Number Of Tardy Jobs Research Articles

Scheduling with deteriorating jobs and learning effects

This paper studies a single machine scheduling problem simultaneously with deteriorating jobs and learning effects. The objectives are to minimize the makespan and the number of tardy jobs, respectively. Two polynomial time algorithms are proposed to solve these problems optimally.

A Pareto-optimal solution procedure for the single-machine scheduling problem with release time and multiple performance measures

This study investigates a single-machine scheduling problem with release times. The objective is to minimize the summation of the weighted earliness and tardiness, subject to the number of tardy jobs. The given n jobs with different earliness and tardiness weights have different release times but the same due date. An algorithm is proposed to efficiently generate Pareto-optimal solutions for any possible number of tardy jobs. The accuracy and run time of our algorithm are discussed. In addition, the results show that the proposed algorithm can eliminate most nodes in the branching tree to efficiently find solutions.

Cross-docking centre operation optimization using simulation-based genetic algorithm

The operational improvement of cross-docking centres in the literature involves job scheduling, layout design and dock assignment. The mentioned research is mainly concerned with makespan, number of tardy jobs or travel distance. However, these measures may not fully represent the main advantages of cross-docking operations. Little has been done to optimize the major performance measures of a cross-docking centre, which substantiates the main advantages of cross-docking technology. In this paper, inventory holding cost, transportation cost and backorder penalty cost are aggregated into total cost and a solution framework has been developed by integrating simulation, genetic algorithm (GA) and smart computing budget allocation (SCBA) for a comprehensive total cost minimization problem. This problem has huge search space even for medium-sized problem scenarios. To address this difficulty, the framework employs simulation to estimate the total cost, GA to search for better design and SCBA to efficiently allocate the simulation budget. Numerical experiments show that the proposed framework operates effectively in cases of different problem scales.

Resource Allocation, Batching and Dispatching in a Stochastic Flexible Job Shop

The problem of resource allocation and scheduling is considered for a flexible job shop composed of several work centers with multiple identical machines. Each machine has its own setup time that depends on the current and the arriving batch types. The optimal number of machines at each center and the optimal batch size for each job type is to be determined for several dispatching rule. The objective of the study is to assist the scheduler in selecting the best dispatching rule with respect to a desired performance measure along with its corresponding batch size and optimum number of machines in each center. Several measures are considered including the average flow time, sum of earliness and tardiness, and the number of tardy jobs. The simulation package ProModel is used to build the model and its optimization tool called SimRunner is used for optimization.

Integrated Production and Distribution Scheduling in Supply Chain Management

This paper studies multiple suppliers’ supply chain scheduling problem. A precise mathematical scheduling model is first built. Moreover, based on the optimal condition analysis, one problem related to the objectives of minimize the number of tardy jobs has been investigated. Furthermore, the corresponding dynamic programming method has been presented. These algorithm has been proved to be efficient by showing its pseudo-polynomial complexity.

Single machine scheduling problems with financial resource constraints: Some complexity results and properties

We consider single machine scheduling problems with a non-renewable resource. These types of problems have not been intensively investigated in the literature so far. For several problems of these types with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), we present some complexity results. Particular attention is given to the problem of minimizing total tardiness. In addition, for the so-called budget scheduling problem with minimizing the makespan, we present some properties of feasible schedules.

Using a Hybrid Genetic Algorithm to Minimize the Number of Tardy Jobs in the Flow Shop

Numerous real-world problems relating to flow shops scheduling are complex. The main problem is that the solution space is very large and therefore the set of feasible solutions cannot be enumerated one by one. Current approaches to solve these problems are metaheuristics techniques, which fall in two categories: population-based search and trajectory-based search. Because of their complexity, recent research has turned to genetic algorithms to address such problems. In this paper we present an effective hybrid approach based on genetic algorithm (GA) for minimizing the number of tardy jobs in a flow shop consisting of m machines. Jobs with processing times and due dates randomly arrive to the system. We assume that job arrival or release dates are not known in advance. The objective is to minimize the number of tardy jobs. Although genetic algorithms have been proven to facilitate the entire space search, they lack in fine-tuning capability for obtaining the global optimum. Therefore the proposed approach incorporates a fitness functions and a population trained by a local improvement search based on tabu search with a candidate list strategy into GA for the problem which belongs to NP-hard class. Experimentation results show that the number of cells and the crossover strategy adapted affect the number of tardy jobs found. The results also indicate that hybrid genetic algorithm approach improves the solution quality drastically.

Effects of bed configurations at a hospital emergency department

This paper analysed and optimised the patient flow of a public hospital emergency department (ED). The simulation model enabled a detailed analysis of variables in the system without the chaos and potential risk that physical changes to the ED would have resulted in. The main performance indicator used throughout the study was compliance with national waiting time standards. The performance of the ED had substantial increases with balancing the utilisation of physicians, treatment areas and critical bed levels. In addition, an optimisation model was built to optimise various aspects of the multi-criteria objectives with a focus on minimising tardiness, number of tardy jobs, weighted percentage tardy jobs and waiting time in the queue. Positive results included an increase in waiting time performance with adjustments to shift allocations and important evaluations of current policies and resources. Performances were increased significantly by the solutions of the optimisation model, particularly when there was a small relaxation of the number of resuscitation beds in exchange for a combination of acute and subacute treatment areas, still ensuring space and cost constraints are met.

Variable neighbourhood search for minimising tardiness objectives on flow shop with batch processing machines

This paper presents the scheduling problem on flow shop with many batch processing machines (BPM) to minimise total tardiness, maximum tardiness and number of tardy jobs, respectively. We propose an efficient variable neighbourhood search (VNS) for the problem, in which job permutation is the only optimisation object and the solutions of batch formation and batch scheduling can be directly obtained by using the permutation. To obtain the promising results, an initial solution of VNS is first produced and then one insertion operation and two swap operations are applied to improve the solution. The proposed VNS is finally tested and the computational results show its good performance on many-BPM flow shop scheduling.

A nondominated ranked genetic algorithm for bi-objective single machine preemptive scheduling in just-in-time environment

Motivated by just-in-time (JIT) manufacturing, we study the bi-objective scheduling problem of minimizing the total weighted earliness and the number of tardy jobs on a single machine, in which machine idle time and preemption are allowed. The problem is known to be NP-hard. In this paper, we propose a new mathematical model, with nonlinear terms and integer variables which cannot be solved efficiently for medium- and large-sized problems. A method combining the new ranked-based roulette wheel selection algorithm with Pareto-based population ranking algorithm, named nondominated ranking genetic algorithm (NRGA), has been presented to find nondominated solutions in a reasonable time. Various operators and parameters of the proposed algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. A number of numerical examples are solved to demonstrate the effectiveness of the proposed approach. The solutions obtained via NRGA are compared against solutions obtained via e-constraint method in small-sized problems. Experimental results show that the proposed NRGA is competitive in terms of the quality and diversity of solutions in medium- and large-sized problems.

Truncation and composition of schedules: A good strategy for solving bicriteria scheduling problems

This paper consider the bicriteria scheduling problem of simultaneously minimizing the total completion time (Ctot) and number of tardy jobs (NT) with release dates on a single machine. A heuristic (called HR7) was proposed for solving this problem and was compared with a heuristic (called HR6) selected from the literature and a branch and bound (BB) method. The proposed heuristic makes use of the idea of truncation and composition of schedules. The three solution methods were tested on 1100 randomly generated problems ranging from 3 to 500 jobs. Performance evaluation, based on both effectiveness and efficiency of the solution methods, were carried out. Experimental results are provided.

Minimizing maximum earliness and number of tardy jobs in the single machine scheduling problem

This paper studies the problem of simultaneous minimization of the two criteria of maximum earliness and number of tardy jobs on a single machine. The goal is to generate the set of efficient sequences with respect to the two criteria. A heuristic algorithm named as H1 is developed for this problem and its efficiency is evaluated against a heuristic algorithm reported in the literature. The two algorithms are executed and applied to a set of instance problems. The computational results for instances with problem sizes of up to 150 jobs show that the H1 heuristic works far more efficiently than the competing heuristic. An exact procedure based on the branch-and-bound approach is also presented for the problem, in which the H1 heuristic is used as the upper bound. A lower bound and some dominance rules proposed in this paper cause the branch-and-bound algorithm to become even more efficient. Computational results of instances with sizes of up to 35 jobs prove the efficiency of the-branch-and bound approach in the optimal solution of the instances.

Minimizing the number of tardy jobs and maximum earliness in the single machine scheduling using an artificial immune system

Nowadays, the importance of timely delivery, which is based on the just in time concept, has caused a number of criteria related to scheduling problems to be taken into consideration. One of the most important of these criteria is maximum earliness to control final costs and number of tardy jobs in an attempt to win customer satisfaction. In this paper, the strongly NP-hard problem of the single machine scheduling with two criteria, i.e., maximum earliness and number of tardy jobs, has been considered. For this purpose, artificial immune system which is inspired by the immunology theory in biology has been used. This algorithm is applied to different instances of small to large sizes and the obtained results is compared with those obtained from a heuristic method and a genetic algorithm reported in the literature. Computational results show a significant preference for the algorithm proposed in this paper.

Algorithms for some maximization scheduling problems on a single machine

In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1?max-ΣT j and for the problem of maximizing the number of tardy jobs 1?maxΣU j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1?max-ΣT j is polynomially solvable. For several special cases of problem 1?maxΣT j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.

Scheduling on parallel machines considering job-machine dependency constraints

Abstract We consider a multi-purpose machine scheduling problem, where jobs should be executed in some machine belonging to a given subset of the set of machines. The problem is P M P M | r j ; p j = 1 | ∑ w j U j , with n independent unit-time jobs, time window constraints, m identical parallel multi-purpose machines, and the minimization of the total weighted number of tardy jobs. The best previous complexity for this problem is O ( n 2 m ( n + log m ) ) , employing network flow techniques. We develop an algorithm that uses basic concepts of computer science to handle more efficiently successive nesting of on-time jobs, with O ( n 3 ) overall time complexity.

Scheduling a deteriorating maintenance activity on a single machine

We study a problem of scheduling a maintenance activity on a single machine. Following several recent papers, the maintenance is assumed to be deteriorating, that is, delaying the maintenance increases the time required to perform it. The following objective functions are considered: makespan, flowtime, maximum lateness, total earliness, tardiness and due-date cost, and number of tardy jobs. We introduce polynomial time solutions for all these problems.

Single-machine scheduling problems with past-sequence-dependent delivery times

We consider single-machine scheduling problems with past-sequence-dependent (p-s-d) job delivery times. The p-s-d delivery time is needed to remove any waiting time-induced adverse effects on the job's condition (prior to delivering the job to the customer) and it is therefore proportional to the job's waiting time. We show that single-machine scheduling problems with p-s-d delivery times and with either completion time-related criteria (such as the makespan or the total job completion time) or due date related criteria (such as the maximum lateness or the number of tardy jobs) can be solved by simple polynomial-time algorithms.

Minimum weighted number of tardy jobs on an m-machine flow-shop with a critical machine

Abstract We study a flow-shop problem, where each of the jobs is limited to no more than two operations. One of these operations is common for all the jobs, and is performed on the same (”critical”) machine. Reflecting many applications, jobs are assumed to be processed in blocks on the critical machine. All the jobs share a common due-date, and the objective is minimum weighted number of tardy jobs. We prove that the problem is NP-hard. Then we formulate the problem as an integer program, and introduce a pseudo-polynomial dynamic programming algorithm, proving that the problem is NP-hard in the ordinary sense. We also propose an efficient heuristic, which is shown numerically to produce very close-to-optimal schedules. Finally, we show that the special case of identical weights is polynomially solvable.

Scheduling time-dependent jobs under mixed deterioration

We consider a new model of time-dependent scheduling. A set of deteriorating jobs has to be processed on a single machine which is available starting from a non-zero time. The processing times of some jobs from this set are constant, while other ones are either proportional or linear functions of the job starting times. The applied criteria of schedule optimality include the maximum completion time, the total completion time, the total weighted completion time, the maximum lateness and the number of tardy jobs. We delineate a sharp boundary between computationally easy and difficult problems, showing polynomially solvable and NP -hard cases.

A dispatching algorithm for parallel machines with rework processes

This paper presents a parallel machine scheduling problem with rework probabilities, due-dates and sequence-dependent setup times. It is assumed that rework probability for each job on a machine can be given through historical data acquisition. Since the problem is NP-hard in the strong sense, a heuristic algorithm is presented, which finds good solutions. The dispatching algorithm named MRPD (minimum rework probability with due-dates) is proposed in this paper focusing on the rework processes. The performance of MRPD is measured by the six diagnostic indicators: total tardiness, maximum lateness, mean flow-time, mean lateness, the number of reworks and the number of tardy jobs. A large number of test problems are randomly generated to evaluate the performance of the proposed algorithm. Computational results show that the proposed algorithm is significantly superior to existing dispatching algorithms for the test problems.