Two due date assignment problems in scheduling a single machine

We study two single-machine scheduling problems: minimizing the sum of weighted earliness, tardiness and due date assignment penalties and minimizing the weighted number of tardy jobs and due date assignment costs. We prove that both problems are strongly NP-hard and give polynomial solutions for some important special cases.     

Scheduling a deteriorating maintenance activity on a single machine

We study a problem of scheduling a maintenance activity on a single machine. Following several recent papers, the maintenance is assumed to be deteriorating, that is, delaying the maintenance increases the time required to perform it. The following objective functions are considered: makespan, flowtime, maximum lateness, total earliness, tardiness and due-date cost, and number of tardy jobs. We introduce polynomial time solutions for all these problems.     

Scheduling to minimize maximum earliness and number of tardy jobs where machine idle time is allowed

We address the bicriteria problem of minimizing the number of tardy jobs and maximum earliness on a single machine where machine idle time is allowed. We show that the problem of minimizing the number of tardy jobs while maximum earliness is kept at its minimum value of zero is polynomially solvable. We present polynomial time algorithms for the maximum earliness problem subject to no tardy jobs and the maximum earliness problem for a given set of tardy jobs. Finally, we discuss the use of the latter algorithm in generating all efficient schedules.     

New solution methods for single machine bicriteria scheduling problem: Minimization of average flowtime and number of tardy jobs

We consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine. This problem, which is known to be NP-hard, is important in practice, as the former criterion conveys the customer’s position, and the latter reflects the manufacturer’s perspective in the supply chain. We propose four new heuristics to solve this multiobjective scheduling problem. Two of these heuristics are constructive algorithms based on beam search methodology. The other two are metaheuristic approaches using a genetic algorithm and tabu-search. Our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature.     

Complexity of single machine scheduling subject to nonnegative inventory constraints

This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine with the minimization of the total weighted completion time, the maximum lateness, and the number of tardy jobs, respectively, as objective and determine their computational complexity. Since the general versions of our problems turn out to be strongly NP-hard, we consider special cases by assuming that different jobs have certain parameter values in common. We determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs.     

一个双目标单机调度问题及其几个多项式可解情形

研究了一个双目标单机调度问题及其几个多项式可解的情形。问题的主目标是延误工件数最小,在此条件下,最小化各工件加权提前期的总和,由于该问题是NP一难的,故研究求解它的一个启发式算法及问题的几个多项式可解的特殊情形。     

Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs

Motivated by just-in-time manufacturing, we consider a single machine scheduling problem with dual criteria, i.e., the minimization of the total weighted earliness subject to minimum number of tardy jobs. We discuss several dominance properties of optimal solutions. We then develop a heuristic algorithm with time complexity O(n³) and a branch and bound algorithm to solve the problem. The computational experiments show that the heuristic algorithm is effective in terms of solution quality in many instances while the branch and bound algorithm is efficient for medium-size problems.     

Algorithm for minimizing weighted earliness penalty in single-machine problem

In this paper, the problem of minimizing the weighted earliness penalty in a single-machine scheduling problem is addressed. For this problem, every job is assumed to be available at time zero and must be completed before or on its deadline. No tardy job is allowed. Each job has its own earliness penalty and deadline. The paper identifies several local optimality conditions for sequencing of adjacent jobs. A heuristic algorithm is developed based on these local optimality conditions. Sample problems are solved and the solutions obtained from the heuristic are compared to solutions obtained from the heuristics developed by Chand and Schneeberger. Also, comparisons are performed between the solutions obtained from the heuristic and the optimal solutions obtained from a mathematical modeling approach for problems involving 10 and 15 jobs. The results show that the developed heuristic produces solutions close to optimal in small size problems, and it also outperforms the Chand and Schneeberger's method.     

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.     

Minimizing earliness and tardiness penalties in a single-machine problem with a common due date

Scheduling problems involving both earliness and tardiness costs have received significant attention in recent years. This type of problem became important with the advent of the just-in-time (JIT) concept, where early or tardy deliveries are highly discouraged. In this paper we examine the single-machine scheduling problem with a common due date. Performance is measured by the minimization of the sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, we propose a tabu search-based heuristic and a genetic algorithm which exploit specific properties of the optimal solution. Hybrid strategies are also analyzed to improve the performance of these methods. The proposed approaches are examined through a computational comparative study with 280 benchmark problems with up to 1000 jobs.     

A note on single-machine scheduling with decreasing time-dependent job processing times

In this note we consider some single-machine scheduling problems with decreasing time-dependent job processing times. Decreasing time-dependent job processing times means that its processing time is a non-increasing function of its execution start time. We present polynomial solutions for the sum of squared completion times minimization problem, and the sum of earliness penalties minimization problem subject to no tardy jobs, respectively. We also study two resource constrained scheduling problems under the same decreasing time-dependent job processing times model and present algorithms to find their optimal solutions.     

带强制工期的可中断平行机排序问题

讨论了在m台同型平行机上,加工带强制工期的n个可中断工件,在机器可空闲条件下,确定一个工件排序,使得提前完工时间和最小.先考虑了问题的复杂性,通过3-划分问题归约,证明了其是强NP-hard的.而后,讨论了强制工期相等的特殊情形,由于工件不允许延迟,问题可能会无可行排序.先讨论了可行性,接着针对可行问题,提出一个算法在多项式时间内获得最优排序.     

An application of the neural network energy function to machine sequencing

We apply a neural network approach for solving a one-machine sequencing problem to minimize either single- or multi-objectives, namely the total tardiness, total flowtime, maximimum tardiness, maximum flowtime, and number of tardy jobs. We formulate correspondingly nonlinear integer models, for each of which we derive a quadratic energy function, a neural network, and a system of differential equations. Simulation results based on solving the nonlinear differential equations demonstrate that our approach can effectively solve the sequencing problems to optimality in most cases and near optimality in a few cases. The neural network approach can also be implemented on a parallel computing network, resulting in significant runtime savings over the optimization approach. This paper should not be disseminated without written permission of the authors.     

极小化最大提前完工时间的两平行机排序问题

讨论了在两台同型平行机上,加工带截止期限的n个工件,在机器可空闲条件下,确定一个工件排序,使得最大提前完工时间最小.由于工件不允许延迟,问题可能会无可行排序.先讨论问题的可行性,通过子集和问题归约,证明了判定问题的可行性是NP-complete的.如果问题可行,接着讨论了问题的复杂性,通过划分问题归约,证明了其是NP-complete的.最后,考虑了工件加工时间相等的特殊情形,提出了一个算法在多项式时间内获得最优排序.     

Complexity results for the linear time–cost tradeoff problem with multiple milestones and completely ordered jobs

We consider two linear project time–cost tradeoff problems with multiple milestones. Unless a milestone is completed on time, penalty costs for tardiness may be imposed. However, these penalty costs can be avoided by compressing the processing times of certain jobs that require additional resources or costs. Our model describes these penalty costs as the total weighted number of tardy milestone. The first problem tries to minimize the total weighted number of tardy milestones within the budget for total compression costs, while the second problem tries to minimize the total weighted number of tardy milestones plus total compression costs. We develop a linear programming formulation for the case with a fixed number of milestones. For the case with an arbitrary number of milestones, we show that under completely ordered jobs, the first problem is NP-hard in the ordinary sense while the second problem is polynomially solvable.     

Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem

We study a static stochastic single machine scheduling problem in which jobs have random processing times with arbitrary distributions, due dates are known with certainty, and fixed individual penalties (or weights) are imposed on both early and tardy jobs. The objective is to find an optimal sequence that minimizes the expected total weighted number of early and tardy jobs. The general problem is NP-hard to solve; however, in this paper, we develop certain conditions under which the problem is solvable exactly. An efficient heuristic is also introduced to find a candidate for the optimal sequence of the general problem. Our illustrative examples and computational results demonstrate that the heuristic performs well in identifying either optimal sequences or good candidates with low errors. Furthermore, we show that special cases of the problem studied here reduce to some classical stochastic single machine scheduling problems including the problem of minimizing the expected weighted number of early jobs and the problem of minimizing the expected weighted number of tardy jobs which are both solvable by the proposed exact or heuristic methods.     

并行机问题的模拟退火调度算法研究

研究了一类调度目标是最小化最大完成时间的并行机调度问题.考虑到此问题的NP-hard特性,引入模拟退火算法思想以获取高质量近优解.分析了现有此问题模拟退火算法的缺陷,定义了关键机器和非关键机器,设计了一个包含局部优化的模拟退火算法.除了交换变换,还引入插入变换以改变各子调度中作业个数.大量的随机数据实验用于验证算法解的质量和计算效率,实验结果表明该模拟退火算法能够在有限时间内为大规模问题求得高质量满意解.     

Minimizing due date related measures for a single machine scheduling problem with outsourcing allowed

This paper considers two single-machine scheduling problems with outsourcing allowed where each job can be either processed on an in-house single-machine or outsourced. They include the problem of minimizing maximum lateness and outsourcing costs, and that of minimizing total tardiness and outsourcing costs. Outsourcing is commonly required as a way to improve productivity in various companies including electronics industries and motor industries. The objective is to minimize the weighted sum of the outsourcing cost and the scheduling measure represented by either one of maximum lateness and total tardiness, subject to outsourcing budget. It is proved that the problem is NP-hard. Some solution properties are characterized to derive heuristic algorithms, and also a branch-and-bound algorithm. Numerical experiments are conducted to evaluate performance of the derived algorithms.     

Minimizing the Number of Tardy Jobs in a Permutation Flowshop Scheduling Problem with Setup Times and Time Lags Constraints

This paper studies the permutation flowshop scheduling problem with sequence dependent setup times and time lags constraints minimizing the number of tardy jobs. Dependent setup times are defined as the work to prepare the machines between two successive jobs. Time lags are defined as intervals of time that must exist between every couple of successive operations of the same job. Two mathematical programming formulations are proposed for the considered problem. A simulated annealing algorithm is also developed to solve the problem. Computational experiments are presented and discussed.     

Minimizing total tardiness in a scheduling problem with a learning effect

Minimizing of total tardiness is one of the most studied topics on single machine problems. Researchers develop a number of optimizing and heuristic methods to solve this NP-hard problem. In this paper, the problem of minimizing total tardiness is examined in a learning effect situation. The concept of learning effects describes the reduction of processing times arising from process repetition. A 0–1 integer programming model is developed to solve the problem. Also, a random search, the tabu search and the simulated annealing-based methods are proposed for the problem and the solutions of the large size problems with up to 1000 jobs are found by these methods. To the best of our knowledge, no works exists on the total tardiness problem with a learning effect tackled in this paper.