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Previously Optimization Probability Review Inventory Models Markov Decision Processes Queues
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Friday Finish simulation Review Post –Sample problems for final –Case to discuss on Monday –Office hour schedule
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Agenda Simulation
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Simulation (Ch 15) Interested in quantity X (it is random) Run simulation to get realizations of X: –X 1, X 2, X 3, …, X n Evaluate output: –look at averageE[X] ≈ AVERAGE(X 1,…,X n ) –standard deviation [X] ≈ STDEV(X 1,…,X n ) –distribution of realizations
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Agenda Confidence intervals –for output evaluation Generating realizations
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Random Numbers ORMM Random Variables add-in –Add RV (to define random variable) –RV_sim(name,seed) or RV_simV(name) RiskSim add-in from book (p562) –functions randnormal, randuniform, …
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Ex. Yield Management (15.7) How many plane tickets to sell? –2 types: full fare and discount –120 seats on plane –Discount tickets sold first Full FareDiscount Fare DemandN(50,20 2 )N(100,30 2 ) Contribution (per seated passenger) $400$150 P(no-show)15%5% Fee for re-booking$0$75 Cost of overbooking$125
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Yield Management 1.Decide ticket availability –q Discount tickets –t Total tickets 2.Demand for Discount tickets –# Reservations –Tickets left 3.Demand for Full-fare tickets –# Reservations 4.# No shows on day of flight: 5.Calculate: –# Overbooked, # Passengers, Profits/Fees
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Stochastic Optimization Approach 1: 1.Pick q, t 2.Estimate E[Profit(q,t)] 3.Go to step 1
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Approach 2 1.Generate n scenarios 2.Calculate Profit(x) for each –x are the decision variables 3.Use Excel to optimize –maximize average Profit(x) –average over all scenarios
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Asset Allocation Example R i = random return of asset class i x i = % allocation to asset class i –decision variable total return = ∑ i R i x i max P(total return > 3%)
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