Flow Shop System Research Articles

Production sequencing in a flow shop system using optimization and heuristic algorithms

abstract: The purpose of the research was to determine the sequencing of the production of n jobs in m operations in a small footwear company in an environment of flow shop machine characteristics, which optimizes the total time of completion of the job in the production system (Makespan). We used heuristic algorithms that were applied through Lekin and WinQSB softwares, and for the optimization algorithm we designed a mathematical model that was solved by Juliabox software. Results show that the integer linear programming and local search minimize the makespan with 3807 minutes, and different production sequences for each algorithm, which consider permutation, which improves the traditional way of programming the production in 97 minutes, however, the optimization presents better results in the performance measures of average waiting time, average time of flow, and average job in process. Application of heuristic algorithms proves to be simple and fast, but the mathematical model of optimization designed and encoded in the software is a flexible and valuable tool for decision making in production programming, which could be applied in other footwear companies, and in other productive sectors whose companies have the same characteristics of the case study, reducing costs and improving delivery times.

Solving a flow shop scheduling problem with missing operations in an Industry 4.0 production environment

Industry 4.0 is a modern approach that aims at enhancing the connectivity between the different stages of the production process and the requirements of consumers. This paper addresses a relevant problem for both Industry 4.0 and flow shop literature: the missing operations flow shop scheduling problem. In general, in order to reduce the computational effort required to solve flow shop scheduling problems only permutation schedules (PFS) are considered, i.e., the same job sequence is used for all the machines involved. However, considering only PFS is not a constraint that is based on the real-world conditions of the industrial environments, and it is only a simplification strategy used frequently in the literature. Moreover, non-permutation (NPFS) orderings may be used for most of the real flow shop systems, i.e., different job schedules can be used for different machines in the production line, since NPFS solutions usually outperform the PFS ones. In this work, a novel mathematical formulation to minimize total tardiness and a resolution method, which considers both PFS and (the more computationally expensive) NPFS solutions, are presented to solve the flow shop scheduling problem with missing operations. The solution approach has two stages. First, a Genetic Algorithm, which only considers PFS solutions, is applied to solve the scheduling problem. The resulting solution is then improved in the second stage by means of a Simulated Annealing algorithm that expands the search space by considering NPFS solutions. The experimental tests were performed on a set of instances considering varying proportions of missing operations, as it is usual in the Industry 4.0 production environment. The results show that NPFS solutions clearly outperform PFS solutions for this problem.

Optimal Sizing of Renewable Microgrid for Flow Shop Systems under Island Operations

This paper addresses a critical question pertaining to manufacturing sustainability: is it economically viable to implement an island microgrid to power a flow shop system under power demand and supply uncertainty? Though many studies on microgrid sizing are available, the majority assume the microgrid is interconnected with main grid. This paper aims to size wind turbine, photovoltaic and battery storage to energize a multi-stage flow shop system in island mode. A mixed-integer, non-linear programming model is formulated to optimize the renewable portfolio and capacity with the goal of minimizing the levelized cost of energy. The island microgrid is tested in three locations with diverse climate profiles. The results show that net zero energy flow shop production is economically feasible in the areas where the average wind speed exceed 8 m/s at 80-meter tower height, or the battery cost drops below $100,000/MWh. Sensitivity analyses are further carried out with respect to installation cost, demand response program, production scalability, and weather seasonality.

Sizing a renewable microgrid for flow shop manufacturing using climate analytics

Abstract A variety of methods have been proposed to assist the integration of microgrid in flow shop systems with the goal of attaining eco-friendly operations. There is still a lack of integrated planning models in which renewable portfolio, microgrid capacity and production plan are jointly optimized under power demand and generation uncertainty. This paper aims to develop a two-stage, mixed-integer programming model to minimize the levelized cost of energy of a flow shop powered by onsite renewables. The first stage minimizes the annual energy use subject to a job throughput requirement. The second stage aims at sizing wind turbine, solar panels and battery units to meet the hourly electricity needs during a year. Climate analytics are employed to characterize the stochastic wind and solar capacity factor on an hourly basis. The model is tested in four locations with a wide range of climate conditions. Three managerial insights are derived from the numerical experiments. First, time-of-use tariff significantly stimulates the wind penetration in locations with medium or low wind speed. Second, regardless of the climate conditions, large-scale battery storage units are preferred under time-of-use rate but it is not the case under a net metering policy. Third, wind- and solar-based microgrid is scalable and capable of meeting short-term demand variation and long-term load growth with a stable energy cost rate.

A fix-and-relax heuristic for the single-item lot-sizing problem with a flow-shop system and energy constraints

This study addresses a new single-item lot-sizing problem for flow-shop configurations by integrating the capacity contract selection problem with multiple energy sources. To the best of our knowledge, this problem has never been tackled before. We introduce a mathematical model which defines optimum production plan and energy contract option regarding the objectives and constraints of the production system and energy supplier contract conditions. Since the problem is NP-Hard, a Fix-and-Relax heuristic is introduced to solve the problem. Two different relaxation procedures are applied and the performance of the solution approach is tested on randomly generated instances. It is seen that the obtained results are quite promising. The applied heuristic approach produces solutions with the optimality gap in average for the small problem sizes such as (N5_T5,N5_T7). For the larger instances, it allows to reach better results than the results obtained by commercial solvers within a shorter time.

Job Scheduling for Hybrid Assembly Differentiation Flow Shop to Minimize Total Actual Flow Time considering Multi-Due-Dates

The hybrid assembly differentiation flow shop is a three-stage flow shop system with machining, assembly and differentiation stages. The machining stage produces k parts in independently unrelated dedicated machines. After k parts of a job completed, they are assembled at the assembly stage and assigned to dedicated machines for a final process. At the end, several types of finished products are resulted. The finished products should be delivered at their respective different due dates. The problem is to find a schedule considering multi due dates, and the criterion of minimizing total actual flow time. This paper proposes a model for job scheduling in a hybrid assembly differentiation flow shops and its algorithm for solving the problems. The initial solution is defined using SPT-based heuristic and it is optimized using variable neighbourhood descend method. The proposed model is tested using a set of hypothetic data. The solution shows that the algorithm can solve the problems effectively.

Multi-scenario scheduling to maximise the weighted number of just-in-time jobs

We study a multi-scenario scheduling problem on a single-machine and a two-machine flow-shop system. The criterion is to maximise the weighted number of just-in-time jobs. We first analyze the case where only processing times are scenario-dependent. For this case, we prove that the single-machine problem is solvable in polynomial time. We also prove that the unit weight two-machine flow-shop problem is solvable in polynomial time if processing times are scenario-dependent only on the second machine, and is ordinary -hard when processing times are scenario-dependent only on the first machine. This ordinary -hard result holds as long as the number of scenarios is fixed. Otherwise, the problem becomes strongly -hard. We then analyze the case where only weights are scenario-dependent. We adopt a multi-criteria approach and define several problem variations. We prove that one of them is polynomial solvable on a single machine and ordinary -hard in a two-machine flow-shop system. We also prove that all other problem variations are ordinary -hard even if there are only two scenarios, and are strongly -hard when the number of scenarios is arbitrary. Finally, we provide two pseudo-polynomial time algorithms for solving all the hard problems when the number of scenarios is fixed.

A Reactive Scheduling Approach Based on Fuzzy Inference for Hybrid Flowshop Systems

A Reactive Scheduling Approach Based on Fuzzy Inference for Hybrid Flowshop Systems

A multi-item multi-packaging model to minimise cost of lost units, unpacking cost and CO2 emissions

This paper presents two multi-objective models that integrate packaging size and production scheduling problems for a flexible flow shop system. The main objective is to find the packaging size of finished product per item and the production schedule that would minimise cost of lost units, unpacking cost, inventory cost, earliness/tardiness penalties and kilograms of carbon dioxide emitted by resources operation. Since the complexity of the proposed models, a Pareto-based hybrid genetic algorithm (HGA) is also developed. A case study was developed to analyse the performance of both models using different instances. Numerical results indicate that the outperformance of one model over the other depends on the demand and the packaging size.

Influence of Workforce Qualification on Service Level in a Flow Shop with two Lines

Abstract Finding the optimal workforce qualification is important in many different industries. Cross-qualifications play an important role if workers are required to perform various tasks during working hours. This is especially crucial in production plants where workforce has to be trained to operate multiple machines throughout the day, and is closely connected to staff planning and job scheduling. In this paper, a flow shop system consisting of two lines is used to analyse various predefined workforce qualification profiles. To measure the performance, a simulation model is applied where the sum of qualifications is compared with the achieved service levels. Scenarios that differ in the number of available workers as well as the amount of transition times needed by workers to switch between stations and lines are analysed. Furthermore, multi-objective simulation-based optimization is conducted in order to find improved qualification profiles. The achieved results from both, the predefined and the optimized qualification profiles, are promising and managerial insight is gained for future research in this domain.

Human factors under uncertainty: A manufacturing systems design using simulation-optimisation approach

Modern manufacturing systems are characterized by waste elimination, cycle time control, and high work specifications. Workers, although being an integral part of manufacturing, are usually neglected or severely simplified in operational research of these systems. Through the years, the need for control over the job in manual manufacturing has been identified as crucial for both system performances and operators’ health. The aim of this research is to integrate time margins, as the mean of control, and human factors under uncertainty into scheduling problem of a multi-product manufacturing system while maintaining performance and workers’ well-being. The proposed method is polynomial and simulation-based, developed in two stages using agent-based methodology. The first stage provides a global schedule with makespan as the objective function and with time margin allocation strategy under uncertainty. The second stage enables rescheduling depending on the human error probability and fatigue level. Experiments and comparisons with the similar literature problem have indicated decrease of human error probability and fatigue. Extended experiments for flow shop system justify the use of this unique approach. The developed tool enables system designers to enhance performance by observing human effects through its factors and different time margins allocation strategies.

Two-machine flow-shop scheduling to minimize total late work: revisited

ABSTRACTThis article revisits the scheduling problem in a two-machine flow-shop system with the total late work criterion, which penalizes parts of jobs executed after their due dates. Firstly, it is shown that a lower bound presented previously in the literature, in the context of a branch-and-bound algorithm proposed for the same problem, is invalid. Then a novel proposal of the branch-and-bound method is given equipped with a new lower-bound technique, as well as an upper-bound and dominance rules. Numerical experiments show that the newly proposed lower-bound technique works well in cutting unpromising branches.

Hybrid flow shop with multiprocessor task scheduling based on earliness and tardiness penalties

PurposeHybrid flow shop with multiprocessor task (HFSMT) has received considerable attention in recent years. The purpose of this paper is to consider an HFSMT scheduling under the environment of a common time window. The window size and location are considered to be given parameters. The research deals with the criterion of total penalty cost minimization incurred by earliness and tardiness of jobs. In this research, a new memetic algorithm in which a global search algorithm is accompanied with the local search mechanism is developed to solve the HFSMT with jobs having a common time window. The operating parameters of memetic algorithm have an important role on the quality of solution. In this paper, a full factorial experimental design is used to determining the best parameters of memetic algorithm for each problem type. Memetic algorithm is tested using HFSMT problems.Design/methodology/approachFirst, hybrid flow shop scheduling system and hybrid flow shop scheduling with multiprocessor task are defined. The applications of the hybrid flow shop system are explained. Also the background of hybrid flow shop with multiprocessor is given in the introduction. The features of the proposed memetic algorithm are described in Section 2. The experiment results are presented in Section 3.FindingsComputational experiments show that the proposed new memetic algorithm is an effective and efficient approach for solving the HFSMT under the environment of a common time window.Originality/valueThere is only one study about HFSMT scheduling with time window. This is the first study which added the windows to the jobs in HFSMT problems.

Multi-agent scheduling in a no-wait flow shop system to maximize the weighted number of just-in-time jobs

ABSTRACTThis article studies a multi-agent scheduling problem on a set of m machines in a no-wait flow shop system, where each agent's objective function is to maximize its own weighted number of just-in-time jobs. Two variants of the problem are investigated. One is the constrained optimization problem and the other is the Pareto optimization problem. When the number of agents is arbitrary, both problems are proved to be strongly -hard. When the number of agents is fixed, pseudo-polynomial time algorithms are first designed to solve them, respectively, then an -approximation algorithm is provided for the former problem, and an -approximate Pareto-optimal frontier is constructed for the latter problem.

On Rescheduling for Two-Machine Flow Shop System with the Arrival of New Jobs

SYNOPTIC ABSTRACTIn this paper, we consider the rescheduling problem for a two-machine flow shop system with the arrival of new jobs, in which a set of original jobs has been given a planned schedule (but has not been executed) on a two-machine flow shop system to minimize the makespan, when a set of new jobs arrives. The production planner needs to insert the new jobs into the planned schedule without excessively disrupting it to minimize the makesapn on the original and the new jobs. The disruption is measured by the maximum time deviation for any given original job, between the original and new schedules. We examine two special models and a general model. In the first special model, the maximum time deviation appears as a constraint. In the second special model, the maximum time deviation appears as the part of the cost objective. In the general model, the maximum time deviation appears both as a constraint and as the part of the cost objective. For the two special models, we prove that they are NP-hard and accordingly the general model is also NP-hard. Furthermore we propose three heuristic algorithms to solve the general model followed by a numerical example.

Proportionate Flow Shop Scheduling with Multi-agents to Maximize Total Gains of JIT Jobs

Different variants of the multi-agent scheduling have been studied in the literature due to its wide applications in artificial intelligence, decision theory, operations research, etc. Most of previous research focused on the single-machine environment and two-agent scheduling. In this paper, we address a multi-agent scheduling problem on a set of m machines in a proportionate flow shop system, where the job processing times are machine independent. Each agent desires to maximize its total gains of JIT jobs which are completed exactly at the due dates. The goal is to find a feasible schedule in which each agent’s cost function value does not less than a given lower bound. When the number of agents is part of the input, we use the reduction method to show that the general problem is strongly $$\mathcal {NP}$$ -complete even if all jobs have unit processing times. When the number of agents is fixed, we first develop a dynamic programming algorithm that runs in pseudo-polynomial time, then we design a fully polynomial time approximation scheme by exploiting the technique of trimming-the-state-space. The results presented in this paper imply that by relaxing each agent’s desired cost function value a small fraction, we can obtain an efficient approximate schedule for the problem with fixed number of agents in polynomial time, while when the number of agents is part of the input, the problem become much intractable, and it needs more sophisticated methods to solve in future research.

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.

Proportionate Flow Shop Scheduling with Rejection

We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time algorithm to solve it and an [Formula: see text] time for the case where the jobs have the same processing time. For the second problem, we first show that it is [Formula: see text]-hard, then we design [Formula: see text] time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

Flow shop scheduling with grid-integrated onsite wind power using stochastic MILP

Over the last decade, manufacturing companies have identified renewable energy as a promising means to cope with time-varying energy prices and to reduce energy-related greenhouse gas emissions. As a result of this development, global installed capacity of wind power has expanded significantly. To make efficient use of onsite wind power generation facilities in manufacturing, production scheduling tools need to consider the uncertainty attached to wind power generation along with changes in the energy procurement cost and in the products’ environmental footprints. To this end, we propose a solution procedure that first generates a large number of wind power scenarios that characterise the variability in wind power over time. Subsequently, a two-stage stochastic optimisation procedure computes a production schedule and energy supply decisions for a flow shop system. In the first stage, a bi-objective mixed integer linear programme simultaneously minimises the total weighted flow time and the expected energy cost, based on the generated wind power scenarios. In the second stage, energy supply decisions are adjusted based on real-time wind power data. A numerical example is used to illustrate the ability of the developed decision support tool to handle the uncertainty attached to wind power generation and its effectiveness in realising energy-related objectives in manufacturing.

Complexity of late work minimization in flow shop systems and a particle swarm optimization algorithm for learning effect

Late work minimization is one of the newer branches in the scheduling theory, with the goal of minimizing the total size of late parts of all jobs in the system. In this paper, we study the scheduling problem in flow shop, which finds many practical applications. First, we prove that the problem with three machines and a common due date is NP-hard in the strong sense. Then we extend this basic model, considering the problem with the arbitrary number of machines, various due dates and learning effect, and propose a particle swarm optimization algorithm (PSO). Computational experiments show that the PSO is an efficient method for solving the problem under consideration, both from algorithm-performance and time-consumption views.