Earliness Penalties Research Articles

Dynamic job shop scheduling with fixed interval deliveries

Most classical scheduling models assume a job is delivered to a customer immediately after job processing is complete. In numerous practical situations, however, multiple delivery dates exist, and the time interval between any two consecutive delivery dates is constant. A finished job is supplied to a customer by truck on the earliest date in a series of fixed delivery dates, typically at or after processing is complete. This fixed delivery strategy results in substantial cost savings when delivery is expensive or complex. The goal of this study is to minimize the sum of due-date cost and earliness penalty associated with jobs scheduling in a dynamic job shop environment. The due date cost for a job is incurred for time spent delivering a job to a customer. Earliness penalty is incurred if a job is completed before the delivery date. This study identifies three dispatching rules, and proposes nine new rules by explicitly considering different due date costs per time unit and the earliness penalty per time unit of a job. The proposed rules are simple and easily implemented without preliminary runs for parameter estimation. Simulation results show that the proposed dispatching rules are significantly superior to their counterparts.

An Iterated Local Search Algorithm for the Lot-Streaming Flow Shop Scheduling Problem

The lot-streaming flow shop scheduling problem plays an important role in modern industry. This paper addresses this problem with the objective of minimizing the total weighted earliness and tardiness penalties and then proposes a simple but effective iterated local search (ILS) algorithm. In the proposed ILS algorithm, an adapted Nawaz–Enscore–Ham (NEH) heuristic is used to generate an initial solution. A local search procedure based on the insertion neighborhood is employed to perform local exploitation. A simulated-annealing-typed acceptance criterion is utilized to determine the start point for next iteration. Extensive experiments are conducted to compare the proposed ILS algorithm with some existing algorithms. The computational results and comparisons demonstrate the effectiveness of the proposed ILS algorithm.

Integrated scheduling and self-reconfiguration for assembly job shop in knowledgeable manufacturing

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling.

Évaluation de la situation épidémiologique de l’infection par le virus de l’hépatite B en Tunisie avant l’introduction de la vaccination

Severe aortic stenosis (AS) results in considerable morbidity and mortality without aortic valve replacement and is expected to increase in prevalence with the aging population. Because AS primarily affects the elderly, many patients with comorbidities are poor candidates for surgical aortic valve replacement (SAVR) and may not be referred. Transcatheter aortic valve replacement (TAVR) has emerged as transformative technology for the management of AS over the past decade. Randomized trials have established the safety and efficacy of TAVR with improved mortality and quality of life compared with medical therapy in inoperable patients, while demonstrating noninferiority and even superiority to SAVR among high-risk operative candidates. However, early studies demonstrated an early penalty of stroke and vascular complications with TAVR as well as increased paravalvular leak as compared with SAVR. Two device platforms have been evaluated and approved for use in the United States: the Edwards SAPIEN and the Medtronic CoreValve. Early studies also suggest cost-effectiveness for TAVR. Ongoing studies are evaluating new iterations of the aforementioned TAVR devices, novel device designs, and applications of TAVR in expanded populations of patients including those with lower risk profiles as well as those with comorbidities that were excluded from early clinical trials. Future improvements in TAVR technology will likely reduce periprocedural and long-term complications. Further studies are needed to confirm device durability over long-term follow-up and explore the applicability of TAVR to broader AS patient populations.

Chemical Reaction Optimization for Earliness-Tardiness Scheduling Problem

This paper studies a job shop scheduling problem on a single machine environment with an objective of minimizing the total weighed earliness and tardiness penalties. Jobs have distinct release dates and distinct due dates. A sequence-dependent setup times exists between two consecutive jobs. Jobs are punished if they are finished either before due dates or after due dates. A chemical reaction optimization method is proposed to solve the problem. An improved optimal timing is applied to fix the start time of each job under given sequence. Experimental results show that the proposed algorithm can solve this problem effectively.

Variable Neighbourhood Search and Mathematical Programming for Just-in-Time Job-Shop Scheduling Problem

This paper presents a combination of variable neighbourhood search and mathematical programming to minimize the sum of earliness and tardiness penalty costs of all operations for just-in-time job-shop scheduling problem (JITJSSP). Unlike classical E/T scheduling problem with each job having its earliness or tardiness penalty cost, each operation in this paper has its earliness and tardiness penalties, which are paid if the operation is completed before or after its due date. Our hybrid algorithm combines (i) a variable neighbourhood search procedure to explore the huge feasible solution spaces efficiently by alternating theswapandinsertionneighbourhood structures and (ii) a mathematical programming model to optimize the completion times of the operations for a given solution in each iteration procedure. Additionally, a threshold accepting mechanism is proposed to diversify the local search of variable neighbourhood search. Computational results on the 72 benchmark instances show that our algorithm can obtain the best known solution for 40 problems, and the best known solutions for 33 problems are updated.

Lot sizing and scheduling problem for production-delivery system with job volume and due date considerations to minimise the total cost while guaranteeing a certain customer service level

This paper considers a lot sizing and scheduling problem where jobs are processed on a batching machine, and then delivered to a customer by a capacitated transporter. Each job is associated with a due date and a volume. In order to guarantee customer service level, each job has to be delivered to customer before or on its due date. It is assumed that the job which is delivered to customer before its due date will occur an earliness penalty. The objective is to minimise the total logistics cost under two kinds of due-date conditions. We formulate the problem as a non-linear model, then develop a Tabu algorithm. To verify performance of this algorithm, we establish a dominance-related exact algorithm for the small-size problems and a lower bound for the large-size problems. Numerical experiments show that the proposed Tabu algorithm performs efficiently in terms of both solution quality and running time.

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.

An Adaptive Assembly Scheduling Approach in Knowledgeable Manufacturing

To address the uncertainty of production environment in aircraft engine assembly, an adaptive optimization scheduling algorithm is designed for an aircraft engine assembly line in knowledgeable manufacturing. A Q-learning adaptive scheduling model of aircraft engine assembly is built on the objective function of minimizing earliness penalty. Simulation experiments indicate that the proposed algorithm outperforms other scheduling rules much. Especially, better results are generally achieved with the increase in number of engines to show good adaptive performance.

Minimising earliness and tardiness penalties in single machine scheduling against common due date using imperialist competitive algorithm

In this paper a novel evolutionary-based approach is utilised for efficiently solving the NP-hard problem of scheduling numerous common-due-date jobs on a single machine. Minimising the sum of earliness and tardiness penalties for all jobs is considered as the target function. The performance of the proposed approach is examined through a computational comparative study with 280 benchmark problems with up to 1000 jobs where the numerical results indicate that it can produce ‘better’ solutions in less computational time when compared to benchmark results and the methods available in the literature, namely genetic algorithm (GA), Tabu search (TS) and differential evolution (DE).

Optimizing the Earliness and Tardiness Penalties in the Single-machine Scheduling Problems with Focus on the Just in Time

The single-machine scheduling problem is the basis of scheduling theories. Because some of the production activities are completed earlier or later than standard time, they create several earliness and tardiness penalties. On the other hand, it is necessary to consider just in time philosophy and its importance in the scheduling problems. Therefore, this study seeks to develop a goal function for optimizing single-machine scheduling problems that combines both earliness and tardiness penalties. This study also is determined to minimize the earliness and tardiness penalties in this area. The restricted due date also has multiple effects on the optimum time. This is why that the present study also was aimed to examine the singlemachine scheduling problems with focus on the earliness and tardiness penalties that considering restricted due date simultaneously. The proposed model of this study is an efficient method for understanding the importance of just in time in the scheduling problems.

Optimal Common Due-Window Assignment with Linear Deteriorating and Resource-Dependent Processing Times under a Deteriorating Maintenance Activitiy

This paper studies single-machine scheduling problems with a due-window assignment under a deteriorating maintenance and time-and-resource-dependent processing times. Jobs completed within the due-window incur no penalties, other jobs incur either earliness or tardiness penalties. The maintenance activity can be scheduled immediately after any of the completed jobs. We assume that once the maintenance activity has been completed, the machine efficiency will be improved and the machine maintenance duration depends on its starting time. The objective is to find the maintenance position, the size and location of the due-window, and the sequence of jobs and resource allocation scheme to minimize a cost function based on the window size and location and the earliness and tardiness of jobs and resource. We propose an algorithm to solve the problem.

On the scheduling with past-sequence-dependent setup times and learning effects on a single machine

This paper deals with a single-machine scheduling problem with setup time and learning effects. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are job-independent and past-sequence-dependent, and the learning effects are job-independent and position-dependent. The objective is to minimize the sum of earliness penalties subject to no tardy jobs. Wang, Wang, Gao, and Huang [Int J Adv Manuf Technol 48: 739–746, 2010] showed that an optimal sequence for this problem could be obtained by arranging jobs in non-increasing order of processing times. In this paper, we first demonstrate that this result is incorrect, and then introduce new exact solution strategies that polynomially solve problems whose earliness penalties are strictly increasing functions of job earliness. Polynomial time solutions are also presented for some special cases.

The morning commute problem with heterogeneous travellers: the case of continuously distributed parameters

We study the morning commute problem with a heterogeneous travelling population whose early/late arrival penalty parameters are continuously distributed. Following Arnott et al.'s (1988) [Schedule delay and departure time decisions with heterogeneous commuters, Transportation Research Record, 1197, 56–67] model, where the ratio of the value of early schedule delay (VESD) over the value of late schedule delay (VLSD) is assumed to be constant across the population, we first derive the user-optimal travel profiles and the corresponding total travel time (TTT) for a one-to-one network with a single route. We show that although every commuter is better off if the bottleneck capacity is enlarged, commuters with high values of early arrival penalty (EAP) benefit more than those with low values. In addition, the homogeneity assumption overestimates the queuing delay and thus the TTT. Then we extend our analysis to a network with two routes, a freeway and an arterial road (AR) connecting a single origin–destination (O–D) pair. In this case, we find that the travellers who weigh schedule delay more will first shift to the AR, prompted by an increase in total demand. However, the critical travel demand at which travellers start to use the AR remains the same if the common EAP for homogeneous users is equal to the expected value of EAP distribution for heterogeneous users. Interestingly, there exists a critical value of EAP parameter, such that all the travellers whose EAP is less than it choose the freeway, and those whose EAP is larger than it choose the AR. Sensitivity analysis on TTT is performed with respect to freeway capacity, AR capacity and free-flow travel time on the AR. The results indicate that enlarging freeway (AR) capacity will always reduce the TTT of the whole network and the TTT of the AR (freeway), and increase the demand share of the freeway (AR). We also show that every commuter is better off if either the freeway capacity or the AR capacity is enlarged. Finally, we provide numerical examples to demonstrate the considerable differences in flow patterns and network performances between a homogeneous and a heterogeneous population.

Single-Machine Scheduling with Due-Window Assignment and Rate-Modifying-Activities under a Deteriorating Maintenance

This paper studies single-machine scheduling problems with a due-window assignment and a rate-modifying activity under a deteriorating maintenance consideration simultaneously. Jobs completed within the due-window incur no penalties, other jobs incur either earliness or tardiness penalties. The maintenance activity can be scheduled immediately after any one of the completed jobs. We assume that once the maintenance activity has been completed, the machine efficiency will be improved and the machine maintenance duration depends on its starting time. The objective is to find the optimal maintenance position as well as the optimal size and location of the due-window, and the sequence of jobs to minimize a cost function based on the window size and window location and the earliness and tardiness of the jobs. We propose a polynomial time algorithm to solve the problem optimally.

A Particle Swarm Optimization Algorithm for Scheduling Against Restrictive Common Due Dates

Focusing on the just-in-time (JIT) operations management, earliness as well as, tardiness of jobs’ production and delivery should be discouraged. In accordance to this philosophy, scheduling problems involving earliness and tardiness penalties are very critical for the operations manager. In this paper, a new population heuristic based on the particle swarm optimization (PSO) technique is presented to solve the single machine early/tardy scheduling problem against a restrictive common due date. This type of scheduling sets costs depending on whether a job finished before (earliness), or after (tardiness) the specified due date. The objective is to minimize a summation of earliness and tardiness penalty costs, thus pushing the completion time of each job as close as possible to the due date. The problem is known to be NP-hard, and therefore large size instances cannot be addressed by traditional mathematical programming techniques. The performance of the proposed PSO heuristic is measured over benchmarks problems with up to 1000 jobs taken from the open literature, and found quite high and promising in respect to the quality of the solutions obtained. Particularly, PSO was found able to improve the 82% of the existing best known solutions of the examined benchmarks test problems.

Fast and meta-heuristics for common due-date assignment and scheduling on parallel machines

This study considers common due-date assignment and scheduling on parallel machines. The problem has three decision variables: assigning the common-due-date, allocating jobs to parallel machines, and sequencing the jobs assigned to each machine. The objective is to minimise the sum of due-date assignment, earliness and tardiness penalties. A mathematical programming model is presented, and then two types of heuristics are suggested after characterising the optimal solution properties. The two types of heuristics are: (a) a fast two-stage heuristic with obtaining an initial solution and improvement; and (b) two meta-heuristics, tabu search and simulated annealing, with new neighbourhood generation methods. Computational experiments were conducted on a number of test instances, and the results show that each of the heuristic types outperforms the existing one. In particular, the meta-heuristics suggested in this study are significantly better than the existing genetic algorithm.

A generalisation model of learning and deteriorating effects on a single-machine scheduling with past-sequence-dependent setup times

This article introduces a general single-machine setup times scheduling model with learning effect and deteriorating jobs simultaneously which is a generalisation of some existing models in the literature. The setup times are proportional to the length of the already processed jobs, i.e. the setup times are past-sequence-dependent (p-s-d). By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The article shows that the problems to minimise the makespan, sum of the kth power of completion times, total lateness and sum of earliness penalties (with common due date) are polynomially solvable under the proposed model. It further shows that the problems to minimise total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties (with common due date) are polynomially solvable under certain conditions.

A hybrid imperialist competitive algorithm for single-machine scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we study single-machine scheduling problem when each job is considered with linear earliness and quadratic tardiness penalties with no machine idle time. Here the objective is to find the best sequence of jobs in the reasonable time. This model was studied in several researches, and some algorithms were proposed to solve it such as genetic algorithm. As the size of problem increased, such algorithms were not effective and efficient. Hence, we proposed the hybrid imperialist competitive algorithm. The proposed algorithm is based upon the imperialist competitive algorithm and genetic algorithm concepts. This algorithm was tested in problems with different sizes. The results denoted that the hybrid algorithm can solve different size of problem in reasonable time. This procedure showed its efficiency in medium- and large-sized problems as compared with other available methods.

Single-machine batch delivery scheduling with an assignable common due window

This paper addresses a batch delivery single-machine scheduling problem in which jobs have an assignable common due window. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find the optimal size and location of the window, the optimal dispatch date for each job, as well as an optimal job sequence to minimize a cost function based on earliness, tardiness, holding time, window location, window size, and batch delivery. We show that the problem can be optimally solved in O(n8) time by a dynamic programming algorithm under a reasonable assumption on the relationships among the cost parameters. A computational experiment is also conducted to evaluate the performance of the proposed algorithm. We also show that some special cases of the problem can be optimally solved by lower order algorithms.