Scheduling time-dependent jobs under mixed deterioration

We consider a new model of time-dependent scheduling. A set of deteriorating jobs has to be processed on a single machine which is available starting from a non-zero time. The processing times of some jobs from this set are constant, while other ones are either proportional or linear functions of the job starting times. The applied criteria of schedule optimality include the maximum completion time, the total completion time, the total weighted completion time, the maximum lateness and the number of tardy jobs. We delineate a sharp boundary between computationally easy and difficult problems, showing polynomially solvable and NP-hard cases.     

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 past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects

In this paper we consider the single machine past-sequence-dependent (p-s-d) setup times scheduling problems with general position-dependent and time-dependent learning effects. By the general position-dependent and time-dependent learning effects, we mean that the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job’s scheduled position. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the θth (θ ? 0) power of job completion times, the total lateness, the total weighted completion time, the maximum lateness, the maximum tardiness and the number of tardy jobs. We show that the problems of makespan, the total completion time, the sum of the θth (θ ? 0) power of job completion times and the total lateness can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, maximum tardiness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

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.     

一致条件下具学习因子的几个单机排序问题

n个工件需在同台机器上依次加工，工件j,j=1，2，…，n所需的正常加工时间为pj,如在某序中工件j第r个加工，则机器对其实际加工的时间为pjr^α，其中α≤0为一学习因子．要求适当排列这n个工件的加工顺序，使某目标函数达最小．本文对加权完工时间之和，最大迟后，延误工件数这三个目标函数，给出了在相应的一致条件下，对应的WSPT规则，EDD规则，修正Moore-Hodgson算法可获最优序，并估计了在一般情况下由该三规则所获序的误差．     

Minimizing Weighted Number of Early and Tardy Jobs with a Common Due Window Involving Location Penalty

This paper studies a single machine scheduling problem to minimize the weighted number of early and tardy jobs with a common due window. There are n non-preemptive and simultaneously available jobs. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. The window size is a given parameter but the window location is a decision variable. The objective of the problem is to find a schedule that minimizes the weighted number of early and tardy jobs and the location penalty. We show that the problem is NP-complete in the ordinary sense and develop a dynamic programming based pseudo-polynomial algorithm. We conduct computational experiments, the results of which show that the performance of the dynamic algorithm is very good in terms of memory requirement and CPU time. We also provide polynomial time algorithms for two special cases.     

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.     

Single-machine scheduling with learning functions

In this study we consider the single-machine scheduling problems with a sum of-processing-times-based learning effect. The sum of-processing-times-based learning effect of a job is assumed to be a function of the sum of the normal processing time of the already processed jobs. The objective is to minimize one of two regular objective functions, namely the weighted sum of completion times and the maximum lateness. We use the weighted shortest processing time (WSPT) rule and the earliest due date (EDD) rule as heuristics for the general cases and analyze their worst-case error bounds. We also provide computational results to evaluate the performance of the heuristics.     

Scheduling a single machine to minimize earliness penalties subject to the SLK due-date determination method

This paper considers a single machine scheduling problem. There are n jobs to be processed on a single machine. The problem is to minimize total earliness penalties subject to no tardy jobs. The problem is NP-complete if the due-dates are arbitrary. We study the problem when the due-dates are determined by the equal slack (SLK) method. Two special cases of the problem are solved in polynomial time. The first one is the problem with equally weighted monotonous penalty objective function. The second one is the problem with weighted linear penalty objective function.     

A Branch and Bound Algorithm to Minimize the Total Weighed Number of Tardy Jobs and Delivery Costs

This paper addresses the production and delivery scheduling integration problem; a manufacturer receives ₋ orders from one customer while the orders need to be processed on one or two machines and be sent to the customer in batches. Sending several jobs in batches will reduce the transportation cost but it may increase the number of tardy jobs. The objective is to minimize the sum of the total weighted number of tardy jobs and the delivery costs. The structural properties of the problem for a single machine and special cases of the two-machine flow shop problem are investigated and used to set up a new branch and bound algorithm. A heuristic algorithm for upper bound calculation and two approaches for lower bound calculation are also introduced. Results of computational tests show significant improvement over an existing dynamic programming method.     

Scheduling linear deteriorating jobs with rejection on a single machine

We consider several single machine scheduling problems in which the processing time of a job is a linear function of its starting time and jobs can be rejected by paying penalties. The objectives are to minimize the makespan, the total weighted completion time and the maximum lateness/tardiness plus the total penalty of the rejected jobs. We show that these problems are NP-hard, and design algorithms based on dynamic programming (including pseudo-polynomial time optimal algorithms and fully polynomial time approximation schemes) to solve them.     

关于总误工损失的两个代理单机排序问题

研究了与总误工损失相关的两个代理的单机排序问题。第一个代理以工件的总误工损失为目标函数,第二个代理以工件的总完工时间或总误工工件数为目标函数。目标是寻找一个排序,使得在第二个代理的目标函数不超过给定的上界的条件下,第一个代理的目标函数值最小。对这两个与总误工损失相关的两个代理的单机排序问题,分别给出它们的拟多项式时间的动态规划算法。     

Single machine scheduling with exponential learning functions

In this paper we consider the single machine scheduling problem with exponential learning functions. By the exponential learning functions, we mean that the actual job processing time is a function of the total normal processing times of the jobs already processed. We prove that the shortest processing time (SPT) rule is optimal for the total lateness minimization problem. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms. It also shows that the problems of minimizing the total tardiness and discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.     

Batch scheduling and common due-date assignment on a single machine

We consider the problem of scheduling n groups of jobs on a single machine where three types of decisions are combined: scheduling, batching and due-date assignment. Each group includes identical jobs and may be split into batches; jobs within each batch are processed jointly. A sequence independent machine set-up time is needed between each two consecutively scheduled batches of different groups. A due-date common to all jobs has to be assigned. A schedule specifies the size of each batch, i.e. the number of jobs it contains, and a processing order for the batches. The objective is to determine a value for the common due-date and a schedule so as to minimize the sum of the due date assignment penalty and the weighted number of tardy jobs. Several special cases of this problem are shown to be ordinary NP-hard. Some cases are solved in O(n log n) time. Two pseudopolynomial dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme.     

有关单机两代理排序问题的两个结果

研究了两个单机两代理排序问题. 在第一个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化最大工件费用. 在第二个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化所有工件的最大完工时间. 证明了第一个问题是强NP-难的, 改进了已有的一般意义NP-难的结果; 对第二个问题给出了一个与现有的动态规划算法不同的动态规划算法.     

Group sequencing around a common due date

The problem of scheduling groups of jobs on a single machine under the group technology assumption is studied. Jobs of the same group are processed contiguously and a sequence independent setup time precedes the processing of each group. All jobs have a common fixed due date, which can be either unrestrictively large or restrictively small. The objective is to minimize the total weighted earliness–tardiness. Properties of optimal solutions are established, and dynamic programming algorithms are derived to solve several special cases of this problem. Computational experiments show that the algorithms can easily solve problems with 500 groups of jobs and each group has 10 to 50 jobs on a standard PC.     

Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect

In this paper we consider the single machine scheduling problems with exponential sum-of-logarithm-processing-times based learning effect. By the exponential sum-of-logarithm-processing-times based learning effect, we mean that the processing time of a job is defined by an exponent function of the sum of the logarithm of the processing times of the jobs already processed. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

Single-machine scheduling with linear decreasing deterioration to minimize earliness penalties

We consider a single-machine scheduling problem with linear decreasing deterioration in which the due dates are determined by the equal slack (SLK) method. By the linear decreasing deterioration, we mean that the job’s processing time is a decreasing function of its starting time. The objective is to minimize the total weighted earliness penalty subject to no tardy jobs. We prove that two special cases of the problem remain polynomially solvable. The first case is the problem with equally weighted monotonous penalty objective function and the other case is the problem with weighted linear penalty objective function.     

并行分批排序综述

并行分批排序起源于半导体芯片制造过程。在并行分批排序中,工件可成批加工,批加工机器最多可同时加工B个工件,批的加工时间为批中所有工件的最大工时。首先根据传统的机器环境和目标函数对并行分批排序已有成果进行分类介绍,主要为单机和平行机的机器环境,以及极小化最大完工时间、极小化总完工时间、极小化最大延迟、极小化误工工件数、极小化总延误和极小化最大延误的目标函数;然后梳理了由基本问题所衍生出来的具有新特点的16类新型并行分批排序,包括差异尺寸工件、多目标、工件加工时间或顺序存在限制、考虑费用和具有特殊机制等情况;最后展望未来的研究方向。     

Minimizing the weighted number of tardy jobs and maximum tardiness in relocation problem with due date constraints

The relocation problem addressed in this paper is to determine a reconstruction sequence for a set of old buildings, under a limited budget, such that there is adequate temporary space to house the residents decanted during rehabilitation. It can be regarded as a resource-constrained scheduling problem where there is a set of jobs to be processed on a single machine. Each job demands a number of resources for processing and returns probably a different number of resources on its completion. Given a number of initial resources, the problem seeks to determine if there is a feasible sequence for the successful processing of all the jobs. Two generalizations of the relocation problem in the context of single machine scheduling with due date constraints are studied in this paper. The first problem is to minimize the weighted number of tardy jobs under a common due date. We show that it is NP-hard even when all the jobs have the same tardy weight and the same resource requirement. A dynamic programming algorithm with pseudo-polynomial computational time is proposed for the general case. In the second problem, the objective is to minimize the maximum tardiness when each job is associated with an individual due date. We prove that it is strongly NP-hard. We also propose a pseudo-polynomial time dynamic programming algorithm for the case where the number of possible due dates is predetermined.