Calculate the yearly cost of waiting time, Operation Research

The Omega company, Brisbane, produces potato chips, corn, cheese twists, and popcorn. These products are made in Brisbane and then shipped to company warehouses and distribution centers located throughout the Midwest.

In the past the company has leased trucks or used common carriers to ship its product, but in 1990 a decision was made to purchase a fleet of trucks and to avoid the use of other more costly means of transportation.

The trucks are kept in a company garage on Langdon Street, and it is there that dispatcher Harold Bascom assigns drivers, loads and destinations. It is not unusual for a truck to be sent to several destinations, dropping off a part of its load at each stop. In these situations Mr. Bascom determines which combination of destinations will be assigned, totals are orders placed by each distribution centre, and loads the trucks with these quantities.  Seldom does this quantity completely fill a truck.  On average, trucks are 80 percent filled. Occasionally, they have been only half filled.

The product is shipped in large cardboard drum containers.  At each stop along the route the driver must first unload the requested number of drums and then load as many empty drums as possible onto the truck.  When the truck returns to Langdon Street, the empty drums are unloaded and stored for reuse.

Recently the shipping department has been unable to keep up with production and warehouse demand. Trucks are in operation for three shifts daily during the 250-day work year, but more trucks are still needed. Consequently Mr. Porter, manager of inventory and transportation, has requested that the company purchase three new trucks. Since business has been unusually strong. Mr. Porter expects quick approval for the vehicles.

Upon receiving this request, Mr Bond, the company president, requested that the accounting department prepare an analysis of the problem and submit a final recommendation with 2 weeks.

To gain some insight into the problem accounting representatives spent several hours observing the shipping department as its Langdon Street location. It became apparent that trucks often had long waits before they were unloaded and loaded. One of the accounting staff asked Mr. Bascom if this was normal. Mr. Bascom replied that on some occasions all the trucks were out and his shippers were idle.  On other occasions, he continued, there were several trucks waiting to be unloaded and loaded. "If we only had trucks during our idle period," he said, "we could increase our shipments."

Upon closer analysis it was determined that the average time between truck arrivals was 4 hours and the average time to unload and load a truck was 3 hours.  The company maintained one shipping platform, and it was in operation 24 hours a day.

But adding more trucks was not the only solution.  The accounting department suspected that the construction of a new shipping platform might be far more effective and economical.  In face, if the trucks were purchased and no new platform was built, the trucks could only add to the bottleneck at the unloading and loading platform.  And waiting time was indeed expensive. They estimated the opportunity cost of waiting at a minimum of $10 per hour. This cost included the lost shipments and subsequent lost sales of Pyramid Products due to stockouts on warehouse shelves.

The accounting staff learned from the building and grounds department that it would be possible to construct another shipping platform identical to the present one. The cost would be $25,000 and would be depreciated on a straight-line basis over 10 years. If the new platform were open three shifts each day, the labour costs would total $20,000 per year, including fringe benefits.


i)      What is the average number of trucks waiting at any time? What assumptions were necessary to make this computation?

ii)     What is the yearly cost of this waiting time?

iii)    If a second loading-unloading platform is built, what will be the average number of trucks waiting at any time?

iv)    What is the yearly cost of waiting for two loading-unloading platforms?

v)     Compare the costs of the two alternatives. Which one would you recommend?

vi)    What other factors could affect the arrival and service time of the trucks and thereby speed the process?

Posted Date: 3/1/2013 5:57:57 AM | Location : United States

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