建筑外文文献及翻译外文原文Study on Human Resource Allocation in Multi-Project Based on thePriority 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 'prsiority.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 as capital , time and human resources oftenoccur .Therefore , it 'csritical 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 .Soenterprises should reasonably and effectively allocate each resource , especially the human resource ,in order to shorten the time and cost of projects and to increase thebenefits .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 theresource-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 resources optimization problem using Genetic Algorithms.These literatures reasonably optimized resources allocation in multi-project, but all had the same prerequisite that the project 'ims portance is the same to each other .This paper will analyze the effects of project 'psriority 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 PROJEC'TS PRIORITYResource sharing is one of the main characteristics of multi-project management .Theallocation of shared resources relates to the efficiency and rationality of the use of resources .When resource conflict occurs ,the resource demand of the project withhighest 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 'bsenefits ,the complexity of project management and technology , and thestrategic influence on the enterprise 'fusture development . The priority weight of the project is the function of the above three categories, as show n in (1). W=f(l,c,s …)(1)Where w refers to project 's priority weight; I refersto 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 ENVIRONMENT3.1Problem DescriptionAccording to the constraint theory, the enterprise should strictly differentiate thebottleneck resources and the non-bottleneck resources to solve the constraint problemof bottleneck resources .This paper will stress on the limited critical humanresources 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 islimited, which cannot be obtained by hiring or any other ways during a certainperiod .when resource conflict among parallel projects occurs, we may allocate the human resource to multi- project according to project 'psriorities .The allocation of non-critical independent human resources is not considered in this paper, whichsupposes 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 occurresource conflict and competition .The paper also supposes that the correspondingnetwork planning of various projects have already been established ,and the peaks of each project 'ressources demand have been optimized .The delay of the critical chain will affect the whole project ' s duration time .3.2Model HypothesesThe following hypotheses help us to establish a mathematical model:(1)The number of mutually independent projects involved in resource allocationproblem 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 ,whichare respectively w 1 ,w2…w n .(3)The total number of the critical human resources is R ,with r ksta nding for each pers on ,while k =1,2, …,R1humanresourcer k toprojectQ i(4)0others(5)Resources capturing by several projects begins on time. t Ei is the expectedduration time of project I that needs the critical resourcesto 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 thecritical resource to finish some task after time t .(6)According to the contract ,if the delay of the project happens the daily cost lossdue to the delay is △c i for project 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 time t ,the time-gapbetween 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 ). Forthere exists resources competition, the time —ap is necessarily a positive number.(8)According to hypotheses (6) and (7), the total cost loss of project I isC i (C i = △ t i* △ C i ).(9)The duration time of activities can be expressed by the workload ofactivities divided by the quantity of resources ,which can beindicated with following expression of t i =n / R i ,」n theexpression , n refers to the workload of projects I during some period ,which issupposed to be fixed and pre-determined by the project managers on projectplanning phase ; R i* refers to the nu mber of the critical huma n resources beingallocated to projects IR•kactually, with the equation R i = ki existing. Due to the resourcek 1competiti on the resource dema nds 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 in crease of the durati on time of activities and the project, while theworkload is fixed.3.3Optimization ModelBased on the above hypotheses, the resource allocation model inmulti-project en vir onment can be established .Here, theoptimizatio n model is :N NF i=min Z i = min i Cii 1 i 1N N=min i t i Gi 1 i 1N Ni 丄E=min i 星-------------- t i Gi 1 i 1kii 1F2 =min Z 2=min t i =min t i EkiWhere wj=max(wi) ,( i, j 1,2,3 N ) (4)NRSubject to : 0 ki =R (5)i 1 k 1The model is a multi-objective one .The two objective functionsare respectively to minimize the total cost loss ,which is toconform to the economic target ,and to shorten the time delayof the project with highest priority .The first objectivefunction can only optimize the apparent economiccost ;therefore the second objective function will help to makeup this limitation .For the project with highest priority ,timedelay will damage not only the economic benefits ,but also thestrategy and the prestige of the enterprise .Therefore weshould guarantee that the most important project be finished ontime 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 getthe comprehensive objective optimized .Therefore the weight of eachsub-objective should be considered .Reference [8] proposed an improvedant colony algorithm to solve this problem .Supposed that the weightsof the two optimizing objectives are a and B ,where a + B =1Then the* *comprehensive goal is F* ,where F*=aF1+BF2.4.2 The Principle of Genetic AlgorithmGenetic Algorithm roots from the concepts of natural selection andgenetics .It a'rasndom search technique for global optimization in acomplex search space .Because of the parallel nature and lessrestrictions ,it has the key features of great currency ,fastconvergence and easy calculation .Meanwhile ,its search scope is notlimited ,so it effective method to solve the resource bala ncingproblem ,as in [9].The mai n steps of GA in this paper are as follow:(1)EncodingAn integer string is short, direct and efficient .According to the characteristics of the model, the huma n resource can be assig ned to be a code object .The string length equals to the total number of huma n resources allocated.(2)Choosing the fitness functionThis paper choose the objective function as the foun dati on offitn ess function .To rate the values of the objectivefunction ,the fitness of the n-th in dividual is 1/ . n 。