Flow shop

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To have a quality multimedia presentation through networks, its presentation lag needs to be controlled. One way to reduce the lag is to prefetch the media objects before their due dates. This paper explores techniques for optimizing the object sequence in a prefetch-enabled TV-like presentation. An optimal solution is the one with which the presentation lag is minimized. We formulate the problem into a two-machine flowshop scheduling problem with a single chain precedence constraint and a player-side buffer constraint. The player-side buffer is "processing time-dependent" and distinguished from the conventional item-based intermediate buffer constraints discussed in previous flowshop studies. We prove the problem to be strongly NP-hard. A branch and bound algorithm equipped with four lower bounds and an NEH-based upper bound is developed. The simulation results show that the average gaps between the overall lower bounds and the NEH-based upper bound are less than 3% for problems with a large buffer size, and less than 13% for problems with a small buffer size and high density of precedence constraints. For applications where the media objects are delivered through extremely busy servers with which only very restricted CPU resources can be allocated for computation, the CDS-based algorithm provides better sequences than the NEH-based algorithm.

Production Scheduling 114 high customer involvement. (2) Operator absence or machine breakdown needs to be carefully controlled to fulfill the critical due dates. (3) Variation in processing times usually happens to an operation, because a highly customized product is rarely repeated. (4) The overflow of work-in-process (WIP) inventories occurs. (5) Production delay on the previous day will affect the production on the current day; so will production earliness. When these problems dynamically happen to an OKP company, the daily production has to be adjusted online, i.e. adaptive production control. Therefore, OKP companies are continuously seeking new methods for adaptive production scheduling and control on shop floors. 1.2 Former research of flow shop production scheduling and control Flow shop production scheduling has been researched for more than five decades since 1954 (Gupta & Stafford, 2006). Early research of flow shop production scheduling was highly theoretical, using optimization techniques to seek optimal solutions for n-job m-machine flow shop scheduling problems. However, the emergence of NP-completeness theory in 1976 (Garey et al., 1976) profoundly influenced the direction of research in flow shop production scheduling. NP-completeness implies that it is highly unlikely to get an optimal solution in a polynomially bounded duration of time, for a given complex problem in general. That is why heuristics are required to solve large problems. Adaptive production control acutely challenges the research of flow shop production scheduling, because the relationship has not been completely revealed, among the number of jobs, the number of machines, job processing times and scheduling objectives. Moreover, the research of flow shop production scheduling is often based on strong assumptions, such as no machine breakdown or operator absence, processing times and some constraints are deterministic and known in advance (MacCarthy & Liu, 1993). During real production, disturbances are manifested in such occurrences as machine breakdown, operator absence, longer than expected processing times, new emergent orders, and so on (McKay et al., 2002), all of which may fail the original offline schedule and then require online rescheduling for adaptive production control. Consequently, heuristics based on strong assumptions are not robust, making production scheduling systems inflexible (Kouvelis et al., 2005), and a large gap exists between theoretical research and industrial applications (Gupta & Stafford, 2006; MacCarthy & Liu, 1993). 1.3 Status of production scheduling and control in OKP Currently, OKP companies primarily use priority dispatching rules (PDRs) to deal with disturbances. It is fast and simple to use PDRs to control production online, but PDRs depend heavily on the configuration of shop floors, characteristics of jobs, and scheduling objectives (Goyal et al., 1995), and no single specific PDR clearly dominates the others (Park et al., 1997). Moreover, the performance of PDRs is poor on some scheduling objectives (Ruiz & Maroto, 2005), and inconsistent when a processing constraint changes (King & Spachis, 1980). Consequently, there is a considerable difference between the scheduled and actual production progress (Ovacik & Uzsoy, 1997), and production may run into an "ad hoc fire fighting" manner (Tu, 1996a, 1996b).

In this paper we consider learning and forgetting effect of workers for flexible flowshop scheduling problem with sequence dependent setup times. The objective is to minimize the weighted sum of maximum completion time and maximum tardiness. The learning effect occurs when operator's (workers) skill increases after repeating similar job causing the decrease of processing time. On the other hand, forgetting effect occurs when an operator relearns the process after an interruption for a batch setup, machine maintenance or operator condition recovery, causing the increase of processing time.

We study the problem of scheduling a single server that processes n jobs in a two-machine flow shop environment. A machine dependent setup time is needed whenever the server switches from one machine to the other. The problem with a given job sequence is shown to be reducible to a single machine batching problem. This result enables several cases of the server scheduling problem to be solved in Oðn log nÞ by known algorithms, namely, finding a schedule feasible with respect to a given set of deadlines, minimizing the maximum lateness and, if the job processing times are agreeable, minimizing the total completion time. Minimizing the total weighted completion time is shown to be NP-hard in the strong sense. Two pseudopolynomial dynamic programming algorithms are presented for minimizing the weighted number of late jobs. Minimizing the number of late jobs is proved to be NP-hard even if setup times are equal and there are two distinct due dates. This problem is solved in Oðn 3 Þ time when all job processing times on the first machine are equal, and it is solved in Oðn 4 Þ time when all processing times on the second machine are equal.

This paper deals with the blocking flow shop problem and proposes new constructive procedures for the total tardiness minimization of jobs. The heuristic has three-phases to build the sequence; the first phase selects the first job to be scheduled, the second phase arranges the remaining jobs and the third phase uses the insertion procedure of NEH to improve the sequence. The proposed procedures evaluate the tardiness associated to the sequence obtained before and after the third phase in order to keep the best of both because the insertion phase can worsen the result. The computational evaluation of these procedures against the benchmark constructive procedures from the literature reveals their good performance.

In this work we study a flowshop scheduling problem in which jobs are not allowed to wait in-between machines, a situation commonly referred to as no-wait. The concerned criterion is to minimize a weighted sum of makespan and maximum lateness. A dominance relation for the case of three-machine is presented and evaluated by experimental designs. Several heuristics and local search methods are proposed for the general m-machine case. The local search methods are based on genetic algorithms and iterated greedy procedures. An extensive computational analysis is conducted where it is shown that the proposed methods outperform existing heuristics and metaheuristics in all tested scenarios by a considerable margin and under identical CPU times.

This paper studies the flowshop scheduling problem with a complex bicriteria objective function. A weighted sum of makespan and maximum tardiness subject to a maximum tardiness threshold value is to be optimized. This problem, with interesting potential applications in practice, has been sparsely studied in the literature. We propose global and local dominance relationships for the three machine problem and a fast and effective genetic algorithm (GA) for the more general m-machine case. The proposed GA incorporates a novel three-phase fitness assignment mechanism specially targeted at dealing with populations in which both feasible as well as infeasible solutions might coexist. Comprehensive computational and statistical experiments show that the proposed GA outperforms the two most effective existing heuristics by a considerable margin in all scenarios. Furthermore, the proposed GA is also faster and able to find more feasible solutions. It should be noted that when the weight assigned to maximum tardiness is zero, then the problem is reduced to minimizing makespan subject to a maximum tardiness threshold value. Heuristics for both problems have been provided in the literature recently but they have not been compared.

Multi-objective optimisation problems have seen a large impulse in the last decades. Many new techniques for solving distinct variants of multi-objective problems have been proposed. Production scheduling, as with other operations management elds, is no dierent. The owshop problem is among the most widely studied scheduling settings. Recently, the Iterated Greedy methodology for solving the single-objective version of the owshop problem has produced state-of-the-art results. This paper proposes a new algorithm based on Iterated Greedy technique for solving the multiobjective permutation owshop problem. This algorithm is characterised by an eective initialisation of the population, management of the Pareto front, and a specially tailored local search, among other things. The proposed multi-objective Iterated Greedy method is shown to outperform other recent approaches in comprehensive computational and statistical tests that comprise a large number of instances with objectives involving makespan, tardiness and owtime. Lastly, we use a novel graphical tool to compare performances of stochastic Pareto fronts based on Empirical Attainment Functions.

Flow shop problem has been addressed by many researchers around the world. Different heuristic methods has been developed to deal with this kind of problems. Nevertheless, it is necessary to explore the impact that the bottleneck machine has on the performance of each heuristic. In this article an F6 || Cmax (Makespan) flow shop is tackled with different well-known heuristics in open literature, such as Palmer, Johnson, Gupta, CDS, NEH and PAS and their impact on Cmax was measure. The methodology used seeks to find the possible relationship between the different bottleneck machines and the result obtained from each of the heuristics. For this experiment, there were 302 scenarios with six machines in series, in which each machine had a parity number of scenarios in which it was the bottleneck. The values of Cmax obtained for each heuristic were compared against the result of corresponding MILP (Mixed Integer Liner Problem) problem. The results show that the performance of the NEH heuristic is superior in each scenario, regardless of the bottleneck, but also shows a variable behavior in each heuristic, taking into account the bottleneck machine.

La conception constitue une des étapes la plus importante dans le cycle de vie d'un atelier de production. Un des problèmes à soulever est le dimensionnement des ressources. Un sur ou un sous dimensionnement provoquera des sur-coûts supplémentaires. Il conditionnera aussi l'ordonnancement pendant la phase d'exploitation. Nous proposons dans ce papier une approche d'optimisation du dimensionnement d'un atelier de production basé sur les ordonnancements des scénarios de production prévisionnels. Nous nous intéressons à une organisation de flow shop hybride à plusieurs étages. En effet, nous proposons un programme linéaire permettant de minimiser conjointement le C max et le nombre de machines dans chaque étage pour un ensemble de jobs types de l'activité prévisionnelle. Un poids est attribué à chacun des objectifs. Au vu des résultats obtenus, cette approche peut fournir des solutions exactes pour des problèmes de petites tailles. Dans le cas où le poids attribué à chaque objectif est le même nous obtenons des solutions dites de « compromis ». Ces solutions de compromis ont permis de minimiser les coûts totaux.

Flow shop problem has been addressed by many researchers around the world. Different heuristic methods has been developed to deal with this kind of problems. Nevertheless, it is necessary to explore the impact that the bottleneck machine has on the performance of each heuristic. In this article an F6 || Cmax (Makespan) flow shop is tackled with different well-known heuristics in open literature, such as Palmer, Johnson, Gupta, CDS, NEH and PAS and their impact on Cmax was measure. The methodology used seeks to find the possible relationship between the different bottleneck machines and the result obtained from each of the heuristics. For this experiment, there were 302 scenarios with six machines in series, in which each machine had a parity number of scenarios in which it was the bottleneck. The values of Cmax obtained for each heuristic were compared against the result of corresponding MILP (Mixed Integer Liner Problem) problem. The results show that the performance of the NEH heuristic is superior in each scenario, regardless of the bottleneck, but also shows a variable behavior in each heuristic, taking into account the bottleneck machine.

Hokkiman is a company which is excel at embroidery based production. Current issues faced by company are unknown standard time for the whole production processes, including machining time for various embroidery's motives, which result in difficulties of calculating final completion time for an order, and necessity to improve current production scheduling system. The purposes of the research are to determine standard time for every production process, improving production scheduling performance by designing an appropriate production scheduling system that allow the company to accept order with due date requirement. Standard time are obtained by collecting primary datas on the production floor using continuous timing method, followed by the calculation for every production process. Standard time calculation for machining are achieved by using simple linear regression analysis. The new production scheduling system is designed by analyzing current system's weaknesses. Proposed production scheduling system are made based on the Shortest Processing Time (SPT) method. Results of the research are as following, the improvement of production scheduling performances which are shortened response time (21,61%), makespan can be reduced by 19,17%, faster mean flowtime (21,47%), within the condition of 14 days due date is applied, the amount of job tardiness and lateness are decreased by 5,88% and 21,32% sequentially.

Flow shop scheduling problem consists of scheduling given jobs with same order at all machines. The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, multi-objective approach for scheduling to reduce the total scheduling cost is important. Hence, in this study, we consider the flow shop scheduling problem with multi-objectives of makespan, total flow time and total machine idle time. Ant colony optimization (ACO) algorithm is proposed to solve this problem which is known as NP-hard type. The proposed algorithm is compared with solution performance obtained by the existing multi-objective heuristics. As a result, computational results show that proposed algorithm is more effective and better than other methods compared.

The present paper studies two stage specially structured flow shop scheduling problem with jobs in a string of disjoint job blocks in which processing times are associated with their respective probabilities, where the optimization criteria is the utilization time of machines. The objective is to minimize utilization time of machines for two the stage specially structured flow shop scheduling problem with jobs in a string of disjoint job blocks. The algorithm proposed in this paper is very simple and easy to understand and also provide an important tool for the decision maker. The algorithm is justified by a numerical illustration.

This paper provides a simple heuristic algorithm to minimize utilization time for specially structured n-job and 2-machine flow shop scheduling problem with jobs in a string of disjoint job blocks having sequence independent setup times separated from processing times each associated with their respective probabilities including job weightage and transportation time where the optimization criteria is the utilization time of machines. In flow shop scheduling the emphasis is on minimization of elapsed time but minimization of elapsed time may not always lead to minimization of utilization time. Here, the objective is to find an algorithm to minimize the utilization time of machines. To minimize the utilization time an algorithm is proposed and a numerical example is given to validate the algorithm.

I. INTRODUCTION Scheduling problems exist in many experimental and real industrial world situations. Scheduling involves determination of the order of processing a set of tasks on machines. In today's manufacturing and distribution systems, scheduling have significant role to meet customer requirements as quickly as possible while maximizing the profits. Flow shop scheduling deals with allocation of resources to tasks over given time periods and its goal is to optimize one or more objectives. The resources and tasks in a system can take different forms. The resources may be machines in a workshop, runways at an airport, crews at a construction site, processing units in a computing establishment etc. The tasks may be operation in a production process, take offs and landings at an airport, phases in a construction work, executions of computer programs etc. The objectives can also take different forms. The common objectives in a flow shop scheduling problems are to minimize some performance measures such as make-span, mean flow time, mean tardiness, mean setup time, number of tardy jobs and mean number of setups. Johnson [1] studied flow shop scheduling in his research paper titled "Optimal two and three stage production schedule with set up times included". Flow shop scheduling has been studied intensively for more than 60 years by various researchers in management, engineering, computer science, operations research etc. Gupta, J.N.D. [2] developed an algorithm to find the optimal sequence for specially structured flow shop scheduling problem. A heuristic algorithm to minimize the rental cost for specially structured two stage flow shop scheduling problem was given by Gupta, D., Sharma, S. & Bala, S. [11]. The concept of job block is significant in scheduling systems where the priority of one job over the other is to be taken into account. The ordering of jobs is also useful when service is done in batches in industries or in service centers. Maggu, P. L. and Das, G. [3] established the basic concept of equivalent job for job block in job sequencing. The string of disjoint job blocks consist of two disjoint job blocks such that in one job block the order of jobs is fixed and in second job block the order of jobs is arbitrary. Heydari [9] studied flow shop scheduling problem with processing of jobs in a string of disjoint job blocks. Singh T.P., Kumar, V. and Gupta, D. [10] studied n×2 flow-shop scheduling problem in which processing time, set up time each associated with probabilities along with jobs in a string of disjoint job blocks. Gupta et al. [14] gave a heuristic method to minimize the utilization time for specially structured two stage flow shop scheduling problem having jobs in a string of disjoint job blocks.

The classical F 2==C max problem is solved optimally by the famous Johnson's algorithm in Oðn à logðnÞÞ where n is the number of jobs. For solving the F =no-idle=C max with a branch and bound algorithm, it is necessary to solve problem closed to the F 2==C max. The only difference is an additive constraint: a set of jobs that cannot be placed in the first (or the last) position. This problem is linear and can be solved by testing systematically all allowed jobs in first position, the other one being scheduled according to Johnson's rule. But this exhaustive procedure (in Oðn 2 Þ) is not satisfying. While it seems natural to think that a single rule (like Johnson's one) can be applied, all intuitive rules can be refuted by counterexamples. Surprisingly, this F 2==C max with this additive constraint appears to be more ''complicated'' than the initial problem, even if it stay linear. Once again, the F 2==C max appears to be a peculiarity in a complex environment.

The purpose of this paper is to consider the problem of scheduling a set of start time-dependent jobs in a two-machine flow shop, in which the actual processing times of jobs increase linearly according to their starting time. The objective of this problem is to minimize the makespan. The problem is known to be NP-hardness; therefore, there is no polynomial-time algorithm to solve it optimally in a reasonable time. So, a branch-and-bound algorithm is proposed to find the optimal solution by means of dominance rules, upper and lower bounds. Several easy heuristic procedures are also proposed to derive near-optimal solutions. To evaluate the performance of the proposed algorithms, the computational experiments are extracted based on the recent literature. Deteriorating jobs lead to an increase in the makespan of the problems; therefore, it is important to obtain the optimal or near-optimal solution. Considering the complexity of the problem, the branch-and-bound algorithm is capable of solving problems of up to 26 jobs. Additionally, the average error percentage of heuristic algorithms is less than 1.37%; therefore, the best one is recommended to obtain a near-optimal solution for large-scale problems.

This study investigates scheduling problems that occur when the weighted number of late jobs that are subject to deterministic machine availability constraints have to be minimized. These problems can be modeled as a more general job selection problem. Cases with resumable, non-resumable, and semiresumable jobs as well as cases without availability constraints are investigated. The proposed efficient mixed integer linear programming approach includes possible improvements to the model, notably specialized lifted knapsack cover cuts. The method proves to be competitive compared with existing dedicated methods: numerical experiments on randomly generated instances show that all 350-job instances of the test bed are closed for the well-known problem 1jr i j P w i U i. For all investigated problem types, 98.4% of 500-job instances can be solved to optimality within 1 hour.

We address a manufacturing environment with the no-wait constraint which is common in industries such as metal, plastic, and semiconductor. Setup times are modelled as uncertain with the objective of minimizing maximum lateness which is an important performance measure for customer satisfaction. This problem has been addressed in scheduling literature for the two-machine no-wait flowshop where dominance relations were presented. Recently, another dominance relation was presented and shown to be about 90% more efficient than the earlier ones. In the current paper, we propose two new dominance relations, which are less restrictive than the earlier ones in the literature. The new dominance relations are shown to be 140% more efficient than the most recent one in the literature. As the level of uncertainty increases, the newly proposed dominance relation performs better, which is another strength of the newly proposed dominance relation. Moreover, we also propose constructive heuristics...

We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.

The scheduling literature is extensive, but much of this work is theoretical and does not capture the complexity of real world systems. Capital goods companies produce products with deep and complex product structures, each of which requires the coordination of jobbing, batch, flow and assembly processes. Many components require numerous operations on multiple machines. Integrated scheduling problems simultaneously consider two or more simultaneous decisions. Previous production scheduling research in the capital goods industry has neglected maintenance scheduling and used metaheuristics with stochastic search that cannot guarantee an optimal solution. This paper presents a novel mixed integer linear programming (MILP) model for simultaneously solving the integrated production and preventive maintenance scheduling problem in the capital goods industry, which was tested using data from a collaborating company. The objective was to minimise total costs including: tardiness and earliness penalty costs; component and assembly holding costs; preventive maintenance costs; and setup, production, transfer and production idle time costs. Thus, the objective function and problem formulation were more extensive than previous research. The tool was successfully tested using data obtained from a collaborating company. It was found that the company's total cost could be reduced by up to 63.5%.

This paper considers a reentrant flow shop with two machines and exact time lag L, in which each task may be processed in this order M1, M2, M1 and there is an identical time lag between the completion time of the first operation and the start time of the second operation on the first machine. The objective is to minimize the total completion time. We prove the NP-hardness of a special case and we give some special subproblems that can be solved in polynomial time.

Application of Multiobjective evolutionary algorithms (MOEAs) in diversified domains has gained popularity in wide area ranging from engineering and computer science to ecology, sociology and medicine field. From these diversified application areas of evolutionary algorithms, computational finance constitutes a very promising field. The use of evolutionary algorithms for solving multi-objective optimization problem emerges as a potential field of research in recent years. This paper deals with application of MOEAs for different problems in computational finance. Different applications are explained briefly and exhaustive simulation study has been carried out for one particular application i.e. investment portfolio optimization. In this paper the Portfolio optimization is solved using two different multi-objective algorithms SPEA2 and NSGA-II. Their performances have been compared in terms of Pareto fronts, the delta, and C and S metrics.

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 sc...

The multi-criteria scheduling problem is one of the main research subjects in the field of multiple objectives programming. Several procedures have been developed to deal with this type of problem where some conflicting criteria have to be optimized simultaneously. The aim of our paper is to propose an aggregation procedure that integrates three different criteria to find the best sequence in a flow shop production environment. The compromise programming model and the concept of satisfaction functions will be utilized to integrate explicitly the manager's preferences according to the deviations between the achievement and the aspiration levels of the following criteria: Makespan, total flow time and total tardiness.

In this study, we deal with a k-stage hybrid flow shop scheduling problem under availability constraints (HFSPAC). In such a problem, machines are not continuously available due to preventive maintenance tasks. Our study aims to provide a good approximate solution to this specific problem with the makespan minimisation as the performance measure. Few studies exist in the literature dealing with the HFSPAC. We consider in this paper two variants to tackle this problem. In the first, the starting times of maintenance tasks are fixed, whereas in the second variant, maintenance must be performed on given time windows. In this last case, a theoretical analysis is elaborated based on the machine idle time to decide which action to perform between left-shifting or right-shifting the maintenance task in the window. Due to the NP-hardness of the HFSPAC, an approximate approach, based on a genetic algorithm (GA), is proposed to minimise the makespan. Computational experiments are performed on randomly generated instances to show the efficiency of the proposed variant (flexibility of the starting times of the maintenance tasks) in terms of makespan minimisation. Moreover, a correlation function computation is proposed to statistically analyse these experiments.

A planning tool that combines the strengths of a propagation prediction tool, CINDOOR, and a particle swarm optimization algorithm (PSO) is presented in this work when applied to optimize wireless networks resources prior to their deployment. For an arbitrary scenario, the approach proposed performs channel allocation, choosing the best set of access points (AP) to be used, including their activation or deactivation to meet a required quality of service (QoS). The CINDOOR software tool provides the heuristic method with data regarding the signal level and delay at each potential receiver point inside a meshed area, associated with any of the potential AP considered. Then, a stochastic binary PSO algorithm is used to meet the following requirements altogether: minimize the interference, maximize the signal-to-interference ratio (SIR) and activate as few AP as possible to maximize the coverage area and reduce interferences. Representative results are included, showing the usefulness of the approach proposed for a real wireless network, considering a certain QoS.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  An exhaustive review of the Non-Permutation Flow-Shop Scheduling problem.  A comprehensive classification in terms of objective functions and the solution methods employed in the literature.  A compilation of problems that, modeled as PFS, do not ensure optimality.  A revision of the main experimental results.  A detailed description of future research lines and literature gaps.

The patient appointment scheduling problem in outpatient chemotherapy clinics is one of the most important and challenging problems due to large numbers of binary variables and thus unrealistic computation times. In this paper, we propose a new approach inspired from cellular manufacturing to reduce the number of binary variables and constraints. The proposed approach consists of two stages: the clustering stage and the mathematical programming stage. In the clustering stage, current clustering algorithms are used to find the optimum cluster members for a given patient mix. The resulted clusters are used in the second stage, namely the mathematical programming stage to optimally assign every nurse to a cluster of patients and a group of chairs at the optimum time slot. The objective function of the mathematical programming model is to achieve the minimum total completion time of all treatments. Compared to the previous models, the proposed approach has the advantage of giving the optimum solution for real problems in much fewer computation time. Another advantage is that a nurse is assigned to each cluster of patients along their treatment durations instead of assigning a nurse just to start up the treatment.

In an industrial environment, manufacturing systems may be subject to considerable uncertainties which could lead to numerous schedule disturbances. These disturbances prevent the execution of a manufacturing schedule as it was planned. The 'groups of permutable operations' method copes with this drawback by proposing a family of schedules instead of a unique one. However, the selection of the appropriate schedule that accounts for real-time disturbances represents a combinatorial optimisation challenge. In this paper, we propose a new decision-aid criterion for selecting the schedule that fits best the real state of the shop. This criterion is measured using a greedy heuristic that anticipates the maximum tardiness in a job shop scheduling environment. Simulation tests performed on benchmark problems show the usefulness of the proposed criterion compared to another frequently used criterion. The final results emphasise the usefulness of this criterion in a bi-criteria decision-aid system.

In an industrial environment, manufacturing systems may be subject to considerable uncertainties which could lead to numerous schedule disturbances. These disturbances prevent the execution of a manufacturing schedule as it was planned. The 'groups of permutable operations' method copes with this drawback by proposing a family of schedules instead of a unique one. However, the selection of the appropriate schedule that accounts for real-time disturbances represents a combinatorial optimisation challenge. In this paper, we propose a new decision-aid criterion for selecting the schedule that fits best the real state of the shop. This criterion is measured using a greedy heuristic that anticipates the maximum tardiness in a job shop scheduling environment. Simulation tests performed on benchmark problems show the usefulness of the proposed criterion compared to another frequently used criterion. The final results emphasise the usefulness of this criterion in a bi-criteria decision-aid system.

Artificial Bee Colony (ABC) algorithm is one of the methods used to solve the flowshop scheduling problem. In order to further investigate the ABC capabilities, we proposed a methodology with the capability of manipulating the onlooker bee approaches in ABC Algorithm for solving flowshop scheduling problem. This paper reviews the analysis of the performance of the ABC algorithm through three different onlooker approaches i.e. method 3+0+0 (three onlooker bees are dedicated to the best employed bee), method 2+1+0 (two onlooker bees are dedicated to the best employed bee and one onlooker bee is dedicated to second best employee bee) and method 1+1+1 (one onlooker bee is dedicated to each employed bee). The simulation results indicated that method 2+1+0 produces best result at low iterations of 102 and below. At high iterations of 204 and above method 3+0+0 dominates the best performance.

The purpose of the Permutation Flowshop Scheduling Problem (PFSP) is to find the best permutation of jobs. PFSP is also considered as an optimization problem and it is often solved using the swarm intelligence approach. In this paper, Artificial Bee Colony (ABC) algorithm is used for solving PFSP. To investigate the effect of trial counter (TC) to the performance of ABC, the TC value was set to six (6), twelve (12) and eighteen (18). Additionally, the percentage of errors was selected as the response. From the experimental results, it can be concluded that ABC algorithm performs best when the TC is set at six (6) because the value of cumulative error percentages is at the lowest. Moreover, the generated data is also located in the smallest spread compared to TC=12 and TC=18. It can also be concluded that the exploration principle works better in a 6 jobs and 3 machines PFSP environment.

The efficiency of wafer sorting scheduling is of particular importance in semiconductor fabrication, especially in the face of strong industry competition. This paper presents a novel hybrid artificial immune system (HAIS) algorithm for solving the wafer sorting scheduling problem, aimed at minimizing the total setup time and the number of testers used. To evaluate the performance of the proposed HAIS algorithm and to compare it with existing approaches, computational experiments were conducted on 480 simulation instances generated from the characteristics of a real wafer probe centre. The experimental results revealed that the proposed HAIS algorithm is highly effective and efficient, as compared with state-of-the-art algorithms on the same benchmark.

In this paper, we present a mixed-integer fuzzy programming model and a genetic algorithm (GA) based solution approach to a scheduling problem of customer orders in a mass customizing furniture industry. Independent job orders are grouped into multiple classes based on similarity in style so that the required number of setups is minimized. The family of jobs can be partitioned into batches, where each batch consists of a set of consecutively processed jobs from the same class. If a batch is assigned to one of available parallel machines, a setup is required at the beginning of the first job in that batch. A schedule defines the way how the batches are created from the independent jobs and specifies the processing order of the batches and that of the jobs within the batches. A machine can only process one job at a time, and cannot perform any processing while undergoing a setup. The proposed formulation minimizes the total weighted flowtime while fulfilling due date requirements. The imprecision associated with estimation of setup and processing times are represented by fuzzy sets.

We consider online as well as offline scheduling of ordered flow shops with the makespan as objective. In an online flow shop scheduling problem, jobs are revealed to a decisionmaker one by one going down a list. When a job is revealed to the decisionmaker, its operations have to be scheduled irrevocably without having any information regarding jobs that will be revealed afterwards. We consider for the online setting the so-called Greedy Algorithm which generates permutation schedules in which the jobs on the machines are at all times processed without any unnecessary delays. We focus on ordered flow shops, in particular proportionate flow shops with different speeds and proportionate flow shops with different setup times. We analyze the competitive ratio of the Greedy Algorithm for such flow shops in the online setting. For several cases, we derive lower bounds on the competitive ratios.

La conception constitue une des étapes la plus importante dans le cycle de vie d'un atelier de production. Un des problèmes à soulever est le dimensionnement des ressources. Un sur ou un sous dimensionnement provoquera des sur-coûts supplémentaires. Il conditionnera aussi l'ordonnancement pendant la phase d'exploitation. Nous proposons dans ce papier une approche d'optimisation du dimensionnement d'un atelier de production basé sur les ordonnancements des scénarios de production prévisionnels. Nous nous intéressons à une organisation de flow shop hybride à plusieurs étages. En effet, nous proposons un programme linéaire permettant de minimiser conjointement le C max et le nombre de machines dans chaque étage pour un ensemble de jobs types de l'activité prévisionnelle. Un poids est attribué à chacun des objectifs. Au vu des résultats obtenus, cette approche peut fournir des solutions exactes pour des problèmes de petites tailles. Dans le cas où le poids attribué à chaque objectif est le même nous obtenons des solutions dites de « compromis ». Ces solutions de compromis ont permis de minimiser les coûts totaux.

In a practical situation, a manufacturer receives different orders from its customers. Different orders may contain different quantities of the product. Therefore, the manufacturer has to decide how to group these orders into different lots based on the capacity of the lot processing machine (such as integrated circuit tester, heated container, etc.) and then decides the sequence of these lots. In this paper, we study a lot scheduling problem with orders which can be split. The objective is to minimize the total completion time of all orders. We show that this problem can be solved in polynomial time.

We consider a two-machine flowshop sequencing problem with limited waiting time constraints. This means that for each job the waiting time between two machines cannot be greater than a given upper bound. The objective is to minimize the makespan. There are efficient algorithms for the special cases of infinite waiting time and zero waiting time. The two-machine flowshop sequencing problem with limited waiting time constraints is shown to be NP-hard. A branch-and-bound algorithm is proposed, and computational experiments are provided.

This paper analyzes a realistic variant of the permutation flow-shop problem (PFSP) by considering a non-smooth objective function that takes into account not only the traditional makespan cost but also failure-risk costs due to uninterrupted operation of machines. After completing a literature review on the issue, the paper formulates an original mathematical model to describe this new PFSP variant. Then, a Biased-Randomized Iterated Local Search (BRILS) algorithm is proposed as an efficient solving approach. An oriented (biased) random behavior is introduced in the well-known NEH heuristic to generate an initial solution. From this initial solution, the algorithm is able to generate a large number of alternative good solutions without requiring a complex setting of parameters. The relative simplicity of our approach is particularly useful in the presence of non-smooth objective functions, for which exact optimization methods may fail to reach their full potential. The gains of considering failure-risk costs during the exploration of the solution space are analyzed throughout a series of computational experiments. To promote reproducibility, these experiments are based on a set of traditional benchmark instances. Moreover, the performance of the proposed algorithm is compared against other state-of-the-art metaheuristic approaches, which have been conveniently adapted to consider failure-risk costs during the solving process. The proposed BRILS approach can be easily extended to other combinatorial optimization problems with similar non-smooth objective functions.

This paper investigates integrated two-stage assembly flow shop problem with preventive maintenance (PM) activities under the multi-objective optimisation approaches. Reliability models are employed to carry out the maintenance activities. This paper attempts to find the appropriate sequence of jobs on machines in order to minimise the makespan and determining when to perform the PM activities in order to minimise the system unavailability. As this problem is proven to be NP-hard two multi-objective optimisation methods that are named non-dominated sorting genetic algorithm II (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are employed to find the Pareto-optimal front. The parameters of proposed algorithms are calibrated by artificial neural network (ANN) and the performances of the algorithms on the problem of various sizes are analysed based on four metrics. The computational results reveal NRGA is statistically better than NSGA-II.

Linear programming is a step or process to get maximum results with existing resources or it can be said the process of looking for optimal value. One part of scheduling is production scheduling. production scheduling is the use of resources that are few but make the most profit. This paper discusses production scheduling using flowshop type production scheduling by taking into account transportation times and work weights. This paper uses the Dannenbring method with the aim of finding the optimal sequence of problems by considering the total production time (makespan) and the average Weigted Mean Flow Time (WMFT). Based on the results of the Dannenbring method, the results of flowshop scheduling are obtained with a total makespan of 75 hours and the WMFT value is 28, 87 hours.

Considering green scheduling and sustainable manufacturing, the energy-efficient hybrid flow shop scheduling problem (EHFSP) with a variable speed constraint is investigated, and a novel multi-population artificial bee colony algorithm (MPABC) is developed to minimize makespan, total tardiness and total energy consumption (TEC), simultaneously. It is necessary for manufacturers to fully understand the notion of symmetry in balancing economic and environmental indicators. To improve the search efficiency, the population was randomly categorized into a number of subpopulations, then several groups were constructed based on the quality of subpopulations. A different search strategy was executed in each group to maintain the population diversity. The historical optimization data were also used to enhance the quality of solutions. Finally, extensive experiments were conducted. The results demonstrate that MPABC can achieve an outstanding performance on three metrics DIR, c and nd for the...

In manufacturing processes where efficiency is crucial to remain competitive, the flowshop is a common configuration in which machines are arranged in series and products are produced individually in stages. In certain production processes, machines are frequently configured in a way that each production stage may contain multiple processing units in parallel or a hybrid configuration. Moreover, along with precedent conditions, sequence dependent setup times may exist. Finally, in the case where there is no buffer, a machine is said to be blocked if the next stage is occupied. In NP-Hard problems, referred to as Blocking Hybrid Flowshop Scheduling Problems with Sequence Dependent Setup/Changeover Times, it is usually not possible to find an exact best solution to satisfy optimization objectives. Thus, it is usually solved by approximate algorithms such as metaheuristics. In this paper, we comparatively investigate the effectiveness of two approaches: a genetic algorithm (GA) and an artificial bee colony (ABC) algorithm. Additionally, we applied an algorithm to improve the GA and ABC algorithms so that they can take advantage of parallel processing resources of modern multiple core processors, while eliminating the need for advance screening of the algorithm optimal parameters. These techniques were applied to solve three problems. In small-sized problems, GA outperformed ABC. For medium-sized problems, the two algorithms appeared to have similar performance. For large-sized problem, ABC performed better than GA because GA is held back by crossover operations. Furthermore, enhancements helped increase the performance of both GA and ABC algorithms.

In the present paper a Flow shop scheduling model in two stage has been studied where the time taken by machines to setup is separately considered from the processing time. The probabilities with the processing times as well as with the setup times are also taken into account. The problem is structured specially for the cases when the minimum of expected processing times on second fictitious machine can never be less than to the maximum of expected processing times on first fictitious machine with the objective of minimizing the total of the waiting time for all the jobs. The two of the jobs has been grouped as a block. The significance of the objective has been made clear by computational experiments in comparison to the existing makespan approaches of Johnson and Palmer.

Selama ini PT. Tlogomas E.P.I menggunakan pendekatan FCFS dan EDD sebagai acuan dalam menentukan prioritas job dan menyusun jadwal produksi dan lebih sering mengandalkan kemampuan manajerial dari supervisor, sehingga jadwal produksi menjadi tidak menentu. Selain itu jadwal produksi masih dirasa kurang efektif, karena proses produksi PT. Tlogomas E.P.I masih sering mengalami overlap job yang menyebabkan basarnya flow time, earliness time dan tardiness time. Sehingga untuk menyelesaikan permasalahan tersebut, dalam penelitian ini akan dikembangkan dua model algoritma penjadwalan produksi yang diharapkan dapat menjadi alternatif metode yang kompetitif untuk menyelesaikan permasalahan optimasi multi tujuan dan dapat diimplementasikan langsung pada PT. Tlogomas E.P.I. Dalam penelitian ini akan dikembangkan dua model algoritma heuristik yaitu berbasis EDD dan MST, masing-masing dari algoritma tersebut akan dimodifikasi dan diintegrasikan dengan konsep algoritma LPT, dengan memperhatikan routing, precedence, dan SDST. Dari hasil pengujian dan analisis disimpulkan bahwa kedua model algoritma yang dikembangkan sesuai dan dapat diimplementasikan pada sistem produksi PT. Tlogomas E.P.I. dan model algoritma yang paling mendekati optimal untuk periode produksi Januari 2014 adalah model algoritma 1 (algoritma heuristik berbasis Earliest Due Date) Kata kunci : Penjadwalan, HFFS/SDST, multi kriteria, algoritma heuristik earliest due date dan minimum slack time.

Persaingan di era globalisasi menyebabkan setiap perusahaan manufaktur harus terus meningkatkan kemampuan produksi dan pelayanan produksi dengan meningkatkan utilitas mesin dan ketepatan dalam penyelesaian produksi agar sesuai dengan waktu yang ditetapkan melalui metode penjadwalan. PT XYZ adalah sebuah perusahaan yang bergerak di bidang otomotif, khususnya pada bidang stamping part atau komponen kendaraan beroda empat. Tujuan penelitian ini adalah untuk meminimalkan waktu proses (makespan) dari proses produksi stamping part ISUZU pada Line B PT XYZ. Metode penjadwalan yang diusulkan terdiri dari dua metode yaitu Campbell, Dudek, and Smith (CDS) dan Nawaz, Enscore and Ham (NEH). Dari kedua metode ini didapatkan urutan job yang berbeda, yang akan dibandingkan dengan penjadwalan yang diterapkan perusahaan. Metode NEH adalah metode yang memiliki waktu makespan yang terbaik, yaitu 4858 menit dan dapat menghemat 252 menit dari penjadwalan perusahaan dengan makespan, yaitu 5110 menit.

Laboratoire d'automatique BP. 230 Faculté des sciences de l'ingénieur Université Abou Bekr Belkaid-Tlemcen. {m_souier,a_hassam,z_sari}@mail.univ-tlemcen.dz RESUME : Cet article présente les résultats d'une étude de simulation d'un système flexible de production (FMS) qui se compose de sept machines, une station de chargement, une station de déchargement, et six types de pièces différentes. En raison de l'existence de centres d'usinage identiques dans le système, les types de pièces ont des routages alternatifs. De plus, au niveau de chaque machine, FIFO (First In First Out) est employé comme règle de séquencement. L'objectif de cette étude est d'analyser l'impact du ré-ordonnancement en temps réel des pièces contenues dans la station de chargement sur les performances du système lorsque les métaheuristiques suivantes (les colonies de fourmis, les algorithmes génétiques, le recuit simulé, la recherche tabou, les essaims particulaires et l'électromagnétisme) sont appliquées pour résoudre le problème de sélection de routages alternatifs en temps réel. Les résultats obtenus ont montré que pour chaque métaheuristique que nous avons étudiée, le ré-ordonnancement améliore les performances pour le taux de production, le taux d'utilisation des machines et du système de transport pour un système flexible de production saturé, même avec la présence de pannes.