New_circuit_board_project[1]

Project

Charter for

New Circuit

Board

Teacher: Sabah Audo

Student: Mansour Ahmadi

Associated Practice of Project Management Course at Mälardalen Högskola (KPP 304)

My Special Thanks to my teacher, Sabah Audo, who thought

and inspired us to use project management science in an

aesthetic manner.

Table of Contents

Introduction .................................................................................................................................................. 3

1. Scope of Work ........................................................................................................................................... 4

2. Work Breakdown Structure (Project WBS) ............................................................................................... 4

3. Project Organization ................................................................................................................................. 6

4. Outsourcing ............................................................................................................................................... 8

5. Project Activities ....................................................................................................................................... 8

6. Tasks’ estimated duration, resources and cost ...................................................................................... 10

7. Tasks’ relationships ................................................................................................................................. 13

7. Project Gantt chart .................................................................................................................................. 15

9. Project Network diagram ........................................................................................................................ 17

10. Project Schedule ................................................................................................................................... 18

11. Critical Path ........................................................................................................................................... 20

12. Project Pert Analysis ............................................................................................................................. 22

12.1 Likelihood of meeting deadline for introducing new circuit board in the local market by 18 month

................................................................................................................................................................ 22

12.2 Likelihood of meeting deadline for introducing new circuit board internationally by 2 years ...... 25

12.3 A short discussion based on Pert Analysis ...................................................................................... 25

13. Project Cost-time trade off (Via Linear Programming) ......................................................................... 26

13.1 How can activities duration be decreased? .................................................................................... 26

13.2 How much should project duration decrease? ............................................................................... 26

13.3 How long can each activity be Crashed and how much does it cost? ............................................ 27

13.4 Linear Programming Model ............................................................................................................ 27

14. Project Resource Loading ...................................................................................................................... 34

15. Resource Leveling By Branch and Bound Algorithm ............................................................................. 37

16. Comulative Cost Diagram ...................................................................................................................... 42

References .................................................................................................................................................. 44

Appendix 1. ................................................................................................................................................. 45

Introduction Competitive industries, high fluctuation in market shares and subsequently shorter product life

cycle obliges companies to promote their product development process. Nowadays, companies

often emerge new products, new processes or new services.

AB is a manufacturer of Circuit Boards in Sweden. According to its strategic plan, AB Company

also developed a new method of attaching electronic components to circuit boards. Now AB

inserts wires from the electronic components through holes and soldering to make the electrical

connection; but via new method, this assembly is going to accomplish by pressing components

into slots in the surface of the board. This leads to more reliable solder less electrical connections

that result in smaller and more durable electronic product.

However, this method has just developed in laboratory and there is a long way until new process

shows itself in the new product. Therefore, AB employed me as the Project Manager in order to

develop the new product and introduce it to the market and here you will find the project charter.

In the charter, firstly Work breakdown and organization structure is described and then project

activities will be introduced with their duration, resource amount and cost estimations.

Relationships among different activities show later and project schedule is calculated via CPM

and Pert methods. Different alternatives for crashing project duration are analyzed afterwards

and resources are assigned and smoothed. In these stages, linear programming is used and

Branch and Bound algorithm is applied to find out the optimum solution for leveling problem.

The last parts elaborated the cost diagram. Because all the figures and charts are inevitable

illustrative parts of different topics, they insert in the text. References for LP methods and

statistical calculations come in the references.

We assume that project started at the beginning of year 2011and the time unit of project is week.

During the stages, MSP, Excel, Word, Visual Basic and Lingo are used to plan the project.

April 2011

Mansour Ahmadi

Project Manager

1. Scope of Work Project starts with Product and process design according to new invented method. The

assembling process of circuit board and the design of final product are going to be changed.

Simultaneously a new facility for this product and its assembling line will be designed and

constructed. The facility equipment also will concurrently be provided. However new facility

demands new investment and therefore finance department of AB Company is responsible for

cost estimation and fundraising.

As soon as facility completed, recruitment for new staffs and marketing for new product would

be begun and hopefully new circuit board will be introduced to local market by 1.5 years.

Marketing department is responsible for getting customer feedbacks before product will be

introduced internationally by two years.

Meanwhile this is the duty of quality department to determine product and process quality

specifications and design corresponding quality assurance forms. The main suppliers and

distributers also are going to be selected and appropriate logistics plans will be considered in

order to minimize the transportation time and cost.

All in all, project object is to introduce product locally by 1.5 years and internationally by 2

years. Since AB Company has some competitors, any delay may lead to lose a big share of future

market. In addition, project should fulfill the expectations of its investors and shareholders. In

fact, AB Company should guarantee the return of investments which is raised in order to

construct new facility and produce new product. Therefore the proposed plan and schedule

should be persuasive and encourage potential shareholders.

Finally, although project different stages were mentioned hereinabove, it is up to project

manager to find any additional stages which were missed. In the other word, project scope of

work contains but not restricted to above-mentioned phases.

2. Work Breakdown Structure (Project WBS) Each project can be broken down to its subdivisions according to different aspects, e.g. time,

place or functionality. Since here project activities are mostly located and performed in the AB

Company, and relatively parallel to each other, time and place don’t seem to be proper aspects

and therefore, project work breaks down functionally.

Based on the mentioned scope of work, whole project is divided to seven main phases: Product

and Process Design, Building New Facility, Marketing, Business Analysis, Recruitment, Quality

Management and Logistics.

As you can see in figure 1, each of these phases, has different stages;

Product and Process Design: Design Products, Design Process, Performing Tests

Building New Facility: Design Facility, procure equipment, construction

Marketing: Advertisement, Market Test

Business Analysis: Fundraising, Pricing

Recruitment: Employment phase, Training Phase

Quality Management: Manufacturing Quality, Product Quality

Logistics: Suppliers, Customers

This classification will be broken down to more detailed activities later. Now this is the

framework of project which should be planned and performed. However it could be change

during the execution phase of project.

3. Project Organization Organization structure can highly influence the project success, by different degree of resource

availability and authority which gives the project manager. There are usually two extremes:

Functional Structure which downgrades the role and power of project manager till almost a

coordinator, and projectized structure which promote the project manager with full availability

and authority on project resources. In between are located Matrix organizations with different

degree, from weak to strong, which distributes the power between functional managers and

project manager.

Although AB Company has sometimes improvements or development projects, it is a producer

of special product rather than a project-wise company; thus a full projectized structure for this

project doesn’t seem appropriate. In addition even though a few project main phases need full-

time devoted staffs, other phases can be done in the parallel with existed work process of AB

Company.

Therefore, a composite structure of functional and projectized can be applied in development

project of new circuit board, as you see in figure 2. Based on the second level of Project WBS,

Building the New Facility phase needs an independent team under the authority of project

manager, but the rest of phases can be done if two or three staffs of related departments will

cooperate with project manager; however here the matrix should be a strong matrix and project

tasks should have more priority in comparison with staffs ordinary duties at functional

departments. Furthermore these staffs should attend periodically meetings which are held for

project coordination in project office. Finally a small team of coordinators, secretaries and

controllers, likely 5 personnel, are required to be under the authority of project manager and fully

devoted to project. This team will be located at project office.

4. Outsourcing There is no company which can do all the facets of its work independently and if there is such a

case, it won’t be beneficial. (The failure of giant companies like Ford that would like to make an

industrial empire is good example!)

Therefore nowadays outsourcing is an inevitable part of companies’ strategic plans. Through

outsourcing, companies can do their works in shorter time, better quality and less risk.

Outsourcing helps companies not to handle all the uncertainties and to cope with emergency

situations of newly fluctuating market. In addition, each company has a specialty which is its core

competency and perhaps its most profitable attribute. In the other word, each company doesn’t

have equal efficiency in its different tasks. Beside there are some jobs that rarely emerged or are

far from company’s specialty and it is not profitable to assign a team or devote a department to

these low frequency tasks. In these circumstances also, outsourcing avails companies.

AB Company is a producer of circuit boards and it has rarely projects such as construction of a

complex or facility. Therefore it has not its specialty or particular teams and staffs. Project

Manager decides to outsource this part of project to an EPC contractor through bidding. EPC

contractor should have constructed lots of factories before and guarantee to hand over the plant

by deadlines. EPC contractor can also outsource some parts of its project. However, all the

subcontractors of project should do their tasks according to the master plan prepared by AB

Company and be under the supervision of AB project manager. (Figure 2)

The same story applies to Advertisement and Transportation and project manager will outsource

them. Advertisement include more detailed tasks such as making suitable video clips, which can

be done totally by an advertising companies, special in using different tricks for attracting people

and be a member of public media lobbies including Radio, T.V and newspapers.

A transportation company can also minimize the costs e.g. by mixing AB packs with other

companies bulks which located in the same region. Moreover, transportation companies usually

have different office in different cities which make the distribution more effective when firstly

other transportation devices like trains should be used.

5. Project Activities Defining the project activities is perhaps the most important part of project planning process.

Missing an activity can later hinder the project to meet deadline. Experts and before done

projects, can be good sources for gathering first data in order to customize according to project

conditions.

Project WBS can be used as the framework and last level breaks down to more detail activities.

Usually it is said project activities shouldn’t be much detailed but comprehensive; and this

generally means 4 levels for the draft plan of project is enough. Further detailing can be done

later during the execution phase by execution team. Right now and during planning phase,

existence of many detailed activities only makes it complicated to be understood by managers

and decision makers.

Here the detailed activities of New Circuit board Project were extracted from similar done

projects and they depict as the fourth level of project WBS. (Table 1) These activities will be

enriched with corresponding duration, predecessors and resources later on.

ID Task Name ID Task Name

1 New Circuit Board Project 40 Make Adjustment Where Necessary

2 Start 41 Sell an initial run of product in local market

3 Product and Process Design 42 Advertisement

4 Design Product 43 Advertisement in T.V.

5 Determine Customer Requirements 44 Advertisement in Radio

6 Specify Design Requirement 45 Advertisement in Newspapers

7 Design Process 46 Introduce the product internationally

8 Specify Parts Design 47 Business Analysis

9 Determine Manufacturing design 48 Pricing

10 Performing Tests 49 Estimate Likely Selling Price

11 Prepare Product Specifications 50 Estimate Sales Volume

12 Test the product 51 Estimate Profitability and Break Even Point

13 Building New Facility 52 Fundraising

14 Procure Equipment 53 Estimate Costs

15 Determine Equipment Specifications 54 Stock Shares

16 Prepare MR(Material Requirement) 55 Bank Loans

17 Request for tenders 56 Recruitment

18 Performing TBE(Technical Bid Evaluation) 57 Employment Phase

19 Select Equipment Vendor 58 Engineers

20 Design Facility 59 Labors

21 Mechanical Design 60 Training Phase

22 Piping Design 61 Engineers

23 Civil Design 62 Labors

24 Electrical Design 63 Quality Management

25 Instrument Design 64 Manufacturing Quality

26 Construction Phase 65 Specify Equipment Quality Specifications

27 Rough grading and compaction 66 Prepare Maintenance Plan

28 Constructing foundations 67 Product quality

29 Installing equipment 68 Specify Quality Specifications

30 Aligning and welding pipes 69 Prepare Quality Assurance Method

31 Cabling and lighting 70 Provide Quality Assurance Forms

32 Instrumentation 71 Logistics

33 Free run test 72 Suppliers

34 Precommissioning 73 Choosing the Least Cost Suppliers for Transportation

35 Commissioning 74 Select the Appropriate Transportation System

36 Marketing 75 Customers

37 Market Test 76 Choosing the Least Cost Distribution Centers

38 Produce a Physical Prototype or mock-up 77 Select the Appropriate Transportation System

39 Conduct Focus Group Customer Interviews 78 Finish

6. Tasks’ estimated duration, resources and cost After task definition, first data estimation should be done for each activity. There are four main

data which are required in order to proceed to other project planning stages; prerequisites,

duration, resources and cost. We will depict activity relationships (include prerequisites) in the

next clause and here other three elements are elaborated.

Duration can be estimated through different information sources e.g. experts, previous projects or

by dividing work volume by doable rate. Here we use data from past projects and estimate

required time for each activity. Durations are mentioned in weeks since project manager believes

more detailed time unit in the planning stage make decision making more complex rather than

any usefulness.

Moreover, in order to perform project activities on time, sufficient resources should be provided

for each task. Therefore a rough estimation of resource demand has to be accompanied with

project activities at the planning stage. Using the resource prices, cost estimation can also be

achieved for each activity.

Using the Pareto analysis, here for New Circuit Board project we consider the three main

resources which consume almost the 80 % of project budget and since project activities are

mostly services being given by human resources, these three are: Engineers, Technicians and

labors. The number of resources are calculated based on ordinary rates exist in the previous done

projects.

Later the corresponding costs are estimated according to the hourly wages of each resource.

These wages are extracted from recruitment websites for year 2011. We assume that each staff

works 8 hours per day and there are 5 working days in a week.

All the estimated information is illustrated in Table 2. It is worthy to inform that activities written

in bold format are summary ones whose data will be calculated by rolling up subordinated tasks

information and will be shown in next clauses. Also here we consider activities individually

rather than as a task of whole project. The resource estimation for whole project and its leveling

will be described as we proceed.

It is assumed that resources are available whenever project demands, since we suppose the

organization structure as strong matrix with high power for project manager. Therefore, there is

no confliction between the tasks and resource calendars. However, we will smooth the whole

project resource loading and assess the effect of fluctuation in resources on the project

termination through the application of Linear Programming and sensitivity analysis later on.

All in all these information are basis for future calculations. Therefore a good estimation can

enhanced the other stages as well as a careless estimation which leads to chaos in reality.

ID Task Name Duration Engineer Technician Labor Cost

1 New Circuit Board Project

2 Start 0 wks $0.00

3 Product and Process Design

4 Design Product

5 Determine Customer Requirements 4 wks 1 1 0.5 $6,560.00

6 Specify Design Requirement 4 wks 1 1 0.5 $6,560.00

7 Design Process

8 Specify Parts Design 4 wks 1 1 0.5 $6,560.00

9 Determine Manufacturing design 4 wks 1 1 0.5 $6,560.00

10 Performing Tests

11 Prepare Product Specifications 4 wks 1 1 0.5 $6,560.00

12 Test the product 4 wks 1 1 0.5 $6,560.00

13 Building New Facility

14 Procure Equipment

15 Determine Equipment Specifications 4 wks 1.5 1 $7,200.00

16 Prepare MR(Material Requirement) 4 wks 1.5 1 $7,200.00

17 Request for tenders 4 wks 1.5 1 $7,200.00

18 Performing TBE(Technical Bid Evaluation) 4 wks 1.5 1 $7,200.00

19 Select Equipment Vendor 4 wks 1.5 1 $7,200.00

20 Design Facility

21 Mechanical Design 12 wks 2 1 $26,400.00

22 Piping Design 12 wks 2 1 $26,400.00

23 Civil Design 12 wks 2 1 $26,400.00

24 Electrical Design 12 wks 2 1 $26,400.00

25 Instrument Design 12 wks 2 1 $26,400.00

26 Construction Phase

27 Rough grading and compaction 1 wk 1 2 3 $3,440.00

28 Constructing foundations 4 wks 1 2 3 $13,760.00

29 Installing equipment 8 wks 1 2 3 $27,520.00

30 Aligning and welding pipes 6 wks 1 2 3 $20,640.00

31 Cabling and lighting 4 wks 1 2 3 $13,760.00

32 Instrumentation 4 wks 1 2 3 $13,760.00

33 Free run test 2 wks 1 2 3 $6,880.00

34 Precommissioning 1 wk 1 2 3 $3,440.00

35 Commissioning 1 wk 1 2 3 $3,440.00

36 Marketing

37 Market Test

38 Produce a Physical Prototype or mock-up 6 wks 2 0.25 $7,920.00

39 Conduct Focus Group Customer Interviews 8 wks 2 0.25 $10,560.00

ID Task Name Duration Engineer Technician Labor Cost

40 Make Adjustment Where Necessary 6 wks 2 0.25 $7,920.00

41 Sell an initial run of product in local market 24 wks 2 0.25 $0.00

42 Advertisement

43 Advertisement in T.V. 12 wks 2 0.25 $15,840.00

44 Advertisement in Radio 12 wks 2 0.25 $15,840.00

45 Advertisement in Newspapers 12 wks 2 0.25 $15,840.00

46 Introduce the product internationally 0 wks $0.00

47 Business Analysis

48 Pricing

49 Estimate Likely Selling Price 3 wks 0.5 1 $3,000.00

50 Estimate Sales Volume 3 wks 0.5 1 $3,000.00

51 Estimate Profitability and Break Even Point 3 wks 0.5 1 $3,000.00

52 Fundraising

53 Estimate Costs 4 wks 0.5 1 $4,000.00

54 Stock Shares 4 wks 0.5 1 $4,000.00

55 Bank Loans 4 wks 0.5 1 $4,000.00

56 Recruitment

57 Employment Phase

58 Engineers 3 wks 2 $3,600.00

59 Labors 3 wks 2 $3,600.00

60 Training Phase

61 Engineers 4 wks 2 $4,800.00

62 Labors 4 wks 2 $4,800.00

63 Quality Management

64 Manufacturing Quality

65 Specify Equipment Quality Specifications 2 wks 1 1 $2,800.00

66 Prepare Maintenance Plan 3 wks 1 1 $4,200.00

67 Product quality

68 Specify Quality Specifications 2 wks 1 1 $2,800.00

69 Prepare Quality Assurance Method 2 wks 1 1 $2,800.00

70 Provide Quality Assurance Forms 4 wks 1 1 $5,600.00

71 Logistics

72 Suppliers

73 Choosing the Least Cost Suppliers for Transportation

2 wks 1 1 $2,800.00

74 Select the Appropriate Transportation System 3 wks 1 1 $4,200.00

75 Customers

76 Choosing the Least Cost Distribution Centers 2 wks $2,800.00

77 Select the Appropriate Transportation System 3 wks 1 1 $4,200.00

78 Finish 0 wks 1 1 $0.00

7. Tasks’ relationships Project tasks usually are done in a sequential manner. In the other word, all the project tasks are related to each other and each has one

or more prerequisites. This dependency can be caused by different reasons; mostly they are technological restrictions that prevent tasks

from being done simultaneously, but there are some time and resource constraints which keep tasks in the sequence.

Here in new circuit board project we consider four different types of relationships; Finish to start, which needs completion of

predecessor; start to finish, which needs beginning of predecessor to finish the task; start to start, which means both tasks will start

together and finish to finish, which caused the concurrent completion of both tasks. In addition to have combinations of these types,

different lags are considered in the manner that negative lag causes the task to begin sooner and positive one delays them. In new

circuit board project the lags are expressed as the percent of predecessor’s duration; therefore for example the phrase “21FS-50%” in

front of one task means it can start when half duration of activity number 21 has passed. Table 3 shows the predecessors with their

relations type for each activity. To be crystal clear, figure 3 shows the whole project as a network. This network was drawn based on

AON-Activity on Node- method.

ID Task Name Predecessors ID Task Name Predecessors

1 New Circuit Board Project 40 Make Adjustment Where Necessary 39

2 Start 41 Sell an initial run of product in local market 40,62

3 Product and Process Design 42 Advertisement

4 Design Product 43 Advertisement in T.V. 41FS-25%

5 Determine Customer Requirements

2 44 Advertisement in Radio 43SS

6 Specify Design Requirement 5 45 Advertisement in Newspapers 44SS

7 Design Process 46 Introduce the product internationally 45

8 Specify Parts Design 6 47 Business Analysis

9 Determine Manufacturing design

8 48 Pricing

10 Performing Tests 49 Estimate Likely Selling Price 40

11 Prepare Product Specifications 9 50 Estimate Sales Volume 49

12 Test the product 11 51 Estimate Profitability and Break Even Point 50

13 Building New Facility 52 Fundraising

14 Procure Equipment 53 Estimate Costs 25FS-50%

15 Determine Equipment Specifications

2 54 Stock Shares 53

16 Prepare MR(Material Requirement)

15 55 Bank Loans 54SS

17 Request for tenders 16 56 Recruitment

18 Performing TBE(Technical Bid Evaluation)

17 57 Employment Phase

19 Select Equipment Vendor 18 58 Engineers 35

20 Design Facility 59 Labors 58SS

21 Mechanical Design 15 60 Training Phase

22 Piping Design 21FS-50% 61 Engineers 58

23 Civil Design 22FS-50% 62 Labors 61SS,59

24 Electrical Design 23FS-50% 63 Quality Management

25 Instrument Design 24FS-50% 64 Manufacturing Quality

26 Construction Phase 65 Specify Equipment Quality Specifications 19

27 Rough grading and compaction 23 66 Prepare Maintenance Plan 65

28 Constructing foundations 27 67 Product quality

29 Installing equipment 28,22 68 Specify Quality Specifications 40

30 Aligning and welding pipes 29 69 Prepare Quality Assurance Method 68

31 Cabling and lighting 30,24 70 Provide Quality Assurance Forms 69

32 Instrumentation 31,25 71 Logistics

33 Free run test 32 72 Suppliers

34 Precommissioning 33 73 Choosing the Least Cost Suppliers for Transportation

51

35 Commissioning 34 74 Select the Appropriate Transportation System

73

36 Marketing 75 Customers

37 Market Test 76 Choosing the Least Cost Distribution Centers

51

38 Produce a Physical Prototype or mock-up

35 77 Select the Appropriate Transportation System

76

39 Conduct Focus Group Customer Interviews

38 78 Finish 12,35,45,55,66,70,74,77,46

7. Project Gantt chart Invented in 1950, Gantt chart is still one of the strong visual tools that show the project activities

and their status in an easy-understanding manner. Managers generally utilize Gantt chart in

decision making meetings since it facilitates the tracking of existing logic among activities. In

Gantt chart activities are shown as date-placed horizontal bars according to their sequence. Here

the Gantt chart of new circuit board project is depicted in figure 4. Left table shows

corresponding activity’s name.

9. Project Network diagram Another visual tool which can show entire project is network diagram. As “network” implies this diagram

shows the project as nodes and arrows and it has two kinds: AON in which activities show on nodes and

AOA in which activities place on arrows.

Here new circuit board project is shown on an AON network diagram in figure 5. Activities which are

connected to each other have relationships and as you see, except first activity, all the other activities

have at least one predecessor. As a logic principle, it is quite important that all activities have at least

one predecessor in order to connect to each other. The importance of this topic will be shown later

during the scheduling of activities and calculation of critical path method.

10. Project Schedule Having the required information for all activities separately, now the scheduling calculations for whole

project can be done. Managers usually want to know when each activity should be start and how long

flexibility they have in order to defer activity beginning. These two time points are called “early start”

and “early finish” and their subtraction which means the time tolerance for each activity, is called

“Slack”. In the other word, each activity slack means the time period which that activity can be delayed

without delaying the whole project. Respectively each activity has early finish and late finish, which are

the summations of early start and late start with activity duration. (Consequently, the difference

between early finish and late finish should give the same slack!)

Here for new circuit board project, these calculations have been done by MSP software and their results

are shown in table 4 below.

ID Task Name Early Start Early Finish Start Slack Late Start Late Finish

1 New Circuit Board Project W52/7 W5/6 0 wks W1/2 W5/6

2 Start W52/7 W52/7 0 wks W1/2 W1/2

3 Product and Process Design W1/2 W24/6 85 wks W34/2 W5/6

4 Design Product W1/2 W8/6 85 wks W34/2 W41/6

5 Determine Customer Requirements W1/2 W4/6 85 wks W34/2 W37/6

6 Specify Design Requirement W5/2 W8/6 85 wks W38/2 W41/6

7 Design Process W9/2 W16/6 85 wks W42/2 W49/6

8 Specify Parts Design W9/2 W12/6 85 wks W42/2 W45/6

9 Determine Manufacturing design W13/2 W16/6 85 wks W46/2 W49/6

10 Performing Tests W17/2 W24/6 85 wks W50/2 W5/6

11 Prepare Product Specifications W17/2 W20/6 85 wks W50/2 W1/6

12 Test the product W21/2 W24/6 85 wks W2/2 W5/6

13 Building New Facility W52/7 W7/6 0 wks W1/2 W1/2

14 Procure Equipment W52/7 W20/6 0 wks W1/2 W1/2

15 Determine Equipment Specifications W52/7 W4/6 0 wks W1/2 W5/2

16 Prepare MR(Material Requirement) W4/6 W8/6 84 wks W37/2 W41/2

17 Request for tenders W8/6 W12/6 84 wks W41/2 W45/2

18 Performing TBE(Technical Bid Evaluation) W12/6 W16/6 84 wks W45/2 W49/2

19 Select Equipment Vendor W16/6 W20/6 84 wks W49/2 W1/2

20 Design Facility W4/6 W40/6 0 wks W5/2 W52/2

21 Mechanical Design W4/6 W16/6 0 wks W5/2 W16/6

22 Piping Design W11/2 W22/6 0 wks W11/2 W22/6

23 Civil Design W17/2 W28/6 0 wks W17/2 W29/2

24 Electrical Design W23/2 W34/6 11 wks W34/2 W45/6

25 Instrument Design W29/2 W40/6 11 wks W40/2 W52/2

26 Construction Phase W29/2 W7/6 0 wks W29/2 W7/6

27 Rough grading and compaction W29/2 W29/6 0 wks W29/2 W29/6

28 Constructing foundations W30/2 W33/6 0 wks W30/2 W33/6

29 Installing equipment W34/2 W41/6 0 wks W34/2 W41/6

30 Aligning and welding pipes W42/2 W47/6 0 wks W42/2 W47/6

31 Cabling and lighting W48/2 W51/6 0 wks W48/2 W51/6

32 Instrumentation W52/2 W3/6 0 wks W52/2 W3/6

ID Task Name Early Start

Early Finish

Start Slack

Late Start

Late Finish

33 Free run test W4/2 W5/6 0 wks W4/2 W5/6

34 Precommissioning W6/2 W6/6 0 wks W6/2 W6/6

35 Commissioning W7/2 W7/6 0 wks W7/2 W7/6

36 Marketing W7/6 W5/6 0 wks W8/2 W5/6

37 Market Test W7/6 W51/6 0 wks W8/2 W51/6

38 Produce a Physical Prototype or mock-up W7/6 W13/6 0 wks W8/2 W14/2

39 Conduct Focus Group Customer Interviews W13/6 W21/6 0 wks W14/2 W22/2

40 Make Adjustment Where Necessary W21/6 W27/6 0 wks W22/2 W28/2

41 Sell an initial run of product in local market W28/2 W51/6 0 wks W28/2 W51/6

42 Advertisement W46/2 W5/6 0 wks W46/2 W5/6

43 Advertisement in T.V. W46/2 W5/6 0 wks W46/2 W5/6

44 Advertisement in Radio W46/2 W5/6 0 wks W46/2 W5/6

45 Advertisement in Newspapers W46/2 W5/6 0 wks W46/2 W5/6

46 Introduce the product internationally W5/6 W5/6 0 wks W5/6 W5/6

47 Business Analysis W35/2 W36/6 61 wks W44/2 W5/6

48 Pricing W27/6 W36/6 16 wks W44/2 W1/2

49 Estimate Likely Selling Price W27/6 W30/6 16 wks W44/2 W47/2

50 Estimate Sales Volume W30/6 W33/6 16 wks W47/2 W50/2

51 Estimate Profitability and Break Even Point W33/6 W36/6 16 wks W50/2 W1/2

52 Fundraising W35/2 W42/6 67 wks W50/2 W5/6

53 Estimate Costs W35/2 W38/6 67 wks W50/2 W2/2

54 Stock Shares W38/6 W42/6 67 wks W2/2 W5/6

55 Bank Loans W38/6 W42/6 67 wks W2/2 W5/6

56 Recruitment W7/6 W14/6 13 wks W21/2 W28/2

57 Employment Phase W7/6 W10/6 13 wks W21/2 W24/2

58 Engineers W7/6 W10/6 13 wks W21/2 W23/6

59 Labors W7/6 W10/6 13 wks W21/2 W24/2

60 Training Phase W10/6 W14/6 13 wks W24/2 W28/2

61 Engineers W10/6 W14/6 13 wks W24/2 W27/6

62 Labors W10/6 W14/6 13 wks W24/2 W28/2

63 Quality Management W20/6 W35/6 81 wks W50/2 W5/6

64 Manufacturing Quality W20/6 W25/6 84 wks W1/2 W5/6

65 Specify Equipment Quality Specifications W20/6 W22/6 84 wks W1/2 W3/2

66 Prepare Maintenance Plan W22/6 W25/6 84 wks W3/2 W5/6

67 Product quality W27/6 W35/6 22 wks W50/2 W5/6

68 Specify Quality Specifications W27/6 W29/6 22 wks W50/2 W52/2

69 Prepare Quality Assurance Method W29/6 W31/6 22 wks W52/2 W2/2

70 Provide Quality Assurance Forms W31/6 W35/6 22 wks W2/2 W5/6

71 Logistics W36/6 W41/6 16 wks W1/2 W5/6

72 Suppliers W36/6 W41/6 16 wks W1/2 W5/6


W36/6 W38/6 16 wks W1/2 W3/2

74 Select the Appropriate Transportation System W38/6 W41/6 16 wks W3/2 W5/6

75 Customers W36/6 W41/6 16 wks W1/2 W5/6

76 Choosing the Least Cost Distribution Centers W36/6 W38/6 16 wks W1/2 W3/2

77 Select the Appropriate Transportation System W38/6 W41/6 16 wks W3/2 W5/6

78 Finish W5/6 W5/6 0 wks W5/6 W5/6

11. Critical Path There are usually many different paths between start and finish and each path is a combination of

diverse activities. Each path’s duration is the summation of its activities’ durations and therefore they

can be equal or less than project duration. (It doesn’t need to be illustrated that project duration is the

longest one!) The paths which tantamount to project duration, are called critical paths, and they could

be one or more. Mathematically critical path is the combination of activities which don’t have any slack

and should be done strictly on time. From the managerial perspective, finding and controlling the critical

activities are much important since they don’t have any flexibility and any delay in their execution can

delay the whole project. Here Table 5 shows whether each activity is critical or not and figure 6 shows

the critical path for new circuit board project.

ID Task Name Critical ID Task Name Critical

1 New Circuit Board Project Yes 40 Make Adjustment Where Necessary Yes

2 Start Yes 41 Sell an initial run of product in local market Yes

3 Product and Process Design No 42 Advertisement Yes

4 Design Product No 43 Advertisement in T.V. Yes

5 Determine Customer Requirements No 44 Advertisement in Radio Yes

6 Specify Design Requirement No 45 Advertisement in Newspapers Yes

7 Design Process No 46 Introduce the product internationally Yes

8 Specify Parts Design No 47 Business Analysis No

9 Determine Manufacturing design No 48 Pricing No

10 Performing Tests No 49 Estimate Likely Selling Price No

11 Prepare Product Specifications No 50 Estimate Sales Volume No

12 Test the product No 51 Estimate Profitability and Break Even Point No

13 Building New Facility Yes 52 Fundraising No

14 Procure Equipment Yes 53 Estimate Costs No

15 Determine Equipment Specifications Yes 54 Stock Shares No

16 Prepare MR(Material Requirement) No 55 Bank Loans No

17 Request for tenders No 56 Recruitment No

18 Performing TBE(Technical Bid Evaluation) No 57 Employment Phase No

19 Select Equipment Vendor No 58 Engineers No

20 Design Facility Yes 59 Labors No

21 Mechanical Design Yes 60 Training Phase No

22 Piping Design Yes 61 Engineers No

23 Civil Design Yes 62 Labors No

24 Electrical Design No 63 Quality Management No

25 Instrument Design No 64 Manufacturing Quality No

26 Construction Phase Yes 65 Specify Equipment Quality Specifications No

27 Rough grading and compaction Yes 66 Prepare Maintenance Plan No

28 Constructing foundations Yes 67 Product quality No

29 Installing equipment Yes 68 Specify Quality Specifications No

30 Aligning and welding pipes Yes 69 Prepare Quality Assurance Method No

31 Cabling and lighting Yes 70 Provide Quality Assurance Forms No

32 Instrumentation Yes 71 Logistics No

33 Free run test Yes 72 Suppliers No

34 Precommissioning Yes 73 Choosing the Least Cost Suppliers for Transportation

No

35 Commissioning Yes 74 Select the Appropriate Transportation System No

36 Marketing Yes 75 Customers No

37 Market Test Yes 76 Choosing the Least Cost Distribution Centers No

38 Produce a Physical Prototype or mock-up Yes 77 Select the Appropriate Transportation System No

39 Conduct Focus Group Customer Interviews Yes 78 Finish Yes

12. Project Pert Analysis Stands for Project Evaluation and Review Technique, since 1950 s, pert has been one of the most

popular methods for dealing with uncertainty in activities’ durations in project management. Assuming

Beta Distribution for activities’ durations, Pert takes three estimated duration as Pessimistic, Most Likely

and Optimistic for each activity and calculate their mean and variance using below formulas:

where O, M and P stand for Optimistic, Most likely and pessimistic respectively. Pert then can estimate

the probability of project completion by a specified duration via simplification of using Central Limit

Theorem and Normal Distribution.

According to given information by AB Company, project manager should introduce the product in local

market by 18 month and internationally by 2 years. Here in the schedule, new circuit board is going to

be introduced locally by 80weeks-19months (Activity number 41) and internationally 109weeks-

25months (activity number 46). However there is uncertainty in activities durations in the real world and

we cannot assure that project wouldn’t meet the deadlines.

Therefore we use Pert Analysis to calculate the likelihood of meeting project deadlines. These

probabilities can guide us through taking proper actions to decrease activities durations if project likely

doesn’t fulfill its deadlines.

12.1 Likelihood of meeting deadline for introducing new circuit board in the

local market by 18 month Table 6 shows the probabilistic information for project activities. According to the Gantt chart the below

critical path leads to activity no. 41 which involves the introduction of new product in the local market.

2 15 21 22 23 27 28 29 30 31 32 33

34 35 38 39 40

It is worthy to mention that here we have some relationships that are not FS (Finish to Start)

and also some lags. Thus the SS precedency won’t be considered and the activities duration

times by lags percentage. Therefore we have:

Mean Path Duration=0+4+12×50%+12×50%+12+1+4+8+6+4+4+2+1+1+6+8+6= 79

Path Variance=0.00+0.11+1.00×50%+1.00×50%+1.00+0.01+0.11+0.44+0.25+0.11+0.11+

0.03+0.01+0.01+0.25+0.44+0.25= 4.13

New circuit board is going to be introduced in the local market by 79 weeks while we want it to be 78

weeks. Therefore using equation z=

while d:Deadline/ µ:Mean duration of corresponding

path/ =standard deviation of corresponding path, we can calculate the probability of meeting deadline

ID Task Name Optimistic Dur.

Expected Dur.

Pessimistic Dur.

Mean Variance Standard Deviation

1 New Circuit Board Project 81.75 wks 109 wks 136.25 wks 109 wks 82.51 wks 9.08 wks

2 Start 0 wks 0 wks 0 wks 0 wks 0 wks 0 wks

3 Product and Process Design 18 wks 24 wks 30 wks 24 wks 4 wks 2 wks

4 Design Product 6 wks 8 wks 10 wks 8 wks 0.44 wks 0.66 wks

5 Determine Customer Requirements 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

6 Specify Design Requirement 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

7 Design Process 6 wks 8 wks 10 wks 8 wks 0.44 wks 0.66 wks

8 Specify Parts Design 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

9 Determine Manufacturing design 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

10 Performing Tests 6 wks 8 wks 10 wks 8 wks 0.44 wks 0.66 wks

11 Prepare Product Specifications 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

12 Test the product 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

13 Building New Facility 44.25 wks 59 wks 73.75 wks 59 wks 24.17 wks 4.92 wks

14 Procure Equipments 15 wks 20 wks 25 wks 20 wks 2.78 wks 1.67 wks

15 Determine Equipment Specifications 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

16 Prepare MR(Material Requirement) 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

17 Request for tenders 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

18 Performing TBE(Technical Bid Evaluation) 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

19 Select Equipments Vendor 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

20 Design Facility 27 wks 36 wks 45 wks 36 wks 9 wks 3 wks

21 Mechanical Design 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

22 Piping Design 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

23 Civil Design 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

24 Electrical Design 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

25 Instrument Design 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

26 Construction Phase 23.25 wks 31 wks 38.75 wks 31 wks 6.67 wks 2.58 wks

27 Rough grading and compaction 0.75 wks 1 wk 1.25 wks 1 wks 0.01 wks 0.1 wks

28 Constructing foundations 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

29 Installing equipements 6 wks 8 wks 10 wks 8 wks 0.44 wks 0.66 wks

30 Aligning and welding pipes 4.5 wks 6 wks 7.5 wks 6 wks 0.25 wks 0.5 wks

31 Cabling and lighting 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

32 Instrumentation 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

33 Free run test 1.5 wks 2 wks 2.5 wks 2 wks 0.03 wks 0.17 wks

34 Precommissioning 0.75 wks 1 wk 1.25 wks 1 wks 0.01 wks 0.1 wks

35 Commissioning 0.75 wks 1 wk 1.25 wks 1 wks 0.01 wks 0.1 wks

36 Marketing 37.5 wks 50 wks 62.5 wks 50 wks 17.36 wks 4.17 wks

37 Market Test 33 wks 44 wks 55 wks 44 wks 13.44 wks 3.67 wks

38 Produce a Physical Prototype or mock-up 4.5 wks 6 wks 7.5 wks 6 wks 0.25 wks 0.5 wks

39 Conduct Focus Group Customer Interviews 6 wks 8 wks 10 wks 8 wks 0.44 wks 0.66 wks

40 Make Adjustement Where Necessary 4.5 wks 6 wks 7.5 wks 6 wks 0.25 wks 0.5 wks

41 Sell an initial run of product in local market 18 wks 24 wks 30 wks 24 wks 4 wks 2 wks

42 Advertisement 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

43 Advertisement in T.V. 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

44 Advertisement in Radio 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

by Normal Distribution as below:

(

) (

√ )

(Appendix 1. Table 1 shows the Normal Distribution)

This means scheduling can meet the deadline for local Market by 31% that is quite weak

probability, and can be interpreted as rarely! Thus project manager must take proper action!

ID Task Name Optimistic Dur.

Expected Dur.

Pessimistic Dur.

Mean Variance Standard Deviation

45 Advertisement in Newspapers 9 wks 12 wks 15 wks 12 wks 1 wks 1 wks

46 Introduce the product internationally 0 wks 0 wks 0 wks 0 wks 0 wks 0 wks

47 Business Analysis 40.5 wks 54 wks 67.5 wks 54 wks 20.25 wks 4.5 wks

48 Pricing 6.75 wks 9 wks 11.25 wks 9 wks 0.56 wks 0.75 wks

49 Estimate Likely Selling Price 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

50 Estimate Sales Volume 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

51 Estimate Profitability and Break Even Point 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

52 Fundraising 6 wks 8 wks 10 wks 8 wks 0.44 wks 0.66 wks

53 Estimate Costs 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

54 Stock Shares 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

55 Bank Loans 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

56 Recruitment 5.25 wks 7 wks 8.75 wks 7 wks 0.34 wks 0.58 wks

57 Employment Phase 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

58 Engineers 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

59 Labors 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

60 Training Phase 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

61 Engineers 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

62 Labors 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

63 Quality Management 50.25 wks 67 wks 83.75 wks 67 wks 31.17 wks 5.58 wks

64 Manufacturing Quality 3.75 wks 5 wks 6.25 wks 5 wks 0.17 wks 0.41 wks

65 Specify Equipement Quality Specifications 1.5 wks 2 wks 2.5 wks 2 wks 0.03 wks 0.17 wks

66 Prepare Maintenance Plan 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

67 Product quality 6 wks 8 wks 10 wks 8 wks 0.44 wks 0.66 wks

68 Specify Quality Specifications 1.5 wks 2 wks 2.5 wks 2 wks 0.03 wks 0.17 wks

69 Prepare Quality Assurance Method 1.5 wks 2 wks 2.5 wks 2 wks 0.03 wks 0.17 wks

70 Provide Quality Assurance Forms 3 wks 4 wks 5 wks 4 wks 0.11 wks 0.33 wks

71 Logistics 3.75 wks 5 wks 6.25 wks 5 wks 0.17 wks 0.41 wks

72 Suppliers 3.75 wks 5 wks 6.25 wks 5 wks 0.17 wks 0.41 wks


1.5 wks 2 wks 2.5 wks 2 wks 0.03 wks 0.17 wks

74 Select the Appropriate Transportation System 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

75 Customers 3.75 wks 5 wks 6.25 wks 5 wks 0.17 wks 0.41 wks

76 Choosing the Least Cost Distribution Centers 1.5 wks 2 wks 2.5 wks 2 wks 0.03 wks 0.17 wks

77 Select the Appropriate Transportation System 2.25 wks 3 wks 3.75 wks 3 wks 0.06 wks 0.24 wks

78 Finish 0 wks 0 wks 0 wks 0 wks 0 wks 0 wks

12.2 Likelihood of meeting deadline for introducing new circuit board

internationally by 2 years Since international introduction of new circuit board is the final activity and main purpose of the

project, its critical path is the same as whole project and therefore as below:

2 15 21 22 23 27 28 29 30 31 32 33

34 35 38 39 40 41 43 44 45 46

According to Table 6, the Mean Duration and Variance of this path are:

MeanPathDuration=0+4+12×50%+12×50%+12+1+4+8+6+4+4+2+1+1+6+8+6+24×75%+

12+0= 109

Path Variance=0.00+0.11+1.00×50%+1.00×50%+1.00+0.01+0.11+0.44+0.25+0.11+0.11+

0.03+0.01+0.01+0.25+0.44+0.25+4×75%+1+0= 8.13

Again the SS (Start to Start) precedency isn’t considered.

The calculation steps are like previous section, but new circuit board was supposed to be

introduced by 104 weeks internationally; so we have:

(

) (

√ )

(Appendix1. Table1 shows the Normal Distribution)

It shows that by 4% project can achieve its goal that means almost impossible! With this

scheduling none of potential shareholders would encourage to invest. In the other word, it is

essential for project manager to take proper action in order to Crash project duration.

12.3 A short discussion based on Pert Analysis Pert analysis shows project manager that corresponding schedule is going to meet two most

important project deadlines by 31% and 4% which means unlikely! Consequently new circuit

board would lose market shares and it could be a disaster for investors.

Therefore, crashing the project duration and increasing the related probabilities of meeting

deadlines is a necessity. For this purpose project manager should determine how much safety

percentage project needs to meet deadlines and which solutions exist in order to Crash activity

durations. This is the topic of next section, where a cost-time trade off will be accomplished via

application of Linear Programming. The results will show us how much it costs for project to

decrease a specified amount of time in an optimum manner.

13. Project Cost-time trade off (Via Linear Programming)

13.1 How can activities duration be decreased?

Decreasing the whole project duration needs to decrease activities duration which usually means

using more resources and subsequently brings about more costs. There is a reverse relation

between cost and time in any project. The short duration increase the cost and long duration

decrease. So project manager should choose the optimum state.

There is also a number of ways in order to increase the resources. Since here and in this project,

our main resources are human resources, we need to specify some ways in order to increase the

human resources in order to Crash the time.

Firstly project manager can outsource some activities to be done concurrently with in progress

activities. This could decrease the project duration effectively while project manager doesn’t

need to engage in their process. Nevertheless, Outsourcing cost usually is much more than hiring

new employees. In addition project manager has already outsourced some parts of project that

don’t need much coordination and for the remained parts; it is hard to be done without much

collaboration with existing project organization.

Second choice is working in the overtime. By increasing the hourly work of each employee via

2-3 hours per day and adding weekends, some activities could be finished earlier and

subsequently their successors can be launched. However besides working in overtime decreases

the efficiency and morale of employees, it costs much due to high overtime coefficient that is

around 2 and times wages.

The third choice is hiring temporary employees. Nowadays employing temporary human

resources even for one day becomes easy through recruitment companies. Even though project

should pay 1.5 times of fixed employees’ salaries to Recruitment company-which usually will

pay a percentage of it to employees themselves- they are flexible and don’t need strict planning

beforehand and afterwards.

Therefore project manager believes that hiring temporary employees by recruitment companies

is the best and most economical solution to fulfill project resources in order to Crash project

duration.

13.2 How much should project duration decrease? In the last section project manager understood that current scheduling can hardly meet the project

deadlines. On the other hand, project stakeholders need a plan which meets project deadlines by

90% percent. Using the normal distribution and project parameters we can calculate the required

duration of project as below:

First deadline: Introducing the New Circuit Board locally

(

) (

√ )

⇒

It means New Circuit board should introduce to the local market by 75 weeks in order to meet 18

month deadline by 90% safety and since it is now by 79 weeks, then corresponding path to this

activity should decrease by 4 weeks!

Second Deadline: Introducing the New Circuit Board Internationally

(

) (

√ )

⇒

It means New Circuit board should introduce internationally by 100 weeks in order to meet 24

month deadline by 90% safety and since it is now by 109 weeks, whole project duration should

Crash by 9 weeks!

So project manager could conclude that “Whole project duration should decrease by 9 weeks

while first deadline should Crash by 4 weeks.”

13.3 How long can each activity be Crashed and how much does it cost? The possible Crashing time for each activity depends on some factors that the most important

one is technological or logical constraints. For example “Request for tenders” cannot be done

less than 4 weeks since it is the period that at least different vendors need to prepare their

documents and take part. The same is for Bank loans and stock shares because of their long

formal process. Some other activities like different discipline designs are also impossible to be

shorter due to mutual dependency with each other and construction.

In addition after determination of possible Crashing time, the corresponding cost for new

duration should be calculated. In New Circuit board project we considered a temporary recruited

crew who helps existing human resources and receives 1.5 times ordinary loans and then

calculate the corresponding cost with the Crashed duration. Table 7 shows the above-mentioned

information.

13.4 Linear Programming Model Having the possible Crashing duration and its corresponding costs, now we can formulate a

linear model in order to find the optimum solution for decreasing the whole project duration.

Again we remind that whole project duration should decrease by 9 weeks while first deadline

should Crash by 4 weeks, assuming the least cost consumption.

We don’t go through the detail of the method since it is described thoroughly in linear

programming books like [1] and it is a well-known model. We made the model in spreadsheet

and solve it by Excel Solver as figure 7 and then come to under-mentioned results.

As you can see in the table 7, the total normal cost and the total crashed cost are:

ID Task Name Normal Duration

Normal Cost

Crashed Duration

Crashed cost Possible Crashing

Crashing cost

Crashing cost per week

2 Start 0 wks $0.00 0 $0.00

5 Determine Customer Requirements 4 wks $6,560.00 4 wks $6,560.00 0 $0.00

6 Specify Design Requirement 4 wks $6,560.00 3 wks $7,380.00 1 wk $820.00 $820.00

8 Specify Parts Design 4 wks $6,560.00 3 wks $7,380.00 1 wk $820.00 $820.00

9 Determine Manufacturing design 4 wks $6,560.00 4 wks $6,560.00 0 $0.00

11 Prepare Product Specifications 4 wks $6,560.00 4 wks $6,560.00 0 $0.00

12 Test the product 4 wks $6,560.00 3 wks $7,380.00 1 wk $820.00 $820.00

15 Determine Equipment Specifications 4 wks $7,200.00 4 wks $7,200.00 0 $0.00

16 Prepare MR(Material Requirement) 4 wks $7,200.00 3 wks $8,100.00 1 wk $900.00 $900.00

17 Request for tenders 4 wks $7,200.00 4 wks $7,200.00 0 $0.00

18 Performing TBE(Technical Bid Evaluation) 4 wks $7,200.00 3 wks $8,100.00 1 wk $900.00 $900.00

19 Select Equipment Vendor 4 wks $7,200.00 3wks $8,100.00 1 wk $900.00 $900.00

21 Mechanical Design 12 wks $26,400.00 12 wks $26,400.00 0 $0.00

22 Piping Design 12 wks $26,400.00 12 wks $26,400.00 0 $0.00

23 Civil Design 12 wks $26,400.00 12 wks $26,400.00 0 $0.00

24 Electrical Design 12 wks $26,400.00 12 wks $26,400.00 0 $0.00

25 Instrument Design 12 wks $26,400.00 12 wks $26,400.00 0 $0.00

27 Rough grading and compaction 1 wk $3,440.00 1 wk $3,440.00 0 $0.00

28 Constructing foundations 4 wks $13,760.00 3 wks $15,480.00 1 wk $1,720.00 $1,720.00

29 Installing equipment 8 wks $27,520.00 7 wks $29,240.00 1 wk $1,720.00 $1,720.00

30 Aligning and welding pipes 6 wks $20,640.00 4 wks $24,080.00 2 wks $1,720.00 $1,720.00

31 Cabling and lighting 4 wks $13,760.00 3 wks $15,480.00 1 wk $3,440.00 $1,720.00

32 Instrumentation 4 wks $13,760.00 3 wks $15,480.00 1 wk $1,720.00 $1,720.00

33 Free run test 2 wks $6,880.00 1 wks $8,600.00 1 wk $1,720.00 $1,720.00

34 Precommissioning 1 wk $3,440.00 1 wk $3,440.00 0 $0.00

35 Commissioning 1 wk $3,440.00 1 wk $3,440.00 0 $0.00

38 Produce a Physical Prototype or mock-up 6 wks $7,920.00 4 wks $9,240.00 2 wks $1,320.00 $660.00


Normal Cost

Crashed Duration

Crashed cost Possible Crashing

Crashing cost

Crashing cost per week

39 Conduct Focus Group Customer Interviews 8 wks $10,560.00 7 wks $11,220.00 1 wk $660.00 $660.00

40 Make Adjustment Where Necessary 6 wks $7,920.00 4 wks $9,240.00 2 wks $1,320.00 $660.00

41 Sell an initial run of product in local market 24 wks $0.00 24 wks $0.00 0 $0.00

43 Advertisement in T.V. 12 wks $15,840.00 12 wks $15,840.00 0 $0.00

44 Advertisement in Radio 12 wks $15,840.00 12 wks $15,840.00 0 $0.00

45 Advertisement in Newspapers 12 wks $15,840.00 12 wks $15,840.00 0 $0.00

46 Introduce the product internationally 0 wks $0.00 0 wks $0.00 0 $0.00

49 Estimate Likely Selling Price 3 wks $3,000.00 2 wks $3,500.00 1 wk $500.00 $500.00

50 Estimate Sales Volume 3 wks $3,000.00 2 wks $3,500.00 1 wk $500.00 $500.00

51 Estimate Profitability and Break Even Point 3 wks $3,000.00 2 wks $3,500.00 1 wk $500.00 $500.00

53 Estimate Costs 4 wks $4,000.00 3 wks $4,500.00 1 wk $500.00 $500.00

54 Stock Shares 4 wks $4,000.00 4 wks $4,000.00 0 $0.00

55 Bank Loans 4 wks $4,000.00 4 wks $4,000.00 0 $0.00

58 Engineers 3 wks $3,600.00 3 wks $3,600.00 0 $0.00

59 Labors 3 wks $3,600.00 3 wks $3,600.00 0 $0.00

61 Engineers 4 wks $4,800.00 4 wks $4,800.00 0 $0.00

62 Labors 4 wks $4,800.00 4 wks $4,800.00 0 $0.00

65 Specify Equipment Quality Specifications 2 wks $2,800.00 2 wks $2,800.00 0 $0.00

66 Prepare Maintenance Plan 3 wks $4,200.00 3 wks $4,200.00 0 $0.00

68 Specify Quality Specifications 2 wks $2,800.00 2 wks $2,800.00 0 $0.00

69 Prepare Quality Assurance Method 2 wks $2,800.00 2 wks $2,800.00 0 $0.00

70 Provide Quality Assurance Forms 4 wks $5,600.00 3 wks $6,300.00 1 wk $700.00 $700.00

73 Choosing the Least Cost Suppliers for Transportation 2 wks $2,800.00 2 wks $2,800.00 0 $0.00

74 Select the Appropriate Transportation System 3 wks $4,200.00 2 wks $4,900.00 1 wk $700.00 $700.00

76 Choosing the Least Cost Distribution Centers 2 wks $2,800.00 2 wks $2,800.00 0 $0.00

77 Select the Appropriate Transportation System 3 wks $4,200.00 2 wks $4,900.00 1 wk $700.00 $700.00

78 Finish 0 wks $0.00 0 $0.00

Total Normal Cost: 457,920 $

Total Crashed Cost: 482,520 $

Overhead Cost: 500$ Per Week

But the problem here is that which activities should be crashed in order to meet deadlines by 90 percent?

Project Manager has the possibility of crashing 22 activities, but according to Linear Model results, the optimum solution involves crashing of 7

activities as table 8 shows:

Table 8 - Optimum Solution for Crashing whole project to 100 weeks while introduce the new circuit board locally by 70 weeks


Normal Cost Crashed Duration

Crashed cost

Possible Crashing

Crashing Cost

Crashing Cost Per Week

Predecessor

29 Installing equipements 8 $27,520.00 7 $29,240.00 1 $1,720.00 $1,720.00 28,22

31 Cabling and lighting 4 $13,760.00 3 $15,480.00 1 $1,720.00 $1,720.00 30,24

32 Instrumentation 4 $13,760.00 3 $15,480.00 1 $1,720.00 $1,720.00 31,25

33 Free run test 2 $6,880.00 1 $8,600.00 1 $1,720.00 $1,720.00 32

38 Produce a Physical Prototype or mock-up 6 $7,920.00 4 $9,240.00 2 $1,320.00 $660.00 35

39 Conduct Focus Group Customer Interviews 8 $10,560.00 7 $11,220.00 1 $660.00 $660.00 38

40 Make Adjustement Where Necessary 6 $7,920.00 4 $9,240.00 2 $1,320.00 $660.00 39

Total Crashing Cost $10,180.00

Then the New circuit board would be introduced to local market by 70 weeks and later internationally by 100 weeks. It is interesting that new

product is going to introduce locally 5 weeks earlier than proposed deadline since all the crashed activities located in its critical path. Table 10

shows the crashed project information. To compare the whole project costs between these two alternatives you can see table 9.

Table 9 - Cost differences between Normal and Crashed Project

Overhead: $500/wk Normal Project Crashed Project Difference

Duration 109 wks 100 wks -9 wks

Variable Cost $457,920.00 $468,131.20 $10,180.00

Fixed Cost $54,500.00 $50,000.00 ($4,500.00)

Total Cost $512,420.00 $518,131.20 $5,711.20

ID Task Name Duration Start Finish Cost Critical

1 New Circuit Board Project 100 wks

W52/7 W48/6 $468,131.20 Yes

2 Start 0 wks W52/7 W52/7 $0.00 Yes

3 Product and Process Design 24 wks W1/2 W24/6 $39,360.00 No

4 Design Product 8 wks W1/2 W8/6 $13,120.00 No

5 Determine Customer Requirements 4 wks W1/2 W4/6 $6,560.00 No

6 Specify Design Requirement 4 wks W5/2 W8/6 $6,560.00 No

7 Design Process 8 wks W9/2 W16/6 $13,120.00 No

8 Specify Parts Design 4 wks W9/2 W12/6 $6,560.00 No

9 Determine Manufacturing design 4 wks W13/2 W16/6 $6,560.00 No

10 Performing Tests 8 wks W17/2 W24/6 $13,120.00 No

11 Prepare Product Specifications 4 wks W17/2 W20/6 $6,560.00 No

12 Test the product 4 wks W21/2 W24/6 $6,560.00 No

13 Building New Facility 55 wks W52/7 W3/6 $281,313.60 Yes

14 Procure Equipment 20 wks W52/7 W20/6 $36,000.00 Yes

15 Determine Equipment Specifications 4 wks W52/7 W4/6 $7,200.00 Yes

16 Prepare MR(Material Requirement) 4 wks W4/6 W8/6 $7,200.00 No

17 Request for tenders 4 wks W8/6 W12/6 $7,200.00 No

18 Performing TBE(Technical Bid Evaluation) 4 wks W12/6 W16/6 $7,200.00 No

19 Select Equipment Vendor 4 wks W16/6 W20/6 $7,200.00 No

20 Design Facility 36 wks W4/6 W40/6 $132,000.00 Yes

21 Mechanical Design 12 wks W4/6 W16/6 $26,400.00 Yes

22 Piping Design 12 wks W11/2 W22/6 $26,400.00 Yes

23 Civil Design 12 wks W17/2 W28/6 $26,400.00 Yes

24 Electrical Design 12 wks W23/2 W34/6 $26,400.00 No

25 Instrument Design 12 wks W29/2 W40/6 $26,400.00 No

26 Construction Phase 27 wks W29/2 W3/6 $113,313.60 Yes

27 Rough grading and compaction 1 wk W29/2 W29/6 $3,440.00 Yes

28 Constructing foundations 4 wks W30/2 W33/6 $13,760.00 Yes

29 Installing equipment 7 wks W34/2 W40/6 $29,136.80 Yes

30 Aligning and welding pipes 6 wks W41/2 W46/6 $20,640.00 Yes

31 Cabling and lighting 3 wks W47/2 W49/6 $15,428.40 Yes

32 Instrumentation 3 wks W50/2 W52/6 $15,428.40 Yes

33 Free run test 1 wk W1/2 W1/6 $8,600.00 Yes

34 Precommissioning 1 wk W2/2 W2/6 $3,440.00 Yes

35 Commissioning 1 wk W3/2 W3/6 $3,440.00 Yes

36 Marketing 45 wks W3/6 W48/6 $77,457.60 Yes

37 Market Test 39 wks W3/6 W42/6 $29,937.60 Yes

38 Produce a Physical Prototype or mock-up 4 wks W3/6 W7/6 $9,240.00 Yes

39 Conduct Focus Group Customer Interviews 7 wks W7/6 W14/6 $11,457.60 Yes

40 Make Adjustment Where Necessary 4 wks W14/6 W18/6 $9,240.00 Yes

41 Sell an initial run of product in local market 24 wks W19/2 W42/6 $0.00 Yes

42 Advertisement 12 wks W37/2 W48/6 $47,520.00 Yes

43 Advertisement in T.V. 12 wks W37/2 W48/6 $15,840.00 Yes

44 Advertisement in Radio 12 wks W37/2 W48/6 $15,840.00 Yes

45 Advertisement in Newspapers 12 wks W37/2 W48/6 $15,840.00 Yes

46 Introduce the product internationally 0 wks W48/6 W48/6 $0.00 Yes

ID Task Name Duration Start Finish Cost Critical

47 Business Analysis 45 wks W35/2 W27/6 $21,000.00 No

48 Pricing 9 wks W18/6 W27/6 $9,000.00 No

49 Estimate Likely Selling Price 3 wks W18/6 W21/6 $3,000.00 No

50 Estimate Sales Volume 3 wks W21/6 W24/6 $3,000.00 No

51 Estimate Profitability and Break Even Point 3 wks W24/6 W27/6 $3,000.00 No

52 Fundraising 8 wks W35/2 W42/6 $12,000.00 No

53 Estimate Costs 4 wks W35/2 W38/6 $4,000.00 No

54 Stock Shares 4 wks W38/6 W42/6 $4,000.00 No

55 Bank Loans 4 wks W38/6 W42/6 $4,000.00 No

56 Recruitment 7 wks W3/6 W10/6 $16,800.00 No

57 Employment Phase 3 wks W3/6 W6/6 $7,200.00 No

58 Engineers 3 wks W3/6 W6/6 $3,600.00 No

59 Labors 3 wks W3/6 W6/6 $3,600.00 No

60 Training Phase 4 wks W6/6 W10/6 $9,600.00 No

61 Engineers 4 wks W6/6 W10/6 $4,800.00 No

62 Labors 4 wks W6/6 W10/6 $4,800.00 No

63 Quality Management 58 wks W20/6 W26/6 $18,200.00 No

64 Manufacturing Quality 5 wks W20/6 W25/6 $7,000.00 No

65 Specify Equipment Quality Specifications 2 wks W20/6 W22/6 $2,800.00 No

66 Prepare Maintenance Plan 3 wks W22/6 W25/6 $4,200.00 No

67 Product quality 8 wks W18/6 W26/6 $11,200.00 No

68 Specify Quality Specifications 2 wks W18/6 W20/6 $2,800.00 No

69 Prepare Quality Assurance Method 2 wks W20/6 W22/6 $2,800.00 No

70 Provide Quality Assurance Forms 4 wks W22/6 W26/6 $5,600.00 No

71 Logistics 5 wks W27/6 W32/6 $14,000.00 No

72 Suppliers 5 wks W27/6 W32/6 $7,000.00 No

73 Choosing the Least Cost Suppliers for Transportation 2 wks W27/6 W29/6 $2,800.00 No

74 Select the Appropriate Transportation System 3 wks W29/6 W32/6 $4,200.00 No

75 Customers 5 wks W27/6 W32/6 $7,000.00 No

76 Choosing the Least Cost Distribution Centers 2 wks W27/6 W29/6 $2,800.00 No

77 Select the Appropriate Transportation System 3 wks W29/6 W32/6 $4,200.00 No

78 Finish 0 wks W48/6 W48/6 $0.00 Yes

In the other word, it costs $5712 more in order to meet project deadlines by 90% assurance. As it

shows in table 10, the critical activities didn’t change the critical path still is:

2 15 21 22 23 27 28 29 30 31 32 33

34 35 38 39 40 41 43 44 45 46 78

From now, we will consider the crashed project as our scheduling since this one can fulfill our

requirements. The other stages will also be done on this version. Obviously it was almost

impossible to calculate by hand and choose the 7 optimum activities among 22 possible ones in

order to crash a project with 78 activities while LP did it in the best manner.

14. Project Resource Loading As it was illustrated in 6, New Circuit Board project has three different resources: Engineer, Technician and labor. It is worthy to

mention that due to considering the Week as time unit, we could allocate fractional number of resources to some activities which

means that resource should devote him/herself to project a percentage of the week which can be a few days. In this section, we will

show the resource loading graph for these three main resources.

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Engineer

Engineer

As you see in figure 8, there is much difference between loadings in different weeks. While the maximum number of needed engineers

is 6.5 per week at the almost beginning of the project, later between weeks 55 and 71, project doesn’t need any engineer and these

fluctuations in resource loadings makes the resource assignment difficult for project manager.

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00

Technician

Technician

Figure 9 shows the loading for Technicians through the entire project. Although it seems smoother than Engineer loadings, still weeks

84-88 don’t need any technician while at the middle of project, we need 6 technicians. Again we need to level technician resources in

order to simplify and minimize the cost of resource allocation.

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Labor

Labor loadings have also differences even though it is almost as smooth as technician. In the middle of the project we need 3 labors

while between weeks 24-29 and 70-88 no labor is required.

All in all, these graphs show us the necessity of resource leveling for the project and this is what we want to do in the next section by

using the activities slacks for stretching or compressing some activities in order to smooth loading of resources.

15. Resource Leveling By Branch and Bound Algorithm In order to level resources, project manager used Branch and Bound Method in order to solve

non-linear programming problem. He assumed the objective function as below:

∑

∑

Yes

Yes No

No

We wrote a code in Visual Basic and firstly execute for resources one by one:

Engineers: We smoothed the Engineer and the result was fantastic. The amount of objective function was decreased by 80 percent and

the number of Max required engineer decreased from 7 to 4. However objective function for other resources increased!

Table 11- Leveling Results for Engineer resource

Objective function before leveling Objective function after leveling

Engineer 526,3475 Engineer 86,8475

Technician 275,76 Technician 511,76

Labor 144,856875 Labor 160,356875

Total 946,964375 Total 758,964375

00,5

11,5

22,5

33,5

44,5

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Engineer

Engineer

Technicians: By smoothing the only technician resource, the amount of its objective function decreased by 50 percent.

Table 12- Leveling Results for Technician resource




Labor 144,856875 Labor 144,856875

Total 946,964375 Total 560,964375

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Technician

Technician

Labors: Algorithm couldn’t find any better objective function for labor resource and the current schedule was the best for it.

Table 13- Leveling Results for Labor resource




Labor 144,856875 Labor 144,856875

Total 946,964375 Total 946,964375

0

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Labor

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Finally we minimize the objective function of total resources. By smoothing total resource profile, the objective function amount for

Engineers, Technicians and Labors decreased respectively by 70%, 40% and 0%. The Objective function for all resources also

decreased by 50 %.

Table 14- Leveling Results for all resources




Labor 144,856875 Labor 146,856875

Total 946,964375 Total 489,464375

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Engineer

Technician

Labor

Project manager chose the last schedule where we smoothed the total resource loading by branch

and bound algorithm. The associated schedule is coming below in Table 15. Interestingly, the

task number 25-instrument design also become critical in the new schedule. (The VB code for

Brach and Bound Algorithm is shown in Appendix 1.)

16. Comulative Cost Diagram In the Figure 16, the comulative cost diagram is showed for Early start dates and Late start dates.

The space between these two curves shows the flexibilty of this schedule for funding the project.

In the other word, project manager can only manuever inside this space while trys to provide

appropriate funds for project.

$0.00

$50,000.00

$100,000.00

$150,000.00

$200,000.00

$250,000.00

$300,000.00

$350,000.00

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$500,000.00

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ek

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Project Comulative Cost

Early Dates

Late Dates

ID Task Name Duration

Critical Early Start

Early Finish

Late Start

Late Finish

Cost

2 Start 0 TRUE 0 0 0 0 $0.00

5 Determine Customer Requirements 4 FALSE 0 4 76 80 $6,560.00

6 Specify Design Requirement 4 FALSE 4 8 80 84 $6,560.00

8 Specify Parts Design 4 FALSE 81 85 84 88 $6,560.00

9 Determine Manufacturing design 4 FALSE 57 61 88 92 $6,560.00

11 Prepare Product Specifications 4 FALSE 61 65 92 96 $6,560.00

12 Test the product 4 FALSE 70 74 96 100 $6,560.00

15 Determine Equipment Specifications 4 TRUE 0 4 0 4 $7,200.00

16 Prepare MR(Material Requirement) 4 FALSE 49 53 79 83 $7,200.00

17 Request for tenders 4 FALSE 66 70 83 87 $7,200.00

18 Performing TBE(Technical Bid Evaluation) 4 FALSE 53 57 87 91 $7,200.00

19 Select Equipment Vendor 4 FALSE 71 75 91 95 $7,200.00

21 Mechanical Design 12 TRUE 4 16 4 16 $26,400.00

22 Piping Design 12 TRUE 10 22 10 22 $26,400.00

23 Civil Design 12 TRUE 16 28 16 28 $26,400.00

24 Electrical Design 12 FALSE 23 35 31 43 $26,400.00

25 Instrument Design 12 TRUE 37 49 37 49 $26,400.00

27 Rough grading and compaction 1 TRUE 28 29 28 29 $3,440.00

28 Constructing foundations 4 TRUE 29 33 29 33 $13,760.00

29 Installing equipment 7 TRUE 33 40 33 40 $29,136.80

30 Aligning and welding pipes 6 TRUE 40 46 40 46 $20,640.00

31 Cabling and lighting 3 TRUE 46 49 46 49 $15,428.40

32 Instrumentation 3 TRUE 49 52 49 52 $15,428.40

33 Free run test 1 TRUE 52 53 52 53 $8,600.00

34 Precommissioning 1 TRUE 53 54 53 54 $3,440.00

35 Commissioning 1 TRUE 54 55 54 55 $3,440.00

38 Produce a Physical Prototype or mock-up 4 TRUE 55 59 55 59 $9,240.00

39 Conduct Focus Group Customer Interviews 7 TRUE 59 66 59 66 $11,457.60

40 Make Adjustment Where Necessary 4 TRUE 66 70 66 70 $9,240.00

41 Sell an initial run of product in local market 24 TRUE 70 94 70 94 $0.00

43 Advertisement in T.V. 12 TRUE 88 100 88 100 $15,840.00

44 Advertisement in Radio 12 TRUE 88 100 88 100 $15,840.00

45 Advertisement in Newspapers 12 TRUE 88 100 88 100 $15,840.00

46 Introduce the product internationally 0 TRUE 100 100 100 100 $0.00

49 Estimate Likely Selling Price 3 FALSE 84 87 86 89 $3,000.00

50 Estimate Sales Volume 3 FALSE 85 88 89 92 $3,000.00

51 Estimate Profitability and Break Even Point 3 FALSE 85 88 92 95 $3,000.00

53 Estimate Costs 4 FALSE 70 74 92 96 $4,000.00

54 Stock Shares 4 FALSE 75 79 96 100 $4,000.00

55 Bank Loans 4 FALSE 78 82 96 100 $4,000.00

58 Engineers 3 FALSE 62 65 63 66 $3,600.00

59 Labors 3 FALSE 55 58 63 66 $3,600.00

61 Engineers 4 FALSE 65 69 66 70 $4,800.00

62 Labors 4 FALSE 58 62 66 70 $4,800.00

65 Specify Equipment Quality Specifications 2 FALSE 35 37 95 97 $2,800.00

66 Prepare Maintenance Plan 3 FALSE 74 77 97 100 $4,200.00

68 Specify Quality Specifications 2 FALSE 86 88 92 94 $2,800.00

69 Prepare Quality Assurance Method 2 FALSE 77 79 94 96 $2,800.00

70 Provide Quality Assurance Forms 4 FALSE 74 78 96 100 $5,600.00


2 FALSE 79 81 95 97 $2,800.00

74 Select the Appropriate Transportation System 3 FALSE 82 85 97 100 $4,200.00

76 Choosing the Least Cost Distribution Centers 2 FALSE 79 81 95 97 $2,800.00

77 Select the Appropriate Transportation System 3 FALSE 81 84 97 100 $4,200.00

78 Finish 0 TRUE 100 100 100 100 $0.00

References

1. F. S. HILLIER, G. J. LIEBERMAN “Introduction to Operation Research” Seventh Edition,

Mac Graw Hill, 2001.

2. K. Neumann , J. Zimmermann “Procedures for resource leveling and net present value

problems in project scheduling with general temporal and resource constraints” European

Journal of Operational Research 127 (2000) 425±443.

3. M. Bandelloni M. Tucci, R. Rinaldi “Optimal resource leveling using non-serial dynamic

programming” European Journal of Operational Research 78 (1994) 162-177 .

Appendix 1. VB code for Resource Leveling

Sub RL()

'

' RL Macro

'

' Keyboard Shortcut: Ctrl+q

'

Dim eng(0 To 100)

Dim tech(0 To 100)

Dim lab(0 To 100)

Dim ID(1 To 54)

Dim t(1 To 54)

Dim z(1 To 54)

Dim est(1 To 54, 1 To 19)

Dim ES(1 To 54)

Dim LS(1 To 54)

Dim slack(1 To 54)

Dim d(1 To 54)

Dim critical(1 To 54) As Boolean

Dim Engineer(1 To 54)

Dim Technician(1 To 54)

Dim Labor(1 To 54)

Dim lst(1 To 54, 1 To 7)

Dim Suc(1 To 54, 1 To 6)

Dim sucvar(1 To 54, 1 To 6)

Dim pre(1 To 54, 1 To 18)

Dim prevar(1 To 54, 1 To 18)

Dim m

Dim fixed(1 To 54) As Boolean

Dim test(1 To 54) As Boolean

Dim engbig(1 To 54, 1 To 100, 1 To 100)

Dim techbig(1 To 54, 1 To 100, 1 To 100)

Dim labbig(1 To 54, 1 To 100, 1 To 100)

Dim ESbig(1 To 54, 1 To 100, 1 To 54)

Dim lsbig(1 To 54, 1 To 100, 1 To 54)

Dim slackbig(1 To 54, 1 To 100, 1 To 54)

Dim criticalbig(1 To 54, 1 To 100, 1 To 54)

Dim zengbig(1 To 54, 1 To 100)

Dim ztechbig(1 To 54, 1 To 100)

Dim zlabbig(1 To 54, 1 To 100)

Dim ztotbig(1 To 54, 1 To 100)

For i = 1 To 54

ID(i) = Cells(i + 1, 1)

d(i) = Cells(i + 1, 12)

Engineer(i) = Cells(i + 1, 31)

Technician(i) = Cells(i + 1, 32)

Labor(i) = Cells(i + 1, 33)

For j = 1 To 6

Suc(i, j) = Cells(i + 1, 2 + j)

Next j

For k = 1 To 18

pre(i, k) = Cells(i + 1, 12 + k)

Next k

Next i

ES(1) = 0

LS(54) = 100

For i = 1 To 54

For j = 1 To 6

sucvar(i, j) = Suc(i, j)

lst(i, j) = 100

Next j

For j = 1 To 18

prevar(i, j) = pre(i, j)

est(i, j) = 0

Next j

Next i

b = 1

t(1) = 1

p = 1

Do While p < 55

m = ID(t(p))

For i = 1 To 54

j = 1

Do While j < 19

If prevar(i, j) = m Then

est(i, j) = ES(t(p)) + prevar(i, j + 1)

prevar(i, j) = "*": prevar(i, j + 1) = "*"

If prevar(i, 1) = "*" And prevar(i, 2) = "*" And prevar(i, 3) = "*" And prevar(i, 4) = "*" And prevar(i, 5) = "*" And prevar(i, 6) = "*" And prevar(i, 7) = "*" And prevar(i, 8) = "*" And prevar(i, 9) = "*" And prevar(i, 10) = "*" And prevar(i, 11) = "*" And prevar(i, 12) = "*" And prevar(i, 13) = "*" And prevar(i, 14) = "*" And prevar(i, 15) = "*" And prevar(i, 16) = "*" And prevar(i, 17) = "*" And prevar(i, 18) = "*" Then

w = 1

Max = 0

Do While w < 19

If Max < est(i, w) Then

Max = est(i, w)

End If

w = w + 2

Loop

ES(i) = Max

b = b + 1

t(b) = i

End If

End If

j = j + 2

Loop

Next i

p = p + 1

Loop

b = 1

z(1) = 54

p = 1

Do While p < 55

m = ID(z(p))

For i = 1 To 54

j = 1

Do While j < 7

If sucvar(i, j) = m Then

lst(i, j) = LS(z(p)) - sucvar(i, j + 1)

sucvar(i, j) = "*": sucvar(i, j + 1) = "*"

If sucvar(i, 1) = "*" And sucvar(i, 2) = "*" And sucvar(i, 3) = "*" And sucvar(i, 4) = "*" And sucvar(i, 5) = "*" And sucvar(i, 6) = "*" Then

w = 1

Min = 100

Do While w < 7

If Min > lst(i, w) Then

Min = lst(i, w)

End If

w = w + 2

Loop

LS(i) = Min

b = b + 1

z(b) = i

End If

End If

j = j + 2

Loop

Next i

p = p + 1

Loop

For i = 1 To 54

Cells(i + 1, 9) = ES(i)

Cells(i + 1, 10) = LS(i)

slack(i) = LS(i) - ES(i)

If slack(i) = 0 Then

critical(i) = True

Else

critical(i) = False

End If

For counter = ES(i) + 1 To ES(i) + d(i)

eng(counter) = eng(counter) + Engineer(i)

Cells(59, counter + 3) = eng(counter)

tech(counter) = tech(counter) + Technician(i)

Cells(60, counter + 3) = tech(counter)

lab(counter) = lab(counter) + Labor(i)

Cells(61, counter + 3) = lab(counter)

Next counter

Cells(i + 1, 34) = slack(i)

Cells(i + 1, 11) = critical(i)

Next i

zeng = 0: ztech = 0: zlab = 0

For counter = 1 To 100

zeng = zeng + (eng(counter) - 2.345) * (eng(counter) - 2.345)

ztech = ztech + (tech(counter) - 3.32) * (tech(counter) - 3.32)

zlab = zlab + (lab(counter) - 1.0575) * (lab(counter) - 1.0575)

Next counter

ztot = zeng + ztech + zlab

Cells(59, 3) = zeng

Cells(60, 3) = ztech

Cells(61, 3) = zlab

Cells(62, 3) = ztot

'The new part'

For i = 1 To 54

If critical(i) = True Then

fixed(i) = True

Else

fixed(i) = False

End If

Next i

d: For i = 1 To 54

If fixed(i) = True Then

test(i) = True

Else

test(i) = False

End If

Next i

b: minslack = 100

minID = 100

For i = 1 To 54

ES(i) = Cells(i + 1, 9)

LS(i) = Cells(i + 1, 10)

slack(i) = Cells(i + 1, 34)

If minslack > slack(i) And test(i) = False Then

minslack = slack(i): minID = i

End If

Next i

If minslack = 100 Then GoTo c

test(minID) = True

fixed(minID) = True

hg = ES(minID)

n = 0

For counter = 1 To slack(minID)

ES(minID) = hg + counter

b = 0

For i = 1 To 54

If fixed(i) = True Then

b = b + 1

t(b) = i

End If

Next i

p = 1

Do While p < 55

m = ID(t(p))

For i = 1 To 54

j = 1

Do While j < 19 And fixed(i) = False

If prevar(i, j) = m Then

est(i, j) = ES(t(p)) + prevar(i, j + 1)

If est(i, j) > 100 Then GoTo a

prevar(i, j) = "*": prevar(i, j + 1) = "*"

If prevar(i, 1) = "*" And prevar(i, 2) = "*" And prevar(i, 3) = "*" And prevar(i, 4) = "*" And prevar(i, 5) = "*" And prevar(i, 6) = "*" And prevar(i, 7) = "*" And prevar(i, 8) = "*" And prevar(i, 9) = "*" And prevar(i, 10) = "*" And prevar(i, 11) = "*" And prevar(i, 12) = "*" And prevar(i, 13) = "*" And prevar(i, 14) = "*" And prevar(i, 15) = "*" And prevar(i, 16) = "*" And prevar(i, 17) = "*" And prevar(i, 18) = "*" Then

w = 1

Max = 0

Do While w < 19

If Max < est(i, w) Then

Max = est(i, w)

End If

w = w + 2

Loop

ES(i) = Max

b = b + 1

t(b) = i

End If

End If

j = j + 2

Loop

Next i

p = p + 1

Loop

b = 0

For i = 54 To 1

If fixed(i) = True And i <> minID Then

b = b + 1

z(b) = i

End If

Next i

p = 1

Do While p < 55

m = ID(z(p))

For i = 1 To 54

j = 1

Do While j < 7 And fixed(i) = False And i <> minID

If sucvar(i, j) = m Then

lst(i, j) = LS(z(p)) - sucvar(i, j + 1)

If lst(i, j) < 0 Then GoTo a

sucvar(i, j) = "*": sucvar(i, j + 1) = "*"

If sucvar(i, 1) = "*" And sucvar(i, 2) = "*" And sucvar(i, 3) = "*" And sucvar(i, 4) = "*" And sucvar(i, 5) = "*" And sucvar(i, 6) = "*" Then

w = 1

Min = 100

Do While w < 7

If Min > lst(i, w) Then

Min = lst(i, w)

End If

w = w + 2

Loop

LS(i) = Min

b = b + 1

z(b) = i

End If

End If

j = j + 2

Loop

Next i

p = p + 1

Loop

n = n + 1

For r = 1 To 100

eng(r) = 0

tech(r) = 0

lab(r) = 0

Next r

For y = 1 To 54

ESbig(minID, n, y) = ES(y)

lsbig(minID, n, y) = LS(y)

slack(y) = LS(y) - ES(y)

If slack(y) = 0 Then

critical(y) = True

Else

critical(y) = False

End If

criticalbig(minID, n, y) = critical(y)

slackbig(minID, n, y) = slack(y)

For Count = ES(y) + 1 To ES(y) + d(y)

eng(Count) = eng(Count) + Engineer(y)

tech(Count) = tech(Count) + Technician(y)

lab(Count) = lab(Count) + Labor(y)

Next Count

Next y

zeng = 0: ztech = 0: zlab = 0

For Count = 1 To 100

engbig(minID, n, Count) = eng(Count)

techbig(minID, n, Count) = tech(Count)

labbig(minID, n, Count) = lab(Count)

zeng = zeng + (eng(Count) - 2.345) * (eng(Count) - 2.345)

ztech = ztech + (tech(Count) - 3.32) * (tech(Count) - 3.32)

zlab = zlab + (lab(Count) - 1.0575) * (lab(Count) - 1.0575)

Next Count

ztot = zeng + ztech + zlab

zengbig(minID, n) = zeng

ztechbig(minID, n) = ztech

zlabbig(minID, n) = zlab

ztotbig(minID, n) = ztot

a: Next counter

If n = 0 Then

fixed(minID) = False: GoTo b

Else

minobject = ztotbig(minID, 1)

opt = 1

For f = 1 To n

If minobject > ztotbig(minID, f) Then

minobject = ztotbig(minID, f)

opt = f

End If

Next f

End If

If minobject < Cells(62, 3) Then

Cells(59, 3) = zengbig(minID, opt)

Cells(60, 3) = ztechbig(minID, opt)

Cells(61, 3) = zlabbig(minID, opt)

Cells(62, 3) = minobject

For i = 1 To 54

Cells(i + 1, 34) = slackbig(minID, opt, i)

Cells(i + 1, 11) = criticalbig(minID, opt, i)

Cells(i + 1, 9) = ESbig(minID, opt, i)

Cells(i + 1, 10) = lsbig(minID, opt, i)

Next i

For i = 1 To 100

Cells(59, i + 3) = engbig(minID, opt, i)

Cells(60, i + 3) = techbig(minID, opt, i)

Cells(61, i + 3) = labbig(minID, opt, i)

Next i

GoTo d

Else

fixed(minID) = False: GoTo b

End If

c: End Sub

Documents

New_circuit_board_project[1]