 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 – – 180 min(X, C) max(X-C, 0)  result: Q * = 106  Excel Program, Java Program Excel 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) (= )

 7  System Reliability  p X = P(X is working)  p A = 0.95; p B = 0.9; p C = 0.9; p D = 0.8; p E = 0.9  independent status  find P(system is working) A B C D E

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

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

 10  Special Usage of Simulation - Estimation of   area of circle =  r 2  area of square = 4r 2  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  D n = delay time of the nth customer; D 1 = 0  S n = service time of the nth customer  T n = inter-arrival time between the nst and the (n+1)st customer  D n+1 = [D n + S n - T n ] +, where [  ] + = max( , 0)