Mine Management Questions and Answers Series (1)

Question 1.

Figure 1. Represents all activities, starting from activity 1 to 12. Event 1 is the beginning and event 12 is the end of my task assigned (thick line represent critical path)

1.      Describe PERT/CPM network analysis, applications, advantages and disadvantages.

Project evaluation and review technique (PERT) is a project – scheduling  tool applied to ensure sequence of different activities eventually lead to a desired completion of a project in consideration. PERT techniques in network analysis is a method of minimizing trouble spots, production bottlenecks, delays associated costs, interruptions and reduce mis-allocations.

Advantages:

PERT is a planning and control technique that uses a network for scheduling and budgeting (time & finance) to accomplish a task.

Disadvantage:

The disadvantage in PERT network is that, an event cannot be accomplished until and unless all activities in a network have been completed. So in a PERT network, we are actually estimating the total project time. The path of the longest duration is called critical path and activities lying this path are critical activities. A delay in any of the activities in the critical path will result in delay, extra costs and resources, redesign, and re – routing of the entire project.

12.      What is the difference between an event an activity in a PERT/CPM network?

Activity is the task allocated to be accomplished towards the total completion oif the project on time. It is represented by an arrow. The tail of the arrow represents the beginning of the activity and its head represents its completion. Whereas,

Event is designation the beginning of one activity and ending of another activity. So the starting and ending points of activities are events.

23.      Describe how you would calculate earliest event (T_E) and latest event (T_L) times and define what they represent.

The earliest event time (T_E) is the earliest time at which the activities originating from an event can be started.

The latest event time (T_L) is the latest event time which activities terminating an event can be competed on scheduled.

So the earliest event time is calculated by adding earliest event time at the tail of activity arrow with the duration or earliest time of activity. Note that when there is more than one activity flowing into an event; choose the maximum value of T_Ej calculated for that event.

The latest event time is calculated by subtracting the T_L of the very last event by the duration/time for activity ij. Subsequently doing the same for rest of the events. When there are more than activities lead to an event, calculate and get the minimum value of T_L

14.      Determine the critical path of the exploration project schedule.

The critical path starts from event   1 to event 3 then to event 5 to 6, from event 6 to event 11 and ends at event 12. At these events the T_E value is equal to T_L at each event given above.

15.      What is a float and slack in PERT/CPM network and state why is having these advantageous in project scheduling?

  Float in PERT network is time available in the non – critical path that could be reallocated towards an activity in the critical path. It is advantageous having float because it represents underutilized time or underutilization of resources. Not only that but also float represents flexibility of an activity and disappearance of float signifies a loss of flexibility for non – critical path activities.

Slack in PERT network is the difference between the earliest and latest times of any event.  Slack is important as it help us to see whether it is a critical or non – critical path by analyzing the T_E and T_L values.

16.      Calculate head slack, tail slack, float, free float and independent float for one non – critical path activity (ij).

Tail slack Ts = T_si = T_Li - T_Ei = 15– 11 = 4 weeks (event 7)

Head slack HS = Tj = T_Lj - T_Ej = 29 – 18 = 11 weeks (event 7)

Float F = (TLj -  TEi) – teij = (29 – 11) – 7 =  11 weeks

Free float FF = (TEj – Tei)  - teij  =  (18 – 11) – 7 = 0

Independent float IF = FF – TS = 0 – 4 = - 4 weeks

Note: a negative independent float is taken as zero for all practical purposes.

17.      Briefly commend on your understandings of three extremes of expected times : (a) optimistic, (b) pessimistic  and (c) most likely time (m) as represented by normal probability distribution curves.

·         Optimistic – is the distribution that satisfy most circumstances at shortest times if execution goes very well.

·         Pessimistic – is    the distribution that satisfy most circumstances at longest times if everything goes bad.

·         Most likely - is the distribution that satisfies most circumstances at normal times or at middle grounds if execution is normal. In other words, it is the mean  of the distribution. 

18.      Complete the following table by calculating the variance (σ²).

Predecessor	Successor	a	M	b	te	σ2
1	2	3	2.5	5	3	0.11
1*	3	5	4.5	13	6	1.78
2	4	7	2	9	4	0.11
2	6	10	10.75	7	10	0.25
4	6	8	1	12	4	0.44
3*	5	5	6.5	11	7	1.00
5*	6	6	7.5	6	7	0.00
3	7	9	2.75	10	5	0.03
7	8	7	2	9	4	0.11
8	9	4	5	12	6	1.78
6*	11	8	12.5	14	12	1.00
9	11	2	5.75	17	7	6.25
7	10	11	5.75	8	7	0.25
10	12	3	14.25	12	12	2.25
11*	12	6	8	6	9	0.00

*critical path.

29.      Calculate Z (number of standard divisions), find corresponding probability value in Z table a conclusion on the probability of implementing your schedule as planned.

Sum of critical path σ² is = σ² _(1-3) + σ²_(3-5) + σ²_(5-6) + σ²_(6-11) + σ²_(11-12)

                                                 1.78  +   1        +  0       +  1         +  0

                                     σ²    = 3.78

                                         σ = (3.78)^0.5 = 1.9442

Assume X = 44 weeks, and µ = 41 weeks

Z = X - µ = (44 – 41)/1.9442 = 1.5431

         σ

Using the table (given), probability of success is: Z value of 1.5431 corresponds to probability of 0.4382 from the table. This means there is 0.9382 (0.4382+0.5) probability or 94% chance of completing the project in 45 weeks or less.

Basing on the probability analysis, I am too optimistic that the project will be completed in 45 weeks or less.

110.      Calculate the total float for the non – critical path.

Total float F_T = (T_Lj – T_Ei) – tij = (29 – 11) – 7 = 11 weeks (from event 7 to event 10)

Note that here, only one total float for only one non – critical path.