Number Of Tardy Jobs Research Articles

Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach

Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under different levels of shop utilization and setup time. The important aspects of the results of the simulation investigation are also discussed in detail.

AN INTEGRATED APPROACH FOR SINGLE MACHINE SCHEDULING WITH SEQUENCE-DEPENDENT SETUP TIMES

This study proposes a multi-choice goal programming for the single machine scheduling problem of minimizing the weighted number of tardy jobs, the total weighted completion time and makespan with sequence-dependent setup times. In this problem, there are n candidate jobs for processing in a single machine, each job has a weight, a due date, a processing time, and also sequence-dependent setup times exist between two consecutive jobs. In the first stage of the proposed methodology, the job weights of each job are determined by using the Analytic Hierarchy Process (AHP) method. In the second stage, a 0-1 mixed integer non-linear programming model is built by considering three objective functions and the ideal point is obtained by minimizing the objectives individually. Then, the multi-choice goal programming is used to allow the decision makers to set multi-choice aspiration levels for each goal. http://dx.doi.org/10.13033/ijahp.v7i1.291

Mathematical Models to Simultaneously Determine Overtime Requirements and Schedule Cells

The problem studied in this paper was inspired from an actual textile company. The problem is more complex than usual scheduling problems in that we compute overtime requirements and make scheduling decisions simultaneously. Since having tardy jobs is not desirable, we allow overtime to minimize the number of tardy jobs. The overall objective is to maximize profits. We present various mathematical models to solve this problem. Each mathematical model reflects different overtime workforce hiring practices. An experimentation has been carried out using eight different data sets from the samples of real data collected in the above mentioned textile company. Mathematical Model 2 was the best mathematical model with respect to both profit and execution time. This model considered partial overtime periods and also allowed different overtime periods on cells. We could solve problems up to 90 jobs per period. This was much more than what the mentioned textile company had to handle on a weekly basis. As a result, these models can be used to make these decisions in many industrial settings.

Analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times

Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90% and setup times less than processing times. Results indicate that shortest setup time (SIMSET) rule provides the best performance for mean flow time and number of tardy jobs measures. The job with similar setup and modified earliest due date (JMEDD) rule provides the best performance for makespan, maximum flow time, mean tardiness, maximum tardiness, total setups and mean setup time measures.

Single-machine scheduling with a variable maintenance activity

We consider the problem of scheduling a maintenance activity and jobs on a single machine, where the maintenance activity must start before a given deadline and the maintenance duration increases with its starting time. We provide polynomial-time algorithms to solve the problems to minimize the makespan, sum of completion times, maximum lateness, and number of tardy jobs.

Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods.

Single Machine Scheduling and due Date Assignment with Past-Sequence-Dependent Delivery Times and General Position-Dependent Processing Times

We studied single machine scheduling problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depended on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyzed these problems with two different due date assignment methods and conclude that the problems are polynomial time solvable.

Single Machine Scheduling and Due Date Assignment with Past-Sequence-Dependent Delivery Times and Position-Dependent Processing Times

This paper considers single machine scheduling and due date assignment problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depends on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyze the problems with two different due date assignment methods and conclude that the problems are polynomial time solvable. We provide a dynamic programming algorithm with O(n3) times for the problems.

IMPACT OF GENETIC ALGORITHM OPERATORS ON ITS PERFORMANCE IN SOLVING FLOW SHOP SCHEDULING PROBL

The primary objective of flow shop scheduling is to obtain the best sequence which optimizes various objectives such as makespan, total flow time, total tardiness, or number of tardy jobs, etc. Due to the combinatorial nature of the flow shop problem (FSP) there is a lot of artificial intelligence methods proposed to solve it. The Genetic Algorithm (GA), one of these methods, is considered a valuable search algorithm capable of finding a reasonable solution in a short computational time. GA operators, (selection, crossover and mutation process), give different forms that can be combined to give various GAs. In this paper we investigate the impact of selection, crossover and mutation process on the quality of the GA solution in solving the flow shop scheduling problems. In this study, four selection methods, seventeen crossover methods and eight mutation methods are investigated. The computational results show that there are significant differences among the investigated methods on the performance of the proposed GA.

Scheduling for fabrication and assembly in a two-machine flowshop with a fixed job sequence

This paper studies a problem of scheduling fabrication and assembly operations in a two-machine flowshop, subject to the same predetermined job sequence on each machine. In the manufacturing setting, there are n products, each of which consists of two components: a common component and a unique component which are fabricated on machine 1 and then assembled on machine 2. Common components of all products are processed in batches preceded by a constant setup time. The manufacturing process related to each single product is called a job. We address four regular performance measures: the total job completion time, the maximum job lateness, the total job tardiness, and the number of tardy jobs. Several optimality properties are presented. Based upon the concept of critical path and block schedule, a generic dynamic programming algorithm is developed to find an optimal schedule in O(n7) time.

A fast heuristic to minimize number of tardy jobs in preemptive open shops

This article considers the problem of scheduling preemptive open shops to minimize the number of tardy jobs. A mixed integer program is presented for solving small-sized problems. An efficient heuristic is constructed for solving large-sized problems. This heuristic can be viewed as a generalization of the well-known Moore’s algorithm for the single machine non-preemptive scheduling problem to the preemptive open shop scheduling problem. A lower bound based on assignment problem is proposed for performance evaluation of the heuristic for large-sized problems. Computational results for randomly generated problems are reported. For small-sized problems, the solution obtained by the heuristic has an average deviation of about 4.02% from the optimal value. The lower bound has an average deviation of about 21.03% from the optimal value. For large-sized problems, the solution obtained by the heuristic has an average deviation of less than 54% from the lower bound.

Scheduling with deteriorating jobs and setup times on a single machine

This paper addresses several single-machine scheduling problems with deteriorating jobs and setup times to minimise the maximum lateness, the weighted number of tardy jobs and the total weighted completion time. The actual job processing times and setup times are both proportional functions of their starting times. For the maximum lateness problem, we first show that the general problem is -hard, which also resolves an open question on its complexity raised in the literature, and then we show that the problem with a fixed number of families is polynomially solvable. For the weighted number of tardy jobs problem, we first present a pseudo-polynomial-time algorithm when the number of families is fixed, and then we provide an O(n2)-time algorithm for the unweighted problem with uniform family due dates. For the total weighted completion time problem, we present a polynomial-time algorithm when the number of families is fixed.

Simulation modelling and analysis of scheduling in robotic flexible assembly cells using Taguchi method

Due to increasing competition in the developing global economy, today’s companies are facing greater challenges than ever to employ flexible manufacturing systems (FMS) capable of dealing with unexpected events and meeting customers’ requirements. One such system is robotic flexible assembly cells (RFACs). There has been relatively little work on the scheduling of RFACs, even though overall scheduling problems of FMS have attracted significant attention. This paper presents Taguchi optimisation method in conjunction with simulation modelling in a new application for dynamic scheduling problems in RFACs, in order to minimise total tardiness and number of tardy jobs (NT). This is the first study to address these particular problems. In this study, Taguchi method has been used to reduce the minimum number of experiments required for scheduling RFACs. These experiments are based on an L9 orthogonal array with each trial implemented under different levels of scheduling factors. Four factors are considered simultaneously: sequencing rule, dispatching rule, cell utilisation and due date tightness. The experimental results are analysed using an analysis of mean to find the best combination of scheduling factors and an analysis of variance to determine the most significant factors that influence the system’s performance. The resulting analysis shows that this proposed methodology enhances the system’s scheduling policy.

The impact of risk on the integrated cellular design and control

Design and control aspects of cellular manufacturing systems (CMSs) have been studied extensively and several robust procedures have been proposed to deal with cell formation and cell scheduling problems, separately. However, less attention has been paid to the interaction between the design and control aspects in the presence of uncertainty. In this paper, stochastic cell formation and cell scheduling problems are jointly studied where product demand and processing times are assumed as probabilistic. First, stochastic CMS design phase is handled and then stochastic cellular control phase is studied. Two stochastic non-linear mathematical models are developed to solve cell formation and cell scheduling problems consecutively. Later, Monte Carlo simulation is utilised to analyse the impact of uncertainty in design phase on the control phase. Various design risk and control risk scenarios are experimented with the proposed hierarchical approach to evaluate the chain impact of the risk taken during the cell formation (design risk) and the risk taken during the cell scheduling (control risk) on the scheduling performance: the number of tardy jobs (nT). A total of 3 cell formation and 300 cell scheduling scenarios are solved and results are summarised by design, control and integration subjects. Results indicate that higher design risk results in more pressure on control, which pushes scheduler to take lower risks during the cellular control. However, when lower design risk is taken, greater control risks can be taken, which provides more flexibility to scheduler. All in all, this paper presents a handy framework to practitioners to deal with modelling the uncertainty prior to design and during the control of CMS and deal with such short- and long-term decisions.

Dynamic set-up rules for hybrid flow shop scheduling with parallel batching machines

An S-stage hybrid (or flexible) flow shop, with sequence-independent uniform set-up times, parallel batching machines with compatible parallel batch families (like in casting or heat treatments in furnaces, chemical or galvanic baths, painting in autoclave, etc.) has been analysed with the purpose of reducing the number of tardy jobs (and the makespan); in Graham’s notation: FPB(m1, m2, …, mS)|p-batch, . Jobs are sorted dynamically (at each new delivery); batches are closed within sliding (or rolling) time windows and processed in parallel by multiple identical machines. Computation experiments have shown the better performance on benchmarks of the two proposed heuristics based on new formulations of the critical ratio (CRsetup) considering the ratio of allowance set-up and processing time in the scheduling horizon, which improves the weighted modified operation due date rule.

Single-machine common due-date scheduling with batch delivery costs and resource-dependent processing times

In this paper we consider the problem of single-machine batch delivery scheduling with an assignable common due date and controllable processing times. The job processing time is either a linear or a convex function of the amount of a continuously divisible and non-renewable resource allocated to the job. Finished jobs are delivered in batches and there is no capacity limit on each delivery batch. The objective is to find a job sequence, a partition of the job sequence into batches, a common due date, and resource allocation that jointly minimise a cost function based on earliness, weighted number of tardy jobs, job holding, due-date assignment, batch delivery, makespan, and resource consumption. We provide some properties of the optimal solution, and show that the problem with the linear and convex resource consumption functions can be solved in and time, respectively. We also show that some special cases of the problem can be solved by lower-order algorithms.

A branch-and-bound algorithm for minimising the number of tardy jobs in a two-machine flow-shop problem with release dates

This article considers the two-machine flow-shop scheduling problem with the objective of minimising the number of tardy jobs in which jobs have release dates. Since the problem under consideration is an NP-hard problem, a branch-and-bound (B&B) algorithm is viable to solve the problem exactly. A heuristic algorithm as an upper bound, some lower bounds and several efficient dominance properties are used to speed up the elimination process of the B&B algorithm. For the evaluation of the performance of the proposed algorithm, computational experiments are performed on test problems and results are displayed. The experimental results show that the proposed B&B algorithm can solve problems with up to 28 jobs in timely manner, and the average percentage gap of the heuristic solutions is about 10%.

A priority scheduling approach for flexible job shops with multiple process plans

This paper considers the job shop scheduling problem with alternative operations and machines, called the flexible job shop scheduling problem. As an extension of previous studies, operation and routing flexibilities are considered at the same time in the form of multiple process plans, i.e. each job can be processed through alternative operations, each of which can be processed on alternative machines. The main decisions are: (a) selecting operation/machine pair; and (b) sequencing the jobs assigned to each machine. Since the problem is highly complicated, we suggest a practical priority scheduling approach in which the two decisions are done at the same time using a combination of operation/machine selection and job sequencing rules. The performance measures used are minimising makespan, total flow time, mean tardiness, the number of tardy jobs, and the maximum tardiness. To compare the performances of various rule combinations, simulation experiments were done on the data for hybrid systems with an advanced reconfigurable manufacturing system and a conventional legacy system, and the results are reported.

Assessment of Possible Survey in Parallel Scheduling Using Non-Convex DEA

An attempt has been investigated to show how applying DEA selected the most efficient among feasible solutions in parallel processing scheduling. One of the most important things between possible solutions is to determine the most efficient one. It will happen in NP-Complete problems when we are compelled to make heuristic algorithms to solve the problem. Maybe the heuristic proposed algorithm gives us some possible solutions. To reach the goal we are supposed to apply one decision maker. DEA model based on linear programming is widely used to make decision. This study will illustrate how DEA works on parallel scheduling problem and select the most efficient solution within which the objective is to minimize completion time and to minimize the number of tardy jobs.

Heuristics for scheduling a two-stage hybrid flow shop with parallel batching machines: application at a hospital sterilisation plant

The model of a two-stage hybrid (or flexible) flow shop, with sequence-independent uniform setup times, parallel batching machines and parallel batches has been analysed with the purpose of reducing the number of tardy jobs and the makespan in a sterilisation plant. Jobs are processed in parallel batches by multiple identical parallel machines. Manual operations preceding each of the two stages have been dealt with as machine setup with standardised times and are sequence-independent. A mixed-integer model is proposed. Two heuristics have been tested on real benchmark data from an existing sterilisation plant: constrained size of parallel batches and fixed time slots. Computation experiments performed on combinations of machines and operator numbers suggest balancing the two stages by assigning operators proportionally to the setup time requirements.