Project management model for constructing a renewable energy plant

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1 Available online at ScienceDirect Procedia Engineering 74 (207 ) Global Congress on Manufacturing and Management Project management model for constructing a renewable energy plant Amy H. I. Lee a, He-Yau Kang b, *, zu-ing Huang b a Department of echnology Management,Chung Hua University, aiwan b Department of Industrial Engineering and Management, National Chin-Yi University of echnology, aiwan Abstract A project management model is developed for constructing a renewable energy plant in this research. Program evaluation and review technique (PER) is applied first to find the critical activities when constructing the plant and to calculate the total project cost and total duration time for the project under normal condition. When some activities are crashed, the total duration time can be reduced. he total project cost and the total duration time for crashing various activities are calculated. he fuzzy PER model is developed by the fuzzy multiple objective linear programming, and the model can devise the project implementation plan to maximize the total degree of satisfaction while minimizing total project cost and total duration time. A case study of a wind turbine construction in aiwan is presented to show the practicality of the proposed models he he Authors. Authors. Published Published by Elsevier by Elsevier Ltd. his Ltd. is an his open is access open article under under the the CC CC BY-NC-ND BY-NC-ND license license ( Peer review under responsibility of the organizing committee of GCMM206 Peer-review under responsibility of the organizing committee of the 3th Global Congress on Manufacturing and Management Keywords: Renewable energy; project management; program evaluation and review technique (PER); fuzzy. * Corresponding He-Yau Kang. el.: Ext address: kanghy@ncut.edu.tw he Authors. Published by Elsevier Ltd. his is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the organizing committee of the 3th Global Congress on Manufacturing and Management doi:0.06/j.proeng

2 46 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) Introduction With an enormous investment in time, capital and effort, the development a renewable energy plant is a very complicated task. A good project management for the construction of a plant is necessary. In a largescale project, the management needs to coordinate numerous activities throughout the organization. Several models, which aim to overcome the disadvantages with critical path method (CPM) and program evaluation and review technique (PER), have been introduced for the scheduling of construction projects, and some examples are vertical method, linear scheduling method and time scheduling method []. PER, developed in the late 950 s, was first applied for the US Navy to plan and control the Polaris missile program, and its emphasis was to complete the program in the shortest possible time. PER has the ability to cope with uncertain activity completion times, and it has the potential to reduce both the time and cost required to complete the project [2]. Some recent works on the project scheduling problem include Chrysafis and Papadopoulos [3], Jeang [4], Creemers et al.[5] and Yaghoubi et al.[6]. he rest of this paper is organized as follows. In section 2, two proposed models are introduced: a discrete PER model and a fuzzy PER model. In section 3, the proposed models are applied in the construction project of a wind turbine in aiwan. Some conclusion remarks are made in the last section. Nomenclature i j (, i j ) Node number, i =,2,,N. Node number, j =,2,,N. Sequence of nodes, j will be processed after i is processed. P C R otal duration time for the project otal cost for the project otal crashing cost for the project. E i Start time for activity i. S Slack time for node (, i j ). K D Direct cost of node (i, j) under normal time. D d Y s s l Normal duration time for node (i, j). Shortest duration time for node (i, j). Duration time for node (i, j). Crash time for node (i, j). Fuzzy crashing cost per unit time for node (i, j). Crashing cost per unit time for node (i, j). Fuzzy penalty cost per unit time.

3 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) l Penalty cost per unit time. 2. Proposed models 2.. Discrete PER model In this section, we assume that there is no uncertainty in implementing the project. hus, the duration time and cost parameters are known and certain. When crashing is considered, the total duration time and cost under various crashing activities can be calculated for the management as a reference. he mathematical model is as follows: D 0, N () Min C K Y s l Max E P i j i j Subject to: E E 0 i, j i j D Y i, j Y D d i, j E 0 E, E,, Y 0 i, j i j 2.2. Fuzzy PER model In this section, we assume that the crashing cost and penalty cost are uncertain. Crashing activities are considered to obtain a compromise solution [7]. he steps of the model are as follows: Step : Consider the fuzziness of crashing cost in each activity. Step 2: Construct a mathematical model. An optimal project planning and cost reduction alternative can be obtained by balancing the project duration time and cost. he original multiple objective linear programing model is as follows, and the objective function is to minimize the total crashing cost, which includes the crashing cost and the penalty cost, for the project: Min R Ys l Max0, EN P (7) Subject to: Eqs. (2)-(6) i j In the objective function, fuzzy crashing cost per unit time for node (i, j), s, and fuzzy penalty cost per unit time, l, are fuzzy in nature and can be represented by triangular fuzzy numbers. Ys is the total direct crashing cost, including the personnel cost, machinery cost, outsourcing cost and overtime cost. l Max{0,( EN P)} is the penalty cost if the project completion time is delayed. Eq. (2) is the constraint for the precedence of activities. Eq. (3) shows that the duration time for a node is the normal duration time for the node minus the crash time for the node. Eq. (4) shows that the crash time for a node must be less than or equal to the normal duration time for the node minus the shortest duration time for the node. Eq. (5) i j (2) (3) (4) (5) (6)

4 48 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) indicates that the start time for the first activity is 0. Eq. (6) ensures that the decision variables are nonnegative Step 3: Establish fuzzy multiple objective functions. () Based on Lai and Hwang [8], use the triangular fuzzy number to represent the crashing cost for l m u each activity, s, i.e. ( s, s, s ), as shown in Fig.. In addition, a fuzzy membership function,, is set to have a value between 0 and. s 0 l s m s u s s Fig.. Fuzzy membership function for the crashing cost, s In real practice, the distribution of triangular fuzzy number can contain three values: the most u l m pessimistic value, ( s ), the most optimistic value ( s ), and the most possible value ( s ). he fuzzy multiple objective linear programing model is as follows: Min GR i x (8) Subject to: Ax B x 0 l m u where G ( R, R, R ) Ri (9) (0) () Because G R i in the objective function is a triangular fuzzy number, its three prominent m u l points, R, R and R, can be used to transform the original fuzzy objective function into three objective functions. hey are to minimize the most possible value of the total crashing cost, G R, maximize the most optimistic value of the total crashing cost, G R 2, and minimize the most pessimistic value of the total crashing cost, G R 3. (2) Calculate the positive ideal solution (PIS) and negative ideal solution (NIS) for each objective function based on Hwang and Yoon [9]. he constraints are then added. (3) Based on the values of PIS and NIS, establish a membership function for each of the three objective functions. Step 4: Based on the membership function values and the fuzzy programming proposed by Zimmermann [0], auxiliary variable is introduced, and the original fuzzy multiple objective linear programming problem can be transformed into a crisp single-goal linear programming problem. By maximizing, a compromise solution can be obtained as follows:

5 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) Max Subject to: ( ) G R ( ) 2 (4) G R 2 G R 3 ( ) 3 E 0 E E 0 i, j i j D Y i, j Y D d i, j E, E,, Y 0 i, j i j 0 Step 5: Analyze the results. After solving the model, a compromise solution can be obtained. () otal crashing cost: R( G G, G, G G ) (22) R R3 R R R2 '' (2) otal project duration time: From P in the model, the optimal total project duration time after crashing activities can be obtained. 3. Case study In this section, the construction project of a wind turbine is used as an example to examine the practicality of the proposed models. he estimated time and costs are shown in able. Under normal condition, the completion time is 245 days. Under uncertain condition, triangular fuzzy number is applied, and the completion time is (70, 245, 255) days. If crashing occurs, a fuzzy crashing cost per unit time for node (i, j), s, incurs. In addition, 20 thousand N dollars or (5.5, 20, 23.5) thousand N dollars of variable penalty costs incurs for each day under normal condition and fuzzy condition, respectively. he network for the project is as depicted in Fig. 2. able. Basic information of the wind turbine project. Normal condition Fuzzy condition Completion time (days) 245 (70, 245, 255) Penalty cost (,000) 20 (5.5, 20, 23.5) (2) (3) (5) (6) (7) (8) (9) (20) (2) 4 Q W Z 2 3 F M 5 O 8 H 9 X 6 7

6 50 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) Fig. 2. Network for the wind turbine project. able 2. Basic construction data for wind turbine. 3.. Discrete PER model Activity Code Activity Duration time (day) Crashing cost per day (,000) W Foundation 84 $ X Generator 42 $ system Z Power 40 $ distribution box Q ower 30 $ M Nacelle 56 $9.4 6 F Rotor blade 84 $ O Wind turbine 7 $ H rial operation 30 $ Possible crashed time (day) he procedure for the discrete PER model in the case study is as follows: Step and 2: Calculate the earliest start time (ES), latest start time (LS), earliest finish time (EF), latest finish time (LF), and slack time of each activity, as shown in able 3. able 3. Four different times and slack time for each activity Activity code ES LS EF LF Slack W X Z Q M F O H Step 3: Find the critical path, which is shown as the dark path in Fig Q W Z 2 3 F M 5 O 8 H 9 X 6 7 Fig.. Critical path of the project.

7 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) Step 4: Based on the critical path depicted in Fig. 3, the total project cost and duration time can be calculated under the normal condition. he total project cost is thousand dollars, and the total duration time is 245 days, as shown in able 4. Next, based on Eqs. ()-(6), the total project cost and duration time with crashing activities can be obtained, as shown in able 4. For example, if the activity H is crashed for one day or two days, the total project cost will increase to and , respectively. able 4. Project duration and cost Project duration(day) Crashing activity and crashing days otal project cost(,000) H H H Z 5H W 3Z 2H W 3Z 2H W 23Z 2H W 24Z 2F 9H W 24Z 2F 9H W 24Z 2F 24H W 24Z 2F 24O H W 24Z 2F 24O 2H Fuzzy PER model he procedure for the fuzzy PER model in the case study is as follows: Step : Consider the fuzziness of crashing costs. able 5. Project activity durations and costs Activity Code Activity Crashing cost per day (,000) (l,m,u) W Foundation (0.64,5.05,6.4) X Generator system (7.38,8.85,2.38) Z Power distribution box (4.23,4.72,8.48) Q ower (5.36,6.32,25.5) M Nacelle (8.5,9.4,3.2) F Rotor blade (4.52,5.2,8) O Wind turbine (63.05,68.77,92.33) H rial operation (.7,2.67,5.47) Step 2Establish an objective function for the project by applying Eq. (7). Min R (0.64,5.05,6.4* Y (7.38,8.85,2.38)* Y (4.23,4.72,8.48)* Y (5.36,6.32,25.5)* Y (8.5,9.4,3.2)* Y (4.52,5.2,8)* Y (63.05,68.77,92.33)* Y (.7, 2.67,5.47)* Y ((5.5, 20, 23.5)* Max 0,(E 73) ) 89 9

8 52 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) Step 3: Establish fuzzy multiple objective functions. () List three objective functions Min G 5.05* Y 8.85* Y 4.72* Y 6.32* Y 9.4* Y R * Y 68.77* Y 2.67* Y (20* Max {0,(E Min G.09* Y 3.53* Y 3.76* Y 9.8* Y 4.06* Y R * Y 2.8* Y 3.5*(E Max G 4.4* Y.47* Y 0.49* Y 0.96* Y 0.64* Y R * Y 5.72* Y.5* Y 4.5*(E (2) Calculate the positive ideal solution (PIS) and negative ideal solution (NIS) for each objective function. he results are shown in able 6. able 6. he PIS and NIS for each objective function. G R G R 2 G R 3 PIS NIS (3) Based on the values of PIS and NIS, establish a membership function for each of the three objective functions. hey are as follows:, GR GR ( GR ), G R , GR , GR GR 2 2( GR ), G R , GR , GR GR ( GR ), G R , GR Step 4: he fuzzy multiple objective linear programming problem can be transformed into a crisp single-goal linear programming problem using Eqs. (2)-(2). By maximizing, a compromise solution can be obtained. Max Subject to G R G R

9 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) G R E =0 E2E2 0 E7E7 0 E223E3 0 E334E4 0 E335E5 0 E445E5 0 E336E6 0 E556E6 0 E668E8 0 E778E8 0 E889E Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y E9 240, Y, E 0 i, j i 0 Step 5: Analyze the results. hey are as follows. () otal project cost: We can obtain dollars, and GR 3 GR thousand dollars, GR thousand thousand dollars. By applying Eq. (22), the total project cost is

10 54 Amy H.I. Lee et al. / Procedia Engineering 74 ( 207 ) R =(668.22, 22.68, ) thousand dollars. (2) otal project duration time: With crashing activities, the optimal duration time is P days. 4. Conclusions In this research, program evaluation and review technique (PER) is adopted to find the critical activities when constructing the plant. he total project cost and total duration time for the project under normal condition are calculated first. When some activities are crashed, the total duration time can be reduced. hus, the total project cost and the total duration time for crashing various activities are obtained for reference. Because the crash time of each activity is usually uncertain, the fuzzy set theory is incorporated with the PER next. A fuzzy multiple objective linear programming is constructed to solve the fuzzy PER model. By maximizing the total degree of satisfaction through minimizing total project cost and total duration time, a compromise solution can be obtained. he practicality of the proposed models is examined by carrying out a case study of a wind turbine construction in aiwan. he proposed model can help the management consider relevant information in the construction process systematically so that resources can be best utilized and costs can be minimized. Acknowledgements his work was supported in part by the Ministry of Science and echnology in aiwan under Grant MOS E MY2. References [] K.A. Chrysafis, B.K. Papadopoulos. Approaching activity duration in PER by means of fuzzy sets theory and statistics. J Intell Fuzzy Syst 204;26(2): [2] A. Azaron, R.. Moghaddam. A multi-objective resource allocation problem in dynamic PER networks. Appl Math Comput 2006;8(): [3] K.A. Chrysafis, B.K. Papadopoulos. Approaching activity duration in PER by means of fuzzy sets theory and statistics. J Intell Fuzzy Syst 204;26(2): [4] A. Jeang. Project management for uncertainty with multiple objectives optimisation of time, cost and reliability. Int J Prod Res 205; 53: [5] S. Creemers, B. DeReyck, R. Leus. Project planning with alternative technologies in uncertain environments. Eur J Oper Res 205;242: [6] S. Yaghoubi, S. Noori, A. Azaron, B. Fynes. Resource allocation in multi-class dynamic PER networks with finite capacity. Eur J Oper Res 205;247: [7].F. Liang,.S. Huang, M.F. Yang. Application of fuzzy mathematical programming to imprecise project management decisions. Qual Quant 202;46: [8] Y.J. Lai, C.L. Hwang. A new approach to some possibilistic linear programming problems. Fuzzy Set Syst 992;49(2):2-33. [9] C.L. Hwang, K. Yoon. Multiple attribute decision making: methods and applications. New York: Springer-Verlag; 98. [0] H.J. Zimmermann. Fuzzy programming and linear programming with several objective functions. Fuzzy Set Syst 978;:45-55.

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