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建筑外文文献及翻译

建筑外文文献及翻译
建筑外文文献及翻译

外文文献:

Study on Human Resource Allocation in Multi-Project Based on the Priority and the Cost of Projects

Lin Jingjing , Zhou Guohua

SchoolofEconomics and management, Southwest Jiao tong University ,610031 ,China Abstract----This paper put forward the affecting factors of project’s 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 Terms—Genetic Algorithm, Human Resource Allocation, Multi-project’s project’s priority .

1.INTRODUCTION

More 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 , it’s 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 reso urces allocation was built to get the project’s duration time and resources distribution, as in [6]. Reference [7] solved the engineering project’s resources optimization problem using Genetic Algorithms. These literatures reasonably optimized resources allocation in multi-project, but all had the same prerequisite that the project’s importance is the same to each other .This paper will analyze the effects of project’s 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 PROJECT’S PRIORITY

Resource 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 project’s priority into three categories ,as the project’s benefits ,the complexity of project management and technology , and the strategic influence on the enterprise’s 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 project’s priority weight; I refers to the benefits of th e 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

ENVIRONMENT

3.1Problem Description

According 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 enterprise’s 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 project’s 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 project’s resources demand have been optimized .The delay of the critical chain will affect the whole project’s 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

Q i,while i=1,2, … N.

(2)The priority weights of multi-project have been determined ,which are

respectively w 1,w 2…w n .

(3) The total number of the critical human resources is R ,with r k standing

for each person ,while k=1,2, …,R

(4) Δk

i = ???others toprojectQ rcer humanresou i k 01 (5) Resources capturing by several projects begins on time. t E i 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 △c i for pr oject I .According to the project’s

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 isn’t 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 △t i ,( △t i =t A i -t E i ). 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 C i

(C i = △t i * △C i ).

(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 t A i =ηi / R i * ,.In the expression , ηi 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 ; R i * refers to the number of the critical human resources being

allocated to projects I actually, with the equation R i *

=∑=R

k ki 1

δ 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 :

F i =min Z i = min

∑∑==N

i i N i Ci 11ω =min i i N

i i N i c t ??∑∑==11ω (2) =min ∑∑==N i i N i 11ω )

E i R i ki i t - ??∑=1δη i c ? 2

F =min Z 2=min ()i t ?=min )

E i R i ki i t -

??∑=1δη (3) Where wj=max(wi) ,(N j i 3,2,1,=?) (4)

Subject to : 0∑∑==≤R k ki N i 11δ=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

ALGORITHM

4.1The 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 αand β ,where α+β=1 .Then the comprehensi ve goal is F* ,where F*=αF1+βF2.

4.2The Principle of Genetic Algorithm

Genetic Algorithm roots from the concepts of natural selection and genetics .It’s 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 it’s 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/n。

(3)Genetic operation

It’s 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 string’s fitness is, the

greater the probability of the string to be selected as a parent will be.

2)Crossover operator

The 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 EXAMPLE

We 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

The 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

From table 2 we can learn that , when αand βchange ,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 project’s 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w

1, w

2

…w

n

(3) 重要人力资源的总数是R ,用r k 代表每个人,而k=1,2, …, R

(4)δk i = ???其他中的人是分配到0r Q 1k i

(5)几个项目共用的资源从时间t s 开始。t E i 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t s 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△C i 。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t s 后,项目i 真正持续时间和预期持

续时间的时间差距为△t i ,( △t i =t A i -t E i )。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C i (C i = △t i * △C i )。

(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t A

i = ηi /R *i 。在这个表达式中, ηi 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R i * =∑=R k ki 1δ。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

基于上述的假设确立多项目环境的资源分配模型。这里的优化模型表示为: F i =min Z i = min

∑∑==N i i N i Ci 11ω =min i i N

i i N i c t ??∑∑==11ω (2)

=min ∑∑==N i i N i 11ω )

E i R i ki i t - ??∑=1δη i c ?

2F =min Z 2=min ()i t ?=min )

E

i R

i ki i t - ??∑=1δη (3) Where wj=max(wi) ,(N j i 3,2,1,=?) (4)

Subject to : 0∑∑==≤R k ki N i 11δ=R (5)

该模型是一个多目标形式的。这两个目标函数一个是为符合经济目标以尽量减少总的成本损失,另一个是以缩短有最高优先权项目的延迟时间。由于第一个目标函数只能优化明显的经济成本,因此第二个目标函数将有助于弥补此限制。对于有最高优先权的项目,时间延迟将会损害的不仅有经济利益,而且也会损害企业的策略和威望。因此,我们应保证最重要的项目应按时完成或提前完成。

4 、用遗传算法求解多目标模型

4.1多目标优化问题是相当普遍。一般来说,应该优化每一个目标,以便获得全面的目标优化。因此每个分目标的比重,应该予以考虑。人们所提出的一种改进的蚁群算法解决这个问题。假定两个优化目标的权重各是α和β,有α+β=1。全面的目标是F *,有F *=α*F 1+β*F 2。

4.2遗传算法的原则

遗传算法起源于自然选择和遗传学的概念。在一个复杂的搜索空间中,遗传算法是一个寻求全局优化的随机搜索技术。因为平行的性质和较少的限制,它有着传播充分、,收敛速度快,且易于计算的主要特点。同时由于遗传算法不局限于的搜索范围,因此它是一个解决资源平衡问题有效的方法。

本文中遗传算法的主要步骤如下:

( 1 )编码

整数串是短期,直接和有效的。根据该模型的特点,每个人力资源可以安排为一个代码对象。字串长度等于人力资源配置的总数。

( 2 )选择的合适的函数

本文选择目标函数作为合适函数的基础。为估计目标函数的价值, N个人的合适性为1/n。这是遗传算法的核心。这个过程中包括三个基本的算子:选择算子、交叉算子和变异算子。

1)选择算子,是选择小组中的优秀个体。一个字符串被作为母体选中的概率与它的合适性是成正比的。字符串越合适被选中的概率也就越高。

2)交叉算子

所谓交叉是指交叉的染色体交换一些基因,而在一些规则下产生两个字符串。我们可以使用统一的交叉,这两个染色体交换基因后,在相同的交叉概率下产生出两个新的个体。

3)变异算子

变异增加了人口的多样性,从而增加了产生更好合适性价值个人的可能性。变异算子决定遗传算法的搜索能力,多样性人口保持能力和避免早产儿的能力。几种整数串的简单的统一变异方法确实存在。

4) 遗传算法的终端标准

在没有人控制的情况下,该算法的演化过程将永远不会结束。人口规模影响着最终的结果和运算速度。如果人口规模越大,则人口的多样性会增加,并且最佳结果也能更易获得。但其效率会降低。最近,在大多数遗传算法的发展过程中,由控制算法的人控制了最大的演化代数。

5)数值例子

我们使用一个数值例子来说明遗传算法的成效。我们假定在同一网络中有三个项目,且每个项目的优先权重也已经提出。每一个项目只存在一个关键路径。数据如表1所示:

表1 三个项目的数据

解决模型遗传算法的步骤如下:

步骤1 :采取整数串将[0,1,2]输入这三个项目。染色体的长度是16即将被分配的人力资源的总数是16。

步骤2:最初的人口大小是50。

步骤3:采取赌轮和精英的策略确定选择算子做遗传操作。后代可以产生均匀交叉,变异算子可以由统一的突变决定。我们假设突变的概率为0.001。

步骤4:采用最高的人口规模是100时终止。

计算机模拟后,我们可以获取两个目标函数不同重要性权重的帕累托结果。如表2所示:

表2 模型的解答结果

从表2我们可以了解,当α和β的变化,结果是不同的。但我们可以取得了一系列的帕累托结果。

6 、结论

人力资源配置,在多项目环境是一个复杂的问题。本文分析项目的优先权在资源配置中的重要性,并在优先次序和项目成本的基础上建立了人力资源分配模型。最后,用遗传算法求解模型。在分配模式下施工过程中,我们提出了一些假设以简化问题。然而,当企业实际分配资源时,他们将面临更多的复杂性,这正是我们未来研究的重点。

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