Scheduling jobs with deterioration effect and controllable processing time

This article considered the single machine scheduling with controllable processing time (resource allocation) and deterioration effect concurrently. It discussed the minimization of three objectives, which involve the weighted sum of the makespan and the total resource consumption cost, the total resource consumption cost under the condition that the makespan (total flow time) is restricted to a fixed constant and the optimal resource allocation and the optimal job sequence is what we need to make decision. Considering the makespan constraint, it proved that these problems can be solved in polynomial time. A special case of the last problem can be solved in polynomial time with respect to the total flow time constraint.

     

Single-machine scheduling with learning effect and resource-dependent processing times

We consider resource allocation scheduling with learning effect in which the processing time of a job is a function of its position in a sequence 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 analyse the problem with two different processing time functions. For each combination of these, we provide a polynomial time algorithm to find the optimal job sequence and resource allocation.     

Two-machine no-wait flowshop scheduling with learning effect and convex resource-dependent processing times

Two-machine no-wait flowshop scheduling problems in which the processing time of a job is a function of its position in the sequence and its resource allocation are considered in the study. The primary objective is to find the optimal sequence of jobs and the optimal resource allocation separately. Here we propose two separate models: minimizing a cost function of makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function of makespan, total waiting time, total absolute differences in waiting times and total resource cost. Since each model is strongly NP-hard, we solve both models by breaking them down to two sub-problems, the optimal resource allocation problem for any job sequence and the optimal sequence problem with its optimal resource allocation. Specially, we transform the second sub-problem into the minimum of the bipartite graph optimal matching problem (NP-hard), and solve it by using the classic KM (Kuhn–Munkres) algorithm. The solutions of the two sub-problems demonstrate that the target problems remain polynomial solvable under the proposed model.     

Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation

We consider various single machine scheduling problems in which the processing time of a job depends either on its position in a processing sequence or on its start time. We focus on problems of minimizing the makespan or the sum of (weighted) completion times of the jobs. In many situations we show that the objective function is priority-generating, and therefore the corresponding scheduling problem under series-parallel precedence constraints is polynomially solvable. In other situations we provide counter-examples that show that the objective function is not priority-generating.     

具有线性恶化加工时间的调度问题

讨论了工件具有线性恶化加工时间的调度问题.在这类问题中,工件的恶化函数为线性 函数.对单机调度问题中目标函数为极小化最大完工时间加权完工时间和,最大延误以及最大费 用等问题分别给出了最优算法.对两台机器极小化最大完工时间的Flowshop问题,证明了利用 Johnson规则可以得到最优调度.对于一般情况,如果同一工件的工序的加工时间均相等,则 Flowshop问题可以转化为单机问题.     

Single-machine group scheduling with both learning effects and deteriorating jobs

In the paper two resource constrained single-machine group scheduling problems with both learning effects and deteriorating jobs are considered. By learning effects, deteriorating jobs and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.     

Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects

In this paper, we study the problem of minimizing the weighted sum of makespan and total completion time in a permutation flowshop where the processing times are supposed to vary according to learning effects. The processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in the sequence. We present heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound. We also adopt an existing algorithm as well as a branch-and-bound algorithm for the general m-machine permutation flowshop problem. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems.     

Single-machine scheduling problems with deteriorating jobs and learning effects

In this paper, we introduce a new scheduling model in which deteriorating jobs and learning effect are both considered simultaneously. By deterioration and the learning effect, we mean that the actual processing time of a job depends not only on the processing time of the jobs already processed but also on its scheduled position. For the single-machine case, we show that the problems of makespan, total completion time and the sum of the quadratic job completion times remain polynomially solvable, respectively. In addition,we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain conditions.     

到达时间依赖于资源分配的单机排序问题*

研究了具有线性退化及学习效应作用下的单机排序问题,对于工件的到达时间是其资源消耗量的正的严格单调递减函数时,考虑了总资源消耗量限定情形下最大完工时间极小化问题,给出了相应的最优算法;也考虑了满足工件最大完工时间限制的条件下极小化资源消耗的总量问题,提出最优资源分配方案。     

Resource-dependent scheduling with deteriorating jobs and learning effects on unrelated parallel machine

The focus of this paper is to analyze unrelated parallel-machine resource allocation scheduling problem with learning effect and deteriorating jobs. The goal is to find the optimal sequence of jobs and the optimal resource allocation separately for minimizing the cost function including the total load, the total completion time, the total absolute deviation of completion time and the total resource cost. We show that the problem is polynomial time solvable if the number of machines is a given constant.     

Flowshop scheduling with a general exponential learning effect

This paper investigates flowshop scheduling problems with a general exponential learning effect, i.e., the actual processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The objective is to minimize the makespan, the total (weighted) completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times, respectively. Several simple heuristic algorithms are proposed in this paper by using the optimal schedules for the corresponding single machine problems. The tight worst-case bound of these heuristic algorithms is also given. Two well-known heuristics are also proposed for the flowshop scheduling with a general exponential learning effect.     

Single-machine scheduling with deteriorating jobs

In this article, we study a single-machine scheduling problem in which the processing time of a job is a nonlinear function of its basic processing time and starting time. The objectives are to minimise the makespan, the sum of weighted completion times and the sum of the kth powers of completion times. We show that the makespan minimisation problem can be solved in polynomial time. However, the total completion time and the sum of the kth powers of completion times minimisation problems can be solved in polynomial time in some cases. Besides, some useful properties are also provided for the sum of weighted completion times problem under certain conditions.     

A note on single-machine scheduling with general learning effect and past-sequence-dependent setup time

In this paper, we study a scheduling model with the consideration of both the learning effect and the setup time. Under the proposed model, the learning effect is a general function of the processing time of jobs already processed and its scheduled position, and the setup time is past-sequence-dependent. We then derive the optimal sequences for two single-machine problems, which are the makespan and the total completion time. Moreover, we showed that the weighted completion time, the maximum lateness, the maximum tardiness, and the total tardiness problems remain polynomially solvable under agreeable conditions.     

Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects

In this paper we introduce a new scheduling model with learning effects in which the actual processing time of a job is a function of the total normal processing times of the jobs already processed and of the job’s scheduled position. We show that the single-machine problems to minimize makespan and total completion time are polynomially solvable. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. Finally, we present polynomial-time optimal solutions for some special cases of the m-machine flowshop problems to minimize makespan and total completion time.     

A bicriterion approach to time/cost trade-offs in scheduling with convex resource-dependent job processing times and release dates

This paper presents a bicriterion analysis of time/cost trade-offs for the single-machine scheduling problem where both job processing times and release dates are controllable by the allocation of a continuously nonrenewable resource. Using the bicriterion approach, we distinguish between our sequencing criterion, namely the makespan, and the cost criterion, the total resource consumed, in order to construct an efficient time/cost frontier. Although the computational complexity of the problem of constructing this frontier remains an open question, we show that the optimal job sequence is independent of the total resource being used; thereby we were able to reduce the problem to a sequencing one. We suggest an exact dynamic programming algorithm for solving small to medium sizes of the problem, while for large-scale problems we present some heuristic algorithms that turned out to be very efficient. Five different special cases that are solvable by using polynomial time algorithms are also presented.     

Integer linear programming-based multi-objective scheduling for scientific workflows in multi-cloud environments

Scientific communities are motivated to schedule the data-intensive scientific workflows in multi-cloud environments, where considerable diverse resources are provided by multiple clouds and resource limitation imposed by individual clouds is overcome. However, this scheduling involves two conflicting objectives: minimizing cost and makespan. In general, dealing with such conflicting criteria is a difficult task. But fortunately recent efficient methods for solving multi-objective optimization problems motivated us to provide a multi-objective model considering minimization of cost and makespan as objectives. For solving this model, we use different scalarization procedures such as weighted-sum, Benson's scalarization and weighted min–max under different scenarios. Moreover, we investigate the stability of obtained solutions and propose a new approach for determining the most stable solution related to weighted-sum and weighted min–max as post-optimality analysis. Results indicate that our proposed weighted-sum approach outperforms the previously developed methods in terms of hypervolume.

     

Makespan minimization subject to flowtime optimality on identical parallel machines

We consider the identical parallel machine problem with makespan minimization subject to minimum total flowtime. First, we develop an optimal algorithm to the identical parallel machine problem with the objective of minimizing makespan. To improve the computational efficiency, two implementation techniques, the lower bound calculation and the job replacement rule, are applied. Based on the algorithm, an optimal algorithm, using new lower bounds, to the considered problem is developed. The result of this study can also be used to solve the bicriteria problem of minimizing the weighted sum of makespan and mean flowtime. Computational experiments are conducted up to six machines and 1000 jobs. Although the proposed algorithm has an exponential time complexity, the computational results show that it is efficient to find the optimal solution.     

一类线性加工时间单机调度问题

讨论一类线性加工时间单机调度问题.在这类问题中,工件具有相同的基本加工时间, 但每个工件的实际加工时间以其开工时间线性增长.对满足无延迟工件条件下极小化提前惩罚 和问题,满足最大完工时间限制条件下极小化资源消耗总量的问题和满足资源消耗总量限制条 件下极小化最大完工时间的问题,分别给出了最优算法.     

Scheduling parallelizable tasks to minimize make-span and weighted response time

This paper presents a generalization to classical scheduling theory by removing the restriction that only one processor can work on a given task at a particular time. Instead, it is assumed that each task can be allocated any number of identical processors from one to the maximum number available, with each task's completion time being a function of the number of processors allocated. Tasks may be started any time, but once started, a task must not have its processor allocation altered or be preempted. Two objective functions are considered: minimizing the overall completion time for the tasks (make-span) and minimizing a weighted sum of the task completion times (weighted response). Both are considered subject to a constraint on the total number of processors available. Suboptimal algorithms are developed for both of these NP-hard problems using Lagrangian relaxation, and their performances are analyzed through extensive simulations. Duality gaps for all problems tested ranged from under 1% to 92%, depending more on the problem size than the specific problem.     

一类资源约束的单机成组调度问题

本文讨论具有连续资源的单机成组调度问题.在这一模型中,工件组的安装时间是所消耗资源的非负严格减少连续函数,工件的加工时间是开工时间的严格增加函数.考虑两个问题,第1个问题是在满足资源消耗总量限制条件下,极小化最大完工时间.第2个问题的目标函数是在满足最大完工时间限制条件下,极小化资源消耗总量.分别对两个问题讨论了最优调度的某些特征,分别给出了求解最优资源分配的方法,并通过数值例子进行说明.