9. The Hindustan Oil Company contains several operating units that comprise its Moradabad and Karnal manufacturing complexes. These units process the crude oil that is pumped through, and transform it into a multitude of hydrocarbon products. The units run 24 hours a day, seven days a week and must be shut down for maintenance for a predetermined schedule. One such unit is Distillation Unit No. 2, or DU2. Pre- vious studies and past records have shown that DU2 can operate only 3 years without major equipment breakdowns and excessive loss of efficiency. Therefore, DU2 is shut down every 3 years for cleaning, inspection, and repairs. DU2 is the only distillation unit for crude oil in the Moradabad complex and its shutdown severely af- fects all other operating units. Some of the production can be compensated by the company's refineries in other locations, but the output must be processed before the shutdown and stored. Without proper planning, a nationwide shortage of its products could occur. The timing of DU2's shutdown is critical and the length of time, the unit is under maintenance, must be kept to a minimum to limit production loss. The company uses PERT as a planning and controlling tool to minimize shutdown time. The first phase of maintenance is to open and clean the equipment. Inspectors examine the damage, if any. Once damages are determined, the needed repairs can be carried out. Repair times depend on what damage the inspection finds out. Based on previous inspection records, some maintenance work is known ahead of time. Thorough cleaning of the equipment is also necessary to improve the unit's operating ef- ficiency. Table 9.10 lists the many maintenance activities and their estimated completion times.

(a) Determine the expected shutdown time and the probability that repairs can be completed one week earlier.

(b) What are the probabilities that the company finishes the maintenance project one, two, three, four, five or six days earlier?

(c) Hindustan Oil is considering increasing the budget to shorten the shutdown. How do you suggest the company should proceed?

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Table 9.10 Preventive Maintenance of DU2 ACTIVITIES Optimistic 1-2 Circulate wash water throughout unit 1 TIME ESTIMATES (IN DAYS) Most Likely 2 Pessimistic 2.5