Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm

Relative to job-shop scheduling problems that optimize makespan or flow time, due-date-related problems are usually much more computationally complex and are classified as strongly NP-hard. In this paper, a hybrid framework integrating a heuristic and a genetic algorithm (GA) is utilized for job-shop scheduling to minimize weighted tardiness. For each new generation of schedules, the GA determines the first operation of each machine, and the heuristic determines the assignment of the remaining operations. Schedules with inferior tardiness are discarded before the next round of evolution. Extensive numerical experiments were conducted for different levels of due-date tightness. The results show that the hybrid framework performs significantly better than does either a heuristic or GA alone. It is also found to be superior to a well-recognized heuristic improvement procedure (lead-time iterations). Specifically, the combination of the R&M heuristic and a GA outperforms a number of heuristics commonly used to minimize total tardiness and weighted total tardiness; this combination is, however, outperformed by the heuristic of Kreipl [Kreipl, S., 2000. A large step random walk for minimizing total weighted tardiness in a job shop. Journal of Scheduling 3, 125–138]. We also develop a generalized hybrid framework that can adapt to different job-shop problems—with or without sequence-dependent setups and with different objectives (e.g., makespan, tardiness, flow time). The new framework allows the interaction of parallel evolutions, extending the GA-heuristic environment to the solving of multi-objective scheduling problems.     

A discrete artificial bee colony algorithm for the no-idle permutation flowshop scheduling problem with the total tardiness criterion

In this paper, we present a discrete artificial bee colony algorithm to solve the no-idle permutation flowshop scheduling problem with the total tardiness criterion. The no-idle permutation flowshop problem is a variant of the well-known permutation flowshop scheduling problem where idle time is not allowed on machines. In other words, the start time of processing the first job on a given machine must be delayed in order to satisfy the no-idle constraint. The paper presents the following contributions: First of all, a discrete artificial bee colony algorithm is presented to solve the problem on hand first time in the literature. Secondly, some novel methods of calculating the total tardiness from makespan are introduced for the no-idle permutation flowshop scheduling problem. Finally, the main contribution of the paper is due to the fact that a novel speed-up method for the insertion neighborhood is developed for the total tardiness criterion. The performance of the discrete artificial bee colony algorithm is evaluated against a traditional genetic algorithm. The computational results show its highly competitive performance when compared to the genetic algorithm. Ultimately, we provide the best known solutions for the total tardiness criterion with different due date tightness levels for the first time in the literature for the Taillard’s benchmark suit.     

粒子群遗传混合算法求解考虑传输时间的FJSP

在某些生产制造场景中,工件在不同机器间的传输时间对车间调度的总拖期具有重要影响,本文基于此扩展了总拖期最小的柔性作业车间调度模型。针对问题模型的复杂性,采用粒子群优化算法和遗传算法的混合算法进行求解。在初始化过程以一定概率优选加工时间和传输时间短的机器并排除调度频繁的机器,使种群在保持多样性的前提下尽量选择优化结果好的个体;采用线性调整的方式动态改变交叉概率和变异概率的值,使种群在遗传算法的不同阶段具有不同的搜索强度;采用粒子群优化算法进行局部搜索,弥补了遗传算法局部搜索能力的不足。最后采用本文方法和其他方法求解柔性作业车间调度问题实例,并对比不同水平层次传输时间下的总拖期,验证了本文方法的有效性。     

A Petri Net based algorithm for minimizing total tardiness in flexible manufacturing systems

Petri Nets have been extensively used for modeling and simulating of the dynamics of flexible manufacturing systems. Petri Nets can capture features such as parallel machines, alternative routings, batch sizes, multiplicity of resources, to name but a few. However, Petri Nets have not been very popular for scheduling in manufacturing due to the Petri Net “state explosion” combined with the NP-hard nature of many of such problems. A promising approach for scheduling consists of generating only portions of the Petri Net state space with heuristic search methods. Thus far, most of this scheduling work with Petri Nets has been oriented to minimize makespan. The problem of minimizing total tardiness and other due date-related criteria has received little attention. In this paper, we extend the Beam A^* Search algorithm presented in a previous work with capability to handle the total tardiness criterion. Computational tests were conducted on Petri Net models of both flexible job shop and flexible manufacturing systems. The results suggest that the Petri Net approach is also valid to minimize due date related criteria in flexible systems.     

基于混沌量子算法和MAGTD的多目标FJSP求解策略

针对多目标环境下柔性作业车间的调度问题,以最小化最大完工时间和惩罚值为目标,建立调度问题的数学模型,提出了基于混沌理论的量子粒子群算法。针对实际生产交货期不确定的特点,在量子粒子群算法基础上,提出引入混沌机制建立初始群的方法;利用混沌机制的遍历性,提出混沌局部优化策略;为获取最优调度方案提出了引入多指标加权灰靶选择策略。通过典型基准算例和对比测试,验证了所提出的算法获得最满意调度方案的可行性和求解多目标柔性作业车间调度问题的有效性。     

Synchronizing production and air transportation scheduling using mathematical programming models

Traditional scheduling problems assume that there are always infinitely many resources for delivering finished jobs to their destinations, and no time is needed for their transportation, so that finished products can be transported to customers without delay. So, for coordination of these two different activities in the implementation of a supply chain solution, we studied the problem of synchronizing production and air transportation scheduling using mathematical programming models. The overall problem is decomposed into two sub-problems, which consists of air transportation allocation problem and a single machine scheduling problem which they are considered together. We have taken into consideration different constraints and assumptions in our modeling such as special flights, delivery tardiness and no delivery tardiness. For these purposes, a variety of models have been proposed to minimize supply chain total cost which encompass transportation, makespan, delivery earliness tardiness and departure time earliness tardiness costs.     

Single-machine scheduling with both deterioration and learning effects

This paper considers a single-machine scheduling problem with both deterioration and learning effects. The objectives are to respectively minimize the makespan, the total completion times, the sum of weighted completion times, the sum of the kth power of the job completion times, the maximum lateness, the total absolute differences in completion times and the sum of earliness, tardiness and common due-date penalties. Several polynomial time algorithms are proposed to optimally solve the problem with the above objectives.     

Single-machine scheduling with accelerating deterioration effects

Scheduling with deterioration effects has been widely investigated in the past two decades. In realistic situations, the deterioration effect might accelerate, especially in the food manufacturing industry. In this paper we propose a scheduling model with an accelerating deterioration effect. We show that the single-machine problems under the model to minimize the makespan, total completion time, total weighted completion time, maximum lateness, maximum tardiness, and total tardiness remain polynomially solvable.     

Multiple-objective heuristics for scheduling unrelated parallel machines

This research proposes two heuristics and a Genetic Algorithm (GA) to find non-dominated solutions to multiple-objective unrelated parallel machine scheduling problems. Three criteria are of interest, namely: makespan, total weighted completion time, and total weighted tardiness. Each heuristic seeks to simultaneously minimize a pair of these criteria; the GA seeks to simultaneously minimize all three. The computational results show that the proposed heuristics are computationally efficient and provide solutions of reasonable quality. The proposed GA outperforms other algorithms in terms of the number of non-dominated solutions and the quality of its solutions.     

A neural network model for scheduling problems

Artificial neural networks (ANNs) have been successfully applied to solve a variety of problems. This paper proposes a new neural network approach to solve the single machine mean tardiness scheduling problem and the minimum makespan job shop scheduling problem. The proposed network combines the characteristics of neural networks and algorithmic approaches. The performance of the network is compared with the existing scheduling algorithms under various experimental conditions. A comprehensive bibliography is also provided in the paper.     

No-wait or no-idle permutation flowshop scheduling with dominating machines

In this paper we study the no-wait or no-idle permutation flowshop scheduling problem with an increasing and decreasing series of dominating machines. The objective is to minimize one of the five regular performance criteria, namely, total weighted completion time, maximum lateness, maximum tardiness, number of tardy jobs and makespan. We establish that these five cases are solvable by presenting a polynomial-time solution algorithm for each case.     

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.     

No-wait flowshops with bicriteria of makespan and total completion time

We consider the m-machine no-wait flowshop scheduling problem with the objective of minimizing a weighted sum of makespan and total completion time. For the two-machine problem, we develop a dominance relation and embed it within a proposed branch-and-bound algorithm. For the m-machine problem, we propose a heuristic. Computational experiments show that the proposed heuristic outperforms the best existing multi-criteria heuristics and the best single criterion heuristics for makespan and total completion time. The efficiency of the dominance relation and branch-and-bound algorithm is also investigated and shown to be effective.     

An Improved Genetic Algorithm for the Distributed and Flexible Job-shop Scheduling problem

The Distributed and Flexible Job-shop Scheduling problem (DFJS) considers the scheduling of distributed manufacturing environments, where jobs are processed by a system of several Flexible Manufacturing Units (FMUs). Distributed scheduling problems deal with the assignment of jobs to FMUs and with determining the scheduling of each FMU, in terms of assignment of each job operation to one of the machines able to work it (job-routing flexibility) and sequence of operations on each machine. The objective is to minimize the global makespan over all the FMUs. This paper proposes an Improved Genetic Algorithm to solve the Distributed and Flexible Job-shop Scheduling problem. With respect to the solution representation for non-distributed job-shop scheduling, gene encoding is extended to include information on job-to-FMU assignment, and a greedy decoding procedure exploits flexibility and determines the job routings. Besides traditional crossover and mutation operators, a new local search based operator is used to improve available solutions by refining the most promising individuals of each generation. The proposed approach has been compared with other algorithms for distributed scheduling and evaluated with satisfactory results on a large set of distributed-and-flexible scheduling problems derived from classical job-shop scheduling benchmarks.     

Four solution techniques for a general one machine scheduling problem: A comparative study

Gelders and Kleindorfer suggested a generalized detailed scheduling cost structure, based on the sum of weighted tardiness and weighted flowtime. They solved the single-machine scheduling problem using a transportation scheme to obtain lower bounds in their branch and bound approach. Recently, Fisher, Baker, Rinnooy Kan and Srinivasan reported attractive computation times with general algorithms adapted to the total tardiness problem for the single-machine case. In this paper four algorithms are adapted to the generalized cost structure mentioned above and extensive computational results are presented.This investigation shows that much is to be expected from the dual approach for more complex scheduling problems while dynamic programming deserves a new research effort because of its efficiency in special structured problems and/or problems where a posteriori precedence relations (dominance criteria) can be developed.     

A tabu search algorithm for the single machine total weighted tardiness problem

In this study, a tabu search (TS) approach to the single machine total weighted tardiness problem (SMTWT) is presented. The problem consists of a set of independent jobs with distinct processing times, weights and due dates to be scheduled on a single machine to minimize total weighted tardiness. The theoretical foundation of single machine scheduling with due date related objectives reveal that the problem is NP-hard, rendering it a challenging area for meta-heuristic approaches. This paper presents a totally deterministic TS algorithm with a hybrid neighborhood and dynamic tenure structure, and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search. The proposed TS approach yields very high quality results for a set of benchmark problems obtained from the literature.     

A partial enumeration heuristic for multi-objective flowshop scheduling problems

This paper addresses the flowshop scheduling problem with multiple performance objectives in such a way as to provide the decision maker with approximate Pareto optimal solutions. It is well known that the partial enumeration constructive heuristic NEH and its adaptations perform well for single objectives such as makespan, total tardiness and flowtime. In this paper, we develop a similar heuristic using the concept of Pareto dominance when comparing partial and complete schedules. The heuristic is tested on problems involving combinations of the above criteria. For the two-machine case, and the pairs of objectives: (i) makespan and maximum tardiness, (ii) makespan and total tardiness, the heuristic is compared with branch-and-bound algorithms proposed in the literature. For two and more than two machines, and the criteria combinations considered in this article, the heuristic performance is tested against constructive heuristics reported in the literature. By means of an illustrative example, it is shown that a genetic algorithm from the literature performs better when starting from heuristic solutions rather than random solutions.     

Single-machine scheduling with deteriorating functions for job processing times

In many realistic scheduling settings a job processed later consumes more time than when it is processed earlier – this phenomenon is known as scheduling with deteriorating jobs. In the literature on deteriorating job scheduling problems, majority of the research assumed that the actual job processing time of a job is a function of its starting time. In this paper we consider a new deterioration model where the actual job processing time of a job is a function of the processing times of the jobs already processed. We show that the single-machine scheduling problems to minimize the makespan and total completion time remain polynomially solvable under the proposed model. In addition, we prove that the problems to minimize the total weighted completion time, maximum lateness, and maximum tardiness are polynomially solvable under certain agreeable conditions.     

模糊环境下的柔性工作车间调度模型的研究

本首先引入了柔性生产系统下的调度过程中存在的不确定性问题，接着对存在模糊操作时间间隔的柔性工作车间调度问题及相关概念进行了描述，并且给出了以最小makespan为目标的基于模糊逻辑和遗传优化的调度模型，最后通过实例验证了模型的可行性。     

Single-machine scheduling problems with an actual time-dependent deterioration

In this paper, we consider the single machine scheduling problems with an actual time-dependent deterioration effect. By the actual time-dependent deterioration effect, we mean that the processing time of a job is defined by increasing function of total actual processing time of jobs in front of it in the sequence. We show that even with the introduction of an actual time-dependent deterioration to job processing times, makespan minimization problem, total completion time minimization problem, the total lateness, and the sum of the quadratic job completion times minimization problem remain polynomially solvable, respectively. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, and the total tardiness minimization problem can be solved in polynomial time under certain conditions.