Dominance rules for single machine schedule with sequence dependent setup and due date

Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.     

Dominance rules for the parallel machine total weighted tardiness scheduling problem with release dates

We address the parallel machine total weighted tardiness scheduling problem with release dates. We describe dominance rules and filtering methods for this problem. Most of them are adaptations of dominance rules based on solution methods for the single-machine problem. We show how it is possible to deduce whether or not certain jobs can be processed by a particular machine in a particular context and we describe techniques that use this information to improve the dominance rules. On the basis of these techniques we describe an enumeration procedure and we provide experimental results to determine the effectiveness of the dominance rules.     

Improved heuristics for the early/tardy scheduling problem with no idle time

A dispatch rule and a greedy procedure are presented for the single machine earliness/tardiness scheduling problem with no idle time and compared with the best of the existing dispatch rules. Both dispatch rules use a lookahead parameter that had previously been set at a fixed value. We develop functions that map some instance statistics into appropriate values for that parameter. We also consider the use of dominance rules to improve the solutions obtained by the heuristics. The computational results show that the function-based versions of the heuristics outperform their fixed value counterparts and that the use of the dominance rules can indeed improve solution quality with little additional computational effort.     

单机序列相关Setup最小化最大拖期算法

研究了一个具有序列相关Setup带交货期的单机调度NP问题,优化目标是最小化最大拖期。提出了一个求解该问题的分枝定界枚举算法,其中包括确定问题上界和下界的方法,以及两条优势规则。计算实验证明了本文提出算法的有效性。     

Earliness–tardiness scheduling with setup considerations

The one-machine scheduling problem with sequence-dependent setup times and costs and earliness–tardiness penalties is addressed. A time-indexed formulation of the problem is presented as well as different relaxations that give lower bounds of the problem. Then, a branch-and-bound procedure based on one of these lower bounds is presented. The efficiency of this algorithm also relies on new dominance rules and on a heuristic to derive good feasible schedules. Computational tests are finally presented.     

The performance of load-selection rules and pickup-dispatching rules for multiple-load AGVs

In this paper, we address the problem of load selection and pickup-dispatching of multiple-load AGVs. Various load-selection rules and pickup-dispatching rules are proposed and studied. The objective of this study is twofold. We want to understand not only the performance of load-selection rules and pickup-dispatching rules in two performance criteria—throughput and tardiness, but also the effects that pickup-dispatching rules and load-selection rules have on each other’s performance. The simulation results indicate the load-selection rule with a selection criterion based on the destination similarity between loads has the best throughput and tardiness performance. Also, the pickup-dispatching rule that dispatches vehicles to the workstation with the greatest queue length has the best throughput and tardiness performance. The simulation results also indicate load-selection rules and pickup-dispatching rules affect each other’s performance. For example, a load-selection rule’s throughput and tardiness performance tends to improve if it is paired with a pickup-dispatching rule that shares similar logic. Furthermore, not all average-time-value-based pickup-dispatching rules are better (in throughput or tardiness) than their respective single-time-value-based pickup-dispatching rules under all load-selection rules.     

A new model for the preemptive earliness–tardiness scheduling problem

This paper addresses a new model for the one-machine earliness–tardiness scheduling problem where jobs can be interrupted. Some dominance rules and a lower bound are derived. A new timing algorithm is also presented and a local search algorithm based on this timing algorithm permits the computation of good feasible solutions. We experimentally compare our timing algorithm with a previously published timing algorithm. The tests show that the execution time of the new timing algorithm is significantly faster, especially for large instances. The values of the solutions are compared to the lower bound.     

Scheduling in dynamic assembly job-shops to minimize the sum of weighted earliness,weighted tardiness and weighted flowtime of jobs

In many manufacturing systems, jobs that are completed early are held as finished-goods inventory until their due-dates, and hence we incur earliness costs. Similarly, jobs that are completed after their due-dates incur penalty. The objective in such situations would, therefore, be to meet the due-dates of the respective jobs as closely as possible, and consequently minimize the sum of earliness and tardiness of jobs because earliness and tardiness of jobs greatly influence the performance of a schedule with respect to cost. In addition, a job incurs holding cost from the time of its arrival until its completion. Most studies on scheduling in such manufacturing systems assume unit earliness cost, unit tardiness cost and unit holding cost of a job. However, in reality such an assumption need not always hold and it is quite possible that there exist different costs of earliness, tardiness and holding for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (i.e. shops that manufacture multi-level jobs) with the consideration of jobs having different earliness, tardiness and holding costs. An attempt is made in this paper to present dispatching rules by incorporating the relative costs of earliness, tardiness and holding of jobs in the form of scalar weights. In the first phase of the study, relative costs (or weights for) earliness and tardiness of jobs are considered, and the dispatching rules are presented in order to minimize the sum of weighted earliness and weighted tardiness of jobs. In the second phase of the study, the objective considered is the minimization of the sum of weighted earliness, weighted tardiness and weighted flowtime of jobs, and the dispatching rules are presented by incorporating the relative costs of earliness, tardiness and flowtime of jobs. Simulation studies have been conducted separately for both phases of the current study, the performance of the scheduling rules have been observed independently, and the results of the simulation study have been reported. The proposed rules are found to be effective in minimizing the mean and maximum values of the measures of performance.     

Scheduling in dynamic assembly job-shops to minimize the sum of weighted earliness,weighted tardiness and weighted flowtime of jobs

In many manufacturing systems, jobs that are completed early are held as finished-goods inventory until their due-dates, and hence we incur earliness costs. Similarly, jobs that are completed after their due-dates incur penalty. The objective in such situations would, therefore, be to meet the due-dates of the respective jobs as closely as possible, and consequently minimize the sum of earliness and tardiness of jobs because earliness and tardiness of jobs greatly influence the performance of a schedule with respect to cost. In addition, a job incurs holding cost from the time of its arrival until its completion. Most studies on scheduling in such manufacturing systems assume unit earliness cost, unit tardiness cost and unit holding cost of a job. However, in reality such an assumption need not always hold and it is quite possible that there exist different costs of earliness, tardiness and holding for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (i.e. shops that manufacture multi-level jobs) with the consideration of jobs having different earliness, tardiness and holding costs. An attempt is made in this paper to present dispatching rules by incorporating the relative costs of earliness, tardiness and holding of jobs in the form of scalar weights. In the first phase of the study, relative costs (or weights for) earliness and tardiness of jobs are considered, and the dispatching rules are presented in order to minimize the sum of weighted earliness and weighted tardiness of jobs. In the second phase of the study, the objective considered is the minimization of the sum of weighted earliness, weighted tardiness and weighted flowtime of jobs, and the dispatching rules are presented by incorporating the relative costs of earliness, tardiness and flowtime of jobs. Simulation studies have been conducted separately for both phases of the current study, the performance of the scheduling rules have been observed independently, and the results of the simulation study have been reported. The proposed rules are found to be effective in minimizing the mean and maximum values of the measures of performance.     

Scheduling rules for dynamic shops that manufacture multi-level jobs

The problem of scheduling in dynamic conventional jobshops has been extensively investigated over many years. However, the problem of scheduling in assembly jobshops (i.e. shops that manufacture multi-level jobs with components and subassemblies) has been relatively less investigated in spite of the fact that assembly jobshops are frequently encountered in real life. A survey of literature on dynamic assembly jobshop scheduling has revealed that the TWKR-RRP rule is the best one for minimizing the mean flowtime and staging delay, and the job due-date (JDD) rule is the best for minimizing the mean tardiness of jobs. However, the objectives of minimizing the maximum flowtime (and maximum staging delay) and standard deviation of flowtime (and standard deviation of staging delay) are as important as the minimization of mean flowtime and mean staging delay. Likewise, the objectives of minimizing the maximum tardiness and standard deviation of tardiness are also as important as the minimization of mean tardiness. The reason is that the maximum and standard deviation values of a performance measure indicate the worst-case performance of a dispatching rule. The present study seeks to develop efficient dispatching rules to minimize the maximum and standard deviation of flowtime and staging delay, and the maximum and the standard deviation of conditional tardiness of jobs. The dispatching rules are based on the computation of the earliest completion time of a job and consequently determining the latest finish time of operations on components/subassemblies of a job. An extensive simulation-based investigation of the performance evaluation of the existing dispatching rules and the proposed dispatching rules has been carried out by randomly generating jobs with different structures and different shop utilization levels. It has been found from the simulation study that the proposed rules are quite effective in minimizing the maximum and standard deviation of flowtime and staging delay, and the maximum conditional tardiness and standard deviation of conditional tardiness.     

Investigating the use of genetic programming for a classic one-machine scheduling problem

Genetic programming has rarely been applied to manufacturing optimisation problems. In this paper the potential use of genetic programming for the solution of the one-machine total tardiness problem is investigated. Genetic programming is utilised for the evolution of scheduling policies in the form of dispatching rules. These rules are trained to cope with different levels of tardiness and tightness of due dates.     

A branch-and-bound algorithm for single machine scheduling with quadratic earliness and tardiness penalties

This paper considers the problem of scheduling a single machine, in which the objective function is to minimize the weighted quadratic earliness and tardiness penalties and no machine idle time is allowed. We develop a branch and bound algorithm involving the implementation of lower and upper bounding procedures as well as some dominance rules. The lower bound is designed based on a lagrangian relaxation method and the upper bound includes two phases, one for constructing initial schedules and the other for improving them. Computational experiments on a set of randomly generated instances show that one of the proposed heuristics, used as an upper bound, has an average gap less than 1.3% for instances optimally solved. The results indicate that both the lower and upper bounds are very tight and the branch-and-bound algorithm is the first algorithm that is able to optimally solve problems with up to 30 jobs in a reasonable amount of time.     

Note on minimizing total tardiness in a two-machine flowshop

This note considers the problem of sequencing jobs to minimize total tardiness in a two-machine flowshop. The note shows how three dominance conditions and a lower bound previously developed for this problem can be improved. The note also proposes a new dominance condition. A branch-and-bound algorithm is developed that uses the improvements and new dominance condition. The algorithm is tested on randomly generated problems and the results of the test show that the improvements and new dominance condition improves the branch-and-bound algorithm's efficiency.     

Minimizing the weighted sum of squared tardiness on a single machine

This paper considers a problem in which there is a set of jobs to be sequenced on a single machine. Each job has a weight and the objective is to sequence the jobs to minimize total weighted squared tardiness. A branch-and-bound algorithm is developed for optimally solving the problem. Several dominance conditions are presented for possible inclusion in the branch-and-bound algorithm. The dominance conditions are included in the branch-and-bound algorithm, which is tested on randomly generated problems of various numbers of jobs, due date tightness and due date ranges. The results show that the dominance conditions dramatically improve the efficiency of the branch-and-bound algorithm.     

Dispatching in flowshops with bottleneck machines

This paper addresses the problem of dispatching in flowshops with bottleneck machines. The presence of bottleneck machines results in the restricted throughput in flowshops. The objective is to develop dispatching rules for scheduling by taking into account the presence of bottleneck machines. The measures of performance are the minimization of total flowtime of jobs, the minimization of the sum of earliness and tardiness of jobs, and the minimization of total tardiness of jobs, considered separately. Many existing conventional dispatching rules and the proposed dispatching rules have been extensively investigated for their performance by generating a large number of problems of various sizes and bottleneck conditions. The results of the experimental investigation show that the proposed dispatching rules emerge to be superior to the conventional dispatching rules.     

Trade-off solutions in a single-machine scheduling problem for minimizing total earliness and maximum tardiness

This paper considers a single-machine scheduling problem involving minimization of the total earliness and the maximum tardiness. Four dominant properties for the precedence relationship between jobs in a search for an optimal solution are proposed. The lower bounds of the total earliness and the maximum tardiness of a subproblem are derived. The dominance properties and the lower bounds are implemented in the branchand-bound algorithm to facilitate the search for an optimal schedule. A heuristic algorithm is then developed to overcome the inefficiency of the branch-and-bound algorithm. Computational performance of the two algorithms is also investigated.     

Heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose several dispatching heuristics, and analyse their performance on a wide range of instances. The heuristics include simple and widely used scheduling rules, as well as adaptations of those rules to a quadratic objective function. We also propose heuristic procedures that specifically address both the earliness and the tardiness penalties, as well as the quadratic cost function. Several improvement procedures were also analysed. These procedures are applied as an improvement step, once the heuristics have generated a schedule.     

Scheduling rules to minimize total tardiness in a parallel machine problem with setup and calendar constraints

Quality control lead times are one of most significant causes of loss of time in the pharmaceutical and cosmetics industries. This is partly due to the organization of laboratories that feature parallel multipurpose machines for chromatographic analyses. The testing process requires long setup times and operators are needed to launch the process. The various controls are non-preemptive and are characterized by a release date, a due date and available routings. These quality processes lead to significant delays, and we therefore evaluate the total tardiness criterion. Previous heuristics were defined for the total tardiness criterion, parallel machines, and setup such as apparent tardiness cost (ATC) and ATC with setups (ATCS). We propose new rules and a simulated annealing procedure in order to minimize total tardiness.     

Minimizing total tardiness in a two-machine re-entrant flowshop with sequence-dependent setup times

We consider a two-machine re-entrant flowshop scheduling problem in which all jobs must be processed twice on each machine and there are sequence-dependent setup times on the second machine. For the problem with the objective of minimizing total tardiness, we develop dominance properties and a lower bound by extending those for a two-machine re-entrant flowshop problem (without sequence-dependent setup times) as well as heuristic algorithms, and present a branch and bound algorithm in which these dominance properties, lower bound, and heuristics are used. For evaluation of the performance of the branch and bound algorithm and heuristics, computational experiments are performed on randomly generated instances, and results are reported.     

The single-machine total weighted tardiness scheduling problem with position-based learning effects

This study addresses the problem of minimizing the total weighted tardiness on a single-machine with a position-based learning effect. Several dominance properties are established to develop branch and bound algorithm and a lower bound is provided to derive the optimal solution. In addition, three heuristic procedures are developed for near-optimal solutions. Computational results are also presented to evaluate the performance of the proposed algorithms.