Programming a project with the CPM - Revision history

Tkokotas at 15:13, 16 November 2018

2018-11-16T15:13:42Z

← Older revision		Revision as of 15:13, 16 November 2018
Line 1:		Line 1:
			''Developed by Konstantinos Terzakis''


	[[Category:Project Management]][[Category:Management]][[Category:CPM]]		[[Category:Project Management]][[Category:Management]][[Category:CPM]]
	==Abstract==		==Abstract==

S161563: /* Big Idea */

2018-02-28T09:25:55Z

Big Idea

← Older revision		Revision as of 09:25, 28 February 2018
Line 5:		Line 5:
	==Big Idea==		==Big Idea==
	"A project is a sequence of unique, complex and connected activities that have  one goal or purpose and that must be completed by a specific time, within a  budget and according to specification." <ref name=kostas21> Robert K. Wysocki, 2009, Effective Project Management: Traditional, Agile, Extreme. Fifth Edition, ISBN: 978-0-470-42367-7. </ref>		"A project is a sequence of unique, complex and connected activities that have  one goal or purpose and that must be completed by a specific time, within a  budget and according to specification." <ref name=kostas21> Robert K. Wysocki, 2009, Effective Project Management: Traditional, Agile, Extreme. Fifth Edition, ISBN: 978-0-470-42367-7. </ref>
	Another definition, according to PM Standard is: “A project is a unique set of processes consisting of coordinated and controlled activities with start and end dates, performed to achieve project objectives. Achievement of the project objectives requires the provision of deliverables conforming to specific requirements”.<ref name=kostas28> (ISO 21500 PM Standard).</ref>		Another definition, according to PM Standard is: “A project is a unique set of processes consisting of coordinated and controlled activities with start and end dates, performed to achieve project objectives. Achievement of the project objectives requires the provision of deliverables conforming to specific requirements”.<ref name=kostas28> ISO 21500 PM Standard.</ref>

	In both of these definitions, it can be observed some key words such as "coordinate", "sequence" "start/end" date. The CPM calculates a single, deterministic early and late start and finish date for each activity based on specified, sequencial network logic and a single duration estimate. The focus of CPM is on calculating the float in order to determine which activities have the least scheduling flexibility. The CPM algorithms are often used in other types of mathematical analysis.<ref name="KOSTAS"> A Guide to the Project Management Body of Knowledge, PMI Standards Committee, ISBN:1-880410-12-5 '' </ref>		In both of these definitions, it can be observed some key words such as "coordinate", "sequence" "start/end" date. The CPM calculates a single, deterministic early and late start and finish date for each activity based on specified, sequencial network logic and a single duration estimate. The focus of CPM is on calculating the float in order to determine which activities have the least scheduling flexibility. The CPM algorithms are often used in other types of mathematical analysis.<ref name="KOSTAS"> A Guide to the Project Management Body of Knowledge, PMI Standards Committee, ISBN:1-880410-12-5 '' </ref>

S161563: /* Big Idea */

2018-02-28T09:25:13Z

Big Idea

← Older revision		Revision as of 09:25, 28 February 2018
Line 5:		Line 5:
	==Big Idea==		==Big Idea==
	"A project is a sequence of unique, complex and connected activities that have  one goal or purpose and that must be completed by a specific time, within a  budget and according to specification." <ref name=kostas21> Robert K. Wysocki, 2009, Effective Project Management: Traditional, Agile, Extreme. Fifth Edition, ISBN: 978-0-470-42367-7. </ref>		"A project is a sequence of unique, complex and connected activities that have  one goal or purpose and that must be completed by a specific time, within a  budget and according to specification." <ref name=kostas21> Robert K. Wysocki, 2009, Effective Project Management: Traditional, Agile, Extreme. Fifth Edition, ISBN: 978-0-470-42367-7. </ref>
	The CPM calculates a single, deterministic early and late start and finish date for each activity based on specified, sequencial network logic and a single duration estimate. The focus of CPM is on calculating the float in order to determine which activities have the least scheduling flexibility. The CPM algorithms are often used in other types of mathematical analysis.<ref name="KOSTAS"> A Guide to the Project Management Body of Knowledge, PMI Standards Committee, ISBN:1-880410-12-5 '' </ref>		Another definition, according to PM Standard is: “A project is a unique set of processes consisting of coordinated and controlled activities with start and end dates, performed to achieve project objectives. Achievement of the project objectives requires the provision of deliverables conforming to specific requirements”.<ref name=kostas28> (ISO 21500 PM Standard).</ref>

			In both of these definitions, it can be observed some key words such as "coordinate", "sequence" "start/end" date. The CPM calculates a single, deterministic early and late start and finish date for each activity based on specified, sequencial network logic and a single duration estimate. The focus of CPM is on calculating the float in order to determine which activities have the least scheduling flexibility. The CPM algorithms are often used in other types of mathematical analysis.<ref name="KOSTAS"> A Guide to the Project Management Body of Knowledge, PMI Standards Committee, ISBN:1-880410-12-5 '' </ref>

	===Methodology===		===Methodology===

S161563: /* Abstract */

2018-02-28T09:07:49Z

Abstract

← Older revision		Revision as of 09:07, 28 February 2018
Line 1:		Line 1:
	[[Category:Project Management]][[Category:Management]][[Category:CPM]]		[[Category:Project Management]][[Category:Management]][[Category:CPM]]
	==Abstract==		==Abstract==
	Many students struggle with the concepts of planning and scheduling when first introduced to it. This struggle extends from the introduction of work breakdown structure to network logic through the meaning of critical activities and continuing with other planning and scheduling topics.<ref name="kostas24"> Weber, Sandra C., Scheduling Construction Projects: Principles and Practices,Prentice Hall, 2005 '' </ref>. The [[Wikipedia:Critical Path Method\|Critical Path Method]] (CPM) was developed in late 1950s and became a very popular tool for Schedule Development. The method, which is broadly used by project managers, is a graphical technique which is known with the generic term Network Modeling and is used to estimate the minimum project duration. This schedule network analysis technique calculates the early start, early finish, late start, and late finish dates for all activities without regard for resource limitations by performing a forward and backward pass analysis through the schedule network. The critical path is the sequence of activities that represents the longest path through a project, which determines the shortest possible project duration. The resulting early and late start and finish dates are not necessarily the project schedule, rather they indicate the time periods within which the activity could be executed, using the parameters set in the schedule model for activity durations, logical relationships, leads, lags, and other known constraints. The CPM is used to calculate the amount of scheduling flexibility on the logical network paths within the schedule model.<ref name="kostas"> A Guide to the Project Management Body of Knowledge (PMBOK® Guide), Fifth Edition, 2013, ISBN-13: 978-1-935589-67-9 '' </ref>. This article describes the CPM methodology, provides an example of this technique so as to be perceivable, while it analyzes how this method responds to the modern business practices as well as which is the evolution of this method.		Many students struggle with the concepts of planning and scheduling when first introduced to it. This struggle extends from the introduction of work breakdown structure to network logic through the meaning of critical activities and continuing with other planning and scheduling topics.<ref name="kostas24"> Weber, Sandra C., Scheduling Construction Projects: Principles and Practices,Prentice Hall, 2005 '' </ref> The [[Wikipedia:Critical Path Method\|Critical Path Method]] (CPM) was developed in late 1950s and became a very popular tool for Schedule Development. The method, which is broadly used by project managers, is a graphical technique which is known with the generic term Network Modeling and is used to estimate the minimum project duration. This schedule network analysis technique calculates the early start, early finish, late start, and late finish dates for all activities without regard for resource limitations by performing a forward and backward pass analysis through the schedule network. The critical path is the sequence of activities that represents the longest path through a project, which determines the shortest possible project duration. The resulting early and late start and finish dates are not necessarily the project schedule, rather they indicate the time periods within which the activity could be executed, using the parameters set in the schedule model for activity durations, logical relationships, leads, lags, and other known constraints. The CPM is used to calculate the amount of scheduling flexibility on the logical network paths within the schedule model.<ref name="kostas"> A Guide to the Project Management Body of Knowledge (PMBOK® Guide), Fifth Edition, 2013, ISBN-13: 978-1-935589-67-9 '' </ref>. This article describes the CPM methodology, provides an example of this technique so as to be perceivable, while it analyzes how this method responds to the modern business practices as well as which is the evolution of this method.

	==Big Idea==		==Big Idea==

S161563: /* Abstract */

2018-02-28T09:07:35Z

Abstract

← Older revision		Revision as of 09:07, 28 February 2018
Line 1:		Line 1:
	[[Category:Project Management]][[Category:Management]][[Category:CPM]]		[[Category:Project Management]][[Category:Management]][[Category:CPM]]
	==Abstract==		==Abstract==
	The [[Wikipedia:Critical Path Method\|Critical Path Method]] (CPM) was developed in late 1950s and became a very popular tool for Schedule Development. The method, which is broadly used by project managers, is a graphical technique which is known with the generic term Network Modeling and is used to estimate the minimum project duration. This schedule network analysis technique calculates the early start, early finish, late start, and late finish dates for all activities without regard for resource limitations by performing a forward and backward pass analysis through the schedule network. The critical path is the sequence of activities that represents the longest path through a project, which determines the shortest possible project duration. The resulting early and late start and finish dates are not necessarily the project schedule, rather they indicate the time periods within which the activity could be executed, using the parameters set in the schedule model for activity durations, logical relationships, leads, lags, and other known constraints. The CPM is used to calculate the amount of scheduling flexibility on the logical network paths within the schedule model.<ref name="kostas"> A Guide to the Project Management Body of Knowledge (PMBOK® Guide), Fifth Edition, 2013, ISBN-13: 978-1-935589-67-9 '' </ref>. This article describes the CPM methodology, provides an example of this technique so as to be perceivable, while it analyzes how this method responds to the modern business practices as well as which is the evolution of this method.		Many students struggle with the concepts of planning and scheduling when first introduced to it. This struggle extends from the introduction of work breakdown structure to network logic through the meaning of critical activities and continuing with other planning and scheduling topics.<ref name="kostas24"> Weber, Sandra C., Scheduling Construction Projects: Principles and Practices,Prentice Hall, 2005 '' </ref>. The [[Wikipedia:Critical Path Method\|Critical Path Method]] (CPM) was developed in late 1950s and became a very popular tool for Schedule Development. The method, which is broadly used by project managers, is a graphical technique which is known with the generic term Network Modeling and is used to estimate the minimum project duration. This schedule network analysis technique calculates the early start, early finish, late start, and late finish dates for all activities without regard for resource limitations by performing a forward and backward pass analysis through the schedule network. The critical path is the sequence of activities that represents the longest path through a project, which determines the shortest possible project duration. The resulting early and late start and finish dates are not necessarily the project schedule, rather they indicate the time periods within which the activity could be executed, using the parameters set in the schedule model for activity durations, logical relationships, leads, lags, and other known constraints. The CPM is used to calculate the amount of scheduling flexibility on the logical network paths within the schedule model.<ref name="kostas"> A Guide to the Project Management Body of Knowledge (PMBOK® Guide), Fifth Edition, 2013, ISBN-13: 978-1-935589-67-9 '' </ref>. This article describes the CPM methodology, provides an example of this technique so as to be perceivable, while it analyzes how this method responds to the modern business practices as well as which is the evolution of this method.

	==Big Idea==		==Big Idea==

S161563: /* Application */

2018-02-28T08:51:29Z

Application

← Older revision		Revision as of 08:51, 28 February 2018
Line 79:		Line 79:


	[[File:3KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|700px\|thumb\|right\|'''Picture 4:''' The network depicts the sequence, the duration, the ES, EF and LS, LF of the actions]].		[[File:3KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|700px\|thumb\|right\|'''Picture 4:''' The network depicts the sequence, the duration, the ES, EF and LS, LF of the actions]]

	'''Slack time and Critical Path'''		'''Slack time and Critical Path'''

S161563: /* The Evolution from CPM to DPM */

2018-02-27T12:44:41Z

The Evolution from CPM to DPM

← Older revision		Revision as of 12:44, 27 February 2018
Line 140:		Line 140:
	[[File:DPM.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|380px\|thumb\|right\|'''Picture 8:''' The Dynamic Progress Method (DPM) compared to CPM. Source: Project Management Institute. <ref name="KOSTASSSS" /> ]]		[[File:DPM.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|380px\|thumb\|right\|'''Picture 8:''' The Dynamic Progress Method (DPM) compared to CPM. Source: Project Management Institute. <ref name="KOSTASSSS" /> ]]

	DPM begins with a fundamental re-evaluation of how input information is used. After defining which tasks are to be done and their dependencies, a project manager begins the process of estimating ~~for~~ each task. For a task, the project manager usually knows about how much work needs to be done, who might do that job, an idea as to how “good” or “effective” that person is, and an idea about the availability of that person. In the example in picture 8, it’s easy to see that an 80-hour task with one assigned resource that is available 8 hours/day and is 100% productive (i.e., for each hour the resource is paid, the resource completes an hour of actual project work) gives a task duration of 10 days. With CPM-based planning tools, the duration is the input. Conversely, with DPM-based tools, the individual task and resource inputs are used instead. In this example, if the resources are actually available at the level of productivity assumed, then the duration will be the same 10 days.<ref name="KOSTASSSS"> https://www.pmi.org/learning/library/going-beyond-critical-path-method-6297 / Project Management Institute '' </ref>		DPM begins with a fundamental re-evaluation of how input information is used. After defining which tasks are to be done and their dependencies, a project manager begins the process of estimating the duration of each task. For a task, the project manager usually knows about how much work needs to be done, who might do that job, an idea as to how “good” or “effective” that person is, and an idea about the availability of that person. In the example in picture 8, it’s easy to see that an 80-hour task with one assigned resource that is available 8 hours/day and is 100% productive (i.e., for each hour the resource is paid, the resource completes an hour of actual project work) gives a task duration of 10 days. With CPM-based planning tools, the duration is the input. Conversely, with DPM-based tools, the individual task and resource inputs are used instead. In this example, if the resources are actually available at the level of productivity assumed, then the duration will be the same 10 days.<ref name="KOSTASSSS"> https://www.pmi.org/learning/library/going-beyond-critical-path-method-6297 / Project Management Institute '' </ref>

	Commercial available tools that use the DPM is the pmBLOX and the [[Wikipedia:Spider Project\|Spider Project]].		Commercial available tools that use the DPM is the pmBLOX and the [[Wikipedia:Spider Project\|Spider Project]].

S161563: /* Limitations of the CPM due to the modern business practices */

2018-02-27T12:43:19Z

Limitations of the CPM due to the modern business practices

← Older revision		Revision as of 12:43, 27 February 2018
Line 125:		Line 125:
	• The usage of a software such as Microsoft Project or Primavera is recommended if the analysis process is extremely complicated.		• The usage of a software such as Microsoft Project or Primavera is recommended if the analysis process is extremely complicated.

	• The method requires time in order to develop the project network and relies heavily on project managers and members ~~involved~~ in that stage. Poorly defined project scope and activities can result in ineffective use of CPM, which becomes difficult to manage.		• The method requires time in order to develop the project network and relies heavily on project managers and members' knowledge and experience in that stage. Poorly defined project scope and activities can result in ineffective use of CPM, which becomes difficult to manage.

	• It is not easy to adjust the method when changes occur in the project plan during the project execution. In that case ~~the~~ we have to redraw the project and start the calculations from the beginning. This is an intertemporal disadvantage of this method.		• It is not easy to adjust the method when changes occur in the project plan during the project execution. In that case we have to redraw the project and start the calculations from the beginning. This is an intertemporal disadvantage of this method.

	• ~~Due to that the~~ CPM is an optimal planning tool, it always assumes that all resources are available for the project at all times, something that does not reflect the reality especially nowadays.		• The CPM is an optimal planning tool, as it always assumes that all resources are available for the project at all times, something that does not reflect the reality especially nowadays.

	To overcome these shortcomings of the critical path, the critical chain method was developed. In the critical chain method resource constraints are also taken into consideration while developing the network diagram.<ref name="KOSTAS" />		To overcome these shortcomings of the critical path, the critical chain method was developed. In the critical chain method resource constraints are also taken into consideration while developing the network diagram.<ref name="KOSTAS" />

S161563: /* Application */

2018-02-27T12:40:03Z

Application

← Older revision		Revision as of 12:40, 27 February 2018
Line 83:		Line 83:
	'''Slack time and Critical Path'''		'''Slack time and Critical Path'''

	Having ES, EF, LS and LF, it is then possible to find the slack times of the actions and identify the critical path. Slack time is the time period during which we can delay an action without affecting the completion time of the project. Obviously the slack time span of any action is the difference between LS and ES or the LF and EF of the action.		Having calculated ES, EF, LS and LF, it is then possible to find the slack times of the actions and identify the critical path. Slack time is the time period during which we can delay an action without affecting the completion time of the project. Obviously the slack time span of any action is the difference between LS and ES or the LF and EF of the action.

	'''Slack time = LS-ES = LF-EF'''		'''Slack time = LS-ES = LF-EF'''
Line 95:		Line 95:
	Thus it is stated that:		Thus it is stated that:

	A critical path in a network of actions is the longest in duration path from network related actions from the start until the end of a project, where any delay in these actions leads to time extension to the completion of the overall project. The critical path can also be defined as the route on the network where all its actions have zero slack time or even the path for which the pairs (ES, EF) and (LS, LF) are ~~identified~~.		A critical path in a network of actions is the longest in duration path from network related actions from the start until the end of a project, where any delay in these actions leads to time extension to the completion of the overall project. The critical path can also be defined as the route on the network where all its actions have zero slack time or even the path for which the pairs (ES, EF) and (LS, LF) are identical.
	The actions that belong to the critical path are also called critical actions. So, if any action ends up with zero slack time, this action is on the critical path. Usually, and especially in some more complex networks, there are many critical routes. Of course, the total time of the critical routes is the same and longer than the total time in any other route of the network. In the example above only action D is not a critical action, and does not belong to the critical path (since it has slack time = 3 ≠ 0). In Picture 5 below it can be seen the critical path, the slack time for action D and the total duration of the project.		The actions that belong to the critical path are also called critical actions. So, if any action ends up with zero slack time, this action is on the critical path. Usually, and especially in some more complex networks, there are many critical routes. Of course, the total time of the critical routes is the same and longer than the total time in any other route of the network. In the example above only action D is not a critical action, and does not belong to the critical path (since it has slack time = 3 ≠ 0). In Picture 5 below it can be seen the critical path, the slack time for action D and the total duration of the project.

Line 107:		Line 107:
	[[File:7KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|500px\|thumb\|right\|'''Picture 7:''' Late Start Schedule for the application depicted in a Gantt chart]]		[[File:7KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|500px\|thumb\|right\|'''Picture 7:''' Late Start Schedule for the application depicted in a Gantt chart]]

	The existence of slack times in actions that do not belong to the critical route, allows for their programming in accordance with the needs and priorities of the overall project. In the example, the action D was reported to have slack time 3 weeks. This allows the start of Action D at any time within the timeline from week 4 (ES = 4) to week 7 (LS = 7). This property of non-critical actions can be better observed if we use the Gantt diagram, where time is depicted in the horizontal axis. Picture 6 shows exactly this, with the non-critical action D that starts at the time that is identical to ES ~~of (ES = 4)~~.		The existence of slack times in actions that do not belong to the critical route, allows for their programming in accordance with the needs and priorities of the overall project. In the example, the action D was reported to have slack time 3 weeks. This allows the start of Action D at any time within the timeline from week 4 (ES = 4) to week 7 (LS = 7). This property of non-critical actions can be better observed if we use the Gantt diagram, where time is depicted in the horizontal axis. Picture 6 shows exactly this, with the non-critical action D that starts at the time that is identical to ES.

	This approach to programming non-critical actions is called '''Early Start Schedule'''. In this case, they are scheduled to begin as soon as possible (ES). With this approach the project and all the individual actions are completed as soon as possible.		This approach to programming non-critical actions is called '''Early Start Schedule'''. In this case, they are scheduled to begin as soon as possible (ES). With this approach the project and all the individual actions are completed as soon as possible.

S161563: /* Application */

2018-02-27T12:31:17Z

Application

← Older revision		Revision as of 12:31, 27 February 2018
Line 34:		Line 34:
	===Application===		===Application===
	[[File:Kk.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|500px\|thumb\|right\|'''Table 1:''' Characteristics of the actions to design the Network (created in MS Excel 2016)]]		[[File:Kk.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|500px\|thumb\|right\|'''Table 1:''' Characteristics of the actions to design the Network (created in MS Excel 2016)]]
	Let’s say that a consulting company carries out a project and the project team decides which individual actions are the main components of the overall project. These may be exploring customer requirements, investigate the case study, preparation of the offer, etc. These actions are shown in the first column of Table 1 ~~below~~. Once established exactly the actions, they are encoded with a letter for facilitating the design of the network (2nd column of the table). Then determine the sequence, that is the order of execution shown in 3rd column of the table, where next to each action is shown which or what actions must precede. Finally, in the fourth column, there is the time required for completion of each action, estimated by the project team. So, the first thing that the project team or the person responsible for the planning must produce, is a table as Table 1.		Let’s say that a consulting company carries out a project and the project team decides which individual actions are the main components of the overall project. These may be exploring customer requirements, investigate the case study, preparation of the offer, etc. These actions are shown in the first column of Table 1. Once established exactly the actions, they are encoded with a letter for facilitating the design of the network (2nd column of the table). Then determine the sequence, that is the order of execution shown in 3rd column of the table, where next to each action is shown which or what actions must precede. Finally, in the fourth column, there is the time required for completion of each action, estimated by the project team. So, the first thing that the project team or the person responsible for the planning must produce is a table as Table 1.


	'''Designing the network.'''		'''Designing the network'''

	Once the above table has been determined, the project manager can proceed with the design of the network. The actions are represented as nodes while arrows from node to node show the sequence of actions. The elements that are written on a node can be seen in Picture 2.		Once the above table has been determined, the project manager can proceed with the design of the network. The actions are represented as nodes while arrows from node to node show the sequence of actions. The elements that are written on a node can be seen in Picture 2.
Line 48:		Line 48:
	When planning a network of actions we need to be sure that the actions are depicted in the proper sequence and that we maintain the logic among them. In the case of the consultancy company we observe two routes, A-B-C-D-F-G and A-B-C-E-F-G.		When planning a network of actions we need to be sure that the actions are depicted in the proper sequence and that we maintain the logic among them. In the case of the consultancy company we observe two routes, A-B-C-D-F-G and A-B-C-E-F-G.

	'''Determination of "Critical Times" of Actions. Early Start Time (ES) - Early Finish Time (EF)'''		'''Determination of "Critical Times" of Actions: Early Start Time (ES) - Early Finish Time (EF)'''

	During the process of identifying the critical route, it is needed to calculate the critical times of the project's actions.		During the process of identifying the critical route, it is needed to calculate the critical times of the project's actions.

	'''Earliest Start Time (ES)''' of the action is the earliest time at which the action may begin. This depends on when the ~~previous or previous~~ actions have been completed.		'''Earliest Start Time (ES)''' of the action is the earliest time at which the action may begin. This depends on when the preceding actions have been completed.

	'''Early Finish Time (EF)''' of the action is the earliest time at which the action ~~may have been~~ completed, and apparently, equals the ES plus the duration of the action.		'''Early Finish Time (EF)''' of the action is the earliest time at which the action could be completed, and apparently, equals the ES plus the duration of the action.

	The ~~shortest~~ end time EF for Action A is ES + 2, since ~~2 weeks is~~ its duration, so EF = 2. The ~~next~~ action is B, which can not begin before Action A has been completed. Therefore, the ES for action B will be identified with EF of the previous action and ES = 2 for action B. As far as it is known that the duration of action B is 1, it is obvious that EF = ES + 1 = 2 + 1 = 3. Following this process and using the duration of actions from Table 1, the network in Picture 3 is produced.		The earliest end time EF for Action A is ES + 2, since its duration is two weeks, so EF = 2. The following action is B, which can not begin before Action A has been completed. Therefore, the ES for action B will be identified with EF of the previous action, and ES = 2 for action B. As far as it is known that the duration of action B is 1, it is obvious that EF = ES + 1 = 2 + 1 = 3. Following this process and using the duration of actions from Table 1, the network in Picture 3 is produced.

	[[File:2KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|700px\|thumb\|right\|'''Picture 3:''' The network depicts the sequence, the duration, the ES and EF of the actions]]		[[File:2KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|700px\|thumb\|right\|'''Picture 3:''' The network depicts the sequence, the duration, the ES and EF of the actions]]

	As a consequence, it is logical that the ~~shorter~~ completion time of the overall project is identical to the EF of the last action. This is the expected completion time of the project. In our case, the company's project has a total project duration of 15 weeks.		As a consequence, it is logical that the earliest completion time of the overall project is identical to the EF of the last action. This is the expected completion time of the project. In our case, the company's project has a total project duration of 15 weeks.

	'''Determination of "Critical Times". Late Start Time (LS) - Late Finish Time (LF)'''		'''Determination of "Critical Times": Late Start Time (LS) - Late Finish Time (LF)'''

	The next step in the process is to calculate the ~~earliest~~ starting and finishing times of the actions.		The next step in the process is to calculate the latest starting and finishing times of the actions.

	'''The Late Finish Time (LF)''' of the action is the latest time when an action can end without extending the completion time of the entire project.		'''The Late Finish Time (LF)''' of the action is the latest time when an action can end without extending the completion time of the entire project.
Line 70:		Line 70:
	'''The Late Start Time (LS)''' of the action is the latest time that an action can start without prolonging the completion time of the entire project and equals to LF minus the duration of the action.		'''The Late Start Time (LS)''' of the action is the latest time that an action can start without prolonging the completion time of the entire project and equals to LF minus the duration of the action.

	Based on the example to define the latest times, we have to start from the end of the network towards the beginning by examining one by one the actions. The ~~shortest~~ completion time of the project, hence the desirable time, is identified by the EF of the last action, and that is 15 weeks~~. So, as long as the total duration of the project does not exceed this achievable time, the latest termination time LF of the action G is 15~~. Consequently, the action G cannot be completed after the 15th week because there will be a time extension for the company’s project. ~~Thus~~, LF ~~= 15~~ for action G~~, and obviously the~~ LS for G ~~will be~~ LS = LF-1 = 15-1 = 14~~, i.e. the latest start time of the action G, is the action LF, minus its duration which in our case is 1~~.
	Regarding action F, ~~as long as the earliest time in which may be triggered by~~ its ~~next associated action G and it’s~~ the ~~14th week (~~LS ~~= 14 for~~ G), ~~cannot end later than~~ the ~~14th week without extending~~ the whole project time~~. Accordingly~~, the ~~latest termination time for the~~ action F is ~~LF =~~ 14 ~~and apparently~~ the ~~earliest start time will be the LF~~ of the action minus ~~its~~ duration~~. Therefore~~, LS ~~= LF-5~~ = 14-5 ~~= 9 for action F~~. Following this procedure and using the duration times of the actions from Table 1, the network in Picture 4 is produced.		Based on the example to define the latest times, we have to start from the end of the network towards the beginning by examining one by one the actions. The earliest completion time of the project, hence the desirable time, is identified by the EF of the last action, and that is 15 weeks. Consequently, the action G cannot be completed after the 15th week because there will be a time extension for the company’s project. Therefore, the LF for action G is 15 weeks. The LS for G is calculated from LF minus the duration of the activity, LS = LF-1 = 15-1 = 14.

			Regarding action F, its LF date depends on the LS of the following action G.
			That means, to avoid the extension of the whole project time, the LF date of action F is 14 weeks. Accordingly, the LS date of the action F is LS minus duration of the activity, LS = 14 - 5.

			Following this procedure and using the duration times of the actions from Table 1, the network in Picture 4 is produced.


	[[File:3KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|700px\|thumb\|right\|'''Picture 4:''' The network depicts the sequence, the duration, the ES, EF and LS, LF of the actions]].		[[File:3KOSTAS.PNG\|link=http://apppm.man.dtu.dk/images/f/f7/1.PNG‎\|700px\|thumb\|right\|'''Picture 4:''' The network depicts the sequence, the duration, the ES, EF and LS, LF of the actions]].