Number Of Tardy Jobs Research Articles

Single Machine Scheduling Model with Total Tardiness Problem

Objectives: In this paper, Five Dispatching Rules and a Branch & Bound algorithm is introduced for Single Machine Total Tardiness Scheduling Problem (SMTTSP) to minimize the total (average) tardiness and number of tardy jobs. Methods/Statistical Analysis: We proposed five dispatching (priority) rules as Shortest Processing Time, Earliest Due Dates, Longest Processing Time, Minimum Slack Time and First Come First Serve for SMTTSP and compared the performance of all the proposed priority rules. Furthermore, a numerical illustrations is also provided to select the best dispatched rule of SMTTSP. Next, we developed a Branch & Bound Algorithm for SMTTSP using best selected dispatching rule. We also developed Branch Tree to understand the Lower bound process of the B& B Algorithm. Findings: The main aim to proposed these dispatching rules and a Branch and Bound Algorithm is to obtain the optimal sequence to optimize the total (average) tardiness and number of total tardy jobs. The comparative analysis of the dispatching rules shows that EDD rule is better than other dispatching rules for minimization of total tardy jobs and tardiness of the jobs while SPT rule is better for minimization of make span. But Dispatching rules do not have the guarantee to give an optimal solution. So in this study, an exact algorithm (Branch & Bound) was developed with EDD rule for finding the optimal solution for SMTTSP. The comparative study between dispatching rules and an exact (B&B) algorithm is being justified by numerical illustrations and we found that the EDD rule and B&B Algorithm give the same results. Hence it was concluded that EDD rule works as an Exact algorithm and gives the optimal solution for SMTTSP. Application/Improvements: The computational results of the proposed (B&B) algorithm and Dispatching rules show that our methodology is more useful than other optimal approach for SMTTSP and it provides an important tool for decision makers.

Multi-agent scheduling on a single machine with a fixed number of competing agents to minimize the weighted sum of number of tardy jobs and makespans

We study the multi-agent scheduling on a single machine with a fixed number of competing agents, in which, the objective function of each agent is either the number of tardy jobs or the makespan, and the goal of the problem is to minimize the weighted sum of agents’ objective functions. In the literature, the computational complexity of this problem was posed as open. By using enumerating, dynamic programming, and schedule-configuration, we show in this paper that the problem is solvable in polynomial time.

Bi-criterion single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times

This paper addresses single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times. Due-window assignment with common flow allowances means that each job has a job-dependent due window, the start time and finish time of which are equal to its actual processing time plus individual job-independent parameters shared by all the jobs, respectively. The processing time of each job can be controlled by extra resource allocation as a linear function of the amount of a common continuously divisible resource allocated to the job. Two criteria are considered, where one criterion is an integrated cost consisting of job earliness, weighted number of tardy jobs, and due-window assignment cost, while the other criterion is the resource consumption cost. Four different models are considered for treating the two criteria. It is shown that the problem under the model where the two criteria are integrated into a single criterion is polynomially solvable, while the problems under the other three models are all NP-hard and an optimal solution procedure is developed for them. Two polynomially solvable cases are also identified and investigated. Finally, numerical studies with randomly generated instances are conducted to assess the performance of the proposed algorithms.

Minimizing the number of tardy jobs in two-machine settings with common due date

We consider two-machine scheduling problems with job selection. We analyze first the two-machine open shop problem and provide a best possible linear time algorithm. Then, a best possible linear time algorithm is derived for the job selection problem on two unrelated parallel machines. We also show that an exact approach can be derived for both problems with complexity $$O(p(n) \times \sqrt{2}^n)$$O(p(n)×2n), p being a polynomial function of n.

A note on efficient sequences with respect to total flow time and number of tardy jobs

AbstractFor the single‐machine scheduling problem with the objective of simultaneously minimizing total flow time and number of tardy jobs, a lower bound on the number of efficient sequences is known. However, the proof thereof, which makes use of a modified version of Smith's algorithm, is unduly lengthy and sophisticated. Adopting a totally new point of view, we present in this short article a much simpler proof based on the naive idea of pairwise interchange. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 346–348, 2016

Single machine SLK/DIF due window assignment problem with job-dependent linear deterioration effects

We consider single machine scheduling problems with deteriorating jobs and SLK/DIF due window assignment, where the deteriorating rates of jobs are assumed to be job-dependent. We consider two different objectives under SLK and DIF due window assignment, respectively. The first objective is to minimise total costs of earliness, tardiness, due window location and due window size, while the second objective is to minimise a cost function that includes number of early jobs, number of tardy jobs and the costs for due window location and due window size. We study the optimality properties for all problems and develop algorithms for solving these problems in polynomial time.

A Genetic Algorithm To Minimize Makespan and Number of Tardy Jobs In Parallel Machine Scheduling Problems

This paper presents a genetic algorithm solution for parallel machine scheduling problems with a real factory case. Various genetic components and operators were examined to design a genetic algorithm for a parallel machine scheduling problem with an objective of minimizing makespan and the number of tardy jobs. A production schedule was optimized using a genetic algorithm and results were compared. The experimental results demonstrated that a genetic algorithm encoding method performed successfully to achieve a solution for parallel machine problems.

An fptas for the weighted number of tardy jobs minimization on a single machine with deteriorating jobs

We consider a single machine scheduling problem in which the processing time of a job is a nondecreasing function of its starting time. The jobs have a common due date. The objective is to minimize the weighted number of tardy jobs. The problem is NP-hard. We present a pseudo-polynomial dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS).

Two-stage flexible flow shop scheduling subject to fixed job sequences

This paper investigates the scheduling problem in a two-stage flexible flow shop, which consists of m stage-1 parallel dedicated machines and a stage-2 bottleneck machine, subject to the condition that nl jobs per type l∈{1, …, m} are processed in a fixed sequence. Four regular performance metrics, including the total completion time, the maximum lateness, the total tardiness, and the number of tardy jobs, are considered. For each considered objective function, we aim to determine an optimal interleaving processing sequence of all jobs coupled with their starting times on the stage-2 bottleneck machine. The problem under study is proved to be strongly NP-hard. An O(m2Πl=1mnl2) dynamic programming algorithm coupled with numerical experiments is presented.

Minimizing the number of tardy jobs on a two-stage assembly flowshop

The objective of minimizing the number of tardy jobs is important as it is directly related to the percentage of on-time shipments, which is often used to rate managers’ performance in many manufacturing environments. To the best of our knowledge, the assembly flowshop scheduling problem with this objective has not been addressed so far, and thus is addressed in this paper. Given that the problem is NP-hard, different heuristics are proposed for the problem in this paper. The proposed heuristics are genetic algorithm (GA), improved genetic algorithm (IGA), simulated annealing algorithm with three different neighborhood structures (SA-1, SA-2, SA-3), Dhouib et al.’s simulated annealing algorithm (DSA), and an improved cloud theory-based simulated annealing algorithm (CSA). The heuristics are evaluated based on extensive computational experiments and all the heuristics were run for the same computational time for a fair comparison. The experiments reveal that the overall average errors of DSA, GA, IGA, CSA, SA-1, SA-2, SA-3 were 20.53, 13.49, 11.64, 3.27, 2.81, 1.92, and 0.56, respectively. Therefore, the proposed heuristic of SA-3 reduces the error of DSA, GA, IGA, CSA, SA-1, SA-2 by about 97, 96, 95, 83, 80, and 71%, respectively. All the results are statistically confirmed.

Group scheduling in a cellular manufacturing shop to minimise total tardiness and nT: a comparative genetic algorithm and mathematical modelling approach

In this paper, family and job scheduling in a cellular manufacturing shop is addressed where jobs have individual due dates. The objectives are to minimise total tardiness and the number of tardy jobs. Family splitting among cells is allowed but job splitting is not. Two optimisation methods are employed in order to solve this problem, namely mathematical modelling (MM) and genetic algorithm (GA). The results showed that GA found the optimal solution for most of the problems with high frequency. Furthermore, the proposed GA is efficient compared to the MM especially for larger problems in terms of execution times. Other critical aspects of the problem such as family preemption only, impact of family splitting on common due date scenarios and dual objective scenarios are also solved. In short, the proposed comparative approach provides critical insights for the group scheduling problem in a cellular manufacturing shop with distinctive cases.

Scheduling comparison between multi-objective mathematical models and genetic algorithms approach in the textile industry

This paper discusses mixed integer mathematical models and genetic algorithms (GAs) approach for finding an optimal schedule of the bottleneck machine for a company in the textile industry. Single-objective and multi-objective mathematical models and GA are used to obtain an optimal solution to minimise the maximum tardiness (Tmax). The comparison is made between mathematical models and GA according to the primary and secondary performance measures. Primary performance measure is Tmax, while secondary performance measure is number of tardy jobs (nt) and total tardiness (TT) values. The experimentation is performed for small and large size problems. All jobs have five different instances except for 150-job and 200-job problems. Due to memory and time limitations, only one sample could be solved for 150-job and 200-job problem. The experimental results indicated that, most of the time GA finds an optimal solution and proposes alternative schedules for both single-objective and multi-objective mathematical models.

Minimizing the weighted number of tardy jobs on multiple machines: A review

We provide an overview of the history, the methods and the people who researched on minimizing the (weighted) number of tardy jobs as a performance measure. The review presents cases on multiple machines: parallel machines (including the identical, uniform and unrelated machines, flow shop, job shop and the open shop). The literature is divided into various sections for proper categorization. This includes setup time, preemption, batching, on-line and off-line scheduling, and other classifications. The complexity status of the various classifications is enumerated with its results and methods. Possible extension for future work is also highlighted.

Multi-criteria M-machine SDST flow shop scheduling using modified heuristic genetic algorithm

The multi-criteria flow shop scheduling problem with sequence dependent setup times (SDST) is one of the most difficult class of scheduling problems. Efficient supervision of heuristics with SDST is one of the significant features to enhance the performance of manufacturing system. In this work, we have formulated multi-criteria decision-making flow shop scheduling problem. It consists of weighted sum of total weighted squared tardiness, makespan, total weighted squared earliness and number of tardy jobs. It is a very effective decision-making for scheduling jobs in modern manufacturing environment. In the present work, three efficient special heuristics based hybrid genetic algorithms (i.e., SHGA1, SHGA2, and SHGA3) are proposed for multi-criteria SDST. Experiments are conducted on the benchmark problems (Taillard, 1993). The performance of three SHGAs are tested, analysed and compared with the help of a defined performance index, known as relative percentage deviation (RPD). The maximum size of the problem is limited to 100 jobs and ten machines. From the results and analysis, the performance of SHGA3 found to be the best.

Assessing the Performance of Dispatching Policies for Hybrid Flowshop Manufacturing Systems

Abstract: This paper considers the problem of scheduling a given set of jobs or tasks in a hybrid flowshop system. Since this problem is known in the literature to be NP-hard, most of academic works has been centered on the analysis of meta-heuristics and hybridized procedures. However, intelligent manufacturing systems in actual industrial practices mostly prefer the use of simple heuristic algorithms, such as dispatching rules. The objective of this paper is to experimentally test the performance of well-known dispatching rules such as FCFS (First Come First Serve), EDD (Earliest Due Date), SLACK, and SRMWK (Slack per Remaining Work). To the best of our knowledge, this is the first work that aimed at this assessment. Various objective functions are considered: makespan, total tardiness, and the number of tardy jobs. Computational experiments are carried out using datasets from the literature.

A hybrid algorithm for unrelated parallel machines scheduling

A B S T R A C T In this paper, a new hybrid algorithm based on multi-objective genetic algorithm (MOGA) using simulated annealing (SA) is proposed for scheduling unrelated parallel machines with sequence- dependent setup times, varying due dates, ready times and precedence relations among jobs. Our objective is to minimize makespan (Maximum completion time of all machines), number of tardy jobs, total tardiness and total earliness at the same time which can be more advantageous in real environment than considering each of objectives separately. For obtaining an optimal solution, hybrid algorithm based on MOGA and SA has been proposed in order to gain both good global and local search abilities. Simulation results and four well-known multi-objective performance metrics, indicate that the proposed hybrid algorithm outperforms the genetic algorithm (GA) and SA in terms of each objective and significantly in minimizing the total cost of the weighted function.

Min-Max Regret Version of the Linear Time–Cost Tradeoff Problem with Multiple Milestones and Completely Ordered Jobs

We consider a linear time–cost tradeoff problem with multiple milestones and uncertain processing times such that all jobs are completely ordered. The performance measure is expressed as the sum of total weighted number of tardy jobs and total crashing cost. The processing times uncertainty is described through two types of scenarios: discrete and interval scenarios. The objective is to minimize maximum deviation from optimality over all scenarios. For the discrete scenario case, we prove its NP-hardness, develop a pseudo-polynomial time approach, and present a polynomially solvable case. Finally, we show that the interval scenario case is also NP-hard.

Some due date determination scheduling problems with two agents on a single machine

This paper addresses some scheduling problems with two competing agents, called agents A and B, respectively, each of which has a set of independent nonpreemptive jobs to be scheduled for processing on a common machine. The due dates of jobs in each job set are considered as given parameters and must be assigned to individual jobs. Each agent wants to minimize a certain objective function that depends on the completion times and due dates of its jobs only. The goal is to find a feasible schedule and determine the due dates for all jobs of the two agents that minimizes the objective of agent A while keeping the objective of agent B below or at a fixed level Q. We consider nine problems arising from different criteria combinations for the two agents, depending on the criterion of each agent including the maximum lateness, total (weighted) tardiness, (weighted) number of tardy jobs, and total weighted tardiness and earliness, and state the complexity results for most of problems under consideration.

Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine

This paper deals with serial-batching scheduling problems with the effects of deterioration and learning, where time-dependent setup time is also considered. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on a single serial-batching machine. The actual job processing time is a function of its starting time and position. In addition, a setup time is required when a new batch is processed, and the setup time of the batches is time-dependent, i.e., it is a linear function of its starting time. Structural properties are derived for the problems of minimizing the makespan, the number of tardy jobs, and the maximum earliness. Then, three optimization algorithms are developed to solve them, respectively.

A Benders decomposition approach to the weighted number of tardy jobs scheduling problem on unrelated parallel machines with production costs

This paper addresses the problem of scheduling on-time jobs on unrelated parallel machines with machine production costs. The objective is to maximise the net profit which is the sum of the weights of on-time jobs and the cost of using the machines. This scheduling problem is very important and frequent in industrial settings. It is herein solved using an exact approach that applies Benders decomposition to obtain tight upper and lower bounds and uses the bounds within a branch and bound. The computational investigation shows the efficacy of the approach in solving large instances. Most importantly, the proposed approach provides a new venue for solving large-scale scheduling problems.