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 ,ChinaAbstract----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.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 ascapital , 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 getthe 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 ANDTHE AFFECTING FACTORS OF PROJECT’S 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 project’s priority into three categories ,as theproject’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-PROJECTENVIRONMENT3.1Problem 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 existseveral 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 wholeproject’s duration time .3.2 Model HypothesesThe 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 Ei is the expected duration time of project Ithat 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’simportance ,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 timet ,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 costloss of project I is C i (C i= △t i* △C i ).(9)The duration time of activities can be expressed bythe 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 projectsI actually, with the equation R i * =∑=Rk ki 1δ existing. Dueto the resource competition the resource demands of projects with higherPriorities 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 ModelBased on the above hypotheses, the resourceallocation 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 ∆ 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)Subjectto : 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 ALGORITHM4.1 The multi-objective optimization problem is quitecommon .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 improvedant 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 AlgorithmGenetic 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)EncodingAn integer string is short, direct andefficient .According to the characteristics of themodel, the human resource can be assigned to be a codeobject .The string length equals to the total numberof human resources allocated.(2)Choosing the fitness functionThis 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。