Session 10 Waiting Line Models II

Session 10 Waiting Line Models II - OSCM356 Operations...

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1 OSCM356 Operations Management Session 10 Waiting Line Models II (Queuing Analysis II) Fuqiang Zhang Olin Business School Washington University in St. Louis Spring 2008 Session Outline Applications of queuing models Analyzing queuing models using Excel (M/M/s) Shcips Inc. Goler City Police Department Wilson Foods Call Center Ways to improve the efficiency of queuing systems Managing waiting lines at theme parks OSCM356, Spring 08, Prof. Zhang Session 10 Slide 2
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2 Multiple-Server Model M/M/s With the multiple-server model, customers form a single line and choose one of s servers when one is available. Customers arrive according to a Poisson process There are s identical servers. The service distribution for each is exponential. Mean service time is 1/ m The service rate ( s m exceeds the arrival rate ( ). OSCM356, Spring 08, Prof. Zhang Session 10 Slide 3 Example: Schips Inc. Problem description: Schips, Inc., a large department store, has recently been experiencing some problems in its receiving and shipping department because of the substantial growth in the store’s sales volume. Currently, the store’s truck dock has only one dock crew who handles one truck at a time. The manager is considering adding more dock crews so that multiple trucks would be loaded and/or unloaded simultaneously. OSCM356, Spring 08, Prof. Zhang Session 10 Slide 4
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3 Example: Schips Inc. The manager has collected the following data: Truck arrivals are not scheduled and occur in an unpredictable fashion at an average of 24 per 8 hour day. When working continuously, each dock crew can service an average of 4 trucks per hour. Suppose that the Schips trucks are operated at a cost of $25 per hour and that a dock crew is paid a total of $30 per hour. OSCM356, Spring 08, Prof. Zhang Session 10 Slide 5 Truck Arrivals Truck dock Loading/ Unloading Queue Question: how many dock crews should be hired to minimize the total cost for Schips? Economic Analysis of Service Level Decision OSCM356, Spring 08, Prof. Zhang Session 10 Slide 6 Total cost Service cost Waiting cost Cost Level of service
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The Economics of Schips Inc. Assume an M/M/s queuing system Data: Arrival rate ( ) = 24/8 = 3 per hour Service rate ( m ) = 4 per hour C1 = truck cost per hour ($25) C2 = crew cost per hour ($30) Let s = number of dock crews (decision variable) L = average number of trucks in the system Cost analysis Total hourly cost for trucks waiting = C1 L Total hourly cost for the dock crews = C2 s Total cost per hour = C1 L + C2 s OSCM356, Spring 08, Prof. Zhang
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Session 10 Waiting Line Models II - OSCM356 Operations...

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