exponential with an average service rate of 12 ship

Referencing Styles : APA Assignment Questions: 1. An integrated petroleum company is considering expansion of its one unloading facility at its Australian refinery. Due to random variations in weather, loading delays, and other factors, ships arriving at the refinery to unload crude oil arrive according to the exponential distribution with an average arrival rate of 8 ships per week. Service time is also exponential with an average service rate of 12 ships per week. (a) What is the average number of ships waiting to gain access to the single unloading facility? (b) What is the average time a ship must wait before beginning to deliver its cargo to the refinery? (c) What is the average total time (waiting plus actual delivery) that a ship spends at the refinery? 2. The company in Problem 1 has under consideration a second unloading berth that could be rented for ✩6,000 per week. The service time for this berth would also be exponential with the same service rate of 12 ships per week as the company’s own berth. The opportunity cost of making a ship wait to unload is ✩30,000 per week. (a) If the second berth is rented, what will be the average number of ships waiting? (b) What would be the average time a ship would wait? (c) Is the benefit (in dollars) of reduced waiting time worth the rental cost for the second berth? 3. An alternative way to improve unloading facilities is for the company of Problem 1 to modify the current operations to speed up the unloading process. Specifically, the new service time would still be exponential, but with a mean service rate of 15 ships per week. The incremental cost of the new operations would be ✩4,000 per week. (a) Compute the (new) average number of ships waiting. (b) Compute the (new) expected waiting time and total time for ships. (c) Is the benefit worth the incremental cost? 4. Crew Soccer Shoes Company is reconsidering its current inventory control system and distri- bution strategy for soccer shoes. The information regarding the shoes is as follows: ❼ Annual Demand = 1000 pairs/year ❼ Lead time = 1 weeks ❼ Order cost = ✩35/order

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