Total Flow Time Research Articles

When serial batch scheduling involves parallel batching decisions: A branch and price scheme

This paper studies a scheduling problem in which serial and parallel batching decisions must be simultaneously taken. There is a single machine with a fixed capacity that can process multiple jobs at the same time (i.e., parallel batching). Throughout the planning horizon, jobs are released at different instants and they belong to different families. Each job requires one unit of the machine capacity and only jobs of the same family can be processed at the same time. Once a group of jobs is decided to be processed, a preparation time occurs and all jobs are considered completed when the last job of the group finishes its processing (i.e., serial batching). We aim to minimize total flow time (i.e., sum of job completion times, ∑Cj) and total weighted tardiness (∑wjTj) objectives. First, we formulate this problem as an integer linear programming model. Then, we develop a column generation algorithm to solve the linear relaxation which is integrated in a branch and bound tree in search for the integer solution. We use a highly efficient heuristic branching technique for ∑wjTj objective and prove its optimality for ∑Cj objective. Numerical test results show that the algorithm can handle large instances in reasonable computational times.

Dynamic mode decomposition of magnetohydrodynamic bubble chain flow in a rectangular vessel

We demonstrate the first application of dynamic mode decomposition (DMD) to bubble flow with resolved dynamic liquid/gas boundaries. Specifically, we have applied DMD to the output of numerical simulations for a system where chains of bubbles ascend through a rectangular liquid metal vessel. Flow patterns have been investigated in the vessel and bubble reference frames. We show how gas flow rate and applied magnetic affect bubble wake flow and larger-scale flow structures within the liquid metal vessel by examining the velocity field mode statistics over trajectory time and total flow time as well as the computed mode velocity fields. The results of this proof-of-concept study indicate that DMD can yield unique insights into various momentum transfer and bubble interaction mechanisms, and that mode analysis can be used to explain the observed flow patterns. In addition, we showcase our own implementation of DMD that combines resilience to data noise, memory efficiency and special pre-processing for input data.

Geometric and harmonic means based priority dispatching rules for single machine scheduling problems

<span lang="ES">This work proposes two new prority dispatching rules (PDRs) for solving single machine scheduling problems. These rules are based on the geometric mean (GM) and harmonic mean (HM) of the processing time (PT) and the due date (DD) and they are referred to as GMPD and HMPD respectively. Performance of the proposed PDRs is evaluated on the basis of five measures/criteria i.e. Total Flow Time (TFT), Total Lateness (TL), Number of Late Jobs (TNL), Total Earliness (TE) and Number of Early Parts (TNE). It is found that GMPD performs better than other PDRs in achieving optimal values of multiple performance measures. Further, effect of variation in the weight assigned to PT and DD on the combined performance of TFT and TL is also examined which reveals that for deriving optimal values of TFT and TL, weighted harmonic mean (WHMPD) rule with a weight of 0.105 outperforms other PDRs. The weighted geometric mean (WGMPD) rule with a weight of 0.37 is found to be the next after WHMPD followed by the weighted PDT i.e. WPDT rule with a weight of 0.76.</span>

A stochastic bi-objective simulation–optimization model for plasma supply chain in case of COVID-19 outbreak

As of March 24, 2020, the Food and Drug Administration (FDA) authorized to bleed the newly recovered from Coronavirus Disease 2019 (COVID-19), i.e., the ones whose lives were at risk, separate Plasma from their blood and inject it to COVID-19 patients. In many cases, as observed the plasma antibodies have cured the disease. Therefore, a four-echelon supply chain has been designed in this study to locate the blood collection centers, to find out how the collection centers are allocated to the temporary or permanent plasma-processing facilities, how the temporary facilities are allocated to the permanent ones, along with determining the allocation of the temporary and permanent facilities to hospitals. A simulation approach has been employed to investigate the structure of COVID-19 outbreak and to simulate the quantity of plasma demand. The proposed bi-objective model has been solved in small and medium scales using ɛ-constraint method, Strength Pareto Evolutionary Algorithm II (SPEA-II), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Grey Wolf Optimizer (MOGWO) and Multi Objective Invasive Weed Optimization algorithm (MOIWO) approaches. One of the novelties of this research is to study the system dynamic structure of COVID-19’s prevalence so that to estimate the required plasma level by simulation. Besides, this paper has focused on blood substitutability which is becoming increasingly important for timely access to blood. Due to shorter computational time and higher solution quality, MOIWO is selected to solve the proposed model for a large-scale case study in Iran. The achieved results indicated that as the plasma demand increases, the amount of total system costs and flow time rise, too. The proposed simulation model has also been able to calculate the required plasma demand with 95% confidence interval.

A population-based iterated greedy algorithm to minimize total flowtime for the distributed blocking flowshop scheduling problem

We consider the distributed blocking flowshop scheduling problem (DBFSP) which is a meaningful generalization of the blocking flowshop scheduling problem in the distributed production environment. The objective of minimizing the total flowtime is relevant and important in the current dynamic manufacturing environment, but, as far as we know, it has not been investigated in the DBFSP previously. In this paper, a population-based iterated greedy (PBIG) algorithm is proposed to solve the DBFSP with the total flowtime criterion, which takes the advantage of both the population-based search approach and the iterated greedy algorithm. First, an effective constructive heuristic is proposed by integrating two existing constructive approaches to initialize the population with a high level of quality and diversity. Second, three different procedures to generate the offspring solutions are tested for the effective exploration capability, each of which rationally combines the destruction, reconstruction and selection operator. Third, the insertion neighborhood and swap neighborhood are investigated to enhance the local exploitation ability and a hybrid local search procedure that utilizes simultaneously both the two neighborhoods are proposed. The comprehensive experimental evaluation based on a total of 720 well-known instances shows that the proposed algorithms outperform the existing effective algorithms at a significant margin.

Scheduling with gaps: new models and algorithms

We consider scheduling problems for unit jobs with release times, where the number or size of the gaps in the schedule is taken into consideration, either in the objective function or as a constraint. Except for several papers on minimum-energy scheduling, there is no work in the scheduling literature that uses performance metrics depending on the gap structure of a schedule. One of our objectives is to initiate the study of such scheduling problems. We focus on the model with unit-length jobs. First we examine scheduling problems with deadlines, where we consider two variants of minimum-gap scheduling: maximizing throughput with a budget for the number of gaps and minimizing the number of gaps with a throughput requirement. We then turn to other objective functions. For example, in some scenarios gaps in a schedule may be actually desirable, leading to the problem of maximizing the number of gaps. A related problem involves minimizing the maximum gap size. The second part of the paper examines the model without deadlines, where we focus on the tradeoff between the number of gaps and the total or maximum flow time. For all these problems we provide polynomial time algorithms, with running times ranging from O(nlog n) for some problems to O(n^7) for other. The solutions involve a spectrum of algorithmic techniques, including different dynamic programming formulations, speed-up techniques based on searching Monge arrays, searching X+Y matrices, or implicit binary search. Throughout the paper, we also draw a connection between gap scheduling problems and their continuous analogues, namely hitting set problems for intervals of real numbers. As it turns out, for some problems the continuous variants provide insights leading to efficient algorithms for the corresponding discrete versions, while for other problems completely new techniques are needed to solve the discrete version.

Data-Driven Dispatching Rules Mining and Real-Time Decision-Making Methodology in Intelligent Manufacturing Shop Floor with Uncertainty.

In modern manufacturing industry, the methods supporting real-time decision-making are the urgent requirement to response the uncertainty and complexity in intelligent production process. In this paper, a novel closed-loop scheduling framework is proposed to achieve real-time decision making by calling the appropriate data-driven dispatching rules at each rescheduling point. This framework contains four parts: offline training, online decision-making, data base and rules base. In the offline training part, the potential and appropriate dispatching rules with managers’ expectations are explored successfully by an improved gene expression program (IGEP) from the historical production data, not just the available or predictable information of the shop floor. In the online decision-making part, the intelligent shop floor will implement the scheduling scheme which is scheduled by the appropriate dispatching rules from rules base and store the production data into the data base. This approach is evaluated in a scenario of the intelligent job shop with random jobs arrival. Numerical experiments demonstrate that the proposed method outperformed the existing well-known single and combination dispatching rules or the discovered dispatching rules via metaheuristic algorithm in term of makespan, total flow time and tardiness.

Adaptive Large Neighborhood Search Heuristic for Mixed Blocking Flowshop Scheduling Problem

Traditional permutation flowshop scheduling problem (PFSP), which has unlimited buffer space, has been interested over the fifty years by several authors to account for many industrial applications. However, some industries, such as the aerospace industry and other sectors processing industrial waste, have different blocking conditions due to the limited or lack of buffer area between their machines. In this study, a mixture of different blocking types is considered to solve PFSP with the total flow time criterion regarding several blocking types. A constraint programming model is proposed to solve the PFSP with mixed blocking constraints (MBFSP). Due to the problem's NP-hard nature of the problem, an adaptive large neighborhood search heuristic is proposed to solve the large size instances. The results of the proposed algorithm are very competitive.

Online Non-preemptive Scheduling on Unrelated Machines with Rejections

When a computer system schedules jobs there is typically a significant cost associated with preempting a job during execution. This cost can be incurred from the expensive task of saving the memory’s state or from loading data into and out of memory. Thus, it is desirable to schedule jobs non-preemptively to avoid the costs of preemption. There is a need for non-preemptive system schedulers for desktops, servers, and data centers. Despite this need, there is a gap between theory and practice. Indeed, few non-preemptive online schedulers are known to have strong theoretical guarantees. This gap is likely due to strong lower bounds on any online algorithm for popular objectives. Indeed, typical worst-case analysis approaches, and even resource-augmented approaches such as speed augmentation, result in all algorithms having poor performance guarantees. This article considers online non-preemptive scheduling problems in the worst-case rejection model where the algorithm is allowed to reject a small fraction of jobs. By rejecting only a few jobs, this article shows that the strong lower bounds can be circumvented. This approach can be used to discover algorithmic scheduling policies with desirable worst-case guarantees. Specifically, the article presents algorithms for the following three objectives: minimizing the total flow-time, minimizing the total weighted flow-time plus energy where energy is a convex function, and minimizing the total energy under the deadline constraints. The algorithms for the first two problems have a small constant competitive ratio while rejecting only a constant fraction of jobs. For the last problem, we present a constant competitive ratio without rejection. Beyond specific results, the article asserts that alternative models beyond speed augmentation should be explored to aid in the discovery of good schedulers in the face of the requirement of being online and non-preemptive.

Optimising the job-shop scheduling problem using a multi-objective Jaya algorithm

This paper presents an effective multi-objective Jaya (EMOJaya) algorithm to solve a multi-objective job-shop scheduling problem, aiming to simultaneously minimise the makespan, total flow time and mean tardiness. A strategy based on grey entropy parallel analysis (GEPA) is developed to assess and select solutions during the search process. To obtain a high-quality reference sequence for GEPA, an opposition-based learning (OBL) strategy is used in parallel. Additionally, the OBL strategy is incorporated into Jaya’s search operation and external archive to enhance the search ability and convergence rate of the algorithm. Computational experiments based on 30 benchmark instances with different scales confirm that GEPA and OBL can significantly improve the performance of our proposed EMOJaya. Experimental results also show that EMOJaya is able to outperform three state-of-the-art multi-objective algorithms in solving the problem at hand in terms of convergence, diversity and distribution. Further, EMOJaya can obtain more high-quality scheduling schemes, which provide more and better options for decision makers.

A batch scheduling model for a three-stage flow shop with job and batch processors considering a sampling inspection to minimize expected total actual flow time

Purpose: This research develops a batch scheduling model for a three-stage flow shop with job processors in the first and second stages and a batch processor in the third stage. The model integrates production process activities and a product inspection activity to minimize the expected total actual flow time.Design/methodology/approach: The problem of batch scheduling for a three-stage flow shop is formulated as a mathematical model, and a heuristic algorithm is proposed to solve the problem. This model applies backward scheduling to accommodate the objective of minimizing the expected total actual flow time.Findings: This research has proposed a batch scheduling model for a three-stage flow shop with job and batch processors to produce multiple items and an algorithm to solve the model. The objective is to minimize total actual time. The resulting production batches can be sequenced between all types of products to minimize idle time, and the batch processor capacity affects the sample size and indirectly affects the production batch size.Originality/value: This research develops a batch scheduling model for a three-stage flow shop constituting job and batch processors and carrying out integrated production and inspection activities to minimize the expected total actual flow time

A green scheduling algorithm for the distributed flowshop problem

In recent years, sustainable development and green manufacturing have attracted widespread attention to environmental problems becoming increasingly serious. Meanwhile, affected by the intensification of market competition and economic globalization, distributed manufacturing systems have become increasingly common. This paper addresses the energy-efficient scheduling of the distributed permutation flowshop (EEDPFSP) with the criteria of minimizing both total flow time and total energy consumption. Considering the distributed and multi-objective optimization complexity, an improved NSGAII algorithm (INSGAII) is proposed. First, we analyze the problem-specific characteristics and designed new operators based on the knowledge of the problem. Second, four constructive heuristic algorithms are proposed to produce high-quality initial solutions. Third, inspired by the artificial bee colony algorithm, we propose a new colony generation method using the operators designed. Fourth, a local intensification is designed for exploiting better non-dominated solutions. The influence of parameter settings is investigated by experiments to determine the optimal parameter configuration of the INSGAII. Finally, a large number of computational tests and comparisons have been carried out to verify the effectiveness of the proposed INSGAII in solving EEDPFSP.

Dynamic contrast-enhanced MRI perfusion quantification in hepatocellular carcinoma: comparison of gadoxetate disodium and gadobenate dimeglumine.

(1) To assess the quality of the arterial input function (AIF) during dynamic contrast-enhanced (DCE) MRI of the liver and (2) to quantify perfusion parameters of hepatocellular carcinoma (HCC) and liver parenchyma during the first 3 min post-contrast injection with DCE-MRI using gadoxetate disodium compared to gadobenate dimeglumine (Gd-BOPTA) in different patient populations. In this prospective study, we evaluated 66 patients with 83 HCCs who underwent DCE-MRI, using gadoxetate disodium (group 1, n = 28) or Gd-BOPTA (group 2, n = 38). AIF qualitative and quantitative features were assessed. Perfusion parameters (based on the initial 3 min post-contrast) were extracted in tumours and liver parenchyma, including model-free parameters (time-to-peak enhancement (TTP), time-to-washout)and modelled parameters (arterial flow (Fa), portal venous flow (Fp), total flow (Ft), arterial fraction, mean transit time (MTT), distribution volume (DV)). In addition, lesion-to-liver contrast ratios (LLCRs) were measured. Fisher's exact tests and Mann-Whitney U tests were used to compare the two groups. AIF quality, modelled and model-free perfusion parameters in HCC were similar between the 2 groups (p = 0.054-0.932). Liver parenchymal flow was lower and liver enhancement occurred later in group 1 vs group 2 (Fp, p = 0.002; Ft, p = 0.001; TTP, MTT, all p < 0.001), while there were no significant differences in tumour LLCR (max. positive LLCR, p = 0.230; max. negative LLCR, p = 0.317). Gadoxetate disodium provides comparable AIF quality and HCC perfusion parameters compared to Gd-BOPTA during dynamic phases. Despite delayed and decreased liver enhancement with gadoxetate disodium, LLCRs were equivalent between contrast agents, indicating similar tumour conspicuity. • Arterial input function quality, modelled, and model-free dynamic parameters measured in hepatocellular carcinoma are similar in patients receiving gadoxetate disodium or gadobenate dimeglumine during the first 3 min post injection. • Gadoxetate disodium and gadobenate dimeglumine show similar lesion-to-liver contrast ratios during dynamic phases in patients with HCC. • There is lower portal and lower total hepatic flow and longer hepatic mean transit time and time-to-peak with gadoxetate disodium compared to gadobenate dimeglumine.

Minimizing makespan and flowtime in a parallel multi-stage cellular manufacturing company

• We formulate an approach for a parallel multi-stage cellular manufacturing system. • Makespan and total flowtime found in reasonable time for large problems. • Genetic algorithm is proposed to improve the efficiency of the cell loading process. • Approach verified by shoes manufacturing case study to yield. • More effective approach offered by using multi-stage solution ways. This study proposes a 3-phase solution approach for a multi-product parallel multi-stage cellular manufacturing company. The study focuses on a case study involving a shoe manufacturing plant in which products are produced according to their due dates. The investigated manufacturing process has three stages, namely lasting cells, rotary injection molding cells, finishing-packaging cells. System performance is measured based on total flowtime and makespan. We propose a 3-phase solution approach to tackle the problem; 1) the first phase of the proposed approach allocates manpower to operations in the lasting cells and finishing-packaging cells, independently. The objective is to maximize the production rates in these cells. 2) The second phase includes cell loading to determine product families based on a similarity coefficient using mathematical modeling and genetic algorithms (GA). The proposed GA algorithm for cell loading performs mutation prior to crossover, breaking from traditional genetic algorithm flow. The performance measures flow time and makespan are considered in this phase. 3) Flow shop scheduling is then performed to determine the product sequence in each (lasting, rotary injection molding, finishing-packaging) cell group. This 3-phase solution approached is repeated with alternative manpower level allocation to lasting and finishing-packaging cells where the total manpower level remains the same.

An iterated local search procedure for the job sequencing and tool switching problem with non-identical parallel machines

In this paper, a new generalization of the uniform job sequencing and tool switching problem is presented. It considers non-identical parallel machines, which differ in tool magazine capacity and setup times. Applications of the problem can be found in the metal working or semiconductor manufacturing industries when the jobs require different tool sets for processing. The paper provides a Mixed Integer Programming formulation for the job sequencing and tool switching problem with machine-dependent processing and tool switching times under the consideration of three conflicting objectives (minimizing the total flowtime, minimizing the makespan and minimizing the total number of tool switches). Different efficient construction heuristics and Iterated Local Search methods are proposed and evaluated, using 640 new and publicly available instances. The results of the construction heuristics, the Iterated Local Search schemes and a Mixed Integer Programming Solver are discussed. The extensive computational experiments show the merit of the perturbation strategy in order to overcome local optima. It is shown that certain methods are more or less suitable depending on the objective function.

A hybrid genetic local and global search algorithm for solving no-wait flow shop problem with bi criteria

This paper addresses the m-machine no-wait Flow Shop Scheduling with Setup Times (NW-FSSWST). Two performance measures: total flow time and makespan are considered. The objective is to find a sequence that minimizing total flow time (sum C_{j}) and makespan (C_{j}) simultaneously. A Hybrid Genetic Local and Global Search Algorithm (HGLGSA) is proposed to solve the NW-FSSWST for two performance criteria. The hybrid genetic algorithm is constructed by insert-search and self-repair algorithm with self-repair function. The proposed HGLGSA is tested on 192 benchmark problems of NW-FSSWST in the literature. A full factorial experimental design is made for determined the best parameter sets that improve the performance of the proposed algorithm. The computational results are compared with the benchmark solutions from the literature. The experimental results demonstrate the effectiveness and efficiency of the proposed HGLGSA for solving NW-FSSWST.

MINIMASI MAKESPAN PADA PERSOALAN PENJADWALAN ORDERED FLOWSHOP MENGGUNAKAN PSO

The production scheduling problem is in the kind of flowshop with n jobs and m machines, to get the order of the schedule for allocating operations of the jobs to the available machines so as to get the minimum total time for completion of all job or commonly called makespan. This study uses an optimization technique approach with the PSO algorithm to get minimum makespan on the ordered flowhop scheduling problem. The performance of the scheduling algorithm presented is evaluated by testing on a benchmark data set of 240 variations in the combination number of jobs and machines. The minimum measure is obtained as a result of scheduling with PSO, whose process stops at a certain iteration when in the last 10 iterations there is no change in the value of a better makespan. The performance of the PSO algorithm is efficient at regular flow scheduling with the use of the most iterations of 19 iterations and the longest execution time of 28.42 seconds or less than half a minute, namely scheduling instances with the largest number of machines and jobs. In this research, only the analysis of the resulting minimal forward and the time of execution was carried out. Further research can be extended by not only measuring the minimum makespan, such as measuring total flowtime, total tardiness, and others.

An Adaptive Iterated Greedy algorithm for distributed mixed no-idle permutation flowshop scheduling problems

Distributed flow shop scheduling is a very interesting research topic. This paper studies the distributed permutation flow shop scheduling problem with mixed no-idle constraints, which have important applications in practice. The optimization goal is to minimize total flowtime. A mixed-integer linear programming model is presented and an Adaptive Iterated Greedy (AIG) algorithm with the sample length changing according to the search process is designed. A restart strategy is also introduced to escape from local optima. Additionally, to further improve the performance of the algorithm, swap-based local search methods and acceleration algorithms for swap neighborhoods are proposed. Referenced Local Search (RLS), which shows better performance in solving scheduling problems, is also used in our algorithm. In the destruction stage, the job to be removed is selected according to the degree of influence on the total flowtime. In the initialization and construction phase, when a job is inserted, the jobs before and after the insertion position are removed and re-inserted into a better position to improve the algorithm search performance. A detailed design experiment is carried out to determine the best parameter configuration. Finally, large-scale experiments show that the proposed AIG algorithm is the best-performing one among all the algorithms in comparison.

Optimizing Lot-Sizes and Scheduling in Terms of Mass Customization

The goal of mass customisation is to offer products tailored to the specific needs of the customers. Even though customers are aware that manufacturers need a certain time to produce and deliver customised products, the companies might guarantee that their products will arrive on time. Then, the objective of manufacturing managers is to minimise the total flow time of parts through the shop. One of the effective ways to reach this objective is to optimise schedules in order to satisfy the due date criterion, which plays a crucial role in the mass customisation environment. This paper, in the first part, outlines methodological tools to tackle the problem of shortening delivery times through scheduling and management of resources. In the second part of the paper, the proposed methodology framework through the theoretical example is applied.

Active learning for multi-objective optimal road congestion pricing considering negative land use effect

The road congestion pricing policy is implemented to alleviate traffic congestion and improve the efficiency of the transportation system during peak hours. However, the negative land use effect caused by this policy could not be ignored. How to design the optimal congestion toll that can not only ensure its positive effect on the transportation system but also reduce its negative effect on land use is an urgent problem to be solved. Given this, this paper proposed a multi-objective bi-level programming road congestion pricing model based on the integrated land use and transportation model to optimize the regional average accessibility, regional average land use diversity, and regional total flow time. Since the proposed problem is NP-hard, this paper innovatively proposed an active learning optimization algorithm based on multi-objective Bayesian optimization, which improves the computation efficiency of the bi-level programming model by automatically finding the next sampling point (candidate solution) according to the probability information. An empirical analysis of Jiangyin City demonstrated the effectiveness of the proposed approach in coordinating the relationship between land use and transportation and alleviating the negative land use effect caused by road congestion pricing. Moreover, the algorithm proposed in this paper can also be used to solve other transportation-related black box problems with high computation complexity.