Fuzzy resource‐constrained project scheduling using taboo search algorithm

This paper proposes a mathematical model to deal with project scheduling problem under vagueness and a framework of a heuristic approach to fuzzy resource‐constrained project scheduling problem (F‐RCPSP) using heuristic and metaheuristic scheduling methods. Our approach is very simple to apply, and it does not require knowing the explicit form of the membership functions of the fuzzy activity times. We first identify two typical activity priority rules, namely, resource over time and minimum slack priority rules. They are used in the F‐RCPS problem and in the initial solution of Taboo search (TS) method. We improved the TS algorithm method for the solution of F‐RCPSP. Our objective is to check the performance of these rules and metaheuristic method in minimizing the project completion time for the F‐RCPS problems. In our study, we use trapezoidal fuzzy numbers (TraFNs) for activity times and activity‐on‐nodes (AON) representation and compute several project characteristics such as earliest, latest, and slack times in terms of TraFNs. The computational experiment shows that the performance of the proposed TS is better than the evaluation and light beam search algorithms in the literature. © 2012 Wiley Periodicals, Inc.     

A basis for the design of a multiattribute heuristic for single resource project scheduling

Two important characteristics of a project network are the network's topology and the amount of resources available. Most published project scheduling procedures take one or both of these two characteristics into account. Project scheduling procedures that are robust over variations of network characteristics are desirable. The degree of robustness is generally gauged by one or more measures of performance.

The objective of this paper is to compare a set of priority rules that are useful for a single resource project scheduling problem. The set of networks suggested by Patterson (1973) is used along with the set of performance measures proposed by Khattab and Choobineh 1991. The result of this comparison allows one to design a multiattribute heuristic for a single resource project scheduling problem.     

Multi-mode resource-constrained project scheduling problems with non-preemptive activity splitting

In this paper, we explore the difference between preemption and activity splitting in the resource-constrained project scheduling problem (RCPSP) literature and identify a new set of RCPSPs that only allows non-preemptive activity splitting. Each activity can be processed in multiple modes and both renewable and non-renewable resources are considered. Renewable resources have time-varying resource constraints and vacations. Multi-mode RCPSP (MRCPSP) with non-preemptive activity splitting is shown to be a generalization of the RCPSP with calendarization. Activity ready times and due dates are considered to study the impact on project makespan. Computational experiments are conducted to compare optimal makespans under three different problem settings: RCPSPs without activity splitting (P1), RCPSPs with non-preemptive activity splitting (P2), and preemptive RCPSPs (P3). A precedence tree-based branch-and-bound algorithm is modified as an exact method to find optimal solutions. Resource constraints are included into the general time window rule and priority rule-based simple heuristics are proposed to search for good initial solutions to tighten bounding rules. Results indicate that there are significant makespan reductions possible when non-preemptive activity splitting or preemptions are allowed. The higher the range of time-varying renewable resource limits and the tighter the renewable resource limits are, the bigger the resulting makespan reduction can be.     

An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem

We present an optimal solution procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem. In this problem, we assume the constrained renewable resources are limited to very expensive equipments and machines that are used in other projects and are not available in all periods of time of a project. In other words, for each resource, there is a dictated ready date as well as a due date such that no resource can be available before its ready date but the resources are permitted to be used after their due dates by paying penalty cost depending on the resource type. We also assume that only one unit of each resource type is available and no activity needs more than it for execution. The objective is to determine a schedule with minimal total weighted resource tardiness penalty costs. For this purpose, we present a branch-and-bound algorithm in which the branching scheme starts from a graph representing a set of conjunctions (the classical finish-start precedence constraints) and disjunctions (introduced by the resource constraints). In the search tree, each node is branched to two child nodes based on the two opposite directions of each undirected arc of disjunctions. Selection sequence of undirected arcs in the search tree affects the performance of the algorithm. Hence, we developed different rules for this issue and compare the performance of the algorithm under these rules using a randomly generated benchmark problem set.     

An exact algorithm for an integrated project staffing problem with a homogeneous workforce

When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability. In resource scheduling problems important assumptions are made with respect to the resource requirements. As projects are typically labour intensive, the underlying (personnel) resource scheduling problems tend to be complex due to different rules and regulations. In this paper, we aim to integrate these two interrelated scheduling problems to minimise the overall cost. For that purpose, we propose an exact algorithm for the project staffing with resource scheduling constraints. Detailed computational experiments are presented to evaluate different branching rules and pruning strategies and to compare the proposed procedure with other optimisation techniques.     

物联网环境下具有顺序约束关系的静态任务表调度算法

针对物联网异构调度环境下并行计算的静态任务调度问题,提出了一种基于最早完成时间策略改变调度顺序的表调度算法HDPTS。该算法针对现有表调度算法在调度前不能准确地确定调度顺序的问题,在IHEFT算法的基础上添加了一个动态优先级调度策略,当节点的前驱任务都已经完成调度任务时,就改变该节点的调度优先级。任务优先级的计算在所有前驱任务到达这个任务的最晚完成时间与所有资源上最大可以使用时间之间取最大值的基础上,同时考虑到分配到各个资源上的任务对后继任务的影响和资源上的负载情况,以及上行权重的计算值和对出口任务的影响,使得优先级计算更加合理,能够根据任务分配动态合理改变任务调度顺序。通过随机生成一个算例进行测试,结果表明HDPTS比IHEFT、HEFT在调度长度方面减少14.29%;对大量随机产生的特定结构的有向无环图(DAG)进行测试,测试结果显示HDPTS算法比IHEFT、HEFT和LDCP算法更有效。     

Augmenting priority rule heuristics with justification and rollout to solve the resource-constrained project scheduling problem

The key question addressed by the resource-constrained project scheduling problem (RCPSP) is to determine the start times for each activity such that precedence and resource constraints are satisfied while achieving some objective. Priority rule-based heuristics are widely used for large problems. Rollout and justification can be integrated with priority rule heuristics to solve the RCPSP. We develop several such procedures and examine the resulting solution quality and computational cost. We present empirical evidence that these procedures are competitive with the best solution procedures described in the literature.     

多启发式规则融合粒子群算法的受限项目调度

在船舶生产的现实背景上,对船舶生产过程中如何利用总装平台这一瓶颈资源建立空间资源受限项目调度的问题模型。利用空间资源和分段任务对象的特性,在最大面积优先、最长边优先、BL（Bottom-Left,一种解决布局问题的启发式规则）规则等启发式规则的基础上,提出多启发式规则融合粒子群算法的空间资源受限项目调度算法。将分段任务对象根据几何特性和拖延惩罚因子赋予不同的权值,确定其实际开始时间,再通过最长边优先和BL规则确定其空间位置。设计了具有初始解集并且能够自动识别的粒子群算法,加速其收敛以更快更优地获取分段任务对象序列。通过和其他几种主流的空间调度方法（分支界定和遗传算法）进行不同规模的实验对比,得出该算法在时间复杂度和平均资源利用率方面都有所提高。     

基于直接后继节点完成时间的异构调度算法

分布式环境下的异构计算系统（HCS）是大数据时代进行数据密集型计算不可或缺的,一个有效的任务调度算法可以提高整个异构计算系统的效率。在对异构环境下的任务调度进行有向无环图（DAG）建模的基础上,提出基于直接后继节点完成时间的异构调度算法（HSFT）。在计算开销和通信开销差异度较大的异构环境中,考虑两者之间的平衡,采用更为合理的以计算均值与标准方差的乘积和通信权值与任务节点出度的比值作为优先权值计算方法,并在考虑最快完成时间（EFT）的基础上,将直接后继节点完成时间（SFT）用于处理器分配策略。实验结果表明,HSFT在不增加算法时间复杂度的情况下,比HEFT、SDBATS、PEFT等算法有更短的调度长度（makespan）、更优的调度长度比和效率。     

Using meta-heuristics for project scheduling under mode identity constraints

Mode identity and resource constrained project scheduling problem (MIRCPSP) is a substantial generalization of the well-known multi-mode problem. It arises when certain activities in the project are interdependent. That is, the set of all activities in the project are partitioned into disjoint subsets where all activities forming one subset have to be processed in the same mode. This paper addresses project scheduling problem with resource and mode identity constraints to minimize the project makespan. This problem is strongly NP-hard and three meta-heuristic algorithms namely imperialist competitive algorithm, simulated annealing and differential evolution are proposed to solve it. In order to improve the quality of the employed algorithms a local search and learning module is combined with the meta-heuristic algorithms. The performance of the algorithms is evaluated on 180 test problems by statistically comparing their solution in term of the objective function and computational times. The obtained computational results indicate that the integration of the learning module and the proposed algorithm is efficient and effective.     

Evaluating project completion time in project networks with discrete random activity durations

Deterministic models for project scheduling suffer from the fact that they assume complete information and neglect random influences, that occur during project execution. A typical consequence is the underestimation of the project duration as frequently observed in practice. This phenomenon occurs even in the absence of resource constraints and has been the subject of extensive research in the scientific community. This paper presents a method for obtaining relevant information about the project makespan for scheduling models, with dependent random processing time available in the form of scenarios.     

基于动态资源权重的多技能项目调度启发式算法

多技能资源受限项目调度问题中,一个资源可同时具备多项技能,相较于传统的单技能项目调度,其资源分配对调度计划的工期影响程度更大,因此在对多技能项目进行排程时更加重视资源的分配.基于此,从资源视角提出一种启发式算法求解工期最短的调度计划.算法以并行调度为主体,并设计一种动态资源权重计算方法,在每一决策点,首先采用二分图最大匹配法确定当前可排活动集,而后将动态资源权重值作为调度过程中资源分配的依据,其核心思想是将资源灵活度高、对后续活动影响大的资源留置,以待下一决策点调用.最后,为验证算法有效性,对不同参数设置下的算例进行实验,结果表明,相较于随机资源分配算法和静态资源权重算法,新算法具有明显优势.     

A neuro-genetic approach to design and planning of a manufacturing cell

In this paper, we propose a neuro-genetic decision support system coupled with simulation to design a job shop manufacturing system by achieving predetermined values of targeted performance measures such as flow time, number of tardy jobs, total tardiness and machine utilization at each work center. When a manufacturing system is designed, the management has to make decisions on the availability of resources or capacity, in our setting, the number of identical machines in each work station and the dispatching rule to be utilized in the shop floor to achieve performance values desired. Four different priority rules are used as Earliest due date (EDD), Shortest Processing Time (SPT), Critical ratio (CR) and First Come First Serve (FCFS). In reaching the final decision, design alternatives obtained from the proposed system are evaluated in terms of performance measures. An illustrative example is provided to explain the procedure.     

云计算环境下科学工作流两阶段任务调度策略

经过对云环境下科学工作流现有的任务调度策略进行分析研究,针对异态最早结束时间(HEFT)算法及其改进算法SHEFT在任务执行过程中出现的资源闲置现象,结合云计算的特点,在SHEFT算法的基础上提出了一种两阶段任务调度策略。该策略在完成时间最少的情况下能够对资源的闲置时间进行尽可能的利用。经过对该算法进行实验和性能分析,表明该策略在完成时间和资源利用方面都有很大改进。     

Minimization of project time and cost under constrained reliability index in the disjunctive project model

Proposed was a reliability model of the network project as a complex technical system where the probability of failure-free execution of an activity (project component) was used as the quantitative index of its reliability, and the resulting guaranteed lower estimate of the project, as its reliability index. This approach underlies the formulation of the problem of scheduling not only under resource constraints, but also with regard for the project reliability index. Consideration was given to minimization of the project execution time (main criterion) in terms of the constrained cost and estimate of the project reliability index, as well as in terms the cost in the determinate network model of the project (second criterion) where project reliability satisfies the guaranteed lower bound both for the OR-network and the special case of the AND-network. This approach enabled formulation of the scheduling problem not only under the resource, but also reliability constraints.     

车联网数据流的多维服务质量改进异构计算最早完成时间调度算法

针对车联网中数据流分布式处理的调度问题,提出了多维服务质量(QoS)改进异构计算最早完成时间(HEFT)调度算法.首先,分别建立了车联网中数据流的分布式处理任务的带权有向无环图模型和车联网分布式计算资源的七维QoS属性带权无向拓扑结构图模型.其次,改进经典的HEFT调度算法中的列表构造方法为最高层最小后继任务优先列表构造方法; 同时,将车联网分布式计算资源的七维QoS属性进行分组、降维,转化为两维综合属性优先权:计算性能优先权和通信性能优先权,形成了两种不同用户偏好的多维QoS改进HEFT调度算法.最后,通过算例分析表明:两种不同用户偏好的多维QoS改进HEFT调度算法综合性能优于经典的HEFT调度算法和轮询调度算法.     

GENRES: An extension of Brooks Algorithm for project scheduling with resource constraints

In project scheduling by network analysis, traditional critical path methods fail to include resource considerations. Other methods must be used to allow for resource considerations. This article explores one area of resource considerations: project scheduling under resource constraints. The specific case investigated is the single resource, single project schedule. A model, entitled the GENRES search model, is developed. The model utilizes Brooks Algorithm (BAG) to generate the project schedule. The criteria used are various weighted combinations of ACTIM and ACTRES (Bedworth, Industrial Systems). The best project schedule is that which gives the least project duration.The GENRES model was found effective in finding project durations equal to or less than that of ACTIM, ACTRES or TIMRES (the combination of ACTIM and ACTRES with each given equal weight). The research also found that when the project completion time found by the algorithm approaches the critical path duration, resource leveling may be preferred.     

An effective shuffled frog-leaping algorithm for multi-mode resource-constrained project scheduling problem

In this paper, an effective shuffled frog-leaping algorithm (SFLA) is proposed for solving the multi-mode resource-constrained project scheduling problem (MRCPSP). In the SFLA, the virtual frogs are encoded as the extended multi-mode activity list (EMAL) and decoded by the multi-mode serial schedule generation scheme (MSSGS). Initially, the mode assignment lists of the population are generated randomly, and the activity lists of the population are generated by the regret-based sampling method and the latest finish time (LFT) priority rule. Then, virtual frogs are partitioned into several memeplexes that evolve simultaneously by performing the simplified two-point crossover (STPC). To enhance the exploitation ability, the combined local search including the multi-mode permutation based local search (MPBLS) and the multi-mode forward-backward improvement (MFBI) is further performed in each memeplex. To maintain the diversity of each memeplex, virtual frogs are periodically shuffled and reorganized into new memeplexes. Computational results based on the well-known benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed SFLA.     

Multi-mode resource constrained project scheduling and contractor selection: Mathematical formulation and metaheuristic algorithms

Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision maker(s) can make a wider variety of decisions in a more flexible manner.     

A new lower bound for the resource-constrained project scheduling problem with generalized precedence relations

In this paper we propose a new lower bound for the resource-constrained project scheduling problem with generalized precedence relationships. The lower bound is based on a relaxation of the resource constraints among independent activities and on a solution of the relaxed problem suitably represented by means of an AON acyclic network. Computational results are presented and confirmed a better practical performance of the proposed method with respect to those present in the literature.