Shale Oil Company Case Study: Project Management

Shale Oil Company Case Study: Project Management
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Introduction
Project management is very important in management of a number of complex projects in organization. This case study is about a crude oil manufacturing company that has a number of operating units. These units are essential in pumping crude oil and change it into several hydrocarbon products. The units run 24 hours a day for 7 days a week. However, due to maintenance purposes it needs to be shut down at some point in time for cleaning. However, the use of visual representation workflow such as Gantt charts and PERT charts are vital in determining the tasks that are to be done. This discussion identifies the time and probability in preventive maintenance case study of Shale Oil Company. For this paper, I shall rely on the below PERT network structure for Shale Oil Company.
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Figure  SEQ Figure \* ARABIC 1: PERT Network of Shale Oil Co. & DUI5
Determine the expected shutdown time and the probability that the shutdown can be completed 1 week earlier
Expected shutdown time
The use of PERT tool serves an important role in project management by managers. The PERT chart contains information related to subprojects and the estimated time of completion. Each of the subprojects is given an estimate time that is particularly based on the probability distributions of the expected time of completion from the start time to finish time. The expected shutdown is calculated by the following equation:
Expected time = (Optimistic Time + 4 x Most likely Time + Pessimistic Time) / 6.
The time estimates for the various activities through the network for the project on preventive maintenance of DU5 are as shown below:

Preventive Maintenance of DU5
Time Estimates (in Days)
EVENTS BEFORE SHUTDOWN TO Tm tp
1–2 Circulate wash water throughout unit 1 2 2.5
2–3 Install blinds 1.5 2 2.5
3–4 Open and clean vessels and columns 2 3 4
3–5 Open and clean heat exchangers; remove tube bundles 1 2 3
3–6 Open and clean furnaces 1 2 4
3–7 Open and clean mechanical equipment 2 2.5 3
3–8 Inspect instrumentation 2 4 5
4–9 Inspect vessels and columns 1 2 3
5–10 Inspect heat-exchanger shells 1 1.5 2
5–11 Inspect tube bundles 1 1.5 2
6–12 Inspect furnaces 2 2.5 3
6–17 Retube furnaces 15 20 30
7–13 Inspect mechanical equipment 1 1.5 2
7–18 Install new pump mechanical seals 3 5 8
8–19 Repair instrumentation 3 8 15
9–14 Repair vessels and columns 14 21 28
10–16 Repair heat-exchanger shells 1 5 10
11–15 Repair tube bundles; retube 2 5 10
12–17 Repair furnaces 5 10 20
13–18 Repair mechanical equipment 10 15 25
14–20 Test and close vessels and columns 4 5 8
15–16 Install tube bundles into heat-exchanger shells 1 2 3
16–20 Test and close heat exchangers 1 2 2.5
17–20 Test and close furnaces 1 2 3
18–20 Test and close mechanical equipment 1 2 3
19–20 Test instrumentation 2 4 6
20–21 Pull blinds 1.5 2 2.5
21–22 Purge all equipment with steam 1 3 5
22–23 Start up unit 3 5 10
Total time estimates 86 112.5 225

Tb is the optimistic time, Tm is the most likely time and Tp is the pessimistic time.
To calculate the expected time before shutdown, we look at the network above, and since there are six standard deviations between them, it follows that:
te = (to + 4tm + tp)/6
However, there exist a number of different paths starting from event 1 to event 23. It is true that different paths have different estimates for maintenance a process which if not completed in time will result to shutdown. In my illustration, there are 11 paths as listed in the table below. Each of the paths from the starting point at 1 to the end point at 23 has different expected shutdown time. The shutdown time will rely on the path that is taken.

Activity in critical path t0tmtpteVariance(d2)1-2122.51.91670.06252-31.522.520.02773-423430.113-51232-3-61242.17-3-722.532.5-3-82453.8-4-912320.1115-1011.521.5-5-1111.521.5-6-1222.532.5-6-1715203020.8-7-1311.521.5-7-183585.16-8-1938157-9-14142128215.44410-1615105.16-11-151015255.33-12-1745810.83-13-1810152515.83-14-201235.330.444415-16122.52-16-201231.916-17-201232-18-202462-19-201354-20-211.522.520.027721-2213530.44422-2335105.51.3611

Generally, the distribution of all the activities above in Preventive Maintenance of DU5 is unknown and need to be estimated. Thus the process of estimating the values follows from the duration times of each activity, optimistic, most likely and pessimistic. These are vital in the next section where the z-score is estimated from the normally distributed activity time.
Expected time= (to + 4tm + tp)/6

Variance = [( tp - to)/6]2
The summation of variance (d2) = 8.0344
However, the duration of the project= 1-2-3-4-9-14-20-21-22-23
Duration of the project (Shutdown time) = 45.7479 days
P (shutdown time can be completed one week earlier)
45.7497-7 = 38.7897
P (t < = 38.7897 - 45.7497/ 2.83450)
=0.00676
The probability that the shutdown can be completed 1 week earlier
=0.00676
2. What are the probabilities that Shale finishes the maintenance project 1, 2, 3, 4, 5, or 6 days earlier?
Estimating the probability of project completion
Activity in critical path t0tmtpteVariance(d2)1-2122.51.91670.06252-31.522.520.02773-423430.113-51232-3-61242.17-3-722.532.5-3-82453.8-4-912320.1115-1011.521.5-5-1111.521.5-6-1222.532.5-6-1715203020.8-7-1311.521.5-7-183585.16-8-1938157-9-14142128215.44410-1615105.16-11-151015255.33-12-1745810.83-13-1810152515.83-14-201235.330.444415-16122.52-16-201231.916-17-201232-18-202462-19-201354-20-211.522.520.027721-2213530.44422-23351...