Question 1:

Billy of Billy's Warehouse in Maine contracts with motor carriers for deliveries however, they assess him with stiff penalties if their trucks have to wait to be unloaded. He thought about investing significantly in technology and equipment to improve productivity. The following facts apply to his situation:

1) Trucks arrive randomly at the average rate of five per hour, with a deviation of plus or minus one.
2) A team of 2 warehouse workers can unload trucks at the rate of 6 per hour, or one every 10 minutes.
3) A team of 4 warehouse workers can unload trucks at the rate of 8 per hour, or one every 7.5 minutes
4) A team of 6 warehouse workers can unload trucks at the rate of 10 per hour, or one every 6 minutes
5) A team of 8 warehouse works can unload trucks at the rate of 12 per hour, or one every 5 minutes.
6) Because of its contract with the carriers, the warehouse must pay the motor carrier that own idle trucks at the rate of $100 per hour while the trucks stand idle, waiting to be unloaded.

7) The number of teams or servers is always 1, although the number varies in terms of costs and output.

Part A: Using the queue theory, for each of the four work team sizes, calculate the expected number of trucks waiting in the queue to be unloaded and calculate the expected time in the queue- that is the expected time a truck has to wait in line to be unloaded. (Lay out all costs in tabular form)

Part B: Using the number of trucks in queue and the expected time a truck has to wait, along with the rate per hour that he must pay for idle time, determine how much Billy is losing with idle trucks with each of the work teams. (Lay out all costs in tabular form)

Part C: Using what you have learned in the text concerning warehouse productivity, how can Billy improve his warehousing productivity without significant investment in technology or equipment?

Question 2

Extreme Hats wanted to bid on a huge festive event of which 6,200 large party hats would be needed. The Style A hats were cylinders that were 11 inches high and 12 inches in diameter and were packed into boxes that were 12 by 12 by 12 inches. The packages cost 80 cents each and weighed 1 pound each. The hats cost $5.00 each to manufacture. They weighed 9 pounds each and 10 pounds packaged. They would be shipped to the Port of Baltimore. The land rate to Baltimore was $2000 per 40 foot container, without regard to weight, although the weight of the load could not exceed 36,000 pounds per loaded container because of highway weight restrictions. The interior dimensions of the intermodal container were 8 feet wide by 8.5 feet high by 40 feet long. Ocean rates from Baltimore to the overseas port were $25 per ton (2,000 pounds), except that the ocean conference used a measurement ton that indicated that for bulky loads every 40 cubic feet would equal 1 ton for rate-making purposes. (That is, a shipment weighing, say 130 pounds and occupying 80 cubic feet would cost as though it weighed 4,000 pounds.) Insurance costs were 5 percent of the value of the shipment ready to be loaded aboard ship in Baltimore. Extreme Hats decided to custom build and came up with an alternative cone-shaped hat design. Style B hats cost $10 per hat to manufacture and could be shipped nested in packages of 8. The package dimensions were 12 by 12 by 48 inches, and when holding 8 hats a package weighed 75 pounds. Each package cost $5, and this included padding between the hats.

Part A: Extreme Hats is debating whether to use private transportation to get the intermodal containers to the port for this order. Based on information from the text, discuss advantages and disadvantages to private transportation.

Part B: How many of style A hats can be loaded in an intermodal container? How many style B hats can be loaded in an intermodal container?

Part C: What are the total costs of delivering Style A hats to the port of importation? What are the total costs of delivery for Style B hats to the port of importation?