基于改进NSGA-II的多项目多技能人力资源调度研究

多项目并行的人力资源管理日益成为研发型企业合理配置各类资源、实现利润最大化的有效方式。从项目成本和多能工满意度角度出发,运用第2代非支配排序遗传算法和蚁群算法对多能工分配问题进行研究。考虑多能工技能组合与项目任务需求之间的匹配以及技能熟练水平对任务作业时间的影响,构建了以实现多项目总工期和多能工间工作量均衡为目标的优化模型。根据模型的约束条件,提出了一系列启发式规则提高算法效率,并结合第2代非支配排序遗传算法和蚁群算法的特点,利用新开发的算法对模型进行求解。通过数值算例验证了模型和算法的有效性。     

Multi-threaded simulated annealing for a bi-objective maintenance scheduling problem

A parallel Simulated Annealing algorithm with multi-threaded architecture is proposed to solve a real bi-objective maintenance scheduling problem with conflicting objectives: the minimisation of the total equipment downtime caused by maintenance jobs and the minimisation of the multi-skilled workforce requirements over the given horizon. The maintenance jobs have different priorities with some precedence relations between different skills. The total weighted flow time is used as a scheduling criterion to measure the equipment availability. The multi-threaded architecture is used to speed up a multi-objective Simulated Annealing algorithm to solve the considered problem. Multi-threading is a form of parallelism based on shared memory architecture where multiple logical processing units, so-called threads, run concurrently and communicate via shared memory. The performance of the parallel method compared to the exact method is verified using a number of test problems. The obtained results imply the high efficiency and robustness of the proposed heuristic for both solution quality and computational effort.     

A multi-objective model for multi-project scheduling and multi-skilled staff assignment for IT product development considering competency evolution

We address a multi-skill project scheduling problem for IT product development in this article. The goal is for product development managers to be able to generate an initial schedule at an early stage of development activities. Due to the complexity of the product structure and functionality, an IT product development effort is divided into multiple projects. Each project includes several tasks, and each task must be completed by an employee who has mastered a certain skill to complete it. A pool of multi-skilled employees is available, and the employees’ skill efficiencies are influenced by both learning and forgetting phenomena. Based on the real-world demands of product development managers, three objectives are simultaneously considered: skill efficiency gain, product development cycle time and costs. To solve this problem, we propose a multi-objective non-linear mixed integer programming model. The Non-dominated Sorting Genetic Algorithm II (NSGA-II)is designed to generate an approximation to the optimal Pareto front of this NP-hard multi-objective optimisation problem. The algorithm produces feasible schedules for all the development projects using the serial schedule generation scheme. We adopt penalty values and individual employee adjustments to address resource conflicts and constraint violations. A weighted ideal point method is used to select the final solution from the approximate Pareto solution set. An application case of a new electrical energy saving product implementation in a leading electrical device company in China is used to illustrate the proposed model and algorithm.     

软件开发项目多技能人力资源均衡调度模型

为了在软件开发项目中同时解决项目活动调度问题和多技能人员指派问题,实现资源均衡分配,本文建立了一个多技能人力资源均衡调度的混合整数规划模型,并以一个软件开发项目为背景开展了算例研究,采用Lingo11软件环境下改良后的分支定界法进行优化求解。优化之后,项目资源强度方差和员工工作量方差大幅度下降。研究结果表明,本文创建的资源均衡调度模型可以显著提高项目周期内员工需求量和员工工作量分配的均衡水平。     

Scheduling Multi-Mode Resource-Constrained Projects Using Heuristic Rules Under Uncertainty Environment

Project scheduling is a key objective of many models and is the proposed method for project planning and management. Project scheduling problems depend on precedence relationships and resource constraints, in addition to some other limitations for achieving a subset of goals. Project scheduling problems are dependent on many limitations, including limitations of precedence relationships, resource constraints, and some other limitations for achieving a subset of goals. Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required, which are known and stable during the implementation process. The concept of deterministic project scheduling conflicts with real situations, in which in many cases, some data on the activity' s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations. Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us. We use the multi-mode resource allocation and scheduling model that takes into account the dynamicity features of all parameters, that is, the scheduling process must be flexible to dynamic environment features. In this paper, we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations, in which we apply the proposed heuristic rules (PHR) for scheduling multi-mode resource-constrained projects. Five projects are considered test problems for the PHR. The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems. The results in many cases of the proposed priority rules are very promising, where they achieve better scheduling dates in many test case problems and the same results for the others. The proposed model is based on the dynamic features for project topography.     

Scheduling and staffing multiple projects with a multi-skilled workforce

We consider the problem of simultaneously scheduling IT-projects and assigning multi-skilled internal and external human resources with resource-specific efficiencies to the project work. The objective is to minimize labor costs. The problem is modeled as a mixed-integer linear program (MIP) with a tight LP-bound. The performance of the model w.r.t. solution gap and computation time is assessed and managerial insight is given concerning different problem parameters such as the time window size of projects, the number of skills of human resources, and the workload. Furthermore, we show the benefit of applying the MIP compared to simple heuristics used in practice in terms of obtaining feasible and low-cost solutions. Finally, we provide insight into the benefit of applying the MIP in case of central compared to decentral planning.     

考虑经济性的多微电网优化调度研究

多微电网并网方式主要有单独并网方式和联合协调并网方式,这2种并网方式下微电网内部的微电源工作状态不同导致发电成本不同。为了减少发电成本,在满足相关微电源约束条件的前提下,建立一种考虑经济性的多微电网能量优化调度模型和单微电网的优化调度模型。由于传统人工鱼群算法精度低,收敛速度慢,提出一种基于模拟退火算法改进的人工鱼群（the artificial fish swarm algorithm based on simulated annealing algorithm,SA_AFSA）算法,该算法克服了传统鱼群算法的缺点。结合具体算例,通过该算法来求解单微电网和多微电网经济性优化调度问题,并比较2种并网方式下的发电成本。实验结果表明,在仅考虑经济性的前提下,多微电网联合协调并网的发电成本低于单微电网单独并网。     

考虑效率差异和流动分配的混流装配线工人优化

本文研究了考虑工人装配水平差异、不同工位之间可以流动分配的装配线工人优化调度，在确定混流装配线的排序后，装配工人在其最擅长的工位工作，在完成本工位的工作后参与其他工位的装配工作，定义相关的优化因素变量和约束条件，建立了考虑工人工位效率差异且可流动分配的混流装配线工人优化数学模型。采用削峰填谷算法和多种群移民算法进行工人的调整和均衡优化，利用一个三层神经网络对削峰填谷的工位进行评估选择，得到工人的最优分配方案，最后通过Matlab对举例进行了验证。算例优化后，减少了2名装配工人，并提高了装配线的平衡率。     

A re-entrant hybrid flow shop scheduling problem with machine eligibility constraints

A production scheduling problem originating from a real rotor workshop is addressed in the paper. Given its specific characteristics, the problem is formulated as a re-entrant hybrid flow shop scheduling problem with machine eligibility constraints. A mixed integer linear programming model of the problem is provided and solved by the Cplex solver. In order to solve larger sized problems, a discrete differential evolution (DDE) algorithm with a modified crossover operator is proposed. More importantly, a new decoder addressing the machine eligibility constraints is developed and embedded to the algorithm. To validate the performance of the proposed DDE algorithm, various test problems are examined. The efficiency of the proposed algorithm is compared with two other algorithms modified from the existing ones in the literatures. A one-way ANOVA analysis and a sensitivity analysis are applied to intensify the superiority of the new decoder. Tightness of due dates and different levels of scarcity of machines subject to machine eligibility restrictions are discussed in the sensitivity analysis. The results indicate the pre-eminence of the new decoder and the proposed DDE algorithm.     

改进遗传算法求解多时间约束的柔性作业车间调度问题

将加工时间、调整时间和移动时间分别作为独立时间因素考虑到柔性作业车间调度模型中,建立以最大完工时间最小、总调整时间最小、总移动时间最小为目标的考虑多时间约束的柔性作业车间调度模型,并提出改进的遗传算法求解该模型。通过测试标准数据集,并对比其他文献算法,验证了改进的遗传算法的可行性和有效性。     

Project scheduling with flexible resources: formulation and inequalities

In this paper, we study a variant of the resource-constrained project scheduling problem in which resources are flexible, i.e., each resource has several skills. Each activity in the project may need several resources for each required skill. We present a mixed-integer linear programming formulation for this problem. Several sets of additional inequalities are also proposed. Due to the fact that some of the above-mentioned inequalities require a valid upper bound to the problem, a heuristic procedure is proposed. Computational experience is reported based on randomly generated data, showing that for instances of reasonable size the proposed model enlarged with the additional inequalities can be solved efficiently.     

Mixed Self-adapting GA Optimal Scheduling Algorithm for a Multiple Resource Job-shop

With an aim at the job-shop scheduling problem of multiple resource constraints, this paper presents mixed self-adapting Genetic Algorithm （ GA ） , and establishes a job-shop optimal scheduling model of multiple resource constraints based on the effect of priority scheduling rules in the heuristic algorithm upon the scheduling target. New coding regulations or rules are designed. The sinusoidal function is adopted as the self-adapting factor, thus making cross probability and variable probability automatically change with group adaptability in such a way as to overcome the shortcoming in the heuristic algorithm and common GA, so that the operation efficiency is improved. The results from real example simulation and comparison with other algorithms indicate that the mixed self-adapting GA algorithm can well solve the job-shop optimal scheduling problem under the constraints of various kinds of production resources such as machine-tools and cutting tools.     

Critical chain project buffer sizing based on resource constraints

Project scheduling is a complex process involving many types of resources and activities that require optimisation. The resource-constrained project scheduling problem is one of the well-known problematic issues when project activities have to be scheduled to minimise the project duration. Consequently, several methods have been proposed for adjusting the buffer size but none of these traditional methods consider buffer sizing accuracy based on resource constraints. The purpose of this paper is to develop a buffer sizing method based on a fuzzy resource-constrained project scheduling problem in order to obtain an appropriate proportionality between the activity duration and the buffer size. Specifically, a comprehensive resource-constrained method that considers both the general average resource constraints (GARC) and the highest peak of resource constraints (HPRC) is proposed in order to obtain a new buffer sizing method. This paper contributes to the research by considering several different aspects. First, this paper adopts a fuzzy method to calculate and obtain the threshold amount. Second, this paper discusses the resource levelling problem and proposes the HPRC method. Third, the proposed method uses a fuzzy quantitative model to calculate the resource requirement. The findings indicate that the project achieved higher efficiency, providing effective protection and an appropriate buffer size.     

不确定资源约束条件下的结构项目排序问题

本文主要建立了具有不确定资源约束条件下的结构项目排序问题的一个数学模型。不确定资源约束主要由固定项目工期、随机项目工期和模糊项目工期组成,其目标函数为项目的整个完工时间(极小)。利用机会约束的置信度(包括某些活动的重要度)和某些有效方法将原不确定问题转化为等价的确定性规划问题。最后我们给出了一个简单的二阶段算法及其数值结果。     

Resource–constrained project scheduling: a heuristic for the multi–mode case

This paper presents a heuristic solution procedure for a very general resource–constrained project scheduling problem. Here, multiple execution modes are available for the individual activities of the project. In addition, minimum as well as maximum time lags between different activities may be given. The objective is to determine a mode and a start time for each activity such that the temporal and resource constraints are met and the project duration is minimized. Project scheduling problems of this type occur e.g. in process industries. The heuristic is a multi–pass priority–rule method with backplanning which is based on an integration approach and embedded in random sampling. Its performance is evaluated within an experimental performance analysis for problem instances of real–life size with 100 activities and up to 5 modes per activity.

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Received: September 22, 2000 / Accepted: May 18, 2001     

Modelling and scheduling analysis of multi-cluster tools with residency constraints based on time constraint sets

This paper is dedicated to the scheduling problem of multi-cluster tools with process module residency constraints and multiple wafer product types. The problem is formulated as a non-linear programming model based on a set of time constraint sets. An effective algorithm called the time constraint sets based (TCSB) algorithm is presented as a new method to schedule the transport modules to minimise the makespan of a number of wafers. In approach, time constraint sets are maintained for all the resources and necessary operations to exploit the remaining production capacities during the scheduling process. To validate the proposed algorithm on a broader basis, a series of simulation experiments are designed to compare our TCSB algorithm with the benchmark with regard to cluster factor, configuration flexibilities and the variation of the processing times and residency constraint times. The results indicate that the proposed TCSB algorithm gives optimal or near optimal scheduling solutions in most cases.     

Design of high-performing hybrid meta-heuristics for unrelated parallel machine scheduling with machine eligibility and precedence constraints

This study involves an unrelated parallel machine scheduling problem in which sequence-dependent set-up times, different release dates, machine eligibility and precedence constraints are considered to minimize total late works. A new mixed-integer programming model is presented and two efficient hybrid meta-heuristics, genetic algorithm and ant colony optimization, combined with the acceptance strategy of the simulated annealing algorithm (Metropolis acceptance rule), are proposed to solve this problem. Manifestly, the precedence constraints greatly increase the complexity of the scheduling problem to generate feasible solutions, especially in a parallel machine environment. In this research, a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. The performance of the proposed algorithms is evaluated in numerical examples. The results indicate that the suggested hybrid ant colony optimization statistically outperformed the proposed hybrid genetic algorithm in solving large-size test problems.     

Dynamic response to demand variability for precast production rescheduling with multiple lines

Production scheduling plays a crucial role in the prefabricated construction productivity and on-time delivery of precast components (PCs). However, previous studies mainly focused on the static scheduling of single production line without considering the demand variability in practice. To achieve dynamic production planning, a Two-level Rescheduling Model for Precast Production with multiple production lines is developed to minimise the rescheduling costs based on genetic algorithm, from the two levels of (1) selection of production line and (2) rescheduling of jobs based on PCs’ priority. Further, two scenarios of different and shared mould types are investigated to represent real-world production environments. Finally, a real case study is conducted to test the validity of proposed rescheduling model. 58.1 and 48.5% cost savings are achieved by comparison to no response to changes and heuristic rescheduling methods, respectively. This research contributes to the precast production theory by expanding the insight into dynamic rescheduling with multiple production lines. The methodology will promote the on-time delivery of PCs and enhance the dynamic precast production management.     

A scheduling problem in glass manufacturing

In this paper, a production scheduling problem in glass manufacturing is studied. The production facility consists of multiple identical production lines and each production line includes a number of serially arranged machines. The production is characterized by semi-ordered processing times in each product family, and the last machine in each production line is a bottleneck machine. Significant changeover times are required when products of different families are produced on a production line. The scheduling problem was modeled as a parallel no-delay flowshop scheduling problem (PNDFSP). The PNDFSP combines the parallel machine scheduling problem (PMSP) with the no-delay flowshop scheduling problem (NDFSP). While PMSP and NDFSP have received considerable attention in the literature, PNDFSP has not been well studied. A mixed-integer programming formulation is developed and an efficient heuristic algorithm is proposed. The sequential heuristic algorithm considers simultaneously the line changeover time, no-delay effect, and line utilization in assigning product families to the production lines. The computational results are reported.