The Sunshine Bottling Company bottles soft drinks that it distributes to retail outlets from nine warehouses in the Michigan area. A single bottling plant is located in Flint, Michigan. The product is shipped from the plant to the nine warehouses in full truckload quantities. The typical plant-to-warehouse movement is to transport a trailer of palletized soft drink to the warehouse, drop off the loaded trailer, and bring a trailer of empty pallets back to the plant. The unloading and hitching of the trailer at the warehouse takes 15 minutes. Since the routes are traveled frequently, travel times, unloading times, and break times are known with a great deal of certainty. The number of trips needed to meet demand and the route times for a typical week are as follows:

It is desirable to schedule trucks to leave the plant at or after 4:00 A.M. and to return no later than 11:00 P.M. the same day. Unloading can take place only when the warehouse is open, which is from 6:30 A.M. until 11:00 P.M.
By sequencing the routes to maximize truck utilization, determine the minimum number of trucks that is needed to serve all the routes. The company was using 10 trucks.

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Warehouse Distance, Number of Driving Unloading Break/Lunch Total Route Location Miles Weekly Trips Time, hr Time, hr. Time, r.Time, hr Flint Alpena Saginaw Lansing Mt. Pleasant W.Branch Pontiac Traverse City Petoskey 1.00 9.00 2.00 3.25 .50 5.00 2.50 9.00 10.00 0.25 0.25 0.25 0.25 0.25 0.25 1.25 10.50 1.25 80 118 185 210 0.25 0.75 0.75 3.75 5.50 376 0.25 0.25 1.25 1.50 10.50 11.75 Round-trip time