Download Test 1 - Summer 2008 | Stochastic Manufacturing and Service Systems | ISYE 3232 and more Exams Systems Engineering in PDF only on Docsity! ISyE 3232 A Stochastic Manufacturing and Service Systems Summer 2008 Sample Test I J. Zhang Test 1 (June 9, 2008) Closed book, closed notes, no electronics. 1. (40 points) A company operates a small call center that is staffed by a single server. When an incoming call finds the server busy, the call is placed into the waiting queue. Assume that there is no limit on the number of waiting calls. (The company has a large number of phone lines available.) It has been observed that, during a normal business day, the interarrival times of phone calls to the center are iid having exponential distribution with mean 3 minutes. Also, the call durations X (namely, the processing times) have the following distribution (in minutes): x 1 2 3 P(X = x) 1/4 1/2 1/4. (a) (8 points) What is the long-run fraction of time that the server is busy? (b) (10 points) What is the the long-run average waiting time of each call in the queue, excluding the processing time? (c) (10 points) What is the average total number of calls in the entire call centers, that is those in queue plus those in service? (d) (6 points) What is the throughput of the center? (e) (6 points) If the interarrival times have mean 1 minute, what is the throughput of the center? 2. (20 points) A company decides to make a production run of part PA360 to be used within the next production period. The demand D for PA360 within one production period is assumed to follow the following distribution d 1 2 3 4 P(D = d) 1/8 1/2 1/4 1/8 . If a shortage of PA360 occurs within the year, it costs $1000 to acquire an item from a third party provider. Each unused item by the end of the period costs $100 to store. The cost of producing each item is $300. Assume for the moment that there is no fixed cost in starting the production run. (a) What is the optimal number of items to produce for the production run? (b) What is the expected total cost if the optimal number of items is produced? 1
