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.     

Single-machine scheduling with time-and-resource-dependent processing times

We consider single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. We show that the problems remain polynomially solvable under the proposed model.     

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。     

Unrelated parallel-machine scheduling with position-dependent deteriorating jobs and resource-dependent processing time

This paper is to analyze unrelated parallel-machine scheduling resource allocation problems with position-dependent deteriorating jobs. Two general resource consumption functions, the linear and convex resource, are investigated. The objectives are to minimize the cost function that includes the weights of total load, total completion time, total absolute deviation of completion time, and total resource cost. Moreover, we try to minimize the cost function that includes the weights of total load, total waiting time, total absolute deviation of waiting time, and total resource cost. Although each job processing time can be compressed through incurring an additional cost, we show that the problems are polynomial time solvable when the number of machines is fixed.     

Scheduling controllable processing time jobs in a deteriorating environment

In many real-life applications, job processing times are a function of the waiting time prior to their execution. In the most general setting, each job comprises of a basic processing time, which is independent of its start time, and a start time-dependent deterioration function. Some common examples of deteriorating systems include fire fighting, pollution containment, and medical treatments. To date, research has focused on scheduling models where the basic processing time of jobs is constant. However, job processing times are often controllable through the allocation of a limited non-renewable resource. We study a single-machine setting that combines these two models under the assumptions of general linear deterioration and convex resource functions. We develop a polynomial time solution for minimizing the makespan. For the total flowtime criterion, we compute the optimal resource allocation policy for a given job instance and show that the sequencing problem is at least as hard as the case with non-controllable jobs. We follow by discussing the properties of several special cases.     

Parallel machines scheduling with deteriorating and learning effects

In this paper parallel identical machines scheduling problems with deteriorating jobs and learning effects are considered. In this model, job processing times are defined by functions of their starting times and positions in the sequence. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. We show that the problems remain polynomially solvable under the proposed model.     

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.     

Scheduling deteriorating jobs with a learning effect on unrelated parallel machines

In this study we consider unrelated parallel machines scheduling problems with learning effect and deteriorating jobs, in which the actual processing time of a job is a function of joint time-dependent deterioration and position-dependent learning. The objective is to determine the jobs assigned to corresponding each machine and the corresponding optimal schedule to minimize a cost function containing total completion (waiting) time, total absolute differences in completion (waiting) times and total machine load. If the number of machines is a given constant, we show that the problems can be solved in polynomial time under the time-dependent deterioration and position-dependent learning model.     

Single machine scheduling problems with controllable processing times and total absolute differences penalties

In this paper, we consider single machine scheduling problem in which job processing times are controllable variables with linear costs. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time, total absolute differences in completion times and total compression cost; minimizing a cost function containing total waiting time, total absolute differences in waiting times and total compression cost. The problem is modelled as an assignment problem, and thus can be solved with the well-known algorithms. For the case where all the jobs have a common difference between normal and crash processing time and an equal unit compression penalty, we present an O(n log n) algorithm to obtain the optimal solution.     

Parallel-machine scheduling with non-simultaneous machine available time

We consider a problem of scheduling n independent jobs on m parallel identical machines. The jobs are available at time zero, but the machines may not be available simultaneously at time zero. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. In this paper, we present polynomial time algorithm to solve this problem.     

带凸资源和恶化效应的单机松弛窗口排序

研究带凸资源和恶化效应的单机窗口指派排序问题,其中窗口指的是松弛窗口,凸资源和恶化效应指的是工件的实际加工时间是其开始加工时间的线性函数,是其资源消耗量的凸函数。目标是确定工件的加工顺序,资源分配量以及窗口的开始加工时间和长度使其在总资源消耗费用(与窗口有关的排序费用)有上界限制的条件下,极小化与窗口有关的排序费用(总资源消耗费用)。获得了求解上述问题的最优算法,证明了该问题是多项式时间可解的。     

A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates

In most deterministic scheduling problems, job-processing times are regarded as constant and known in advance. However, in many realistic environments, job-processing times can be controlled by the allocation of a common resource to jobs. In this paper, we consider the problem of scheduling jobs with arbitrary release dates and due dates on a single machine, where job-processing times are controllable and are modeled by a non-linear convex resource consumption function. The objective is to determine simultaneously an optimal processing permutation as well as an optimal resource allocation, such that no job is completed later than its due date, and the total resource consumption is minimized. The problem is strongly NP\mathcal{NP}-hard. A branch and bound algorithm is presented to solve the problem. The computational experiments show that the algorithm can provide optimal solution for small-sized problems, and near-optimal solution for medium-sized problems in acceptable computing time.     

Single-machine group scheduling with processing times dependent on position,starting time and allotted resource

This article considers scheduling problems on a single machine with learning effect, deteriorating jobs and resource allocation under group technology (GT) assumption. We assume that the actual processing time of a job depends on the job position, the group position, the starting time and the amount of resource allocated to them concurrently, and the actual setup times of groups depend on the group position and the amount of resource allocated to them concurrently. Two resource allocation functions are examined for minimizing the weighted sum of makespan and total resource cost. We prove that the problems have polynomial solutions under the condition that the number of jobs in each group are the same.     

Some single-machine scheduling with sum-of-processing-time-based and job-position-based processing times

The single-machine scheduling problems with position and sum-of-processing-time based processing times are considered. The actual processing time of a job is defined by function of its scheduled position and total normal processing time of jobs in front of it in the sequence. We provide optimal solutions in polynomial time for some special cases of the makespan minimization and the total completion time minimization. We also show that an optimal schedule to be a V-shaped schedule in terms of the normal processing times of jobs for the total completion time minimization problem and the makespan minimization problem.     

Single-machine scheduling problems with past-sequence-dependent delivery times and position-dependent processing times

This paper considers single-machine scheduling problems with job delivery times where the actual job processing time of a job is defined by a function dependent on its position in a schedule. We assume that the job delivery time is proportional to the job waiting time. We investigate the minimization problems of the sum of earliness, tardiness, and due-window-related cost, the total absolute differences in completion times, and the total absolute differences in waiting times on a single-machine setting. The polynomial time algorithms are proposed to optimally solve the above objective functions. We also investigate some special cases of the problem under study and show that they can be optimally solved by lower order algorithms.     

Single machine scheduling with a time-dependent learning effect and deteriorating jobs

The paper deals with the single machine scheduling problems with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the processing time of a job is defined by function of its starting time and total normal processing time of jobs in front of it in the sequence. It is shown that even with the introduction of a time-dependent learning effect and deteriorating jobs to job processing times, the single machine makespan minimization problem remain polynomially solvable. But for the total completion time minimization problem, the classical shortest processing time first rule or largest processing time first rule cannot give an optimal solution.     

A Heuristic Solution Procedure to Minimize Makespan on a Single Machine with Non-linear Cost Functions

We consider the static single-facility scheduling problem where the processing times of jobs are a nondecreasing and differentiable function of their starting (waiting) times and the objective is to minimize the total elapsed time (makespan) in which all jobs complete their processing. We give a criterion for optimality of two jobs to be scheduled next to each other, and based on this criterion we propose a heuristic algorithm to solve the problem. The effectiveness of the algorithm is empirically evaluated for quadratic and exponential cost functions. In the quadratic case it is compared with the static heuristic algorithm proposed by Gupta and Gupta.     

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 scheduling problems with an aging effect

This paper considers single machine scheduling problems where the processing time of a job increases as a function of its position in the sequence. In this model, the later a given job is scheduled in the sequence, the longer its processing time. It is shown that the optimal schedule may be very different from that of the classical version of the problem. We introduce polynomial solutions for the makespan minimization problem, the sum of completion times minimization problem and the sum of earliness penalties minimization problem. For two resource constrained problems, based on the analysis of the problems, the optimal resource allocation methods are presented, respectively.     

带有退化效应和序列相关运输时间的排序问题

考虑带有退化效应和序列相关运输时间的单机排序问题. 工件的加工时间是其开工时间的简单线性增加函数. 当机器单个加工工件时, 极小化最大完工时间、(加权)总完工时间和总延迟问题被证明是多项式可解的, EDD序对于极小化最大延迟问题不是最优排序, 另外, 就交货期和退化率一致情形给出了一最优算法. 当机器可分批加工工件时, 分别就极小化最大完工时间和加权总完工时间问题提出了多项式时间最优算法.