Network Diagrams, Start and Finish Times and Crashing

Wild Cat Petroleum Company has struck oil on their latest drilling project in central Africa. You are responsible for developing a minimum cost schedule to bring the first wellhead into production. Unfortunately, local workers are not available due to the continuing unrest in the surrounding territory (a lingering civil war). Therefore, you must rely on crews of expatriate workers to complete your project. The project should not generate any interference from the warring parties because all sides to the conflict favor the development of this oil field. However, your insurance carrier has insisted that you hire a security detail (at a cost of $1000 per day) while your workers are on site.

The project can commence with three simultaneous activities:

A concrete slab must be poured at the wellhead location. The project supervisor estimates that this task would take 11 days with a standard crew. However, it can be reduced to as few as 9 days by renting a small bulldozer at a cost of $300 per day.

The pumping unit must be ordered. This requires that the specifications for the unit be drafted and faxed to the supplier. This normally takes one day and cannot be substantially reduced.

The field-clearing crew can begin cutting a swath through the jungle for the pipeline and electrical service. The swath must run a distance of four miles from the wellhead to the loading station. Judging from the distance and density of the forest, this task should take 8 days to complete. However, with a little luck and by hiring a special stump-pulling crew for $600 per day, it can be reduced to as little as 6 days.

After pouring the slab, it will take two days to set and cure the cement. Because weather conditions do not vary during this time of year in central Africa, it is unlikely that this activity will be delayed (or shortened).

The supplier can deliver the pumping unit to the wellhead location from their warehouse in South Africa within 9 days of receiving the specifications. The supplier can make special delivery arrangements to shorten delivery time, but it will cost $250 for each day the order is expedited. The minimum delivery time is 5 days.

Once the slab cures and the pumping unit delivered, a crew must mount the unit on the slab. This normally takes 5 days. However, you can save one day if the crew rents a special crane to hoist the unit into place. The crane costs $165 per day to rent.

When the swath is cut through the jungle, an electric crew can run the electrical service from the loading station to the well location. At the same time, another crew can run the pipeline. The electric line should take 6 days to complete. Running the pipeline should take 11 days. Either of these tasks (electric line or pipeline) may be shortened by one day for an additional expense of $450 (if both are shortened it costs $900).

When the pipeline is complete, it must be connected to the installed pumping unit. This requires one day and cannot be reduced.

After the pipeline is connected to the pumping unit, the electrical service must be connected. This takes one day and cannot be reduced.

1. Identify and state the duration for each activity. Label each activity with letters.
In a table format state the following: label (letter), activity description, predecessor, normal duration, minimum duration, and crash cost/day.

NOTE: some of the activities may not be crashed. Hence, their normal duration and minimum duration may be the same.

2. Prepare the network diagram of the project schedule using Excel

3. Before any crashing takes place, state all paths through the network and their associated duration. State the normal completion time (before crashing) of the project.

4. Before any crashing takes place, calculate the earliest start time (ES) , earliest finish time (EF), latest start time (LS), latest finish time (LF) for each activity.

5. Before any crashing takes place, determine the slack time for each path.

6. Crash the network to determine the minimum cost completion time for the project. (Note: use the $1000 per day cost). Report the activities that should be expedited to crash the project. Also give the order in which the activities should be crashed and the associated cost for each activity.

Please note the costs associated with crashing in this system are the crash cost per day. The crash costs do not have to be paid over the entire length of the activity, but rather only for the days that are being crashed.