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Outline

Outline. simulation exercises yield management project management system reliability integration estimation of  GI / G /1 queue. Yield Management. Airline AAA provides service from HK to Beijing no show for some passengers capacity wastage to improve observe the system

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Outline

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  1. Outline • simulation exercises • yield management • project management • system reliability • integration • estimation of  • GI/G/1 queue

  2. Yield Management • Airline AAA provides service from HK to Beijing • no show for some passengers • capacity wastage • to improve • observe the system • formulate a model (define the scope of the model; then the objective functions, variables, and constraints) • carry out simulation to determine optimal booking • implement the optimal decisions

  3. Yield Management • airline AAA ticket from HK to Beijing: $1,600 • capacity of the plane: 100 • fixed cost to fly the plane $40,000 • variable cost per passenger $180 • overbooked penalty incurred on airline AAA: $2,500 / passenger • from record, P(no-show) of a passenger = 0.05 • objective: maximize expected profit • decision: # of reservations for the plane

  4. Yield Management • C = capacity of plane • Q = # of reservations allowed • X = actual # of passengers appear • ~ Binomial (Q, 0.95) • V= net profit • = 1600X – 40000 – 180 min(X, C)- 2500 max(X-C, 0) • result: Q* = 106 • Excel Program, Java Program

  5. Project Management • 3 activities in a term project • A: data collection; B: programming; C :implementation • A and B can be done concurrently • C after the completion of A and B • X, Y and Z be the time (days) for A, B & C • distributions N(10, 2), N(15,3), and N(6,1) • independent • question: expected time to finish the project? P(taking more than 24 days for it)?

  6. Project Management • T = the project completion time • T = max(X, Y) + Z • generate samples (random variates) of T from those of X, Y and Z • estimate E(T) (= 21.09) and P(T > 24) (= 0.1735)

  7. D A B C E System Reliability • pX = P(Xis working) • pA= 0.95; pB= 0.9; pC= 0.9; pD= 0.8; pE= 0.9 • independent status • find P(system is working)

  8. Special Usage of Simulation - Integration • can we integrate by simulating? • for X ~ unif(0, 4),

  9. density of exp(): density of Erlang (n, ): Special Usage of Simulation - Integration • How about

  10. Special Usage of Simulation - Estimation of  • area of circle = r2 • area of square = 4r2 • area of circle/area of square = /4 • possible to estimate ? • a related question: how to generate a point whose location ~ uniformly in the circle?

  11. Simulation a GI/G/1 Queue by its Special Properties • Dn = delay time of the nth customer; D1 = 0 • Sn = service time of the nth customer • Tn = inter-arrival time between the nst and the (n+1)st customer • Dn+1 = [Dn + Sn - Tn]+, where []+ = max(, 0)

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