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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

外文原文

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 resources 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 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

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 proje ct 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 1δ 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 11

ω =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

4.1 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 α and β ,where α+β=1 .Then the comprehensive goal is F* ,where F*=αF1+βF2.

4.2 The 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 β 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 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:

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