic algorithm to solve large-sized problem. According to the computational experiments, the GA can reach good-quality solutions in reasonable computational time, and can be used to solve large scale problems effectively.

A PSO-Based Hybrid Metaheuristic for Permutation Flowshop Scheduling Problems

This paper investigates the permutation flowshop scheduling problem (PFSP) with the objectives of minimizing the makespan and the total flowtime and proposes a hybrid metaheuristic based on the particle swarm optimization (PSO). To enhance the exploration ability of the hybrid metaheuristic, a simulated annealing hybrid with a stochastic variable neighborhood search is incorporated. To improve the search diversification of the hybrid metaheuristic, a solution replacement strategy based on the pathrelinking is presented to replace the particles that have been trapped in local optimum. Computational results on benchmark instances show that the proposed PSO-based hybrid metaheuristic is competitive with other powerful metaheuristics in the literature.

Performance study of parallel kanban-base stock for a high-mix multi-stage production system with the entrance of rework

The present study evaluates the performance of parallel kanban-base stock (PKB) system to regulate the production of high-mix items in a multi-stage shared-machine facility with the entrance of rework. The high-runner products are handled using a kanban system and low-runner products using a base stock system. The PKB systems were differentiated in terms of the model driver, loading rule, and rework entrance policy. The performance measures adopted the total output, average work-in-process, flow times and average machine utilisations. Discrete-event simulations were conducted with an analysis constituted of multi-factor ANOVA and response surface methodology. From the analysis, there is a specific R(LR) value that gives desired performance, and at the same time, its dependency is solely on accuracy of regression equation. Between rework policies, predominantly merge rework entrance policy yields more desirable results as observed within performance measures, compared to original rework entrance policy.

Parallel-batch scheduling and transportation coordination with waiting time constraint.

This paper addresses a parallel-batch scheduling problem that incorporates transportation of raw materials or semifinished products before processing with waiting time constraint. The orders located at the different suppliers are transported by some vehicles to a manufacturing facility for further processing. One vehicle can load only one order in one shipment. Each order arriving at the facility must be processed in the limited waiting time. The orders are processed in batches on a parallel-batch machine, where a batch contains several orders and the processing time of the batch is the largest processing time of the orders in it. The goal is to find a schedule to minimize the sum of the total flow time and the production cost. We prove that the general problem is NP-hard in the strong sense. We also demonstrate that the problem with equal processing times on the machine is NP-hard. Furthermore, a dynamic programming algorithm in pseudopolynomial time is provided to prove its ordinarily NP-hardness. An optimal algorithm in polynomial time is presented to solve a special case with equal processing times and equal transportation times for each order.

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).

Scheduling controllable processing time jobs in a deteriorating environment

In many real-life applications, job processing times are a function of the waiting time prior to their execution. In the most general setting, each job comprises of a basic processing time, which is independent of its start time, and a start time-dependent deterioration function. Some common examples of deteriorating systems include fire fighting, pollution containment, and medical treatments. To date, research has focused on scheduling models where the basic processing time of jobs is constant. However, job processing times are often controllable through the allocation of a limited non-renewable resource. We study a single-machine setting that combines these two models under the assumptions of general linear deterioration and convex resource functions. We develop a polynomial time solution for minimizing the makespan. For the total flowtime criterion, we compute the optimal resource allocation policy for a given job instance and show that the sequencing problem is at least as hard as the case with non-controllable jobs. We follow by discussing the properties of several special cases.

Improved sheep flock heredity algorithm and artificial bee colony algorithm for scheduling m-machine flow shops lot streaming with equal size sub-lot problems

The objective of this paper is to develop intelligent search heuristics to solve n-jobs, m-machines lot streaming problem in a flow shop with equal size sub-lots where the objective is to minimise makespan and total flow time independently. Improved sheep flock heredity algorithm (ISFHA) and artificial bee colony (ABC) algorithms are applied to the problem above mentioned. The performance of these algorithms is evaluated against the algorithms reported in the literature. The computational analysis shows the better performance of ISFHA and ABC algorithms.

An improved memetic algorithm based on a dynamic neighbourhood for the permutation flowshop scheduling problem

The permutation flowshop scheduling problem (PFSP) has been extensively studied in the scheduling literature. In this paper, we present an improved memetic algorithm (MA) to solve the PFSP to minimise the total flowtime. In the proposed MA, we develop a stochastic local search based on a dynamic neighbourhood derived from the NEH method. During the evolution process, the size of the neighbourhood is dynamically adjusted to change the search focus from exploration to exploitation. In addition, we introduce a new population generation mechanism to guarantee both the quality and diversity of the new populations. We also design a diversity index for the population to monitor the diversity of the current population. If the diversity index is less than a given threshold value, the current population will be replaced by a new one with good diversity so that the proposed MA has good ability to overcome local optima. We conduct computational experiments to test the effectiveness of the proposed algorithm. The computational results on randomly generated problem instances and benchmark problem instances show that the proposed MA is effective and superior or comparable to other algorithms in the literature.

A hybrid particle swarm optimization algorithm for a no-wait flow shop scheduling problem with the total flow time

This paper proposes a particle swarm optimization (PSO) algorithm based on memetic algorithm (MA) that hybridizes with a local search method for solving a no-wait flow shop scheduling problem. The main objective is to minimize the total flow time. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as global search. In addition, a self-organized random immigrant's scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in search space. The experimental study over the moving peaks benchmark problem shows that the proposed PSO-based MA is robust. Finally, the analysis of the computational results and conclusion are given.