【正文】 her the priority is. 3. HUMAN RESOURCE ALLOCATION MODEL IN MULTIPROJECT 畢業(yè)設(shè)計外文文獻(xiàn)及譯文 3 ENVIRONMENT Problem Description According to the constraint theory, the enterprise should strictly differentiate the bottleneck resources and the nonbottleneck resources to solve the constraint problem of bottleneck resources .This paper will stress on the limited critical human resources being allocated to multiproject 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 multiproject according to project’s priorities .The allocation of noncritical 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 petition .The paper also supposes that the corresponding work 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 . 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 multiproject is N. Each project is indicated with Qi ,while i=1,2, … N. (2) The priority weights of multiproject have been determined ,which are 畢業(yè)設(shè)計外文文獻(xiàn)及譯文 4 respectively w1,w2…w n . (3) The total number of the critical human resources is R ,with rk standing for each person ,while k=1,2, …,R (4) Δki= ??? ot he r stop r oj e c tQr c e rhu m an r e sou ik01 (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 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 timegap between the real and expected duration time of project I that needs the critical resources to finish some task is △ ti ,( △ ti =tA itEi ). For there exists resources petition, 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 =ηi / Ri* ,.In the expression , ηi refers to the workload of projects I during some period ,which is supposed to be fixed and predetermined by the project managers on project planning phase 。 Ri* refers to the number of the critical human resources being 畢業(yè)設(shè)計外文文獻(xiàn)及譯文 5 allocated to projects I actually, with the equation Ri* =??Rk ki1? existing. Due to the resource petition the resource demands of projects with higher Priorities may be guarantee, while those projects with lower priorities m