Project task flow optimisation and departmental flow ...

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Int. J. Logistics Systems and Management, Vol. 15, No. 1, 2013

Project task flow optimisation and departmental flow analysis using design structure matrix and genetic algorithm Shi-Jie Chen* Department of Industrial and Systems Engineering, Northern Illinois University, 590 Garden Rd., EB 234, DeKalb, IL 60115, USA Fax: (815)-753-0823 E-mail: [email protected] *Corresponding author

Lukasz M. Mazur Department of Radiation Oncology – School of Medicine, University of North Carolina, Campus Box 7512, 101 Manning Drive, Chapel Hill, NC 27514, USA E-mail: [email protected]

Michał Sąsiadek Department of Mechanical Engineering, Institute of Computer Science and Production Management, University of Zielona Gora, Prof. Szafrana 4, Zielona Gora, Poland E-mail: [email protected] Abstract: Engineering projects often require a great deal of effort during the planning and designing stages to eliminate any unnecessary rework. To achieve satisfactory results in complex projects, project managers need to consider every possible rework (or feedback connections) throughout the entire project life cycle in addition to establishing the best project task flow. Therefore a project can be completed in a shorter time and lower cost without sacrificing the quality of the outcome. The objective of this paper is to develop an optimisation process for project task coordination using design structure matrix (DSM) and genetic algorithm (GA). DSM helps identify the relationships among project tasks. GA is used to help coordinate/optimise the project task structure in terms of task cost, task time and their coupling strength. This paper also shows our developed method is able to help the managers to enhance the level of cooperation among the related departments by a departmental flow analysis. The effectiveness of this model is demonstrated by an industry example. Keywords: project management; project task flow analysis; departmental flow analysis; genetic algorithm; GA; design structure matrix; DSM.

Copyright © 2013 Inderscience Enterprises Ltd.

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Reference to this paper should be made as follows: Chen, S-J., Mazur, L.M. and Sąsiadek, M. (2013) ‘Project task flow optimisation and departmental flow analysis using design structure matrix and genetic algorithm’, Int. J. Logistics Systems and Management, Vol. 15, No. 1, pp.68–92. Biographical notes: Shi-Jie (Gary) Chen is an Associate Professor of Industrial and Systems Engineering at Northern Illinois University. He received his PhD in Industrial Engineering from the State University of New York at Buffalo. His research interests are in the areas of healthcare systems engineering, concurrent engineering and management, project team management, production systems, and lean manufacturing. He has published refereed research articles in Concurrent Engineering: Research and Applications, IEEE Transactions on Engineering Management, Health Care Management Science, International Journal of Industrial and Systems Engineering, Innovative Higher Education, Journal of Industrial Engineering and Management, International Journal of Production Research, Computers in Industry, Computers and Industrial Engineering, and Journal of Intelligent Manufacturing, and Computer Integrated Manufacturing Systems. Lukasz M. Mazur is a Research Assistant Professor of Radiation Oncology Department at University of North Carolina. He received his PhD in Industrial Engineering from Montana State University. His research and practical work is focused on three areas: applying and evaluating quality improvement and patient safety models in healthcare settings; applying and evaluating healthcare systems improvement education; and concurrent engineering project management. He has published refereed research articles in Health Care Management Science, Engineering Management Journal, International Journal of Industrial and Systems Engineering, Journal of Industrial Engineering and Management, Seminars of Radiation Oncology, and International Journal of Radiation Oncology, Physics and Biology. Michał Sąsiadek is an Assistant Professor of the Institute of Computer Science and Production Management in the Department of Mechanical Engineering at University of Zielona Gora. He received his PhD in Mechanical Engineering, Machine Construction and Exploitation from University of Zielona Gora. He has published research articles in the areas of design engineering, planning and organising of manufacturing processes.

1

Introduction

Engineering projects often require a great deal of effort during the planning and designing stages to eliminate any unnecessary rework. The difficulties in coordinating project task structure do not simply arise from engineering complexity, but also steam from cooperation capabilities between the departments. For example, a design of an aircraft can involve the coordination of hundreds of thousands of tasks and engineers from different departments that have to work together and make millions of decisions over months or years. To achieve satisfactory results in such complex projects, project managers need to consider every possible rework (or feedback connections) throughout the entire project life cycle in addition to establishing the best project task flow. Therefore a project can be completed in a shorter time and lower cost without sacrificing the quality of the outcome. The methods such as design structure matrix (DSM) and

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genetic algorithms (GAs) have been found effective in revealing the entire project task structure and optimising the task flow (Steward, 1981a, 1981b; Eppinger et al., 1994; Rogers, 1996, 1997; Liu et al., 2008; Aleisa and Lin, 2009; Gunawan and Ahsan, 2010; Bagloee and Tavana, 2012; Yang et al., 2012). The major objective in this research is to develop an optimisation process for project task coordination using DSM and GA. DSM helps identify the relationships among project tasks (i.e., independent, dependent, and interdependent relations). GA is used to help coordinate/optimise the project task structure in terms of task time, cost and their coupling strength. The effectiveness of this model is demonstrated by an industry example where the two methods, DSM and GA, are working together to help reduce the project time and cost. In addition, this paper also shows our developed method is able to help the managers to enhance the level of cooperation among the related departments (due to task dependencies), and thus avoid unnecessary rework, by a departmental flow analysis.

2

Design structure matrix

There are three basic types of relationships among project tasks: independent, dependent, and interdependent. To identify these three basic task types inherent in the whole complex process system, DSM proposed by Steward (1981a, 1981b) is a useful tool. Much research has demonstrated the effectiveness of DSM in the past (Kusiak et al., 1994, 1995; Rogers and Bloebaum, 1994; Kusiak and Larson, 1995; Krishnan, 1996; Krishnan et al., 1997; McCulley et al., 1997; Ahmadi et al., 2001; Browning, 2001; Cho, 2001; Liu et al., 2008; Aleisa and Lin, 2009; Gunawan and Ahsan, 2010; Yang et al., 2012). DSM divides the design project into n individual tasks in an n×n matrix. Similar to an adjacency matrix, DSM is a square matrix with n rows, n columns, and m non-zero elements, where n is the number of nodes and m is the number of edges. If there exists an edge from node i to node j, the value of element ij is a unity or a marked sign in the matrix. Otherwise, the value of the element is zero or empty. Information links among individual tasks are revealed clearly by the systematic mapping, regardless of the number of tasks. Figure 1 shows a 17-task DSM example with 31 task relations/connections including 20 progressive connections (above the diagonal) and 11 feedback connections (below the diagonal). In recent years, DSM has been used as a management aid as well as an engineering tool to guide the organisational structure of design projects (Yassine et al., 2000, 2001; Dong and Whitney, 2001; Eppinger, 2001; Eppinger and Salminen, 2001; Chen and Lin, 2002, 2003). According to Steward’s partitioning algorithm, Rogers (1989) developed an expert system tool called design manager’s aide for intelligent decomposition (DeMAID) that can perform DSM analysis in determining the task sequences and their relationships. DeMAID has been claimed to be a very useful tool in assisting task sequencing (Rogers and Bloebaum, 1994; McCulley and Bloebaum, 1996). Sobieszczanski-Sobieski (1989, 1993) combined DSM with a mathematical model of the physical problem to form a hierarchical, constrained non-linear optimisation problem. Eppinger et al. (1990, 1994) analysed task interactions to create design task groupings using DSM in order to find an alternative sequence and structure of a project. Kusiak and Wang (1993a, 1993b, 1993c) decomposed tasks in design using DSM and group technology to identify how tasks should be divided into groups. Guo et al. (1995) developed an algorithm for DSM to

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carry out the planning tasks. Smith and Eppinger (1997a, 1997b) used DSM to represent each task with deterministic duration and probabilistic repetition in order to identify controlling features of engineering design iterations. Chen and Lin (2002, 2003) used DSM for interdependent task group decomposition and project task coordination model for team organisation in concurrent engineering. Aleisa and Lin (2009) used DSM to identify time-consuming iterative design cycles that cause critical delays within the design development process. Gunawan and Ahsan (2010) used DSM to address the interdependency of feedbacks and iterations that help reduced the project duration of the petroleum oil field development. According to their proposed algorithm, Yang et al. (2012) showed that DSM is able to improve the concurrency and collaboration of product development tasks for automotive case studies. Figure 1

Design structure matrix (see online version for colours)

The advantages of using DSM are: 1

DSM overcomes the size and complexity limitations of digraphs in visualising the entire project task structure

2

DSM is easy to understand and able to handle the processes in their entirety

3

the matrix format is suitable to programme and calculate using a computer

4

not only can the entire sequences among project tasks be identified, but also the underlying structure of the project can be analysed by rearranging the task sequences.

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Even though the current DSM literature provides little on its disadvantages and/or limitations, it should be noted that DSM has been mostly used to capture and represent the complexity of project task structure. In complex projects, coordination of project tasks often depends on multiple variables. Therefore, further analysis on the outcomes of DSM is needed in order to reach the optimal project solution (Kusiak et al., 1995; Yassine et al., 2001; Chen and Lin, 2002, 2003; Liu et al., 2008; Aleisa and Lin, 2009; Gunawan and Ahsan, 2010; Yang et al., 2012).

3

Genetic algorithm

Invented by Holland in 1975 and later developed by Goldberg (1989), GA is a programming technique that mimics biological evolution as a problem-solving strategy, which has proved to be very effective in optimising the project task flows (Goldberg, 1989; Syswerda, 1990; Gebala and Eppinger, 1991; Thomas and Eppinger, 1994; Rohatyński and Kielec, 2001; Rohatyński at el., 2002; Bagloee and Tavana, 2012). The concept of GA is simple. First, an initial population of solution is randomly generated and serves as a group of potential candidates for optimal solutions. Next, GA selects/eliminates those candidates based on a user-defined selection method with a user-designed fitness function for evaluating the individual solutions. Crossing and mutation processes are used to create multiple variations of the selected solution, which are later subjected to the next fitness evaluation and selection. The expectation is that the fitness average of the population will improve each round, and therefore, by repeating this process for hundreds or thousands of generations, an optimal solution or some near optimal solutions to the problem will be obtained. The advantages of using GA for complex systems optimisation are: 1

Ability for multiple direction search: GA can explore the solution space in multiple directions at once. If one direction turns out to be a dead end, it can easily be eliminated and GA continues to work on more promising paths, which will provide a better chance to reach the optimal solution (Koza et al., 1999).

2

Efficient performance in complex problems: GA is particularly well-suited for solving complex problems where the solution space is large and is difficult to search exhaustively in any reasonable amount of time (Haupt and Haupt, 1998).

3

Effective to escape the local optima and to discover the global optimum for even a very rugged and complex fitness landscape (Coello, 2000)

4

No prior knowledge requirements: GA knows anything about the problems it is deployed to solve.

Instead of using previously known domain-specific information to guide each step and making changes with a specific eye towards improvement, as human designers do, GA is a ‘blind watchmaker’ that makes random changes to candidate solutions and then uses fitness function to determine whether those changes produce an improvement (Dawkins, 1996; Koza et al., 2003). There are also some problems and limitations of using GA for complex systems optimisation (Goldberg, 1989; Syswerda, 1990; Forrest, 1993; Dawkins, 1996; Mitchell, 1996; Haupt and Haupt, 1998; Romeo et al., 2008a, 2008b):

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1

Code representation: some changes (usually mutations) to an individual’s genes can produce an unintelligible result if code representation is poorly designed.

2

Fitness function design: if fitness function is chosen poorly or defined imprecisely, the GA may be unable to find a solution to the problem, or may end up solving the wrong problem.

3

Selection of the population size: it is crucial to establish the size of the population that will lead to an optimal solution for a particular problem. In general, the more complex the problem is, the larger the population size should be chosen. It is usually recommended to test the developed GA with its fitness function to make sure the proper population size to be used.

4

Premature convergence: this problem is usually related to the chosen selection method for the algorithm and usually occurs when a solution becomes the dominant over the others. The problem can be avoided by controlling the strength of selection, so as not to give excessively fit individuals too much advantage.

To deal with potential issues of GA, researchers developed unique solutions to deal with potential issues related to code representation, fitness function design and/or solution generation. For example, Wang et al. (2008) presented a novel coding format of chromosomes, with random bit crossing to solve multi-team weapon target assignment problem. Azizi et al. (2009) compared their new hybrid simulated annealing algorithm tailored for flow shop scheduling with other techniques including a conventional simulated annealing, a standard GA, and a hybrid GA. Fan et al. (2009) used the multi-objective GA with a bi-objective 0-1 programming model for selecting suitable members for facilitating the success of research and development projects using the individual and collaborative information. Azadeh et al. (2009) identified a conventional time series using integrated GA algorithm as the best model for future oil production forecasting because of its dynamic structure, whereas previous studies assume that GA always provides the best solutions. Lee et al. (2010) proposed an integer programming model and a GA-based solution procedure for allowing express couriers to maximise their incremental profit. Min and Guo (2010) combined game theory with GA to promote a compromise between the conflicting interests of the carrier and the shipper, while optimally balancing the shipper’s desire to contain cost against the carrier’s desire to increase profit. Zhou and Min (2011) proposed a non-linear mixed-integer programming model and GA that can solve the stochastic network design problem in a closed-loop supply chain.

4

Methodology – the GA optimisation process

In this paper, we develop a GA to optimise the task flow for the entire project structure based on the information of task time, cost and their coupling strength. At first, we need to encode each potential solution, which is the task sequence or task structure represented by DSM, in a form that GA can process. One common approach is to encode each solution as a binary string (i.e., a sequence of 0’s and 1’s) where the digit at each position represents the value of some aspect of the solution. Virtually every combination of solution can be represented by genetic code as a binary string called chromosome. Figure

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2(a) represents a DSM containing five tasks in a sequence, where Figure 2(b) shows the representation of the same sequence in the genetic and binary form. Figure 3 shows the overall procedure of this GA optimisation process. Steps 1 to 7 in the following highlight some important details of the GA optimisation process. Figure 2

Genetic and binary representation of DSM, (a) design structure matrix (b) genetic representation (see online version for colours)

(a) Figure 3

(b)

The GA optimisation process 1. Generate the Population of Chromosomes

2. Selection of Chromosomes

3. Reproduction Process of Crossing and Mutation

4. Fitness Function Evaluation

5. Creation of New Population

6. Check for Stoppage Conditions

7. Selection of the Best Chromosome

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4.1 Generate the population of chromosomes The algorithm randomly generates the initial population of chromosomes, which serves as a group of candidates or potential solutions.

4.2 Selection of chromosomes The algorithm uses the tournament selection method. One major reason of using tournament selection is its ability to prevent the algorithm from the premature convergence. In every reproduction step, two chromosomes are selected from the new generated population (chi, chj ⊂ Pt) for the tournament selection. The winner of the tournament is the chromosome with a higher fitness value, Wj, which is then copied to the next population. The tournament selection continues until the population meets a user-defined size. The following example shows two chromosomes (ch1 and ch5) are selected among six chromosomes in a population for the tournament selection where ch5 with a higher fitness value wins the tournament and will advance to the next population. ch1 = [1 2 3 4 5]

ch2 = [3 1 2 4 5]

ch3 = [5 3 4 2 1]

ch4 = [2 1 3 4 5] ch5 = [4 1 3 2 5] ch6 = [4 5 3 2 1]

W j ( ch1 ) = 0.4672

W j ( ch5 ) = 0.8452

4.3 Reproduction process by crossing and mutation Multi-points crossing is used in the algorithm. Multi-point crossing introduces a higher variability than single-point crossing when creating new chromosomes, so that the final solution tends to have a less chance to be a local optimum. For each randomly selected pair of chromosomes in the population, the positions of the genes to cross are selected according to the following conditions:

L p > 0.5 → Stay; L p ≤ 0.5 → Cross where Lp – generated random number for crossing probability. Figure 4

Crossing process (see online version for colours)

CHROMOSOME 1

5

3

4

2

1

Crossing output

5

4

3

2

1

CHROMOSOME II

2

4

5

3

1

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76 Figure 5

Mutation process (see online version for colours) Chosen for mutation

Chosen for mutation

5

4

3

2

1

CHROMOSOME BEFORE MUTATION

5

2

3

4

1

CHROMOSOME AFTER MUTATION

For example, a new chromosome is generated as shown in Figure 4 where tasks (or ‘genes’) 5 and 2 in chromosome 1 stay in the same position because they are the only two tasks whose Lp values are higher than 0.5, while Tasks 4, 3, and 1 in chromosome 2 are crossing to the new positions in sequence. The probability of mutations, that is a pair of genes within the chromosome switching their positions, usually is very low in the GA optimisation process (i.e., about 0.1%). Figure 5 shows the mutation of Tasks 4 and 2.

4.4 Fitness function evaluation The fitness function shown below evaluates the fitness (or quality) of every chromosome in the population by calculating the fitness value, Wj. The chromosomes with higher fitness values are the better chromosomes. W j = ( wt ⋅ T + wc ⋅ C ) −4 ⊗

where T

task time

C

task cost

wt, wc weights (from 0 to 1).

4.5 Creation of the new population The chromosomes generated by the reproduction process will join the new population and each of them will be reevaluated by the fitness function. In general, the best chromosome from the old population replaces the chromosome with the lowest fitness value in the new population. And then the rest of the chromosomes in the new population replace the chromosomes in the old population.

4.6 Check for the stoppage conditions There are three stoppage conditions in the algorithm. First, the stoppage occurs when the fitness average of the current population is equal or greater than the global best

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chromosome times a user-defined threshold, Zp (1 by default), which is expressed mathematically as follows: n pop

∑W

j

n pop ≥ global W j • Z p

i =1

where Wj the fitness value Zp the user-defined threshold. Second, the stoppage also occurs if there is no further improvement in the fitness function for a certain number of generations (e.g., 10% of the maximum number of generations pre-defined by the users). Third, the algorithm stops after the pre-defined maximum number of generations.

4.7 Selection of the best chromosome (or solution) If one of the stoppage conditions is met, the GA optimisation process is stopped and the optimal solution is the chromosome with the highest fitness value.

5

An illustrative example

The example is taken from an industry company that designs, manufactures and distributes different types of industrial and commercial furnaces. The main purpose of this example is to present the significant improvement of time and cost after the GA optimisation process. We will also show that our developed method is able to help the managers to enhance the level of cooperation among the related departments by a departmental flow analysis. First, the entire project is decomposed into 27 tasks and the relationships among them are also established, which are done by meeting with managers and members from different functional departments involved in the new furnace design and manufacturing. It should be noted that the project decomposition and task relationship establishment provide critical information for the study that have to be handled by the experienced managers and engineers with care if satisfactory results are desired. Table 1 shows the project task information including task relationship, time, cost, and the responsible department of each task. For example, Task 1 (customer order/price negotiations) is related to Task 5 and needs to provide information input to Task 5. The estimated time and cost for Task 1, which is to be executed in selling department (SD), are 150 and 40 units, respectively.

5.1 Project task flow before the GA optimisation process According to the task input/output relationships in Table 1, Figure 6 shows the current project task flow using DSM before the GA optimisation process (with 43 progressive and eight feedback connections).

Project design documentation

Project components documentation

Project specification check

User manual documentation

Past experience technology consultation

Technology documentation

Evaluation/selection of procurement partners

Material procurement ordering

8

9

10

11

12

13

5

7

Project initiation

4

6

Technical concept proposition

Price evaluation

3

14

100

42

324

8, 12, 16, 17, 18, 19, 20, 21, 22 13, 15

45

86

308

16

1,619

30

40

60

16

150

Time

11

24

9, 10, 26

11

8, 9, 10

6, 7

1

1

1

Order specification analysis for production feasibility

2

Relationship 5

Task description

Customer order/price negotiations

1

35

35

40

28

40

40

40

40

40

40

40

80

40

Cost

Department(s) responsible for task realisation

Selling department (SD)

Selling department (SD)

Technology department (TD)

Archival office (AO)

Design department (DD)

Design department (DD)

Design department (DD)

Design department (DD)

Procurement department (PrcD) Technology department (TD) Planning coordinator (PC) Design testing department (DTD)

Selling department (SD)

Selling department (SD)

Design testing department (DTD) Design department (DD) Services and installation department (SID)

Selling department (SD)

Table 1

Task number

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Project task information

Disassembly and painting

Transportation

Assembly over the customer site

Furnace assembly inspection

Final meeting

25

26

27

Final testing

22

24

Final assembly

21

23

Assembly of furnace subparts

Assembly of main furnace part

Detail analysis of firms value proposition

18

20

Detail analysis of supply chain management value proposition

17

19

17

Evaluation/selection of supply chain management partners

16

-

8, 27

26

25

24

8, 23

8, 22

21, 22

20, 21, 22

19, 22

19, 22

8

15, 17, 18, 20, 21

Material procurement receiving

Project material evaluation/specification changes

15

Relationship

14

Task description

12

259

353

288

347

250

537

2,387

1,622

270

1,892

452

5

100

Time

40

32

84

28

28

32

28

28

28

28

28

40

35

28

Cost

Technical director (TD)

Service and installation department (SID)

Service and installation department (SID)

Distribution department (DistD)

Production department (PD)

Service and installation department (SID)

Production department (PD)

Production department (PD)

Production department (PD)

Production department (PD)

Supply chain management department (SCMD)

Supply chain management department (SCMD)

Design testing department (DTD)

Inventory department (ID)

Department(s) responsible for task realisation

Table 1

Task number

Project task flow optimisation and departmental flow analysis 79

Project task information (continued)

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80 Figure 6

Project task flow before optimisation using DSM (see online version for colours)

Cluster A 1 2 3 4 5 6 7

Cluster B 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A simple example consisting of four tasks is used to illustrate the calculations of project time and cost. Table 2 shows the task information of time, cost and their relationships for this four-task process example and Figure 7 presents the DSM task flow for the example. It is important to note that when estimating the project time and cost, feedback connections and concurrency among tasks should be considered. In the example, we assume that every feedback loop can only be executed once. The total time and cost of this example are calculated as follows: T = (T1 + T3 ) + (T1 + T3 ) + T4 + (T1 + T3 + T4 ) = 220

C = ( C1 + C2 + C3 ) + ( C1 + C2 + C3 ) + C4 + ( C1 + C2 + C3 + C4 ) = 390

Please note that Task 2 is not included in the calculations of project total time. This is because Task 2 and Task 3 can be undertaken concurrently and the shorter time of these two tasks, Task 2, therefore is not included in the calculation.

Project task flow optimisation and departmental flow analysis Table 2

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Four-task process example

Tasks number

Relationship

Time

Cost

1

2, 3

15

40

2

-

35

45

3

1

45

25

4

1

20

30

T = 115

C = 140

n

∑ i =1

Figure 7

Task flow of four-task process example (see online version for colours)

1 2 3 4 In the same way, the total time and cost of the entire project can be calculated by following the task flows revealed in DSM where the progressive and feedback flows are considered along with the concurrency among some tasks. For example, assuming that each feedback connection will cause only one rework (or iteration), the time units required to complete the tasks in cluster A and in the feedback loop between Tasks 8 and 11 (see Figure 6) can be calculated as follows, respectively: TclusterA = Tlongest (1,2,3,4) + T1 = 150 + 150 = 300

(

T feedback (8−11) = 2 × T8 + Tlongest (9,10) + T11

)

= 2 × ( 308 + 86 + 324 ) = 2 × 718 = 1,436

Calculating the cost is much simpler because there is no need to consider the concurrency among tasks. For example, the total cost units for the project are calculated in the following by adding up the costs of 27 tasks and the sums of five feedback loops: 27

Ctotal =

∑ t =1

11

Ct +

∑ t =8

15

Ct +

∑ t =8

21

Ct +

∑ t =8

22

Ct +

∑ t =8

26

Ct +

∑C

t

= 3, 273

t =8

It should be noted that more feedback connections entail more potential rework. Additionally, the more tasks in the feedback loop the more expensive and lengthy rework will be needed, which usually result in higher cost and longer time for a project to complete. Table 3 shows the time and cost needed for each feedback loop as well as the total time and cost for the entire project before the GA optimisation process.

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82 Table 3

Project time and cost before optimisation 19

18

17

16

15

14

13

12

11

10

9

2,387

1,622

270

1,892

452

5

100

100

42

324

45

86

308

32

28

28

28

28

28

40

35

28

35

35

40

28

40

40

1

20

537

28

2

21

250

28

3

22

347

84

4

23

288

32

5

24

353

40

6

25

12

259

7

26

8

27

Tasks

40

40

80

60

40

40

40

150

30

40

40

16

16

1,619

Time

Cost

11,156

Time (1-27)

1,025

Cost (1-27)

150

Time (1-4)

200

Cost (1-4)

Time (8-11)

148

Cost (8-11)

965

Time (8-15)

281

Cost (8-15)

7,608

Time (8-21)

461

Cost (8-21)

7,558

Time (8-22)

493

Cost (8-22)

9,105

Time (8-26)

665

Cost (8-26)

37,110

Total time

3,273

Total cost

Project time and cost before optimisation

718

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83

5.2 Project task flow after the GA optimisation process The main goal in this section is to establish the best DSM task structure by our GA optimisation process based on the information of task time and cost. Figure 8 shows the optimal project task flow after optimisation, which becomes very different from the original structure. The optimised DSM contains only two feedback connections comparing to eight feedbacks before optimisation. The optimal solution is reached with the following parameters used in the GA optimisation process: the number of generations = 1,500, the number of populations = 100, Mutation % = 0.01, Zp = 0.9, wt = 1, and wc = 1. The stoppage condition occurred at the generation number 1245 with the generation fitness average exceeding the global best chromosome Wj times Zp (see Figure 9). Figure 8

Project task flow after optimisation using DSM (see online version for colours)

2 3 4 1 5 7 6

Cluster B 10 11 12 16 13 14 18 15 17 19 20 21 22 8 23 9 24 25 26 27

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84 Figure 9

GA optimisation progress GA Optimization Progress

9.00E-17 8.00E-17 7.00E-17 6.00E-17 5.00E-17 4.00E-17 3.00E-17 2.00E-17 1.00E-17 0.00E+00 1

10

20

40

Global Best Wj

60

80

100

200

300

400

500

600

700

800

900

1000

1100

1200

1245

generation

Generation Average

Table 4 shows the time and cost needed for each feedback loop as well as the total time and cost for the entire project after the GA optimisation process. It should be noted that the second feedback loop between Tasks 8 and 26 in Figure 8 contains only six tasks comparing to 19 tasks in the original loop before optimisation, thus the extra rework time and cost required for this new feedback loop are significantly reduced after optimisation (time units decreased from 9,105 to 1,294 and cost units decreased from 665 to 252). Finally after the optimisation process, we are able to reduce the total project time from 37,110 to 19824 time units (46.58% time reduction) and the cost units from 3,273 to (47.14% cost saving).

5.3 Project departmental flow analysis In order to further analyse and manage the project completion time and cost more accurately, project managers have to consider the ‘weight’ of each feedback connection in the project, such as the probability of a feedback to happen and/or the number of loops (or iterations) that a feedback connection should incur. A higher feedback probability with more feedback iterations means a stronger weight should be given to the feedback connection, which will significantly increase the project time and cost. Figures 10 and 11 present the task flows among departments before and after the GA optimisation. Task numbers from 1 to 27 are within circles. The abbreviations within squares stand for the names of the departments where the tasks are performed. The solid and dashed lines represent the progressive and feedback connections, respectively. Performing departmental flow analysis helps us to evaluate the weights of feedback connections (possible rework). In general, the feedback connections involving the tasks that belong to the same department tend to have less iteration than those feedbacks with the tasks from different departments. In addition, those departments being willing to share and cooperate with each other in a feedback loop are also likely to have less iteration than the departments that lock themselves up from cooperation.

Project task flow optimisation and departmental flow analysis Table 4

85

Project time and cost after optimisation

7

16

40

6

1,619

40

10

45

28

11

324

40

12

42

35

16

452

40

13

100

35

14

100

28

18

270

28

15

5

35

17

1892

28

19

1622

28

20

2387

28

21

537

28

22

250

32

8

308

40

23

347

28

9

86

40

24

288

28

25

353

84

26

259

32

27

12

40

Total cost

40

1,730

30

Total time

5

19,824

40

Cost (8–26)

150

252

1

Time (8–26)

40

1,294

40

Cost (10–8)

4

453

40

Time (10–8)

60

7,817

3

Cost (1–27)

80

1,025

16

Time (1–27)

Cost

2

10,713

Time

Task number

Project time and cost after optimisation

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Figure 10 Project departmental flow before optimisation

ID

SD

1

14

SID DD DTD

4

3

2

SCMD

PD

17

DTD

18

15 8

PrcD pc DTD TD

19

SD

5

20

21 8 8

SID

Project Realization Flow

DD

6

7

22 8

PD

8

23

AO

9 24

TD

10

24

TD

11

25 SID

26

SCMD

16

12 SD td

13

27

Project task flow optimisation and departmental flow analysis

87

Figure 11 Project departmental flow after optimisation SID

DTD

SCMD

PD

DD SD

DTD

4

3

15

17

18

2

1

19 20

PrcD pc DTD TD

8

SD

21

5 SID

Project Realization Flow

22

DD

6

7

PD

8

23

DD AO

10

9

TD TD

11

24 SID

SCMD

12

16

25

SD

26 13

27

ID

14

td

88

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In Figure 10, Tasks 3 and 4 (both having a feedback connection to Task 1) are expected to receive better coordination and cooperation with Task 1 because these three tasks belong to the same department (SD). However, handling the feedback connection from Task 2 to Task 1 is more difficult because Task 2 involves three different departments (DTD, DD, and SID) that all have to deal with the department (SD) of Task 1. Therefore, the feedback connection of Task 2 to Task 1 is given a stronger weight than the feedbacks of Task 3 to Task 1 and Task 4 to Task 1. Compared the departmental flow of Figure 10 (before optimisation) with Figure 11 (after optimisation), it can be seen that the level of cooperation among departments is much improved after optimisation which should lead to significant rework elimination. The feedback loops in Figure 10 involve six functional departments (DTD, DD, SID, SD, TD, and PD) for cooperation, which will be difficult for managers to coordinate: DTD, DD, and SID with SD (between Tasks 1 and 2); TD with DD (between Tasks 8 and 11); DTD with DD (between Tasks 8 and 15); PD with DD (between Tasks 8 and 21); SID with DD (between Tasks 8 and 22); and SID with DD (between Tasks 8 and 26). In contrast, the two feedback loops in Figure 11 need only three functional departments (DD, AO and SID) to cooperate with each other during the project execution: DD with AO (between Tasks 8 and 10) and SID with DD (between Tasks 8 and 26). For example, Task 10, when undertaken by the AO department, is expected to maintain a close communication with the DD department where Task 8 belongs in order to avoid the unnecessary rework. Moreover, Task 6, which provides information input to Task 10, also belongs to the DD department. Therefore managers should give more emphasis to the level of cooperation and communication between the departments of AO and DD. The above examples show that departmental flow analysis based on the optimised DSM project task structure is able to improve the project task flow that results in less bureaucratic processes, better coordination for the information exchange, and thus reduces the total time and cost of the project by eliminating unnecessary rework.

6

Conclusions

For complex projects, it is critical to consider the feedback connections among tasks because much rework (or iteration) will be involved that usually leads to a significant increase of the project time and cost. The major contributions of this study are: 1

the DSM method, which reveals the entire project task structure and task relations, overcomes the limitation of traditional PERT/CPM method that cannot handle task rework/iteration

2

the GA optimisation process is able to help improve the project task flow and reduce the number of feedbacks in DSM so that the overall project time and cost are reduced.

The results from the illustrative example demonstrate the effectiveness of the optimisation process. Some managerial implications include: 1

the departmental flow analysis highlights the areas of close-related departments where much attention should be paid by the managers in order to enhance the level of cooperation and avoid unnecessary rework

Project task flow optimisation and departmental flow analysis 2

89

managers should make sure that the appropriate communication and information exchange channels are well established for all the feedback connections in DSM to facilitate the effective cooperation among the related departments.

Although the use of heuristics with GA has been proved to be very effective in solving the similar type of NP-hard problems (i.e., project task sequencing and scheduling), in this paper we have no intention to suggest that GA is ‘the best’ approach for solving such problems. Other computerised problem-solving techniques or heuristics (i.e., calculus-based algorithms, enumerative methods, random methods, hill-climbing methods, simulated annealing, tabu search, and neural network, etc.) could also be applied to this problem. One future research direction will be to compare our GA optimisation process with the other search methods (i.e., tabu search, neural network, and random search, etc.) to see if comparable or better results can be achieved by a shorter computational time. Various examples from different industries are also to be studied.

Acknowledgements The authors are grateful to the anonymous reviewers and the editor for their valuable comments and suggestions.

References Ahmadi, R., Roemer, T. and Wang, R. (2001) ‘Structuring product development processes’, European Journal of Operational Research, Vol. 130, No. 3, pp.539–558. Aleisa, E. and Lin, L. (2009) ‘Sequencing of design tasks based on the degree of permissible concurrency’, International Journal of Applied Management Science, Vol. 1, No. 4, pp.367–387. Azadeh, A., Aramoon, M. and Saberi, M. (2009) ‘An integrated GA-time series algorithm for forecasting oil production estimation: USA, Russia, India, and Brazil’, International Journal of Industrial and Systems Engineering, Vol. 4, No. 4, pp.368–387. Azizi, N., Liang, M. and Zolfaghari, S. (2009) ‘Hybrid simulated annealing in flow shop scheduling: a diversification and intensification approach’, International Journal of Industrial and Systems Engineering, Vol. 4, No. 3, pp.326–348. Bagloee, S.A. and Tavana, M. (2012) ‘An efficient hybrid heuristic method for prioritising large transportation projects with interdependent activities’, International Journal of Logistics Systems and Management, Vol. 11, No. 1, pp.114–142. Browning, T.R. (2001) ‘Applying the design structure matrix to system decomposition and integration problems: a review and new directions’, IEEE Transactions on Engineering Management, Vol. 48, No. 3, pp.292–306. Chen, S.J. and Lin, L. (2002) ‘A project task coordination model for team organization in concurrent engineering’, Concurrent Engineering: Research and Applications, Vol. 10, No. 3, pp.187–203. Chen, S-J. and Lin, L. (2003) ‘Decomposition of interdependent task group for concurrent engineering’, Computers & Industrial Engineering, Vol. 44, No. 3, pp.435–459. Cho, S-H. (2001) An Integrated Method for Managing Complex Engineering Projects using the Design Structure Matrix and Advanced Simulation, MS thesis, Mechanical Engineering Department, MIT, Cambridge, MA. Coello, A. (2000) ‘An updated survey of GA-based multiobjective optimization techniques’, ACM Computing Surveys, Vol. 32, No. 2, pp.109–143.

90

S-J. Chen et al.

Dawkins, R. (1996) The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design, W. W. Norton & Co, New York, NY. Dong, Q. and Whitney, D. (2001) ‘Designing a requirement driven product development process’, Proceedings of the 13th International Conference on Design Theory and Methodology, Pittsburgh, PA. Eppinger, S.D. (2001) ‘Innovation at the speed of information’, Harvard Business Review, Vol. 79, No. 1, pp.149–158. Eppinger, S.D. and Salminen, V. (2001) ‘Patterns of product development interactions’, International Conference on Engineering Design, Glasgow, Scotland. Eppinger, S.D., Whitney, D.E., Smith, R.P. and Gebala, D.A. (1990) ‘Organizing the tasks in complex design projects’, ASME Design Theory and Methodology, Vol. 27, pp.39–46. Eppinger, S.D., Whitney, D.E., Smith, R.P. and Gebala, D.A. (1994) ‘A model-based method for organizing tasks in product development’, Research in Engineering Design, Vol. 6, No. 1, pp.1–13. Fan, Z., Feng, B., Jiang, Z. and Fu, N. (2009) ‘A method for member selection of R&D teams using the individual and collaborative information’, Expert Systems with Applications, Vol. 36, No. 4, pp.8313–8323. Forrest, S. (1993) ‘Genetic algorithms: principles of natural selection applied to computation’, Science, Vol. 261, No. 5123, pp.872–878. Gebala, D.A. and Eppinger, S.D. (1991) ‘Methods for analyzing design procedures’, ASME Design Theory and Methodology, Vol. 31, pp.227–233. Goldberg, D. (1989) Genetic Algorithms in SEARCH, Optimization and Machine Learning, Addison-Wesley Publishing Co., New York, NY. Gunawan, I. and Ahsan, K. (2010) ‘Project scheduling improvement using design structure matrix’, International Journal of Project Organisation and Management, Vol. 2, No. 4, pp.311–327. Guo, W., Cha, J., Fang, Y. and Woo, T.C. (1995) ‘Concurrent design: an algebraic perspective’, International Journal of Information Technology, Vol. 1, No. 1, pp.17–32. Haupt R.L. and Haupt, S. E. (1998) Practical genetic algorithms, John Wiley & Sons, New York, NY. Koza, J., Bennett, F., Andre, D. and Keane, M. (1999) Genetic programming III: Darwinian Invention and Problem Solving, Morgan Kaufmann Publishers, San Francisco, CA. Koza, J., Keane, M., Streeter, M., Mydlowec, W., Yu, J. and Lanza, G. (2003) Genetic Programming IV: Routine Human-competitive Machine Intelligence, Kluwer Academic Publishers, Dordrecht, Netherlands. Krishnan, V. (1996) ‘Managing the simultaneous execution of coupled phases in concurrent product development’, IEEE Transactions on Engineering Management, Vol. 43, No. 2, pp.210–217. Krishnan, V., Eppinger, S.D. and Whitney, D.E. (1997) ‘A model-based framework to overlap product development activities’, Management Science, Vol. 43, No. 4, pp.437–451. Kusiak, A. and Larson, T.N. (1995) ‘Decomposition and representation methods in mechanical design’, Journal of Mechanical Design, Vol. 117, No. 3, pp.17–24. Kusiak, A. and Wang, J. (1993a) Decomposition in Concurrent Design. Concurrent Engineering: Automation, Tools, and Techniques, John Wiley & Sons, New York, NY. Kusiak, A. and Wang, J. (1993b) ‘Efficient organizing of design activities’, International Journal of Production Research, Vol. 31, No. 4, pp.753–769. Kusiak, A. and Wang, J. (1993c) ‘Decomposition of the design process’, Journal of Mechanical Design, Vol. 115, No. 4, pp.687–695. Kusiak, A., Larson, T.N., and Wang, J. (1994) ‘Reengineering of design and manufacturing process’, Computers and Industrial Engineering, Vol. 26, No. 3, pp.521–536.

Project task flow optimisation and departmental flow analysis

91

Kusiak, A., Wang, J., He, D.W., and Feng, C. (1995). ‘A structured approach for analysis of design processes’, IEEE Transactions on Components, Packaging, and Manufacturing Technology – Part A, Vol. 18, No. 3, pp.664–673. Lee, H.J., Ko, H.J., Sohn, Y.H. and Ko, C.S. (2010) ‘Profit-based reconfiguration of express courier service network with multiple consolidation terminals’, International Journal of Logistics Systems and Management, Vol. 6, No. 4 pp.442–457. Liu, T., Chen X., Chen X. and Zou X. (2008) ‘R&D task programming of electromechanical product in networked manufacturing environment’, International Journal of Industrial and Systems Engineering, Vol. 3, No. 1, pp.3–17. McCulley, C. and Bloebaum, C.L. (1996) ‘A genetic tool for optimal design sequencing in complex engineering systems’, Structural Optimization, Vol. 12, Nos. 2/3, pp.186–201. McCulley, C., Hulme, K., and Bloebaum, C.L. (1997) ‘Simulation-based development of heuristic strategies for complex system convergence’, Applied Mechanics Review, Vol. 50, No. 11, pp.117–124. Min, H. and Guo, Z. (2010) ‘Developing bi-level equilibrium models for the global container transportation network from the perspectives of multiple stakeholders’, International Journal of Logistics Systems and Management, Vol. 6, No. 4 pp.362–379. Mitchell, M. (1996) An introduction to Genetic Algorithms, MIT Press, Cambridge, MA. Rogers J.L. (1997) ‘Reducing design cycle time and cost through process resequencing’, International Conference on Engineering Design, Tampere, Finland. Rogers, J.L. (1989) ‘A knowledge-based tool for multilevel decomposition of a complex design problem’, NASA TP-2903. Rogers, J.L. (1996) ‘Integrating a genetic algorithm into a knowledge-based system for ordering complex design processes’, NASA, Hampton, VA, TM-110247. Rogers, J.L. and Bloebaum, C.L. (1994) ‘Ordering design tasks based on coupling strengths’, 5th AIAA Symposium on Multidisciplinary Analysis and Optimization, pp.708–717. Rohatyński R. and Kielec, R. (2001) ‘Artificial evolution in design process optimization’, International Conference of Computer Integrated Manufacturing, Zakopane, Poland. Rohatyński, R., Kielec, R. and Sąsiadek, M. (2002) ‘Implementation of matrix method and evolution algorithm for reorganization of design processes’, Third International Seminar and Workshop on Engineering Design in Integrated Product Development, Zielona Góra-Łagów, Poland. Romeo, M.M., Lee, H.S. and Luong, R.A. (2008a) ‘Optimization of distribution networks using genetic algorithms. Part 1 – problem modeling and automatic generation of solutions’, International Journal of Manufacturing Technology and Management, Vol. 15, No. 1, pp.64–84. Romeo, M.M., Lee, H.S. and Luong, R.A. (2008b) ‘Optimization of distribution networks using genetic algorithms. Part 2 – the genetic algorithm and genetic operators’, International Journal of Manufacturing Technology and Management, Vol. 15, No. 1, pp.84–101. Smith, R.P. and Eppinger, S.D. (1997a) ‘Identifying controlling features of engineering design iteration’, Management Science, Vol. 43, No. 3, pp.276–293. Smith, R.P. and Eppinger, S.D. (1997b) ‘A predictive model of sequential iteration in engineering design’, Management Science, Vol. 43, No. 8, pp.1104–1120. Sobieszczanski-Sobieski, J. (1989) ‘Multidisciplinary optimization for engineering systems: achievements and potential’, NASA Technical Memorandum 101566. Sobieszczanski-Sobieski, J. (1993) ‘Multidisciplinary design optimization: An emerging new engineering discipline’, NASA Technical Memorandum 107761. Steward, D.V. (1981a) System Analysis and Management: Structure, Strategy and Design, Petrocelli Books, Inc., Princeton, NJ. Steward, D.V. (1981b) ‘The design structure system: a method for managing the design of complex systems’, IEEE Transactions on Engineering Management, Vol. 28, No. 3, pp.71–74.

92

S-J. Chen et al.

Syswerda, G. (1990) Handbook of Genetic Algorithms: Schedule Optimization using Genetic Algorithms, Van Nostran Reinhold, NY. Thomas, U.P. and Eppinger, S.D. (1994) ‘Integration analysis of product decompositions’, ASME Design Theory and Methodology, Vol. 68, pp.343–351. Wang, W., Cheng, S. and Zhang, Y. (2008) ‘Research on approach for a type of weapon target assignment problem solving by genetic algorithm’, Systems Engineering and Electronics, Vol. 30, No. 9, pp.1708–1711. Yang, Z., Zhou, J., Deng, C. and Shao, X. (2012) ‘Development of a design structure matrix partitioning method towards effective design collaboration’, International Journal of Manufacturing Technology and Management, Vol. 25, No. 4, pp.177–190. Yassine, A., Whitney, D. and Zambito, T. (2001) ‘Assessment of rework probabilities for design structure matrix (DSM) simulation in product development management’, 13th International Conference on Design Theory and Methodology, Pittsburgh, PA. Yassine, A., Whitney, D., Lavine, J. and Zambito, T. (2000) Do-It-Right-First-Time (DRAFT) Approach to Design Structure MATRIX (DSM) restructuring, MIT, Center for Technology, Policy and Industrial Development, Cambridge, MA. Zhou, G. and Min, H. (2011) ‘Designing a closed-loop supply chain with stochastic product returns: a Genetic Algorithm approach’, International Journal of Logistics Systems and Management, Vol. 9, No. 4 pp.397–418.