Group Scheduling Problems Research Articles

A Hybrid Metaheuristic Approach for Minimizing the Total Flow Time in A Flow Shop Sequence Dependent Group Scheduling Problem

Production processes in Cellular Manufacturing Systems (CMS) often involve groups of parts sharing the same technological requirements in terms of tooling and setup. The issue of scheduling such parts through a flow-shop production layout is known as the Flow-Shop Group Scheduling (FSGS) problem or, whether setup times are sequence-dependent, the Flow-Shop Sequence-Dependent Group Scheduling (FSDGS) problem. This paper addresses the FSDGS issue, proposing a hybrid metaheuristic procedure integrating features from Genetic Algorithms (GAs) and Biased Random Sampling (BRS) search techniques with the aim of minimizing the total flow time, i.e., the sum of completion times of all jobs. A well-known benchmark of test cases, entailing problems with two, three, and six machines, is employed for both tuning the relevant parameters of the developed procedure and assessing its performances against two metaheuristic algorithms recently presented by literature. The obtained results and a properly arranged ANOVA analysis highlight the superiority of the proposed approach in tackling the scheduling problem under investigation.

Single-machine bicriterion group scheduling with deteriorating setup times and job processing times

This paper considers a group scheduling problem with two ordered criteria where both setup times and job-processing times are increasing functions of their starting times. It is assumed that the jobs be classified into several groups and the jobs of the same group have to be processed contiguously. We consider two objectives where the primary criterion is the total weighted completion time and the secondary criterion is the maximum cost. A polynomial time algorithm is presented to solve this bicriterion group scheduling problem with deteriorating setup times and job-processing times. This algorithm can also solve single-machine group scheduling problems with deteriorating setup times and job-processing times in several ordered maximum cost and arbitrary precedence.

Joint optimization of a flow-shop group scheduling with sequence dependent set-up times and skilled workforce assignment

Flow-shop sequence-dependent group scheduling (FSDGS) problem has been extensively investigated in the literature also due to many manufacturers who implemented the concept of group technology to reduce set-up costs, lead times, work-in-process inventory costs, and material handling costs. On the other hand, skilled workforce assignment (SWA) to machines of a given shop floor may represent a key issue for enhancing the performance of a manufacturing system. As the body of literature addressing the group scheduling problems ignored up to now the effect of human factor on the performance of serial manufacturing systems, the present paper moves in that direction. In particular, an M-machine flow-shop group scheduling problem with sequence-dependent set-up times integrated with the worker allocation issue has been studied with reference to the makespan minimization objective. First, a Mixed Integer Linear Programming model of the proposed problem is reported. Then, a well-known benchmark arisen from the literature is adopted to carry out an extensive comparison campaign among three properly developed metaheuristics based on a genetic algorithm framework. Once the best procedure among those tested is selected, it is compared with an effective optimization procedure recently proposed in the field of FSDGS problems, being this latter properly adapted to run the SWA issue. Finally, a further analysis dealing with the trade-off between manpower cost and makespan improvement is proposed.

Efficient upper and lower bounding methods for flowshop sequence-dependent group scheduling problems

In this research, a permutation flowshop sequence-dependent group scheduling problem with minimisation of total completion time is considered. Since the problem is shown to be strongly NP-hard, a hybrid genetic (HG) algorithm is proposed. The only available lower bounding (LB) method for the proposed research problem in the literature based on branch and price (B&P) algorithm is also enhanced by proposing efficient method to solve sub-problems and proposing a better branching rule. A statistical comparison shows that both the proposed HG algorithm and the proposed LB have better performance than the other methods from the literature with an average 5.96% percentage gap.

Group scheduling and job-dependent due window assignment based on a common flow allowance

We study a single-machine group scheduling and job-dependent due window assignment problem in which each job is assigned an individual due window based on a common flow allowance. In the group technology environment, the jobs are divided into groups in advance according to their processing similarities and all the jobs of the same group are processed consecutively in order to improve production efficiency. A sequence-independent machine setup time precedes the processing of the first job of each group. A job completed earlier (later) than its due window will incur an earliness (tardiness) penalty. Our goal is to find the optimal sequence for both the groups and jobs, together with the optimal due window assignment, to minimize the total cost that comprises the earliness and tardiness penalties, and the due window starting time and due window size costs. We give an O(nlogn)time algorithm to solve this problem.

A new encoding scheme-based hybrid algorithm for minimising two-machine flow-shop group scheduling problem

This article investigates the two-machine flow-shop group scheduling problem (GSP) with sequence-dependent setup and removal times, and job transportation times between machines. The objective is to minimise the total completion time. As known, this problem is an NP-hard problem and generalises the typical two-machine GSPs. In this article, a new encoding scheme based on permutation representation is proposed to transform a random job permutation to a feasible permutation for GSPs. The proposed encoding scheme simultaneously determines both the sequence of jobs in each group and the sequence of groups. By reasonably combining particle swarm optimisation (PSO) and genetic algorithm (GA), we develop a fast and easily implemented hybrid algorithm (HA) for solving the considered problems. The effectiveness and efficiency of the proposed HA are demonstrated and compared with those of standard PSO and GA by numerical results of various tested instances with group numbers up to 20. In addition, three different lower bounds are developed to evaluate the solution quality of the HA. Limited numerical results indicate that the proposed HA is a viable and effective approach for the studied two-machine flow-shop group scheduling problem.

Modeling Group Scheduling Problems in Space and Time by Timed Petri Nets

Dealing with cyber-physical systems CPS puts a strong emphasis on the interaction between computing and non-computing elements. Since the physical world is characterized by being strongly distributed and concurrent, this is also reflected in the computational world making the design of such systems a challenging task. If a number of tasks shall be executed on a CPS which are bound to time and space, may have dependencies to other tasks and requires a specific amount of computing devices, a solution requires a four-dimensional space-time schedule which includes positioning of the devices resulting in an NP-hard problem. In this paper, we address the problem of spatial-temporal group scheduling using Timed Petri nets. We use Timed Petri nets in order to model the spatial, temporal, ordered and concurrent character of our mobile, distributed system. Our model is based on a discrete topology in which devices can change their location by moving from cell to cell. Using the time property of Petri nets, we model movement in a heterogeneous terrain as well as task execution or access to other resources of the devices. Given the modeling, we show how to find an optimal schedule by translating the problem into a shortest path problem, which is solvable with the known method of dynamic programming.

Single machine group scheduling with time and position dependent processing times

In the paper two resource constrained single-machine group scheduling problems with time and position dependent processing times are considered. By time and position dependent processing times and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

An efficient tabu search algorithm for flexible flow shop sequence-dependent group scheduling problems

In this paper, the flexible flow shop sequence-dependent group scheduling problem (FFSDGS) with minimisation of makespan as the criterion (FFm | fmls, Splk | C max) is investigated. For the first time a mathematical model for the proposed research problem is developed. Since the problem is shown to be NP-hard, six metaheuristic algorithms based on tabu search (TS) are developed to efficiently solve the problem. The proposed metaheuristics are different to the only available metaheuristic algorithm in the literature based on TS. By applying randomised complete block design and using available test problems in the literature, the best of the proposed TS algorithms in this research is identified. The performance of the best developed metaheuristic algorithm is then compared with the existing algorithm in the literature by solving the test problems, also available in the literature, ranging in size from small, medium, to large. A comparison based on paired t-test at 95% confidence interval, shows that the best proposed algorithm in this research has a better performance than the existing algorithm in the literature with an average percentage deviation of around 1.0% for medium and large size problems.

Single-machine group scheduling with time-dependent learning effect and position-based setup time learning effect

As to learning effect, it may be more appropriate to assume that position-based learning takes place during machine setups only, while sum-of-processing-time-based learning occurs in considering the experience that workers have gained from producing jobs. Thus, in this paper, we consider sum-of-processing-time-based learning on job processing time and position-based learning on setup time in single-machine group scheduling problems. The objectives are to minimize the makespan and the total completion time, respectively. We provide two polynomial time algorithms to solve the makespan minimization problems. On the other hand, we also provide two polynomial time algorithms to solve the total completion time minimization problems under certain conditions.

Single‐Machine Group Scheduling Problems with Deterioration to Minimize the Sum of Completion Times

We consider two single‐machine group scheduling problems with deteriorating group setup and job processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. Jobs in each group have the same deteriorating rate. The objective of scheduling problems is to minimize the sum of completion times. We show that the sum of completion times minimization problems remains polynomially solvable under the agreeable conditions.

Optimisation of manufacturing cell formation with extended great deluge meta-heuristic approach

The concepts of cellular manufacturing system (CMS) and cell scheduling (CS) have been widely used to meet various production needs. The CMS is a particular case of group technology (GT) applied to improve the production efficiency and reduce operational costs. This work addresses the machine/part grouping and group scheduling problems. The cell formation problem has long been recognised as the most challenging problem in realising the concept of cellular manufacturing. It belongs to the class of NP-hard problems. One of the most important problems in the area of production management is the scheduling problem which has also been proven to be NPhard. To solve this scheduling problem an Extended Great Deluge (EGD) metaheuristic approach is employed. The results of the proposed approach show a major improvement when compared with the results of one of the best algorithms developed so far by other researchers.

Permutation flowshops in group scheduling with sequence-dependent setup times

This paper focuses on the flow shop sequence dependent group scheduling (FSDGS) problem with minimisation of total completion time as the criterion (Fm|fmls, prmu, Splk|∑Cj). The research problem is formulated in form of two different mixed integer linear programming (MILP) models. Comparing with the latest MILP model for the proposed problem in the literature, the complexity size of the proposed models are significantly reduced. One of the proposed mathematical models is so effective that even medium-sized instances (problems up to 60 jobs in all groups) are solved to optimality in a reasonable amount of time. Moreover, a metaheuristic hybridising genetic and simulated annealing algorithm, called GSA, is proposed to solve the problems heuristically. All the results and analyses show the high performance of the proposed mathematical models as well as the proposed metaheuristic algorithm compared to the available ones in literature. (Received 11 February 2010; Revised 24 May 2010; Accepted 30 September 2010)

Single-machine group scheduling with general deterioration and learning effects

In this paper we consider single-machine group scheduling problems with effects of learning and deterioration at the same time. By effects of learning and deterioration, we mean that the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent and time-dependent learning effects. The objective of scheduling problems is to minimize the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.

A fast hybrid particle swarm optimization algorithm for flow shop sequence dependent group scheduling problem

A Particle Swarm Optimization (PSO) algorithm for a Flow Shop Sequence Dependent Group Scheduling (FSDGS) problem, with minimization of total flow time as the criterion (Fm|fmls,Splk,prmu|∑Cj), is proposed in this research. An encoding scheme based on Ranked Order Value (ROV) is developed, which converts the continuous position value of particles in PSO to job and group permutations. A neighborhood search strategy, called Individual Enhancement (IE), is fused to enhance the search and to balance the exploration and exploitation. The performance of the algorithm is compared with the best available meta-heuristic algorithm in literature, i.e. the Ant Colony Optimization (ACO) algorithm, based on available test problems. The results show that the proposed algorithm has a superior performance to the ACO algorithm.

Group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine

Group technology is important to manufacturing as it helps increase the efficiency of production and decrease the requirement of facilities. In this paper we investigate group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine setting. The learning phenomenon is implemented to model the setup time of groups. Three models of deteriorating for the job processing time within a group are examined. We show that all the problems studied are polynomially solvable with or without the presence of certain conditions where the objective is to find an optimal schedule for minimizing the makespan. We also investigate the minimization of the total completion time. We proved that one of the deterioration models examined in this study can also be solved in a polynomial time algorithm under certain conditions.

Single-machine group scheduling with both learning effects and deteriorating jobs

In the paper two resource constrained single-machine group scheduling problems with both learning effects and deteriorating jobs are considered. By learning effects, deteriorating jobs and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

Multi-objective group scheduling with learning effect in the cellular manufacturing system

Article history: Received 18 December 2010 Received in revised form 14 February 2011 Accepted 15 February 2011 Available online 15 February 2011 Group scheduling problem in cellular manufacturing systems consists of two major steps. Sequence of parts in each part-family and the sequence of part-family to enter the cell to be processed. This paper presents a new method for group scheduling problems in flow shop systems where it minimizes makespan (Cmax) and total tardiness. In this paper, a position-based learning model in cellular manufacturing system is utilized where processing time for each part-family depends on the entrance sequence of that part. The problem of group scheduling is modeled by minimizing two objectives of position-based learning effect as well as the assumption of setup time depending on the sequence of parts-family. Since the proposed problem is NP-hard, two meta heuristic algorithms are presented based on genetic algorithm, namely: Non-dominated sorting genetic algorithm (NSGA-II) and non-dominated rank genetic algorithm (NRGA). The algorithms are tested using randomly generated problems. The results include a set of Pareto solutions and three different evaluation criteria are used to compare the results. The results indicate that the proposed algorithms are quite efficient to solve the problem in a short computational time. © 2011 Growing Science Ltd. All rights reserved

Note on “A note on single-machine group scheduling problems with position-based learning effect”

In a recent paper, Lee and Wu [W.-C. Lee, C.-C. Wu, A note on single-machine group scheduling problems with position-based learning effect, Appl. Math. Model. 33 (2009) 2159–2163] proposed a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. They investigate the makespan and the total completion time minimization problems on a single-machine. As for the total completion time minimization problem, they assumed that the numbers of jobs in each group are the same and the group normal setup and the job normal processing times are agreeable. Under the assumption conditions, they showed that the total completion time minimization problem can be optimally solved in polynomial time solution. However, the assumption conditions for the total completion time minimization problem do not reflect actual practice in many manufacturing processes. Hence, in this note, we propose other agreeable conditions and show that the total completion time minimization problem remains polynomially solvable under the agreeable conditions.

Single-machine group scheduling problems under the effects of deterioration and learning

This paper investigates single-machine group scheduling problems with simultaneous considerations of deteriorating and learning effects to minimize the makespan and the total completion time of all jobs. The group setup time is assumed to follow a simple linear time-dependent deteriorating model. Two models of learning for the job processing time are examined in this study. We provided polynomial time solutions for the makespan minimization problems. We also showed that the total completion time minimization problems remain polynomially solvable under agreeable conditions.