PROJECT ACTIVITY ANALYSIS WITHOUT THE NETWORK MODEL

This paper presents a new procedure for analysing and managing activity sequences in projects. The new procedure determines critical activities, critical path, start times, free floats, crash limits, and other useful information without the use of the network model. Even though network models have been successfully used in project management so far, there are weaknesses associated with the use. A network is not easy to generate, and dummies that are usually associated with it make the network diagram complex – and dummy activities have no meaning in the original project management problem. The network model for projects can be avoided while still obtaining all the useful information that is required for project management. What are required are the activities, their accurate durations, and their predecessors.


INTRODUCTION
Networks have been used successfully in project management since the 1950s.Networks graphically show the total amount of time needed to complete a project, the sequence in which the tasks must be carried out, the critical tasks that need close attention, and which tasks can be carried out simultaneously [2] [4] [6] [8].A project manager can also shorten the project duration by adding more resources to certain tasks in an attempt to get them done faster.The network diagram has proved to be a useful tool for scheduling activities in a project [1] [7].When unexpected circumstances cause slight changes in durations -for example, a worker strike, resources supply problems, or unpredictable weather -such problems require the rescheduling of activities and rapid computation.Changing networks are called protean networks [3], and for very large projects a slight delay in decisionmaking can be costly.The network diagram can be avoided while still obtaining the same scheduling decisions.This paper presents a novel procedure for analysing and managing activity sequences in projects.The procedure determines critical activities, the critical path, start times, free floats, crash limits, and other useful information without using a network model.Even though the network model has been used successfully so far in project management, there are weaknesses associated with it.A network is not easy to generate, and dummies that are usually associated with it make the network diagram complex -and they have no meaning in the original project management problem.One can avoid the network model for projects and still get all the useful information that is required for project management.What are required are the activities, their accurate duration estimates, and their predecessors.The proposed procedure changes are only incorporated into the affected activities; unaffected activities are not considered.As a result of this, technique calculations are rapidly carried out, resulting in timeous decisions.

Consider a given activity
i A , its ri predecessors, and an accurate duration estimate, as shown in Table 1 below.

Activity
Predecessor Accurate duration estimate where The data in Table 1 can be used to determine the critical activities, critical path, start and end times, free floats, crash limits, and other useful information that is required for project management without the use of a network diagram.

GENERATING THE LATEST END TIME
The latest end time (1) http://sajie.journals.ac.zawhere i LEj T is the end time for j th of the ri predecessors.In this case ri j ,..., 2 , 1 =

Immediately after obtaining
i LE T all the predecessors must have the same end time value of , where The process is called 'updating', and changes the latest end times of all predecessors to .i LE T

CRITICAL ACTIVITIES
The activity giving the largest end time is the critical activity.The set of critical activities in chronological order is the critical path.This path is conveniently traced from the bottom of the table, going backwards.The latest start time of an activity is the latest end time of its predecessor.

GENERATING THE EARLIEST END TIME i EE T FOR ACTIVITY i A
The earliest end time where si EEj T and sj d are the earliest end time and duration of the successor activity si A respectively.
. ,..., 2 , 1 k j = The updated end times and critical activities are shown in Table 2.

CRASHING ACTIVITY DURATIONS
'Crashing' refers to a technique used in project management for the purpose of decreasing the total project duration.Crashing is done after a careful and thorough analysis of all activities, their sequences and importance, so as to obtain the most convenient duration at the least additional cost.There are several approaches to crashing a project schedule.One of these is the minimum incoming weight label (MIWL) method proposed by Munapo et al. [5].This method selects only those activities that are affected by crashing, and uses them to calculate the crash limit.It is efficient, but it does not make start and end times readily available, and it is also directly based on the project network diagram.The other and most common approach is the use of the smallest free float selected from all the noncritical activities as the crash limit.A serious drawback of this approach is that it uses all the noncritical activities to determine the crash limit.Some of these noncritical activities are not affected by the crashing, and as a result may give very small values.The technique proposed in this paper is efficient, it selects only those activities that are affected by crashing, and it uses them to calculate the crash limit.Both activity start and end times are also made readily available.Suppose activity i A Suppose activity i A is critical: then it is denoted by an asterisk, as follows: The earliest end times are updated as shown in Table 3.

Activity Predecessor
Accurate duration estimate  3 http://sajie.journals.ac.zaAssume the crash limit to be .cl The duration i d for the critical activity i A is reduced by cl units, and the necessary recalculations made are shown in Table 4.

Activity
Predecessor Accurate duration estimate This duration is also equal to the project duration given by the second best critical path.
The second best critical path is the critical path that is obtained after ignoring activity When determining the new critical path, there is no need to start from the first node.Some of the activities are not affected by this change, and so they need not be used in the computations.

Earliest end times
The earliest end times are generated as shown in Table 8.From Table 6 the critical activity , 9 A selected for crashing, is reduced by cl , and recalculations are done in terms of cl as presented in Table 9.

Activity
Predecessor Duration (in days) The project duration ) ( P cl T , which is in terms of cl , is given by   The new project duration

A
best critical activities and new project duration are determined by ignoring activity 9 , as presented in Table10 . http://sajie.journals.ac.za

Table 7
is obtained by updating the latest end times.