In 1998, Samir Khaldoun, after receiving an MBA degree from a leading university in the United States, returned to Jeddah, Saudi Arabia, where his family has extensive business holdings. Samir’s first assignment was to stabilize and develop a newly formed, family-owned transport company--Abjar Transport.

An immediate problem facing Samir was the determination of the number of trucks needed to handle the forecasted freight volume. Heretofore, trucks were added to the fleet on an “as-needed” basis without comprehensive capacity planning. This approach created problems of driver recruitment, truck service and maintenance, and excessive demurrage (that is, port fees) because of delays at unloading docks and retention of cargo containers.

Samir forecasts that Abjar’s freight volume should average 160,000 tons per month with a standard deviation of 30,000 tons. Freight is unloaded on a uniform basis throughout the month. Based on past experience, the amount handled per month is assumed to be normally distributed, as seen in the following table:

Less Than (Tons)Probability

100,000 ........0.02

130,000 ........0.16

160,000 ........0.50

190,000 ........0.84

220,000 ........0.98

After extensive investigation, Samir concluded that the fleet should be standardized to 40-foot Mercedes 2624 2 3 4 tractor-trailer rigs, which are suitable for carrying two 20-foot containers, one 30-foot container, or one 40-foot container. Cargo capacity is approximately 60 tons per rig. Each tractor-trailer unit is estimated to cost 240,000 riyals. Moreover, they must meet Saudi Arabian specifications—double cooling fans, oversized radiators, and special high-temperature tires. Historical evidence suggests that these Mercedes rigs will operate 96% of the time.

Approximately 25% of the freight handled by these tractor-trailer rigs is containerized in container lengths of 20, 30, and 40 feet. (The balance of the freight—75%—is not containerized.) The 20-foot containers hold approximately 20 tons of cargo, the 30-foot containers hold 45 tons, and the 40-foot containers hold 60 tons of freight. Approximately 60% of the containerized freight is shipped in 40-foot units, 20% is shipped in 30-foot units, and 20% is transported in 20-foot units.

Abjar Transport picks up freight at the dock and delivers it directly to customers, or warehouses it for later delivery. Based on his study of truck routing and scheduling patterns, Samir concluded that each rig should pick up freight at the dock three times each day.

How many tractor-trailer rigs should make up the Abjar Transport fleet?