Scheduling when resources are limited
An activity with no float will have no flexibility in scheduling these activity. In the table above, we
observe that the activity (1-2) and (2-5) have no float, this means that there is no flexibility in
scheduling these activity. The earliest start time and the latest start time is also the same and also
the earliest finish time is same as latest finish time. For non critical activities, however, some float is
available and this provide flexibility in scheduling them. The choice available in this respect is
bounded by two schedules: the early start schedule and the late start schedule.
The Bounding schedule: The early start schedule and the late start schedule- The early start
schedule refer to the schedule in which all activity start as early as possible. In this schedule :
(i)
(ii)
(iii)
All events occur at at their earliest because all activity start at their earliest starting time
and finish at their earliest finishing time;
There may be time lags between the completion of certain and the occurrence of events
which these activities lead to.
All activities emanating from an event begin at the same time.
The early start schedule suggests a cautious attitude towards the project and a desire minimize the
possibility of delay. It provides a greater measure of protection against uncertainties and adverse
circumstances. Such a schedule, however, calls for an earlier application of resources.
The late start schedule refers to the schedule arrived at when all activities are started as late as
possible.In this schedule:
i.
ii.
iii.
All events occur at their latest because all activities start attheir latest starting time.
Some activities may start after a time lag subsequent to the occurrence of previous events.
All activities leading to an event are completed at the same time.
The late start schedule reflects a desire to commit resources late- as late as possible. However, such a
schedule provides no elbow room in the wake of adverse developments. Any unanticipated delay
results in increased project duration.
These two types of schedules(early start and late start schedules )are shown in figure below:
Here the project schedules are shown as graph with horizontal time scale.
Choice of Schedule in view of resource constraints:
In our earlier network diagram, we have considered a project which is technically feasible, which
does not violate the logical relationship among activities –can be adopted. For generating various
schedules, early start schedule, late start schedule, or any other schedule lying between the two
bounds, information was required
regarding only network logic and
activity duration.
The above type of scheduling assume
that adequate resources are available,
so that each activity can be started
anywhere between earliest starting
time or late starting time. In real life
however, there are many restrictions,
manpower may not be adequate, or
not got in time, budgets may be
restricted. Under such restrictions,
various schedules may have to be
considered to be find which schedule is
most appropriate under these conditions. Here are two examples under restrictions of resources.
Ex-1: Schedule to match availability of manpower: Here in the network diagram the duration is
shown above the arrow and the manpower is shown below the arrow. Considering the resource
limitation as 12 manpower.
The early start schedule of this project is shown as a graph on the horizontal time scale.
Looking at the manpower requirement for early start schedule we find that the manpower
requirement (20 for first day, 14 for second day, 15 for 3rd day, 5 for4th day and 5 for the fifth day) is
calculated as:
1st day (a, b, c): activity (1-2) 10 manpower + activity (1-3_ 2 manpower + activity (1-5) 8 manpower
= 20 manpower
2nd day(d,b,c): activity (1-2) 10 manpower + activity (2-5) 4 manpower = 10+4= 14 manpower
3rd day (d,e,f): activity (2-5) 4 manpower + activity (3-5) 6 manpower) + activity (3-4) 5 manpower
=15 manpower
4th day(f): activity( 3-4) 5 manpower
5th day(f): activity (3-4) 5 manpower
Looking at the manpower constraint this schedule is unacceptable. So we consider shifting of
activities. Even shifting the activities, with project duration fixed to 5 only, shifting of activity don’t
help in completing the project with
the constraint of manpower.
So, with the same constraint of
manpower, let us assume that we
have freedom of extending the
project by one day. Now we see that the schedule shown below become feasible.
Ex-2: Schedule to match the release of fund:
Table below shows the cost estimates of various activities.
Activity
1-2
1-3
2-4
3-4
2-5
4-5
Duration in Month
13
12
2
8
15
2
Cost per month
200,000
500,000
1,000,000
250,000
100,000
750,000
Total
Cost
2,600,000
6,000,000
2,000,000
2,000,000
1,500,000
1,500,000
15,600,000
The funds were released in the following manner:
Rs. 6,900,000 in 1st year
6,800,000 in 2nd year
1,900,000 in 3rd year
It has also been stipulated that the unspent amount would lapse and hence cannot be carried
forward.
Before developing a project schedule, a preliminary question may be asked: Is it possible to extend
prima facie to schedule this project beyond 28 months, which is the minimum time required given
the network logic and activity duration?
To answer this question let us look at the funds requirement for the early start schedule and the late
start schedule
Late Start Schedule
In both the figures the activities are represented by bars; the length of bar corresponds to the
duration of the activity in month in the figures.
The monthly fund requirement is shown above the bars for each activity assuming that the
expenditure is uniformly spread over its duration. The requirement of the project expenditure
month wise and cumulative is also shown in the figures.
Let us now look at the commulative funds release pattern for the above project. This lies between
the early start schedule requirement and late start schedule requirement. OS prima facie it suggests
that a feasible schedule without extending the project duration can be developed. Let us proceed
further and consider scheduling year by year. The activities that begin in year 1 according to the
early start schedule are (1-2) and (1-3). If both these activities are are commenced as early as
possible, the fund requirement for year 1 would be 8.4 million. Since the amount exceeds 6.9
million, the amount to be released in year 1, the expenditure in year 1 has to be reduced by 1.5
million. For this we consider the shifting the activities to subsequent period. Looking at activities (12) and (1-3) we find that activity (1-2) is on the critical path, so there is no flexibility available with
respect to it. Activity (1-3) can however be shifted as it is not on the critical path. Since activity (1-3)
requires 0.5 million per month, it has to be shifted by three months so that the amount spent in
year 1 is equal to the amount released in year 1. Since there is no free float of six months for
activity (1-3), we shift it by 3 months.
Now going to year 2. The effect of shifting activity(1-3) by three months are as follows:
i.
ii.
iii.
The funds requirement for year 2 on account of activity (1-3) increases by 1.5 million over
and above what it is for early strat schedule.
The earliest starting time for activity (3-4) moves to 15 months from 12 months and the
earliest finishing time moves to 23 months from 20 months. Since this shift occurs within
year2, there is no change in funds requirement on account of activity (3-4)
The earliest starting time for activity (4-5)moves to 23 months from 20 months and the
earliest finishing time for activity (4-5) moves to 25 months from 23 months. This decreases
the fund requirement by 0.75 million . The net effect, therefore, is to increase funds
requirement by 0.75 million over and above what it is for the earliest starting schedule.
Hence the total requirement becomes 6.8 million +0.75 million = 7.55 million. However, the
fund budgeted for year2 are only 6.8 million. So we consider the possibility of shifting some
activites to year 3. We find that by shifting activity (4-5) to year 3 the expenditure in year 2
can be reduced to 6.8 million, the budget of the year. As a result of this shifting, the
expenditure for year 3 (first four months of year 3) equals the budgeted funds release for
year 3. The final schedule is shown below:
Problems of Real Life Projects:
In real life projects, there are hundred of activities with several constrains. The problem of
scheduling in such cases tend to become very complex. For solving such complex problems the
techniques of linear programming may be used. Linear programming can be informationally intensive
and computationally intensive. If linear programming is not suitable then some heuristics programming
may be used. A heuristic is a rule of thumb like “schedule critical activities first” or schedule the
activities which has the largest independent float in the end.
A heuristic program consist of a collection of such heuristics. In recent years, many heuristic
programmes have been developed- they are formulated usually as computer programs. These programs
may be broadly divided into two types:
I.
II.
Resource leveling programme
resource allocation programmes
A resource leveling programme seek to level resource requirement, given a constraint on project
duration.
A resource allocation programme tries to find the shortest project schedule, given fixed resource
availabilities.