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。     

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.     

Two-machine flowshop scheduling to minimize the number of tardy jobs

We consider the two-machine flowshop problem with the objective of minimizing the total number of tardy jobs. Since this problem is known to be strongly NP-hard, algorithms are described for four polynomially solvable special cases. In addition, several heuristic algorithms are developed to find optimal or near optimal schedules. Results of computational tests in solving problems up to 60 jobs are reported and directions for future research are provided.     

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 mean tardiness subject to unspecified minimum number tardy for a single machine

In this paper we propose a hybrid branch and bound algorithm for solving the problem of minimizing mean tardiness for a single machine problem subject to minimum number of tardy jobs. Although the minimum number of tardy jobs is known, the subset of tardy job is not known. The proposed algorithm uses traditional branch and bound scheme where lower bounds on mean tardiness are calculated coupled with using the information that the number of tardy jobs is known. It also uses an insertion algorithm which determines the optimal mean tardiness once the subset of tardy jobs is specified. An example is solved to illustrate the developed procedure.     

Minimum weighted number of tardy jobs on an m-machine flow-shop with a critical machine

We study a flow-shop problem, where each of the jobs is limited to no more than two operations. One of these operations is common for all the jobs, and is performed on the same (”critical”) machine. Reflecting many applications, jobs are assumed to be processed in blocks on the critical machine. All the jobs share a common due-date, and the objective is minimum weighted number of tardy jobs. We prove that the problem is NP-hard. Then we formulate the problem as an integer program, and introduce a pseudo-polynomial dynamic programming algorithm, proving that the problem is NP-hard in the ordinary sense. We also propose an efficient heuristic, which is shown numerically to produce very close-to-optimal schedules. Finally, we show that the special case of identical weights is polynomially solvable.     

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.     

最小化提前/延误赋权工件数及时窗惩罚的排序问题

研究赋权提前/延误工件数的公共时窗单机排序问题,时窗的位置和大小待定且由惩罚费用衡量.首先给出最优排序的一些性质,进而提出一个多项式时间算法以最小化这些费用的和.     

工件加工时间是开工时间线性函数的单机排序问题

研究了具有线性恶化工件的单机排序问题,其中线性恶化工件指的是工件的加工时间是开工时间的线性增长函数.在一般情况下,对目标函数为极小化完工时间平方和与极小化总误工数问题分别给出了最优算法.此外,在分段情况下,对目标函数为极小化最大完工时间问题也给出了最优算法.     

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.     

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.     

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.     

Approximation results in parallel machnies stochastic scheduling

We consider scheduling a batch of jobs with stochastic processing times on parallel machines. We derive various new formulae for the expected flowtime and weighted flowtime under general scheduling rules. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time provides a natural heuristic for this problem. We obtain a bound on the worst case difference between the expected weighted flow time under Smith's Rule and under an optimal policy. For a wide class of processing time distributions, this bound is of oderO(1) and does not increase with the number of jobs.This research was supported in part by NSF Grant ECS-8712798.     

Single machine scheduling to minimize weighted earliness subject to no tardy jobs

This paper considers the single machine scheduling problem where the objective is to minimize the total weighted earliness subject to no tardy jobs. Known results for a well researched single machine scheduling problem where the objective is to minimize the weighted completion time subject to no tardy jobs have been used in analyzing this problem. Several important results are proved and both exact and approximate methods are developed to solve this problem.     

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.     

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.     

一类变工时的单机排序问题

提出了一类可变加工时间的单台机器排序问题,着重考虑如下的目标函数：最小化工件排序长度、完工时间之和误工工件数等等,且用受束的等规模划分问题证明了可变加工时间的单台机器排序问题是ＮＰ－完全的。     

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.     

Scheduling linear deteriorating jobs to minimize the number of tardy jobs

In this paper a problem of scheduling a single machine under linear deterioration which aims at minimizing the number of tardy jobs is considered. According to our assumption, processing time of each job is dependent on its starting time based on a linear function where all the jobs have the same deterioration rate. It is proved that the problem is NP-hard; hence a branch and bound procedure and a heuristic algorithm with O(n ²) is proposed where the heuristic one is utilized for obtaining the upper bound of the B&B procedure. Computational results for 1,800 sample problems demonstrate that the B&B method can solve problems with 28 jobs quickly and in some other groups larger problems are also solved. Generally, B&B method can optimally solve 85% of the samples which shows high performance of the proposed method. Also it is shown that the average value of the ratio of optimal solution to the heuristic algorithm result with the objective ??(1 ? Ui) is at most 1.11 which is more efficient in comparison to other proposed algorithms in related studies in the literature.