具有恶化效应和凸资源分配关系的单机排序问题

研究工件加工时间具有恶化效应和凸资源关系的单机排序问题,其中工件的实际加工时间是其正常的加工时间,工件开工时间(具有恶化效应)及消耗资源量的函数。目标为在最大完工时间(总完工时间、总等待时间、完工时间总绝对差与等待时间总绝对差)小于或等于给定常数的条件下找到工件的最优排序和最优的资源分配使工件的总资源消耗量最少。在单机状态下,证明了此问题是多项式时间可解的,并给出了求解该问题的算法和数值实例。     

优化交货期窗口的两阶段供应链排序问题

研究一类优化交货期窗口的两阶段供应链排序问题. 优化交货期窗口是指交货期窗口的开始与结束时刻是决策变量, 不是输入常量. 两阶段是指工件先加工, 后运输: 加工阶段是一台加工机器逐个加工工件;运输阶段是无限台车辆分批运输完工的工件. 工件的开始运输时刻与完工时刻之差定义为工件的储存时间, 且有相应的储存费用. 若工件的运输完成时刻早于(晚于)交货期窗口的开始(结束)时刻, 则有相应的提前(延误)惩罚费用. 目标是极小化总提前惩罚费用、总延误惩罚费用、总储存费用、总运输费用以及与交货期窗口有关的费用之和. 针对单位时间的延误惩罚费用不超过单位时间的储存费用、单位时间的储存费用不超过单位时间的提前惩罚费用的情形, 给出了时间复杂性为O(n^{8})的动态规划算法.     

储存时间有上限的两阶段供应链排序问题

研究一类储存时间有上限的两阶段供应链排序问题.两阶段是指工件先加工,后运输:加工阶段是一台加工机器逐个加工工件;运输阶段是无限台车辆分批运输完工的工件.工件的运输完成时刻与完工时刻之差定义为工件的储存时间,且有相应的储存费用,且任意工件的储存时间都不超过某一常数.若工件的运输完成时刻早于(晚于)交货期窗口的开始(结束)时刻,则有相应的提前(延误)惩罚费用.目标是极小化总提前惩罚费用、总延误惩罚费用、总储存费用、总运输费用以及与交货期窗口有关的费用之和.先证明该问题是NP-难的,后对单位时间的储存费用不超过单位时间的延误惩罚费用的情形给出了伪多项式时间算法.     

具有CON/SLK交货期指派的一类单机排序问题

研究工件的实际加工时间既具有指数学习效应,又依赖所消耗资源的准时制排序问题.在模型中,探讨了共同交货期(CON)和松弛交货期(SLK)两种情形.管理者的目标是确定最优序、最优资源分配方案和最佳工期(共同交货期或松弛交货期)以便极小化工件的总延误、总提前、总工期和资源消耗费用的总和.对于工件的实际加工时间是资源消耗量的线性函数的排序问题,通过将其转化为指派模型,给出了时间复杂性为O(n~3)的算法,从而证明该类排序问题是多项式时间可求解的.针对工件的实际加工时间是资源消耗量的凸函数的排序问题,也给出了多项式算法.     

具有学习效应的非同类机资源约束排序问题研究

研究具有学习效应和资源约束的非同类平行机排序,即工件的加工时间与所排机器,所排位置和所用资源都有关系.目地是确定每台机器所分配的工件及其排序和所用的资源量,使所有工件的总完工时间和总资源消耗费用的加权和最小.在非同类机的数量给定的情况下,证明了这个问题能够在多项式时间内解决,并给出了一个例子来说明问题是如何求解的.     

具有资源约束的工期指派排序问题

研究在资源有限情况下,工件加工具有学习效应和凸资源依赖的单机排序问题,其中工件的实际加工时间与正常的加工时间,工件所排位置,学习因子及资源分配量都有关,为资源消耗量的一个凸函数.在模型中,讨论了两种情形::共同交货期(CON),共同松弛交货期(SLK).目标为确定工件的排序,资源分配和工件的工期,使得工件的提前、延误、工期费用的总和最小.在分配资源量有限情况下,证明了这两个问题都是多项式时间可解的,并给出了相应的算法.     

带学习效应和资源依赖的单机排序模型

在工业生产中,随着员工操作技能的熟练程度的增加,对于相同的任务越往后加工,所花的时间将会减少。 同时,为了尽早完工,管理者也会考虑给加工工件分配一定量的额外资源来缩短工件加工时间。 本文基于以上实例,讨论了工件的实际加工时间既具有学习效应又依赖所分配资源的单机排序问题。 在问题中,假设工件的学习效应是之前已加工工件正常加工时间和的指数函数。 同时随着分配给工件资源量的增加,工件的实际加工时间呈线性减少,所需费用呈线性增加。对这一排序模型,主要探讨以下五个目标函数:最小化最大完工时间与资源消耗量总费用的和;最小化总完工时间与资源消耗量总费用的和;最小化加权总完工时间与资源消耗量总费用的和;最小化总提前、总延误、总共同交货期与资源消耗量总费用的和以及最小化总提前、总延误、总松弛交货期与资源消耗量总费用的和。 本文对前三个目标函数相应的排序问题给出了多项式时间可求解的算法。 对后两个目标函数所涉及的排序问题借助于指派问题分别给出了时间复杂性为O(n³)的算法。     

具有凸资源约束的单机指数学习效应问题

研究在所有工件的正常加工时间均相同的情况下具有指数学习效应和凸资源约束的单机排序问题.给出了两种模型:在资源消耗总费用有限的情况下,以工件的最大完工时间为目标函数;在工件的最大完工时间有限的情况下,以资源消耗总费用为目标函数.求两种模型下的最优排序和最优资源分配,使得目标函数最小.证明这两个问题都是多项式时间可解的,并给出了相应的算法.     

平行机的供应链排序

研究平行机环境下的供应链排序,即研究如何安排工件在平行机上加工,把加工完毕的工件分批发送给下游客户,使得生产排序费用和发送费用总和最少。这里,生产排序费用是用工件送到时间的函数表示;发送费用是由固定费用和与运输路径有关的可变费用两部分组成。研究以工件带权送到时间和作为生产排序费用的供应链排序问题,给出多项式时间近似算法,并分析算法性能比。     

工期窗口安排与具有退化效应和维修活动的单机排序

考虑具有工件相关的退化效应和维修活动的单机排序模型,讨论了工期窗口安排问题.在这一模型中,机器在加工过程中产生退化使效率降低,工件的实际加工时间不仅与其所在排序中的位置有关并且与其本身的退化率有关;然而,维修活动能使机器的加工效率得到恢复.工期窗口的开始时间是已给定的常量,而工期窗口的结束时间是需要确定的变量.目标是得到安排维修活动的最佳时间、最佳工期窗口的大小和最优排序以便最小化流时间、提早、延误和工期窗口大小的总处罚函数.对这一问题,给出了一多项式算法.     

Single machine common flow allowance scheduling with deteriorating jobs and a rate-modifying activity

We study a single machine slack due date assignment (usually referred to as SLK) scheduling problem with deteriorating jobs and a rate-modifying activity. The deterioration effect manifest such that the job processing time is a function of its starting time in a sequence. The rate-modifying activity is an activity that changes the processing rate of machine, i.e., the machine performs a rate-modifying activity. Hence the actual processing time of a job is a variable, which depends not only on its starting time in a sequence but also on whether it is scheduled before or after a rate-modifying activity. The goal is to schedule the rate-modifying activity, the optimal common flow allowance and the sequence of jobs to minimize the total earliness, the total tardiness and the common flow allowance cost. We show that the problem remains polynomially solvable under the proposed model.     

Single-machine scheduling with convex resource dependent processing times and deteriorating jobs

In this study, we consider scheduling problems with convex resource dependent processing times and deteriorating jobs, in which the processing time of a job is a function of its starting time and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately. This paper focus on the single-machine problems with objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. It shows that the problems remain polynomially solvable under the proposed model.     

Unrelated parallel machines scheduling with deteriorating jobs and resource dependent processing times

We consider unrelated parallel machines scheduling problems involving resource dependent (controllable) processing times and deteriorating jobs simultaneously, i.e., the actual processing time of a job is a function of its starting time and its resource allocation. Two generally resource consumption functions, the linear and convex resource, were investigated. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. This paper focus on the objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. If the number of unrelated parallel machines is a given constant, we show that the problems remain polynomially solvable under the proposed model.     

具有退化工件和工期窗口安排的排序问题

针对具有退化工件的排序模型,考虑了单机排序和两台机器流水作业的工期窗口安排问题,在这一模型中,工件的加工时间是与其开工时间和退化率有关的一个线性函数。目标是找到一个最优排序和确定工期窗口的开始时间及大小以便最小化所有工件的费用函数,费用函数由四部分组成:提前、延误、工期窗口开始时间和工期窗口大小。对所研究的单机问题,详细地讨论了符合现实情况的几种类型问题,并得到了问题的最优解;对两台机器流水作业问题,给出了多项式算法。     

Optimal due-date assignment problem with learning effect and resource-dependent processing times

In this paper, we consider a single-machine earliness-tardiness scheduling problem with due-date assignment, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The due date assignment methods studied include the common due date, and the slack due date, which reflects equal waiting time allowance for the jobs. For each combination of due date assignment method and processing time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes earliness, tardiness, due date assignment, and total resource consumption costs.     

Single-machine group scheduling with deteriorating jobs and allotted resource

In this paper, we consider single-machine scheduling problems with deteriorating jobs and resource allocation in a group technology environment. In the proposed model of this paper the actual processing time of a job depend on its starting time and the amount of resource allocated to it, and the actual setup time of a group depend on its starting time and the amount of resource allocated. Deterioration effect and two resource allocation functions are examined for minimizing the weighted sum of makespan and total resource cost. For the linear resource allocation function and the convex resource allocation function, we show that the problem remains polynomially solvable 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.     

Single-machine scheduling to minimize total absolute differences in waiting times with deteriorating jobs

In this paper we consider a single-machine scheduling problem with simple linear deterioration. By simple linear deterioration, we mean that the processing time of a job is a simple linear function of its execution starting time and its deterioration rate. The objective is to find a schedule that minimizes total absolute differences in waiting times. We show that the optimal schedule is V-shaped: jobs are arranged in descending order of their deterioration rates if they are placed before the job with the smallest deterioration rate, but in ascending order of their deterioration rates if placed after it. We prove other several properties of an optimal schedule, and introduce two efficient heuristic algorithms that are tested against a lower bound. We also provide computational results to evaluate the performance of the heuristic algorithms.