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.     

Efficient constructive and composite heuristics for the Permutation Flowshop to minimise total earliness and tardiness

In this paper we address the problem of scheduling jobs in a permutation flowshop with a just-in-time objective, i.e. the minimisation of the sum of total tardiness and total earliness. Since the problem is NP-hard, there are several approximate procedures available for the problem, although their performance largely depends on the due dates of the specific instance to be solved. After an in-depth analysis of the problem, different cases or sub-problems are identified and, by incorporating this knowledge, four heuristics are proposed: a fast constructive heuristic, and three different local search procedures that use the proposed constructive heuristic as initial solution.The proposed Prod. Type: FLPheuristics have been compared on an extensive set of instances with the best-so-far heuristic for the problem, as well as with adaptations of efficient heuristics for similar scheduling problems. The computational results show the excellent performance of the proposed algorithms. Finally, the positive impact of the efficient heuristics is evaluated by including them as seed sequences for one of the best metaheuristic for the problem.     

Dispatching heuristics for the single machine early/tardy scheduling problem with job-independent penalties

In this paper, we consider the single machine earliness/tardiness scheduling problem with job-independent penalties, and no machine idle time. Several dispatching heuristics are proposed, and their performance is analysed on a wide range of instances. The heuristics include simple scheduling rules, as well as a procedure that takes advantage of the strengths of each of those rules. We also consider early/tardy dispatching procedures, and a heuristic method based on existing adjacent precedence conditions. An improvement procedure that can be used to improve the schedules generated by the heuristics is also proposed.

The computational tests show that the best results are given by the early/tardy dispatching rules. These heuristics are also quite fast, and are capable of quickly solving even very large instances. The use of the improvement procedure is recommended, since it improves the solution quality, with little additional computational effort.     

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.     

Minimizing maximum earliness on parallel identical machines

This paper addresses the scheduling problem of minimizing maximum earliness (or more generally — maximizing minimum lateness) on parallel identical machines. We prove that the two-machine case is NP-hard in the ordinary sense, and introduce a pseudo-polynomial dynamic programming algorithm for this case. When the number of machines is arbitrary, the problem is shown to be NP-hard in the strong sense. Then we introduce an efficient heuristic and two simple upper bounds on the optimal minimum lateness value. Finally we provide an extensive numerical study which indicates that the heuristic performs well in various job and machine settings.Scope and purposeIn recent years many researchers have focused on minimizing both earliness and tardiness costs. Only a few studies have considered problems with (maximum or total) earliness as the sole performance measure. We believe that the earliness measure is appropriate for many real-life settings, where the main cost component is the earliness (inventory) cost, and the tardiness (positive lateness) cost component is negligible. Our paper studies the scheduling problem of minmax earliness on parallel identical machines: we analyze the complexity of the problem, and introduce an efficient heuristic and simple bounds on the optimal cost.     

Exact and heuristic procedures for single machine scheduling with quadratic earliness and tardiness penalties

The present paper studies the single machine, no-idle-time scheduling problem with a weighted quadratic earliness and tardiness objective. We investigate the relationship between this problem and the assignment problem, and we derive two lower bounds and several heuristic procedures based on this relationship. Furthermore, the applicability of the time-indexed integer programming formulation is investigated. The results of a computational experiment on a set of randomly generated instances show (1) the high-quality results of the proposed heuristics, (2) the low optimality gap of one of the proposed lower bounds and (3) the applicability of the integer programming formulation to small and medium size cases of the problem.     

Benchmarks for scheduling on a single machine against restrictive and unrestrictive common due dates

We consider the NP-hard problem of scheduling jobs on a single machine against common due dates with respect to earliness and tardiness penalties. The paper covers two aspects: Firstly, we develop a problem generator and solve 280 instances with two new heuristics to obtain upper bounds on the optimal objective function value. Secondly, we demonstrate computationally that our heuristics are efficient in obtaining near-optimal solutions for small problem instances. The generated problem instances in combination with the upper bounds can be used as benchmarks for future approaches in the field of common due-date scheduling.Scope and purposeIn connection with just-in-time production and delivery, earliness as well as tardiness penalties are of interest. Thus scheduling against common due dates has received growing attention during the last decade. Many algorithms have been developed to solve the different variants of this problem. But whenever a new algorithm for scheduling against common due dates is proposed, its quality is assessed only on a few self-generated examples. Hence it is difficult to evaluate the various approaches, particularly in comparison with each other. Therefore the goal of this paper is to present numerous benchmark problems together with some upper bounds on the optimal objective function value.     

Scheduling job classes on uniform machines

We study a scheduling problem with job classes on parallel uniform machines. All the jobs of a given class share a common due-date. General, non-decreasing and class-dependent earliness and tardiness cost functions are assumed. Two objectives are considered: (i) minmax, where the scheduler is required to minimize the maximum earliness/tardiness cost among all the jobs and (ii) minmax-minsum, where the scheduler minimizes the sum of the maximum earliness/tardiness cost in all job classes. The problem is easily shown to be NP-hard, and we focus here on the introduction of simple heuristics. We introduce LPT (Largest Processing Time first)-based heuristics for the allocation of jobs to machines within each class, followed by a solution of an appropriate non-linear program, which produces for this job allocation an optimal schedule of the classes. We also propose a lower bound, based on balancing the load on the machines. Our numerical tests indicate that the heuristics result in very small optimality gaps.     

Genetic algorithms for the optimal common due date assignment and the optimal scheduling policy in parallel machine earliness/tardiness scheduling problems

Earliness/tardiness scheduling problems with undetermined common due date which have wide application background in textile industry, mechanical industry, electronic industry and so on, are very important in the research fields such as industry engineering and CIMS. In this paper, a kind of genetic algorithm based on sectional code for minimizing the total cost of assignment of due date, earliness and tardiness in this kind of scheduling problem is proposed to determine the optimal common due date and the optimal scheduling policy for determining the job number and their processing order on each machine. Also, simulated annealing mechanism and the iterative heuristic fine-tuning operator are introduced into the genetic algorithm so as to construct three kinds of hybrid genetic algorithms with good performance. Numerical computational results focusing on the identical parallel machine scheduling problem and the general parallel machine scheduling problem shows that these algorithms outperform heuristic procedures, and fit for larger scale parallel machine earliness/tardiness scheduling problem. Moreover, with practical application data from one of the largest cotton colored weaving enterprises in China, numerical computational results show that these genetic algorithms are effective and robust, and that especially the performance of the hybrid genetic algorithm based on simulated annealing and the iterative heuristic fine-tuning operator is the best among them.     

准时化生产计划的半无限规划模型与模拟退火方法

半无限规划模型是描述ＪＩＴ环境下，提前／拖期生产计划问题的一种数学模型。因为目标函数是非线性的、有无限多约束和约束的非凸性，所以求解比较困难。用模型退火结合启发式方法和最速下降法求解半无限规划模型，与遗传算法进行比较，计算结果表明用模拟退火方法求解更有效。     

Minimizing total earliness and tardiness on a single machine using a hybrid heuristic

This paper focuses on scheduling jobs with different processing times and distinct due dates on a single machine with no inserted idle time as to minimize the sum of total earliness and tardiness. This scheduling problem is a very important and frequent industrial problem that is common to most just-in-time production environments. This NP hard scheduling problem is herein solved using a hybrid heuristic which combines local search heuristics (dispatching rules, hill climbing and simulated annealing) and an evolutionary algorithm based on genetic algorithms. The heuristic involves low and high, relay and teamwork hybridization. Computational results reflect the sizeable solution quality improvement induced by hybridization, and assess the impact of each type of hybridization on the efficiency of the hybrid heuristic.     

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 scheduling in flowshops and flowline-based manufacturing cells to minimize the sum of weighted flowtime and weighted tardiness of jobs

The problem of scheduling in two different types of flowshops (all jobs available at time zero, different job availability times known a priori) and in flowline-based manufacturing cells is considered with the objective of minimizing the sum of weighted flowtime and weighted tardiness of jobs. First, heuristic preference relations are developed by the consideration of lower bounds on the completion times, operation due-dates, and weights for holding and tardiness of jobs. A heuristic algorithm for scheduling is then proposed by making use of the heuristic preference relations. Two more heuristic algorithms are developed by implementing an improvement scheme to enhance the quality of the solution given by the first heuristic algorithm. The proposed and the existing heuristics are evaluated with respect to the three problem classes under consideration by solving a large number of randomly generated problems. The results of an extensive computational investigation for various problem sizes are presented. It has been observed that all three proposed heuristics perform better than the existing heuristics in giving a solution of superior quality and that the first proposed heuristic yields a good solution by requiring a negligible CPU time. In addition, an experimental investigation is carried out to evaluate the effectiveness of the improvement scheme when implemented in the existing heuristics, and also the effectiveness of heuristics based on simulated annealing. The results are discussed in detail.     

A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet. Several genetic algorithms based on this approach are presented. These versions differ on the generation of the initial population, as well as on the use of local search. The proposed procedures are compared with existing heuristics, as well as with optimal solutions for the smaller instance sizes.     

Local and global dominance conditions for the weighted earliness scheduling problem with no idle time

In this paper, we present dominance conditions for the single machine weighted earliness scheduling problem with no idle time. We also propose an algorithm that can be used to improve upper bounds for the weighted earliness criterion and lower bounds for an earliness/tardiness problem. The computational tests show that the algorithm is superior to an initial heuristic schedule and an existing adjacency condition.     

Local and global dominance conditions for the weighted earliness scheduling problem with no idle time

In this paper, we present dominance conditions for the single machine weighted earliness scheduling problem with no idle time. We also propose an algorithm that can be used to improve upper bounds for the weighted earliness criterion and lower bounds for an earliness/tardiness problem. The computational tests show that the algorithm is superior to an initial heuristic schedule and an existing adjacency condition.     

A performance comparison of heuristics for the total weighted tardiness problem

The single machine total weighted tardiness problem is an NP-hard problem that requires the use of heuristic solution procedures when more than 50 jobs are to be scheduled. In the literature, a well-tuned simulated annealing method and a descent heuristic with zero interchanges (DESO) both generated the best solutions for a large set of randomly generated problems. Due dates are generated by defining two parameters: the relative range of due dates (RDD) and the average tardiness factor (TF). In this paper, we define several heuristics based on dynamic programming and then use these and DESO heuristics to solve 50-job, 100-job, 200-job, and 500-job problems.     

Exact and heuristic algorithms for the just-in-time scheduling problem in a batch processing system

Batch processing systems are commonly used in many different environments such as chemical and semiconductor industries. In this research, a just-in-time scheduling problem in a batch processing system is investigated. Minimization of total earliness and tardiness of the jobs with respect to a common due date is considered as the objective function. First, the research problem is formulated as a mixed integer linear programming model. Then, to find the optimal schedule for a predetermined set of batches, a dynamic programming algorithm is proposed. Based on the proposed dynamic programming algorithm, several heuristics are also developed. A lower bounding method is presented, and then a branch and bound algorithm is proposed to solve the problem optimally. To demonstrate the performance of the proposed algorithms, several computational experiments are conducted.     

Filtered and recovering beam search algorithms for the early/tardy scheduling problem with no idle time

In this paper, we present filtered and recovering beam search algorithms for the single machine earliness/tardiness scheduling problem with no idle time, and compare them with existing neighbourhood search and dispatch rule heuristics. Filtering procedures using both priority evaluation functions and problem-specific properties have been considered.The computational results show that the recovering beam search algorithms outperform their filtered counterparts, while the priority-based filtering procedure proves superior to the rules-based alternative. The best solutions are given by the neighbourhood search algorithm, but this procedure is computationally intensive and can only be applied to small or medium size instances. The recovering beam search heuristic provides results that are close in solution quality and is significantly faster, so it can be used to solve even large problems.     

解决并行多机提前/拖后调度问题的混合遗传算法方法

研究了带有公共交货期的并行多机提前/拖后调度问题.提出了一种混合遗传算法 方法,以便于确定公共交货期和每台机器上加工的任务代号及其加工顺序,即找到一个最优 公共交货期和最优调度,使加工完所有任务后交货期安排的成本、提前交货成本和拖后交货 成本的总和最小.数值计算结果表明了该混合遗传算法优于启发式算法,并能适用于较大规 模并行多机提前/拖后调度问题.算法计算量小,鲁棒性强.