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
73 Choosing the Least Cost Suppliers for Transportation
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
73 Choosing the Least Cost Suppliers for Transportation
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
ID Task Name Normal Duration
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
ID Task Name Normal Duration
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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k 1
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.
0
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1.5
2
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3
3.5W
eek
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Labor
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
Wee
k 1
Wee
k 5
Wee
k 9
Wee
k 1
3
Wee
k 1
7
Wee
k 2
1
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k 2
5
Wee
k 2
9
Wee
k 3
3
Wee
k 3
7
Wee
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1
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5
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9
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3
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7
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3
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7
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3
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7
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
Objective function before leveling Objective function after leveling
Engineer 526,3475 Engineer 286,3475
Technician 275,76 Technician 129,76
Labor 144,856875 Labor 144,856875
Total 946,964375 Total 560,964375
0
1
2
3
4
5
6
7
Wee
k 1
Wee
k 5
We
ek
9
Wee
k 1
3
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7
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k 2
1
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k 2
5
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k 2
9
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3
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7
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1
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3
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7
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1
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3
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7
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1
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5
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9
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3
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7
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
Objective function before leveling Objective function after leveling
Engineer 526,3475 Engineer 526,3475
Technician 275,76 Technician 275,76
Labor 144,856875 Labor 144,856875
Total 946,964375 Total 946,964375
0
0,5
1
1,5
2
2,5
3
3,5
Wee
k 1
Wee
k 5
Wee
k 9
Wee
k 1
3
Wee
k 1
7
Wee
k 2
1
Wee
k 2
5
Wee
k 2
9
Wee
k 3
3
Wee
k 3
7
Wee
k 4
1
Wee
k 4
5
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k 4
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3
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k 5
7
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1
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k 6
5
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k 7
3
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7
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1
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k 8
5
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k 8
9
Wee
k 9
3
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k 9
7
Labor
Labor
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
Objective function before leveling Objective function after leveling
Engineer 526,3475 Engineer 152,8475
Technician 275,76 Technician 189,76
Labor 144,856875 Labor 146,856875
Total 946,964375 Total 489,464375
0
1
2
3
4
5
6
7
Wee
k 1
Wee
k 5
Wee
k 9
Wee
k 1
3
Wee
k 1
7
Wee
k 2
1
Wee
k 2
5
Wee
k 2
9
Wee
k 3
3
Wee
k 3
7
Wee
k 4
1
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k 4
5
Wee
k 4
9
Wee
k 5
3
Wee
k 5
7
Wee
k 6
1
Wee
k 6
5
Wee
k 6
9
Wee
k 7
3
Wee
k 7
7
Wee
k 8
1
Wee
k 8
5
Wee
k 8
9
Wee
k 9
3
Wee
k 9
7
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
$400,000.00
$450,000.00
$500,000.00
We
ek
01
We
ek
05
We
ek
09
We
ek
13
We
ek
17
We
ek
21
We
ek
25
We
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29
We
ek
33
We
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37
We
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41
We
ek
45
We
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49
We
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53
We
ek
57
We
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61
We
ek
65
We
ek
69
We
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73
We
ek
77
We
ek
81
We
ek
85
We
ek
89
We
ek
93
We
ek
97
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
73 Choosing the Least Cost Suppliers for Transportation
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