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DiscreteEventSimulation 4xgs

DiscreteEventSimulation 4xgs - Two Useful Modeling...

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Discrete Event Simulation Peter L. Jackson Professor School of O.R. and I.E. 2/14/2011 Industrial Data and Systems Analysis 1 Two Useful Modeling Approaches Functional Modeling Behavioral Modeling Initialize Arrival Start OvenIsEmpty InterarrivalTime CookiesInQueue Finish OvenCycleTime 2/14/2011 Industrial Data and Systems Analysis 2 Key Lessons (Preview) Discrete event simulation is a highly Discrete event simulation is a highly flexible method of describing the behavior of a system Basic simulation services can be implemented in MS Excel, but require user coding in VBA Th t t f i l ti d l The structure of a simulation model can be described with an event graph B ildi i d l i Building, running, and analyzing a simulation model is a structured process 2/14/2011 Industrial Data and Systems Analysis 3 Overview • Motivation: The Cookie Problem Motivation: The Cookie Problem A Model of Behavior: Discrete Event A Model of Behavior: Discrete Event Simulation A Graphical Language Programming a Simulation in MS Excel 2/14/2011 Industrial Data and Systems Analysis 4

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Before You Buy a Simulation P k Package See how you would use it to model See how you would use it to model the following situation: An oven takes 13.5 minutes to bake cookies. The oven can h ld t t t f ki Th b f t i th hold up to two trays of cookies. The number of trays in the oven does not affect baking time. The trays can be of different types of cookies but you cannot open the door while the cookies are baking. That is, you can put trays into the oven only after the current oven cycle has ended. Trays of chocolate chip cookies arrive every t c minutes. Trays of peanut butter cookies arrive every t p minutes. What is the average number of trays of peanut butter What is the average number of trays of peanut butter cookies waiting to be cooked, assuming t c is uniformly distributed over [9,18] and t p is uniformly distributed over [12,16]? 2/14/2011 Industrial Data and Systems Analysis 5 The Cookie Problem Trays of c.c. Oven cycle is arrive every 13.5 minutes on average 13.5 minutes but cannot be interrupted Maximum throughput is 2 trays every 13 5 Queues of trays can build up due trays every 13.5 minutes can build up due to randomness of arrivals Trays of p.b. arrive every 14 minutes on Oven capacity is two trays (can be of mixed type) 2/14/2011 Industrial Data and Systems Analysis 6 average Questions Maximum throughput is 2 trays/13.5 min. What will be the average throughput ? Easy, determined by average arrival rate If th i d h t ill b th If there is no randomness, what will be the maximum number of trays in queue? 2/14/2011 Industrial Data and Systems Analysis 7 Questions (continued) If arrivals are random (uniformly distributed), what will be the average number of trays in queue?
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