A Resources Allocation Model for Multi-Project Management

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1 A Resources Aocaton Mode for Mut-Proect Management Hamdatou Kane, Aban Tsser To cte ths verson: Hamdatou Kane, Aban Tsser. A Resources Aocaton Mode for Mut-Proect Management. 9th Internatona Conference on Modeng, Optmzaton & SIMuaton, Jun, Bordeaux, France. <ha-7599> HAL Id: ha Submtted on Aug HAL s a mut-dscpnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are pubshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from pubc or prvate research centers. L archve ouverte purdscpnare HAL, est destnée au dépôt et à a dffuson de documents scentfques de nveau recherche, pubés ou non, émanant des étabssements d ensegnement et de recherche franças ou étrangers, des aboratores pubcs ou prvés.

2 9 e Conférence Internatonae de Modésaton, Optmsaton et SIMuaton - MOSIM 6 au Jun - Bordeaux - France «Performance, nteropérabté et sécurté pour e déveoppement durabe» A Resource Aocaton Mode for Mut-Proect Management H. KANE & A. TISSIER Département des Scences admnstratves, Unversté du Québec en Outaouas, rue Sant-Jean-Bosco, C.P. 5 Succ. Hu, Gatneau (Québec), JX X7, Canada (Te : # 99; e-ma : ABSTRACT: In ths paper, we propose a mathematca mode whch can be used n the phases of pannng and organzng of a mut-proect program. The mode w optmze the costs of competng a group of nked proects whe speedng up the reazaton of the whoe program n order to save tme. We mprove substantay a mode that Wey et a. (99) had eaborated, and adapt t to the current requrements of the mut-proect manager s work, ncudng the extensve use of subcontractng companes. We tested the mode through a mut proect case to ensure t w be effcent and safe n pannng compex mut-proect programs. We focused expcty and practcay on the optmzaton of shared human resources among the varous proects n order to save tme and ower the costs of the whoe proect. KEYWORDS: Mut-proect management, Resource aocaton, Mathematca programmng. INTRODUCTION The mut-proect management, aso desgnated as management by proects, conssts n pannng, coordnatng and controng a program that comprses severa parae proects (PMI, ). Mut-proect management s a growng fed of research. More and more companes manage severa proects n order to carry out ther actvtes (Tsser ; Frame, 995). To be effcent, mut-proect managers have to optmze tme management and resource aocaton. Tme management s the most mportant stake n proect management. Speedng up the reazaton of proects saves money, respects tme schedue n case of actvtes that ncur deay, and wns contracts by proposng the best tme of devery n a busness competton. Speedng up the reazaton of proects s therefore a key chaenge. Few works have been pubshed on ths subect (see secton ). Among them, ony a sma number of papers dea specfcay wth mutproect management. Resource aocaton s the second man task n potng proects. A terature revew shows the aocaton of resources ssue has been wdey deat n many research reports n the case of managng a unque proect. Methods and modes have been deveoped to formaze resource aocaton work (Gordon & Tup, 997). In mut-proect management, ths work s more compex. In fact, the aocaton of resources s one of the man ssues of mut-proect management (Payne, 995). Most of the tme, resources are mted and have to be shared among proects ed n parae. Ths paper deas wth the genera topc of mut-proect management. It nvestgates more specfcay resource aocaton works. Wthn companes, human, fnanca and matera resources are mted, as s the tme aocated to acheve the proect. The man obectve of ths research s to hep mut-proect managers speed up ther proects and aocate the proper amount of resources to make the acceeraton of ther proects possbe. We have focused on the phases of pannng and organzaton of the proect wthn a company that performs mut-proect management. The specfc am of our research was to create a mathematca mode that aows optmzng the costs of performng a group of proects whe speedng up the reazaton of the whoe program n order to save tme. Wey et a. (99) eaborated a mathematca mode to reduce tme spent n carryng out a program of severa proects and aocate resources at the owest cost possbe. We rewrote t to adapt t to the current requrements of the mut-proect manager works. For exampe, we took nto account the use of subcontractng companes achevng tasks n proects ed n a mut-proect program. Our mode has been spt n two dfferent parts. The frst part deas wth the acceeraton of the proect. In ths paper, ths frst part of the mode w not be descrbed (Tsser ). Ony ts resuts w be showed. The second part deas excusvey wth the aocaton of the resources. The second part s our man contrbuton n deveopng the former mode proposed by Wey et a. (99). That s why ths paper ony presents ths part n detas. A our deveopments were conducted to smpfy the understandng of the mode and ts use by the mut-proect managers. To vadate the mode, we tested t through a compex case ncudng many condtons. Ths case deas wth the reazaton of three proects, the characterstcs of whch (the duraton, the budget, the number of operators and the quanttes of work) are dfferent from one proect to the other. Wth ths approach, we demonstrate that the mode can be apped to a arge number of rea cases. In next secton, we revew the reated terature whch aowed us to consder and understand a the ponts of vew about the acceeraton of proects and the aocaton of resources n mut-proect envronment. Secton outnes the mode formuaton on mut-proect resource aocaton. Secton presents the case of study. Secton 5 concudes ths paper wth a revew of the works and suggests some orentatons for further research.

3 MOSIM - 6 au Jun - Bordeaux - France LITERRATURE REVIEW Many researchers have worked on topcs reated to the acceeraton of proects and the aocaton of resources. Semens (97) deveoped a mode on tme and cost parameters to acceerate a proect. The mode acceerates some tasks and not others n functon of ther cost by unts of tme. Wth ths method, the duraton of proect reazaton s reduced. However, the cost of the proect ncreases after acceeraton and the crtca path of the proect may change. It woud be more effcent to reduce duraton wth keepng the same crtca path. It aso appeared thought-provokng to save tme at the owest possbe cost. Isam et a. () consder t s more dffcut to make busness decson now than n the past. Currenty, more aternatves have to be taken nto account, n order to make a busness choce. Moreover, the fnanca mpact of a bad decson s more mportant, and ess toerabe n companes nowadays than n the past. That s why the authors consdered that the decson process has to be ratonazed. Then, they deveoped a near mathematca mode to reduce tme for competng a proect. The mode acceerates proects soey on the bass of fnanca consderatons, owerng the cost as much as possbe. However, suppes of addtona resources are needed for acceeraton, and the mode does not specfy these resources and ther extra costs. Moreover, the mode deas wth a unque proect management and not wth mut-proect management. Azondékon () examned the trade-off between task duraton ncrease or decrease and the aocaton of resources. The author estmated t s more effcent to consder the trade-off between tme and resources than the trade-off between tme and the costs of the tasks. The trade-off between tme and the costs of the tasks s an aggregaton of cost of human resources and other costs. It s not detaed. Azondékon s mode uses a dfferent trade-off between the tme and the resources for each type of resource human or matera - whch acts n a However, the mode does not determne the amount of resources. Gordon & Tup (997) sted dfferent modes and methods for the aocaton of resources from 959 to 997. Those modes and methods try to aocate - human, fnanca or matera - resources under restrcton of resources and tme. However, the authors expaned that those modes and methods were rarey adapted to the reaty of proect management. Azaron et a. (6) presented a non-near mode to aocate resources. Athough the mode s consdered as versate by ts creators, t s based on restrctve hypothess. Consequenty, the resuts gven by the mode are reevant ust for a restrctve number of case studes. Moreover, the mode gves no deta on the type of resources n ts outputs. Most of the researchers studed unque proects, whereas companes are currenty managng mut-proects. Moreover, many of these authors consder the acceeraton of proects as a cost-ncreasng factor. Acceeratng a task or a proect s obtaned by provdng more resources n order to acheve the work faster. Consequenty, costs ncrease. However, we can aso consder deceeraton of tasks. Proects contan crtca and non-crtca tasks. Crtca path ncudes a the crtca tasks of a proect. Non-crtca tasks can be acheved n a onger duraton and be performed wth fewer human resources than ntay panned. In ths way, the deceeratons of non-crtca tasks can provde addtona human resources to the crtca tasks. The chaenge s to re-aocate human resources from a task to another to speed up the proects. Usng the fewest new externa human resources speeds up the proects at the owest possbe cost. In ths paper, we propose a mode that deas wth resource aocaton or re-aocaton to make the program acceeraton possbe. Re-aocaton of human resources from a proect to another n mut-proect program s the man way to acceerate at the owest possbe cost. MULTI-PROJECT RESOURCE ALLOCATION MODEL Our frst contrbuton n deveopng a mode from Wey et a. (99) was to respond to the current requrements of mut-proect managers. For exampe, proects n program can be ed by dfferent companes. Consequenty n our mode, overhead proect costs appeared as dfferent costs as they are reated to dfferent companes. We propose a mathematca mode to formaze the aocaton of resources n mut-proect program. Varabes of the mode c : number of human resources of type to be added to - or to be taken off from - task (,) n order to acheve t. Parameters B r : budget of the program dedcated to human resource fundng B rk : budget of proect k dedcated to human resource fundng I: the set of connected arcs (,) n the program I k : the set of connected arcs (,) n proect k ; I k I, k T : norma duraton of task (,) y : maxma quantty of tme unts on whch task (,) s acceerated z : maxma quantty of tme unts on whch task (,) s deceerated E : quantty of human resources of type, whch s aocated to task (,) before ts acceeraton or deceeraton h : cost of human resources of type per tme unt and per person, n norma condtons S : cost of human resources of type per tme unt and per person, whch are aocated to speed up the task (,) V : cost of human resources of type per tme unt and per person, whch are aocated to the deceeraton of task (,) C maxma quantty of human resources of type avaabe on the program C k maxma quantty of human resources of type avaabe on proect k.

4 MOSIM - 6 au Jun - Bordeaux - France () Obectve functon: Mn z = (S y c V z c ) Mnmzng the vaue of the obectve functon s frameworked by constrants: () Human resources program budget: (h T E + S y c V z c ) B r, and (, ) I In the most restrctve case: B r = h T E, and (, ) I. In the ess restrctve case: B r h T E, and (, ) I. () Maxma quantty of type human resource avaabe on the program: (E ± c ) C, and (, ) I + f task (, ) can ony be acceerated, - f task (, ) can ony be deceerated. In the most restrctve case: C = E, and (, ) I. Human resources deducted from deceerated tasks are then re-aocated to speeded-up tasks and ±c =. In the ess restrctve case: C E, and (, ) I. Human resources deducted from deceerated tasks and human resources aocated to speeded-up tasks are not specfcay the same and ±c () Human resources proect k budget: (h T E + S y c V z c ) B rk, and (, ) I k In the most restrctve case: B rk = h T E, and (, ) I k. In the ess restrctve case: B rk h T E, and (, ) I k. (5) maxma quantty of type human resource avaabe on the proect k: (E ± c ) C k, and (, ) I k + f task (, ) can ony be acceerated, - f task (, ) can ony be deceerated. In the most restrctve case: C k = E, and (, ) I k. Human resources deducted from deceerated tasks are then re-aocated to speeded-up tasks and ±c =. In the ess restrctve case: C k E, and (, ) I k. Human resources deducted from deceerated tasks and human resources aocated to speeded-up tasks are not specfcay the same and ±c. (6) Lower bound of c for speedng-up task (, ) c, y T E (7) Upper bound of c to deceerate task (, ) If z s ower than T then we consder the foowng constrant: c z (E T ), If z s bgger than T then we consder the foowng constrant: c () Non-negatvty c T (E z ), NUMERICAL APPLICATION Mut-proect management s reay a common type of management n constructon companes or n ar-space frms. However, ths type of management s recommended to every company, whch wants to rease bg achevements n a very mted duraton. The case study presentaton w be spt n three parts. Frst, a mutproect program and ts characterstcs w be presented. Then, mode resuts concernng ths context w be presented. Fnay, those resuts w be anaysed.

5 MOSIM - 6 au Jun - Bordeaux - France Program presentaton We consder a program made up of three proects (A, B and C). Each proect has a set of precedence constrants dctated by the program network n Fg.. A the three proects have the same competon date. The assumpton s that each task begns at the earest possbe date n the proects. Ony the data necessary for the mode w be presented. We are usng the PERT network ustraton method. Arrows (aso desgnated as arcs) represent tasks and nodes represent begnnng or competon dates. Crtca tasks are doube-ned. A the nodes are numbered. Fg.. Program PERT network

6 MOSIM - 6 au Jun - Bordeaux - France The characterstcs of the proect A, B and C are presented n the foowng tabes. Tabe. Works breakdown structure of the proect A Name Fna Hum. Res. Hum. Res. Norma Norma Task duratons of type, of type, Predecesors duraton T (, ) cost T [days] -y +z E D [days] [$] E [persons] [persons] A A -- B A A A C A A A 6 D A 5 A A 6 6 E A 6 B A 6 F A 56 B A, C A, D A G A B A 5 H A 6 E A, F A 6 crtca 7 days new crtca 5 days 57$ Hum. Res. of type, E [persons] Tabe. Works breakdown structure of the proect B Name Norma Fna Hum. Res. Hum. Res. Norma Task duraton duratons of type, of type, Predecesors cost (, ) T T -y +z E D [days] [days] [$] E [persons] [persons] A B B B A B 7 C B 9 A B D B 9 C B E B B B F B B B, D B G B 9 C B H B G B, F B I B E B, H B crtca days new crtca 7 days 76$ Hum. Res. of type, E [persons]

7 MOSIM - 6 au Jun - Bordeaux - France Tabe. Works breakdown structure of the proect C Name Norma Fna Hum. Res. Hum. Res. Norma Task duraton duratons of type, of type, Predecesors cost (, ) T T -y +z E D [days] [days] [$] E [persons] [persons] A C B C 56 A C C C 67 B C 5 56 D C 6 B C 9 E C 7 C C, D C 5 F C 69 B C G C E C, F C H C G C I C H C J C I C crtca 9 days new crtca 7 days 79$ Hum. Res. of type, E [persons] Tabe. Common parameters across the three proects Human resources types Type Type Type Maxma quantty of human resource (type ) avaabe on the program [persons] 6 66 Costs of type human resource [$/day] h = h = h = Costs of added type human resource, n case of acceeraton [$/day] S =6 S = S = Costs of wthdrawn type human resource, n case of deceeraton [$/day] V = V =9 V =6 program budget dedcated to human resources fundng B ra + B rb + B rc = B r $5 9 + $77 + $ = $ The foowng tabe (Tabe 5) presents resuts from the mode to the program of proects A, B and C. These resuts aowed proposng human resources to work on the program n addton to the human resources aready workng on the program. Hrng s then a second factor of aocaton, after the re-aocaton of human resources from a task to another. Moreover we notced the acceeraton of tasks has a better chance to nduce an ncrease of quantty of human resources than the deceeraton of tasks has to nduce a decrease of quantty of human resources on a task team. Two reasons can expan ths phenomenon. Frst, we cannot remove resources from a team of ony one person; otherwse the task woud not be acheved. In our case study, many deceerated tasks are performed by ony one person. That s why re-aocaton s not reay possbe. Second, the mode does not reduce the quanttes of human resources to ther mnma vaues, because t not ony chooses the optma fnanca vaues to acceerate the whoe program, but aso reduces the addtona cost on every task. Fnay, the mode aows detang for each task how the aocaton or re-aocaton of human resources can nduce addtona costs and gans.

8 MOSIM - 6 au Jun - Bordeaux - France Tabe 5. Human resources comparson between nta statement and mode resuts nta states Mode resuts Tasks Proet A Proet B nta duraton Proet C E E.day E E.day E E.day fna duraton E ± c (E ± c ).day E ± c (E ± c ).day E ± c (E ± c ).day Totas gaps 5 6 gaps (%) +, +,9 +6, Note: ± means + n case the task s acceerate and means n case the task s deceerate.

9 MOSIM - 6 au Jun - Bordeaux - France 5 CONCLUSION The aocaton of resources s a dffcut chaenge n mut-proect management. It s many due to the nteracton of tme and resources between the proects ncuded n the same program. However, ther benefts can aow companes to ncrease ther capactes to succeed n the current goba competton. We aso presented how t can propose an aocaton of resources to make ths acceeraton possbe. Moreover, the mode presents resuts that mnmze addtona costs from the nta budget and maxmze gans by deceeratng tasks. A our work was based on the w to make our mode as understandabe and user-frendy as possbe for managers. However, our mode can be mproved. We ony consdered human resources n our work. Further research coud nvestgate other resources n proect management. By evauatng matera resources - for exampe - n addton to human resources researchers coud be abe to present a more detaed mode that w be abe to propose more detaed resuts. 6 REFERENCES Ahn, T., & Erenguc, S.S. (99). The resource constraned proect schedung probem wth mutpe crashabe modes: A heurstc procedure, European Journa of Operatona Research, Vo. 7, A-bour, S. (). Effects of resource management regmes on proect schedue. Internatona Journa of Proect Management, Vo., Anav-Isakow, S., & Goany, B. (). Managng mutproect envronments through constant work-nprocess. Internatona Journa of Proect Management, Vo., 9-. Azaron, A., Katagr, H., Sakawa, M., Kato, K., & Memaran, A. (6). A mut-obectve resource aocaton probem n PERT networks. European Journa of Operatona Research, Vo. 7, -5. Azondékon, S. (). A Way to Dea Wth Tme/Resource Trade-Off Probem. Ffth Internatona Conference of the Internatona Research Network on Organzng by Proect (IRNOP V). Renesse, The Netherands. Burns, S. A., Lu, L., & Feng, C. (996). The LP/IP hybrd method for constructon tme-cost trade-off anayss. Constructon Managment and Economcs, Vo., Cohen, I., Mandebaum, A., & Shtub, A. (). Mutproect schedung and contro: A process-based comparatve study of the crtca chan methodoogy and some aternatves. Proect Management Journa, Vo. 5, 9-5. Demeuemeester, E. L., Herroeen, W. S., & Emaghraby, S. E. (996). Optma procedures for the dscrete tme/cost trade-off probem n proect networks. European Journa of Operatona Research, Vo., 5-6. Eonen, S., & Artto, K. (). Probems n managng nterna deveopment proects n mut-proect envronments. Internatona Journa of Proect Management, Vo., 95-. Engwa, M., & Jerbrant, A. (). The resource aocaton syndrome: The prme chaenge of mutproect management. Internatona Journa of Proect Management, Vo., -9. Eskerod, P. (996). Meanng and acton n mut-proect envronment. Internatona Journa of Proect Management, Vo., Fatem Ghom, S. M. T., & Ashar, B. (). A smuaton mode for mut-proect resource aocaton. Internatona Journa of Proect Management, Vo., 7-. Frame, J. D. (995). Le nouveau management de proet. Pars : AFNOR. Gordon, J., & Tup, A. (997). Resource schedung. Internatona Journa of Proect Management, Vo. 5, Isam, M. N., Rana, B. Md., Rafque, S., & Azza, T. (). Crashng proect tme wth east cost: A near programmng approach. Journa of Busness Research, Vo. 6,. Payne, J. (995). Management of mutpe smutaneous proects: A state-of-the-art revew. Internatona Journa of Proect Management, Vo., 6-6. Proect Management Insttut (). Gude du Corpus des connassances en management de proet. PMI Goba Standard. Semens, N. (97). A smpe CPM tme-cost trade-off agorthm. Management Scence, Vo. 7 No. 6, 5-6. Spüher, R. W., & Bagn, R. G. (99). The roe and weaknesses of top management n nterna proects. In R. Gares (Éds). Handbook of management by proects. Venne : Manzsche Verag. Tsser, A. (). Accéératon de proets et aocaton de ressources : Des eneux de a geston mut-proet. Thèse de Maîtrse. Unversté du Québec en Ourtaouas. Wey, V. D., Deckro, R. F., & Jackson, J. A. Jr. (99). Optmzaton anayss for desgn and pannng of mut-proect programs. European Journa of Operatona Research, Vo. 7, Zka-Vktorsson, A., Sundström, P., & Engwa, M. (6). Proect overoad: An exporatory study of work and management n mut-proect settngs. Internatona Journa of Proect Management, Vo., 5-9.

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