he Houston Port Authority has engaged you as a consultÂ¬ant to advise it on possible changes in the handling of wheat exports. At present, a crew of dockworkers using conventional belt conveyors unloads hopper cars containÂ¬ing wheat into cargo ships bound overseas. The crew is known to take an average of 30 minutes to unload a car. The crew is paid a total wage of $50 per hour. Hopper car arrivals have averaged 12 per 8-hour shift. The railroad asÂ¬sesses a demurrage charge from time of arrival to release at a rate of $20 per hour on rolling stock not in service. ParÂ¬tially unloaded cars from one shift are first in line for the folÂ¬lowing shift.
A chi-square “goodness-of-fit” analysis of arrival rates for the past months indicates a Poisson distribution. Data on unloading times for this period may be assumed to follow a negative exponential distribution. Because of excessive demurrage charges, adding anÂ¬other work crew has been proposed. A visit to the work area indicates that both crews will be unable to work together on the same car because of congestion; however, two cars may be unloaded simultaneously with one crew per car. During your deliberations, the industrial engineering staff reports that a pneumatic handling system has become available. This system can transfer wheat from cars to cargo ships at a constant rate of three cars per hour, 24 hours per day, with the assistance of a skilled operator earning $20 per hour. Such a system would cost $400,000 installed. The Port Authority uses a 10 percent discount rate for capital imÂ¬provement projects. The port is in operation 24 hours per day, 365 days per year. For this analysis, assume a 10-year planning horizon, and prepare a recommendation for the Port Authority.
In your report, evaluate each of the three alternatives (continue operating with one crew; add an additional work crew; or purchase a pneumatic handling system). Determine the cost of service for each alternative and describe the model you would use in each instance.