Concept Check 1 solutions.pdf - University of Chicago Booth School of Business Ozan Candogan ASSIGNMENT Concept Check#1 KEY 1[5(Capacity analysis

# Concept Check 1 solutions.pdf - University of Chicago Booth...

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University of Chicago Booth School of Business Ozan Candogan ASSIGNMENT Concept Check #1 - KEY 1. [5] (Capacity analysis.) Question Capacity (jobs/minute) CT (minutes) a. 1/5 5 b. 1/5 8 c. 1/3 6 d. 1/3 + 1/5 = 8/15 3(1/3)/(8/15) + 5(1/5)/(8/15) = 15/4* e. 1/5 5 Note: In part d, we assume that flow is routed according to the relative capacity along an arc. Thus, (1/3)/(8/15) of the total flow is served by the “top” server (which operations at a rate of one job every 3 minutes) and (1/5)/(8/15) of the total flow is served by the “bottom” server. 2.[5](Little’s Law.) The number of cars that can be served in a 90 minute period (32) is estimated incorrectly. This is because the throughput rate is incorrectly estimated to be 1/167.9 cars per second (which when multiplying by 5400 yields 32 cars in 90 minutes. The error is evident from Little’s Law where we know that INV = λCT; that is, λ= INV/CT. Having a throughput rate λof 32 cars per minute incorrectly assumes that INV = 1. From our experience, we know that more than a single car can be kept “in inventory” between the speakers and pick-up windows during rush periods.