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建筑大学毕业设计外文文献及译文外文原文Study on Human Resource Allocation in Multi-Project Based on the Priority and the Cost of ProjectsLin Jingjing , Zhou GuohuaSchoolofEconomics and management, Southwest Jiao tong University ,610031 ,China Abstract-This paper put forward the affecting factors of projects priority. which is introduced into a multi-objective optimization model for human resource allocation in multi-project environment . The objectives of the model were the minimum cost loss due to the delay of the time limit of the projects and the minimum delay of the project with the highest priority .Then a Genetic Algorithm to solve the model was introduced. Finally, a numerical example was used to testify the feasibility of the model and the algorithm. Index TermsGenetic Algorithm, Human Resource Allocation, Multi-projects projects priority .1. INTRODUCTIONMore and more enterprises are facing the challenge of multi-project management, which has been the focus among researches on project management. In multi-project environment ,the share are competition of resources such as capital , time and human resources often occur .Therefore , its critical to schedule projects in order to satisfy the different resource demands and to shorten the projects duration time with resources constrained ,as in 1.For many enterprises ,the human resources are the most precious asset .So enterprises should reasonably and effectively allocate each resource , especially the human resource ,in order to shorten the time and cost of projects and to increase the benefits .Some literatures have discussed the resource allocation problem in multi-project environment with resources constrained. Reference 1 designed an iterative algorithm and proposed a mathematical model of the resource-constrained multi-project scheduling .Based on work breakdown structure (WBS) and Dantzig-Wolfe decomposition method ,a feasible multi-project planning method was illustrated , as in 2 . References 3,4 discussed the resource-constrained project scheduling based on Branch Delimitation method .Reference 5 put forward the framework of human resource allocation in multi-project in Long-term ,medium-term and short-term as well as research and development(R&D) environment .Based on GPSS language, simulation model of resources allocation was built to get the projects duration time and resources distribution, as in 6. Reference 7 solved the engineering projects resources optimization problem using Genetic Algorithms. These literatures reasonably optimized resources allocation in multi-project, but all had the same prerequisite that the projects importance is the same to each other .This paper will analyze the effects of projects priority on human resource allocation ,which is to be introduced into a mathematical model ;finally ,a Genetic Algorithm is used to solve the model. 2. EFFECTS OF PROJECTS PRIORITY ON HUMAN RESOUCE ALLOCATION AND THE AFFECTING FACTORS OF PROJECTS PRIORITYResource sharing is one of the main characteristics of multi-project management .The allocation of shared resources relates to the efficiency and rationality of the use of resources .When resource conflict occurs ,the resource demand of the project with highest priority should be satisfied first. Only after that, can the projects with lower priority be considered.Based on the idea of project classification management ,this paper classifies the affecting factors of projects priority into three categories ,as the projects benefits ,the complexity of project management and technology , and the strategic influence on the enterprises future development . The priority weight of the project is the function of the above three categories, as shown in (1). W=f(I,c,s) (1)Where w refers to projects priority weight; I refers to the benefits of the project; c refers to the complexity of the project, including the technology and management; s refers to the influence of the project on enterprise .The bigger the values of the three categories, the higher the priority is.3. HUMAN RESOURCE ALLOCATION MODEL IN MULTI-PROJECT ENVIRONMENT3.1 Problem DescriptionAccording to the constraint theory, the enterprise should strictly differentiate the bottleneck resources and the non-bottleneck resources to solve the constraint problem of bottleneck resources .This paper will stress on the limited critical human resources being allocated to multi-project with definite duration times and priority.To simplify the problem, we suppose that that three exist several parallel projects and a shared resources storehouse, and the enterprises operation only involves one kind of critical human resources. The supply of the critical human resource is limited, which cannot be obtained by hiring or any other ways during a certain period .when resource conflict among parallel projects occurs, we may allocate the human resource to multi-project according to projects priorities .The allocation of non-critical independent human resources is not considered in this paper, which supposes that the independent resources that each project needs can be satisfied.Engineering projects usually need massive critical skilled human resources in some critical chain ,which cannot be substituted by the other kind of human resources .When the critical chains of projects at the same time during some period, there occur resource conflict and competition .The paper also supposes that the corresponding network planning of various projects have already been established ,and the peaks of each projects resources demand have been optimized .The delay of the critical chain will affect the whole projects duration time . 3.2 Model Hypotheses The following hypotheses help us to establish a mathematical model:(1) The number of mutually independent projects involved in resource allocation problem in multi-project is N. Each project is indicated with Qi ,while i=1,2, N.(2) The priority weights of multi-project have been determined ,which are respectively w1,w2wn .(3) The total number of the critical human resources is R ,with rk standing for each person ,while k=1,2, ,R(4) ki= (5) Resources capturing by several projects begins on time. tEi is the expected duration time of project I that needs the critical resources to finish some task after time t ,on the premise that the human resources demand can be satisfied .tAi is the real duration time of project I that needs the critical resource to finish some task after time t .(6) According to the contract ,if the delay of the project happens the daily cost loss due to the delay is ci for project I .According to the projects importance ,the delay of a project will not only cause the cost loss ,but will also damage the prestige and status of the enterprise .(while the latent cost is difficult to quantify ,it isnt considered in this article temporarily.)(7) From the hypothesis (5) ,we can know that after time t ,the time-gap between the real and expected duration time of project I that needs the critical resources to finish some task is ti ,( ti =tAi-tEi ). For there exists resources competition, the time gap is necessarily a positive number.(8) According to hypotheses (6) and (7), the total cost loss of project I is Ci (Ci = ti* Ci ). (9) The duration time of activities can be expressed by the workload of activities divided by the quantity of resources ,which can be indicated with following expression of tAi =i / Ri* ,.In the expression , i refers to the workload of projects I during some period ,which is supposed to be fixed and pre-determined by the project managers on project planning phase ; Ri* refers to the number of the critical human resources being allocated to projects I actually, with the equation Ri* = existing. Due to the resource competition the resource demands of projects with higher Priorities may be guarantee, while those projects with lower priorities may not be fully guaranteed. In this situation, the decrease of the resource supply will lead to the increase of the duration time of activities and the project, while the workload is fixed.3.3 Optimization Model Based on the above hypotheses, the resource allocation model in multi-project environment can be established .Here, the optimization model is :Fi=min Zi = min =min (2) =min =min Z2=min=min (3) Where wj=max(wi) ,() (4)Subject to : 0=R (5)The model is a multi-objective one .The two objective functions are respectively to minimize the total cost loss ,which is to conform to the economic target ,and to shorten the time delay of the project with highest priority .The first objective function can only optimize the apparent economic cost ;therefore the second objective function will help to make up this limitation .For the project with highest priority ,time delay will damage not only the economic benefits ,but also the strategy and the prestige of the enterprise .Therefore we should guarantee that the most important project be finished on time or ahead of schedule . 4. SOLUTION TO THE MULTI-OBJECTIVE MODEL USING GENETIC ALGORITHM4.1 The multi-objective optimization problem is quite common .Generally ,each objective should be optimized in order to get the comprehensive objective optimized .Therefore the weight of each sub-objective should be considered .Reference 8 proposed an improved ant colony algorithm to solve this problem .Supposed that the weights of the two optimizing objectives are and ,where +=1 .Then the comprehensive goal is F* ,where F*=F1+F2.4.2 The Principle of Genetic Algorithm Genetic Algorithm roots from the concepts of natural selection and genetics .Its a random search technique for global optimization in a complex search space .Because of the parallel nature and less restrictions ,it has the key features of great currency ,fast convergence and easy calculation .Meanwhile ,its search scope is not limited ,so its an effective method to solve the resource balancing problem ,as in 9.The main steps of GA in this paper are as follow:(1) Encoding An integer string is short, direct and efficient .According to the characteristics of the model, the human resource can be assigned to be a code object .The string length equals to the total number of human resources allocated.(2) Choosing the fitness function This paper choose the objective function as the foundation of fitness function .To rate the values of the objective function ,the fitness of the n-th individual is 1/ 。 (3) Genetic operation Its the core of GA .This process includes three basic operators: selection operator, crossover operator, and mutation operation.1) Selection operation is to select the good individuals among the group .The probability of a string to be selected as a parent is proportional to its fitness .The higher the strings fitness is, the greater the probability of the string to be selected as a parent will be.2) Crossover operatorThe so-called crossover is that the paten chromosomes exchange some genes to yield two offspring strings in some rule .We can use uniform crossover ,that the two chromosomes exchange the genes on the same positions with the same crossover probability to yield two new individuals.3) Mutation operator Mutation adds to the diversity of a population and thereby increases the likelihood that the algorithm will generate individuals with better fitness values .The mutation operator determines the search ability of GA ,maintain the diversity of a population ,and avoid the prematurity .There are several mutation is quite easy .4) Standard for the terminal of GA Without human control ,the evolution process of the algorithm will never end .The population size affects the final result and the operation speed .If the size is greater ,the diversity of the population can be added ,and the best result can be obtained easier .However ,the efficiency is reduced .Recently ,in most GA progress , the biggest evolvement algebra is determined by human-beings to control the course the algorithm.5. NUMERICAL EXAMPLEWe use a numerical example to illustrate the effectiveness of Genetic Algorithm . Assume that there are three projects with the same network ,and the priority weights have been put forward .There is only one critical path in each project . The data we have known are shown in Table 1. Table 1 Data of the Three Projects ProjectPriority weight wtECost loss(human yuan/day)Workload (person*day)10.421010010020.3181508030.271280120The steps of Genetic Algorithm to solve the model are as follow:Step1: An integer string is adopted .Encode with 0,1,2 for there are three projects .The length of the chromosome is 16 ,the total number of human resource to be allocated .Step 2: The initial population size is 50.Step 3: Doing genetic operation .Adopt Roulette Wheel and Elitist tactic to determined selection operator .The offspring can be yielded by uniform cross-over .The mutation operator can be determined by uniform mutation .We assume that the mutation probability equal to 0.001 .Step 4: Adopt the maximum population size is 100 when terminated.After the computer simulation, we can obtain the Pare-to results with different importance weights of the two objective functions, as shown in Table 2 :Table 2 The Solution Result of the Model R1*R2*R3*F1(Hundred Yuan)F2(Day)=1,=0655911.22.8=0.7,=0.3754940.81.8=0.4,=0.68441051.81.05=0.1,=0.910331472.80From table 2 we can learn that , when and change ,the result is different .However we can obtain a series of Pareto results.6. CONCLUSION Human resource allocation in multi-project environment is a complicated problem .This paper analyzes the importance of projects priority in resource allocation and establishes a human resource allocation model based on priority and cost of projects .Finally, genetic Algorithm is adopted to solve the model.During the construction process of the allocation model, we have put forward some hypotheses in order to simplify the problem .However, when the enterprises practically allocate the resources, hey will face more complexity, which is the focus of our future study.中文翻译：在项目优先权和成本的基础上对多项目中人力资源配置的研究林晶晶，周国华 中国西南交通大学经济和管理学院，610031摘要-本文提出项目优先次序的影响因素，为多项目环境配置人力资源引入一个多目标优化模型。这一模型的目标是使得由于项目时间限制的延误损失的成本最低和具有最高优先顺序项目的延迟最小。然后用遗传算法求解该模型。最后，用一个数值例子证明该模型和算法的可行性。 关键字-遗传算法;人力资源配置;多项目、项目的优先权;1 、引言越来越多的企业面临的挑战是多项目管理，这已经成为项目管理研究的焦点。多项目环境中，诸如资金，时间和人力等资源的共享和竞争经常发生。因此合理安排项目的进度，以满足不同资源的需求并缩短项目造成的资源约束。对于许多企业来说，人力资源是最宝贵的资产。所以企业应合理有效分配每个资源，尤其是人力资源，用以缩短时间减少项目的成本和增加效益。一些文献中曾讨论的存在资源约束的多项目环境中资源分配问题。设计一个迭代算法，并提出了资源约束的多项目调度的数学模型。基于工作分解结构（ wbs ）和dantzig -wolf的分解方法，人们曾演示过一个可行的多项目规划方法。讨论基于分支定界的方法的资源受限项目的调度。提出在长期、中期和短期的多项目及研究和开发（ R D ）环境中人力资源配置框架。在gpss语言的基础上，为了获得该项目的持续时间和资源的分配而建立仿真模型的资源配置。用遗传算法解决了工程项目的资源优化问题。这些文献虽然合理优化了多项目的资源配置，但它们都有相同的先决条件即该项目的重要性是一样。本文将引进数学模型用以分析项目优先权在人力资源配置中的作用。最后，用遗传算法求解这一模型。2. 项目优先权对人的资源分配的作用和影响项目优先权的因素资源共享是是多项目管理一个主要特点。共享资源的分配涉及到资源使用的效率和合理性，当资源发生冲突时，应该首先满足最高优先权项目的资源的需求。在此之后，较低优先权的项目才予以考虑。基于项目分类管理的思想，本文将归类项目的优先次序的影响因素分为三类。正如项目的利润一样，复杂的项目管理和技术以及战略都影响着企业的未来发展。优先权的重量级取决于该项目上述三大类因素。公式为：W=f(I,c,s) (1)其中w是指项目的优先权重；i指该项目的利润，; c指项目中技术和管理的复杂性; s指该项目对企业的影响。三类因素的价值越大，其优先级越高。3 、在多项目环境下的人力资源分配模型。3.1、问题描述 根据约束理论，企业应严格区分瓶颈资源和非瓶颈资源来解决瓶颈资源的约束问题。本文将着力研究被分配在多项目中有限且关键的人力资源，而这些多项目都有明确的期限和时代优先权。为了简化问题，我们假设存在平行的几个项目和一个共享的资源库，且企业的运作只涉及一种重要的人力资源。关键人力资源的供应是有限的，在一定期限内是不能通过雇用或凭借任何其他方式获得的。当资源之间的冲突在并行项目中发生时，我们可能会根据项目的优先次序分配人力资源。本文不考虑非关键独立的人力资源的配置问题，这是假定这些独立的资源可以满足每个项目的需求。工程项目通常在一些关键链需要大量的关键技术熟练的人力资源，而这些资源是由其他人力资源所不能取代。在某时期内，当项目的几个关键环节同时需要同一种关键性人力资源时就会发生资源的冲突和竞争。本文还假设认为，各个项目已经建立相应的网络规划，并且每个项目的资源需求的高峰期已得到优化。关键环节的延误将会影响整个项目的持续时间。3.2 模型假设以下假说帮助我们建立一个数学模型：(1) 介入多项目的资源分配问题的相互独立项目的数量是N。 每个项目Q用表示，而i=1,2， N。(2) 确定了多项目优先权重量，各自是w1， w2wn。(3) 重要人力资源的总数是R，用rk代表每个人，而k=1,2， ， R(4)ki= (5)几个项目共用的资源从时间ts开始。tEi是人力资源的需求可以得到满足的前提下项目i的预计持续时间，项目i在ts 后需要关键资源来完成某些任务。(6)根据合同，如果该项目延误则由延误对项目i造成的每日成本损失为Ci。根据该项目的重要性，工程延误后不但会造成成本的损失，而且还会损害企业的威望和地位。 （而潜在的成本是难以量化的，这在本文中暂时不做考虑）。(7)从假说（ 5 ） ，我们可以知道在时间ts后，项目i真正持续时间和预期持续时间的时间差距为ti ,( ti =tAi-tEi )。由于存在着资源的竞争，时间的差距必然是一个正数。(8)根据假说(6)和(7)，项目i总的成本损失是Ci (Ci= ti* Ci)。(9)活动持续时间可以用活动的工作量除以资源的数量表达，用下面的表达式表示为tAi = i/R*i。在这个表达式中， i指在某一时期项目i的工作量，它应该是固定和预先确定的。R*i是指在项目经理对项目的规划阶段被实际上分配给项目i中的关键人力资源的数量。于是存在方程Ri* =。由于资源的竞争，具有较高优先权项目的资源需求可能得到保障，而那些较低的优先权的项目可能无法得到充分保障。在这种情况下当工作量是固定的，减少了资源的供应将导致活动和项目持续时间的增加。3.3优化模型基于上述的