Tardiness Scheduling Research Articles

Minimizing tardiness scheduling measures with generalized due-dates and a maintenance activity

We study single machine scheduling problems with the following features: (i) Generalized due-dates are considered, i.e., the j-th due-date is assigned to the j-th completed job; (ii) A fixed maintenance activity during which no production is feasible is assumed; (iii) The objective functions are minimizing various tardiness measures. Specifically, four objective functions are considered: total tardiness, maximum tardiness, the number of tardy jobs and total late work. We introduce pseudo-polynomial solution algorithms for these NP-hard problems. Our numerical tests indicate that instances of medium size of all four problems are solved in very reasonable running times.

Dispatching Rules for Minimizing Deviation from JIT Schedule Using the Earliness -Tardiness Scheduling Problem with Due Windows Approach

In Earliness-Tardiness (E/T) scheduling approach, the Just-In-Time (JIT) schedule is a schedule with zero earliness and zero tardiness. However, this is an optimal schedule and even notional in some instances where tardiness and earliness are inevitable. However, minimizing the deviation at the upper region (tardiness) and the lower region (earliness) from the JIT schedule is a challenge. This work proposes solutions. Two proposed heuristics; TA1 and TA2 as well as some existing heuristics were explored to solve simulated problems ranging from 5≤n≤400 and the results obtained were benchmarked against the JIT schedule. The results obtained show that one of the heuristics, TA2 yielded JIT schedules for many problem sizes at the lower and upper deviation than other solution methods.

Three classes of Earliness-Tardiness (E/T) scheduling problems

In this work, the tolerance window defined as the variations of gains and penalty associated with the earliness component of the Linear Composite Objective Function (LCOF) of Earliness–Tardiness (E/T) scheduling problems were explored to establish three different classes of the problem. Two variants of E/T problems has been established in the literature; the problems with unknown due-date with the objective of optimizing jobs due-date and the problems with a known due-date for optimizing the E/T cost function. The latter variant considered in this work applies the concept of Just-In-Time (JIT) as the basis for optimizing the E/T cost function. However, while the ideal JIT schedule which tends towards zero LCOF is notional, the deviation is a function of the tolerance window. To the best of the researchers’ knowledge, there is a gap between the measures of the deviation called the delivery reliability or penalty cost function and the tolerance window. This work closes the gap. A numerical example was solved to demonstrate the three problem classes’ utility using the Early Due Date (EDD) algorithm as the hypothetical solution.

Structural properties and algorithms for earliness and tardiness scheduling against common due dates and windows: A review

This paper deals with earliness and tardiness scheduling around common due dates and windows. Related problems share a strong practical importance due to the endogenous and exogenous cost structures that occur within just-in-time production systems. Despite of their significance, there are no survey papers that holistically address the two main variants of the problems in terms of the common due date (window) approach. We contribute to the field with a survey that covers problems where the common due date (window) is a given constraint as well as the ones where it is a decision variable. First, a framework is provided to segment the current literature and then a planning protocol establishes the boundaries of the survey. Searches conducted in a well-known scientific database identified more than 200 related papers and 170 of them were classified and summarized in comprehensive tables according to the objective function of the problem, the due date or due window approach, and the complexity of the available algorithms. Moreover, we discuss 26 structural properties that characterize optimal solutions shared by problems from single, parallel, and flow-shop machine environments. Our analysis shows that a lot of effort was directed to combine machine scheduling with other phenomena such as resource allocation, learning, deterioration, and rate-modifying activities specially in the single machine context, however, research on job shops and open shops is still scarce.

Hybrid algorithms for the earliness–tardiness single-machine multiple orders per job scheduling problem with a common due date

In this paper, we study an earliness–tardiness scheduling problem for a single machine that is motivated by process conditions found in semiconductor wafer fabrication facilities (wafer fabs). In modern 300-mm wafer fabs, front opening unified pods (FOUPs) transfer wafers. The number of FOUPs is limited to avoid a congestion of the Automated Material Handling System. Several orders can be grouped in one FOUP. A nonrestrictive common due date for all the orders is assumed. Only orders that belong to the same family can be processed together in a single FOUP at the same time. We present a Mixed Integer Linear Programming (MILP) formulation for this problem. Moreover, we show that this scheduling problem is NP-hard. We propose several simple heuristics based on dispatching rules and assignment strategies from bin packing. Moreover, genetic algorithms are designed that assign the orders to the set of early and tardy orders, respectively. In addition, a random key genetic algorithm (RKGA) is described that proposes order sequences. The different algorithms are hybridized with job formation and sequencing heuristics. A more specialized algorithm that is based on the generalized assignment problem is presented for the special case of a single order family. Results of computational experiments based on randomly generated problem instances are presented. They demonstrate that the genetic algorithms perform well with respect to solution quality and computing time under a broad range of experimental conditions.

A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems

This work proposes a unified heuristic algorithm for a large class of earliness–tardiness (E–T) scheduling problems. We consider single/parallel machine E–T problems that may or may not consider some additional features such as idle time, setup times and release dates. In addition, we also consider those problems whose objective is to minimize either the total (average) weighted completion time or the total (average) weighted flow time, which arise as particular cases when the due dates of all jobs are either set to zero or to their associated release dates, respectively. The developed local search-based metaheuristic framework is quite simple, but at the same time relies on sophisticated procedures for efficiently performing local search according to the characteristics of the problem. We present efficient move evaluation approaches for some parallel machine problems that generalize the existing ones for single machine problems. The algorithm was tested in thousands of instances of several E–T problems and particular cases. The results obtained show that our unified heuristic is capable of producing high-quality solutions when compared to the best ones available in the literature that were obtained by specific methods. Moreover, we provide an extensive annotated bibliography on the problems related to those considered in this work, where we not only indicate the approach(es) used in each publication, but we also point out the characteristics of the problem(s) considered. Beyond that, we classify the existing methods in different categories so as to have a better idea of the popularity of each type of solution procedure.

A tutorial of integrating duality and branch and bound in earliness–tardiness scheduling with idle insertion time problems

We present a conceptual tutorial of the value of the dual representation to branching strategies of idle insertion time in a single-machine scheduling problem. We consider the problem where scheduling generally occurs in two phases: a sequence of activities is first determined, then idle time is inserted into the schedule to minimise the sum of early and tardy costs. Typically, the sequence of jobs is determined first using a heuristic method. The idle time insertion problem is solved via linear programming to establish starting and ending times of the activities. In this paper, we show how the dual of the idle time insertion problem can be used as a means of generating insights for earliness–tardiness sequencing algorithms. We provide an extended tutorial on a new way of branching based on dual information. We find that in our simple examples, the search space can be vastly reduced, improving the feasibility of branch-and-bound improvements to heuristic solutions. We suggest that the dual approach is a useful and intuitive way to improve scheduling solutions in short order.

Efficient local search limitation strategy for single machine total weighted tardiness scheduling with sequence-dependent setup times

This paper concerns the single machine total weighted tardiness scheduling with sequence-dependent setup times, usually referred as 1|sij|∑wjTj. In this NP-hard problem, each job has an associated processing time, due date and a weight. For each pair of jobs i and j, there may be a setup time before starting to process j in case this job is scheduled immediately after i. The objective is to determine a schedule that minimizes the total weighted tardiness, where the tardiness of a job is equal to its completion time minus its due date, in case the job is completely processed only after its due date, and is equal to zero otherwise. Due to its complexity, this problem is most commonly solved by heuristics. The aim of this work is to develop a simple yet effective limitation strategy that speeds up the local search procedure without a significant loss in the solution quality. Such strategy consists of a filtering mechanism that prevents unpromising moves to be evaluated. The proposed strategy has been embedded in a local search based metaheuristic from the literature and tested in classical benchmark instances. Computational experiments revealed that the limitation strategy enabled the metaheuristic to be extremely competitive when compared to other algorithms from the literature, since it allowed the use of a large number of neighborhood structures without a significant increase in the CPU time and, consequently, high quality solutions could be achieved in a matter of seconds. In addition, we analyzed the effectiveness of the proposed strategy in two other well-known metaheuristics. Further experiments were also carried out on benchmark instances of problem 1|sij|∑Tj.

Single Machine Scheduling Model for Total Weighted Tardiness

Objectives: We proposed two heuristic algorithms for Total Weighted Due Date Tardiness Scheduling (TWDDTS). The main aim of this paper is to optimize the weighted tardiness based criteria. Methods/Statistical Analysis: The first one heuristic algorithm for 'TWDDTS' is based on dispatching rule (EDD-Earliest Due Date) and the second one heuristic algorithm for Modified Total Weighted Due Date Tardiness Scheduling (MTWDDTS) is based on modified weighed due dates. We equated the effectiveness of both the proposed heuristic algorithms with the help of numerical illustrations. Findings: The main aim to propose these heuristic algorithms is to obtain the optimal solution of the problem related to weighted tardiness scheduling based criteria, when processing times of the jobs are also associated with probabilities. These heuristic algorithms are justified by numerical illustrations and comparative study of both the heuristic algorithms (with the help of numerical example) show that an improved heuristic algorithm for MTWDDTS is outperform and give better results than a TWDDTS heuristic algorithm. We also found that when we measure the mean completion time of jobs by both the heuristic algorithms then we observed that the MTWDDTS heuristic algorithm gives the best result as compared to a TWDDTS heuristic algorithm. So we find that MTWDDTS gives the best result for minimization the weighted tardiness based criteria as well as makespan. Application/Improvements: The proposed MTWDDTS algorithm is more useful than the EDD dispatching rule for weighted tardiness based scheduling problems. It is easy to understand and provide an important tool for decision makers.

Single-machine earliness–tardiness scheduling with two competing agents and idle time

ABSTRACTTwo-agent scheduling has gained a lot of research attention recently. Two competing agents who have their own objective functions have to perform their respective set of jobs on one or more shared machines. This study considers a two-agent single-machine earliness and tardiness scheduling problem where jobs have distinct due dates and unforced idleness in between any two consecutive jobs is allowed. The objective is to minimize the total earliness and tardiness of jobs from one agent given that the maximum earliness–tardiness of jobs from the other agent cannot exceed an upper bound. In other words, each job from the second agent has a hard due window, whereas each job from the first agent will incur a penalty if completed either before or after its due date. Two mathematical models of the problem are presented, and several necessary optimality conditions are derived. By exploiting the established dominance properties, heuristic algorithms are developed for the problem. Finally, computational experiments are conducted to assess the models and heuristic procedures.

A discrete artificial bee colony algorithm for single machine scheduling problems

This paper presents a discrete artificial bee colony algorithm for a single machine earliness–tardiness scheduling problem. The objective of single machine earliness–tardiness scheduling problems is to find a job sequence that minimises the total sum of earliness–tardiness penalties. Artificial bee colony (ABC) algorithm is a swarm-based meta-heuristic, which mimics the foraging behaviour of honey bee swarms. In this study, several modifications to the original ABC algorithm are proposed for adapting the algorithm to efficiently solve combinatorial optimisation problems like single machine scheduling. In proposed study, instead of using a single search operator to generate neighbour solutions, random selection from an operator pool is employed. Moreover, novel crossover operators are presented and employed with several parent sets with different characteristics to enhance both exploration and exploitation behaviour of the proposed algorithm. The performance of the presented meta-heuristic is evaluated on several benchmark problems in detail and compared with the state-of-the-art algorithms. Computational results indicate that the algorithm can produce better solutions in terms of solution quality, robustness and computational time when compared to other algorithms.

A hybrid cuckoo search metaheuristic algorithm for solving single machine total weighted tardiness scheduling problems with sequence dependent setup times

In this paper, we present a hybrid algorithm based on cuckoo search algorithm to solve the single machine total weighted tardiness (SMTWT) scheduling problems with sequence dependent setup times which have been proved to be strongly NP-hard. Three different dispatching rules are incorporated with the initial random solutions of the cuckoo search (CS) algorithm to improve the solution quality. Computational results show that the proposed algorithm is very competitive to many metaheuristic algorithms in the literature.

Ant colony systems for the single-machine total weighted earliness tardiness scheduling problem

Single-machine weighted earliness tardiness scheduling is a prevalent problem in just-in-time production environments. Yet, the case with distinct due dates is strongly NP-hard. Herein, it is approximately solved using ASV, an ant colony-based system with a reduced number of ants and of colonies and with daemon actions that explore the search space around the ants using a variable neighborhood search (VNS). The numerical investigation provides computational proof of the utility of the daemon actions. In addition, it infers that these latter can be applied either to the initial or to subsequent colonies. Furthermore, it highlights the importance of using ant colony optimization as the multiple restart engine of VNS. Finally, it shows that ASV obtains the optimum for most small-sized instances. It has a 0.2 % average deviation from the optimum over all benchmark instances.

Parallel Machine Scheduling with Fuzzy due Date Using Improved Simulated Annealing in Lean Production

Tardiness scheduling problems in the lean production has received extensive attention recently, and in most tardiness scheduling problems job due dates are regarded as invariable and known in advance. The study deals with fuzzy tardiness scheduling for parallel machines with fuzzy job due dates, where the objective is to minimize the average penalty cost of jobs tardiness. To describe the tardy degree of job clearly, a novel tardiness measure index is introduced based on the possibility and necessity measures in the study. And further, the mixed integer programming scheduling model of parallel machines is constructed for jobs tardiness. Since this problem is NP-hard, an improved simulated annealing is proposed and designed to solve the model. Finally, a numerical experiment is presented to illustrate the feasibility and effectiveness of the proposed method.

Single-machine due date assignment problem with deteriorating jobs and resource-dependent processing times

We study a single-machine earliness–tardiness scheduling problem with due date assignment, in which the processing time of a job is a function of its starting time and its resource allocation. We analyze the problem with two different processing time functions and three different due date assignment methods. The goal is to minimize an integrated objective function, which includes earliness, tardiness, due date assignment, and total resource consumption costs. For each combination of due date assignment method and processing time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations.

Type-2 fuzzy hybrid expert system for prediction of tardiness in scheduling of steel continuous casting process

This paper addresses an interval type-2 fuzzy (IT2F) hybrid expert system in order to predict the amount of tardiness where tardiness variables are represented by interval type-2 membership functions. For this purpose, IT2F disjunctive normal forms and fuzzy conjunctive normal forms are utilized in the inference engine. The main contribution of this paper is to present the IT2F hybrid expert system, which is the combination of the Mamdani and Sugeno methods. In order to predict the future amount of tardiness for continuous casting operation in a steel company in Canada, an autoregressive moving average model is used in the consequents of the rules. Parameters of the system are tuned by applying Adaptive-Network-Based Fuzzy Inference System. This method is compared with IT2F Takagi–Sugeno–Kang method in MATLAB, multiple-regression, and two other Type-1 fuzzy methods in literature. The results of computing the mean square error of these methods show that our proposed method has less error and high accuracy in comparison with other methods.

Tardiness Scheduling with Fuzzy Processing Time Using Tabu Search

In this paper, we address unrelated parallel machines scheduling problem with fuzzy processing times considering the minimization of the total tardiness cost. The tardiness credibility index of jobs is given to estimate the possibility of job’s tardiness, and a mixed integer programming model (MIP) is formulated for total tardiness cost based on fuzzy theory. Solving the MIP problem is NP-hard, thus a tabu search is designed to solve such a difficult problem. The results of computational test show the feasibility and effectiveness of the developed model and algorithm.

Parallel Machine Tardiness Scheduling Based on Improved Discrete Differential Evolution

To study the identical parallel machine scheduling problem with total tardiness objective, an improved discrete differential evolution DDE_VND is presented. The proposed algorithm hybridizes discrete differential evolution (DDE) with variable neighborhood descent (VND) to enhance its local search ability. Moreover, a constructive heuristic MDD is employed to generate an initial solution in the algorithm to accelerate the convergence of the algorithm. At last, the experimental results based on 50 benchmark instances validate the effectiveness of the DDE_VND algorithm

Parallel Machine Tardiness Scheduling Based on Improved Discrete Differential Evolution

To study the identical parallel machine scheduling problem with total tardiness objective, an improved discrete differential evolution DDE_VND is presented. The proposed algorithm hybridizes discrete differential evolution (DDE) with variable neighborhood descent (VND) to enhance its local search ability. Moreover, a constructive heuristic MDD is employed to generate an initial solution in the algorithm to accelerate the convergence of the algorithm. At last, the experimental results based on 50 benchmark instances validate the effectiveness of the DDE_VND algorithm

The single machine earliness and tardiness scheduling problem: lower bounds and a branch-and-bound algorithm

This paper addresses the single machine scheduling problem with a common due date aiming to minimize earliness and tardiness penalties. Due to its complexity, most of the previous studies in the literature deal with this problem using heuristics and metaheuristics approaches. With the intention of contributing to the study of this problem, a branch-and-bound algorithm is proposed. Lower bounds and pruning rules that exploit properties of the problem are introduced. The proposed approach is examined through a computational comparative study with 280 problems involving different due date scenarios. In addition, the values of optimal solutions for small problems from a known benchmark are provided. Mathematical subject classification: 90C11, 62P30, 90B35.