MGT 239, SPRING 2009

Posted in TEACHING by longgao on 04/01/2009

MGT 239, SIMULATION FOR BUSINESS, CLASS SPRING 2009

In simulation we believe if something talks like a duck, walks like a duck, it is a duck.

COURSE SCHEDULE

WEEK I
1. Syllabus and the tentative schedule
2. Introduction of simulation: system, analytical and simulation model
3. A review of probability models:
  1. Key concepts: random variable, probability, frequency, histogram, distribution, and CDF $F(x)$ ;
  2. distributions: uniform, Bernoulli, Poisson, normal, exponential, triangle, Erlang, Gamma, etc.
  3. stochastic processes: Poisson, renewal, nonstationary arrival processes
WEEK II
1. Monte Carlo Simulation:
  1. Select inputs: uncertain parameters and probability distributions;
  2. Specify outputs measurements;
  3. Run a simulation for replications N (sample size);
  4. Analyze outputs, draw insights and make recommendations;
2. random variates generation:
  1. building block $U[0,1]$ (RAND( ))
  2. the inverse transform method $F^{-1}(U)$
  3. continuous (e.g, NORMSINV(RAND()))
  4. discrete cases (e.g., VLOOKUP( ) )
3. EXCEL modeling:
  sampling and simulation: iid $\{X_i\}_{i=1}^N$ , $\mathbb{P}(X=x) \approx \frac{\sum_i \mathbb{I}(X_i=x)}{N}$ , $\mathbb{E}[X] \approx \frac{\sum_i X_i}{N}$ ;
  HW 2.13: random sample size (N), indicator function $\mathbb{I}_A$ and binary variable (IF(A,1,0));
  For Excel: hit F1 for help, or click menu ‘Help’ for help, or stop by my office…
WEEK III
1. Inventory management and the newsvendor model:
  1. mathematical formulation: let $(x)^+=\max(x,0)$
    $\min_{Q\ge 0} TC(Q)= \mathbb{E}[TC(Q,D)]$ , $TC(Q,D)= C_o (Q-D)^+ + C_u (D-Q)^+$
  2. analytical solution $Q^*$ satisfies $F(Q^*)=\frac{C_u}{C_o+C_u}$
  3. insights: tradeoff between shortage and overage, matching supply and demand
2. Spreadsheet simulation optimization: MGT239_NW.XLS on iLearn
3. Next Monday, April 13: watch @RISK tutorial, prepare financial models (chapter 3)
4. HW2 due on April 15; reading: chapter 3, 10, and push your project.
WEEK IV
1. Risk management and financial hedging:
  1. risk: adverse consequence and prob; variance; downside risk;
  2. derivatives: forward & future (obligation), options (right), e.g., American, European, Asian;
  3. geometric random walk stock price model: $S_t = S_0 e^{(\mu - \sigma^2/ 2) t + \sigma \sqrt{t} Z}$
  4. pricing European call and put options: $\mathbb{E}[R_0]$ , $R_0= (S_t - K)^+ e^{-r t}$ , $R_0= (K-S_t)^+ e^{-r t}$
  5. hedging a stock with put options;
2. Exercise 1: simulate stock price processes; distribution; confidence interval; downside risk;
3. Exercise 2: evaluate investment strategies: stock v.s. stock with put option hedging;
4. HW3 due on Wed (iLearn, at 9am); proposal due on Wed (iLearn at 9 am);
5. Midterm I, May 6, week 6; midterm II, May 27, week 9;
6. Project meeting: April 24, 4-6pm, 221 Anderson Hall
WEEK V
1. Dynamic simulations:
  1. key concepts: state variable $X_t$ , recursion dynamics $X_{t+1}= f(X_t)$ ;
  2. sample path $\{X_t: X_{t+1}=f(X_t), t=1, \dots, T\}$ ;
  3. nonstationary, fixed and variable time advance mechanisms, etc.
2. Exotic options:
  1. pricing Asian options over T periods: fair price $\mathbb{E}[R_0]$ , $S_{t+\Delta t} = S_0 e^{(\mu - \sigma^2/ 2) \Delta t + \sigma \sqrt{\Delta t} Z}$ , $S_{ave}=\sum_t S_t/T$ , $R_0= (S_{ave} - K)^+ e^{-r t}$ , $R_0= (K-S_{ave})^+ e^{-r t}$
3. Multi-period inventory management:
  1. $X_t=(S-D_{t-1})^+$ , $TC_t(S, D_t, X_t) = p(S-X_t)^+ + C_o(S-D_t)^+ + C_u (D_t -S)^+$ , $TC(S,D,X_1) = \sum_{t=1}^{T} TC_t(S,D_t,X_t)$ , $\min_{S\ge 0}\mathbb{E}[ TC(S,D,X_1) ]$
4. Exercise 3: pricing Asian put and call options;
5. Exercise 4: evaluate multi-period nonstationary inventory systems under base stock policy;
WEEK VI
1. Monday, May 4th:
  1. No lecture or office hours;
  2. Project meeting;
  3. Prepare midterm 1;
2. Tuesday, May 5th, Office hours for midterm I, 10-12pm
3. Wednesday, May 6th, Midterm I: open book/notes, bring a functional Excel, 9:40am to 11:30am;
  1. Solution: 1, 2, 3.
WEEK VII
1. Review midterm I
2. Service systems:
  1. service processes;
  2. customer integration and process strategies;
  3. techniques for improving service productivity;
3. Queueing theory:
  1. 3 main parts: arrival, waiting line, service;
  2. queueing system structures;
  3. operating characteristics, analytical models and Little’s Law:
    $\rho= \lambda/\mu$ , $W=1/(\mu - \lambda)$ , $W_q=\rho/(\mu-\lambda)$ , $L=\lambda\cdot W$ , $L_q=\lambda\cdot W_q$ ;
4. Discrete-Event simulation;
5. Exercise 5: simulate a bank lobby system with Arena;
WEEK VIII
1. Exercise 6: simulate a barbershop with cost parameters (Arena);
2. Auctions and bidding:
  1. 1st- and 2nd-price, sealed-bid auctions, Dutch and English auctions;
  2. Optimal bidding strategies for 1st(Ducth) and 2nd(English) price, sealed-bid auctions;
    $b^*(v)= v - \frac{\int_0^v P(s)ds}{P(v)}$ , $b^*(v)=v$ , $P(v) = F^{N-1}(v)$ , $v_i\sim F$ , $i=1,\dots, N$
  3. Revenue equivalence theorem: (i) allocation $y_i(v_i, v_{-i})$ is increasing in $v_i$ ; (ii) zero valuation has zero expected surplus, then
    $\mathbb{E} [\sum_{i=1}^N J(v_i) y_i(v_i, v_{-i})]$ , $J(v) = v - \frac{1-F(v)}{f(v)}$
3. Exercise 7: optimal bidding strategies and expected revenues;
  1. Solution;
4. Project interim report due on Wednesday;
5. HW6 due on Friday;
WEEK IX
1. Review;
2. Midterm II
  1. open book/notes;
  2. bring a functional PC with Arena and Excel;
  3. 9:40am to 11:40am;
WEEK X
1. Dress code for project final presentation
2. Monday, project final presentation schedule (submit slides on iLearn at 9am)
  1. An Application of Monte Carlo Simulation in Retirement Investment Planning, Haiying Chen, Wei Chen, Sunny Yang;
  2. Human Resource Budgeting Tool, Pei-Chen Hsiao, Chih-Yuan Chen;
  3. Modeling Notebook Service Center, Chieh-Yu Wei, Chia-Yen Kao, Hong-Tao Hsieh;
  4. TV Panel Plant Simulation, Chen-Yi Lee, Wan Wen Hung, and Yenming Lu;
  5. Simulated Fair Valuation of Credit Default Swap (CDS), Kai Chung, Sandy Chang, Claudia Lee;
3. Wednesday, project final presentation schedule (submit slides on iLearn at 9am)
  1. UPS Air Freight Traffic Simulation for Pacific Gateway Cargo Center, Kamarat Jermsirisakpong, Animat Adesanya;
  2. Valuation of MBA, Mung Fei Hung, Zhi Yang, Jingtao Ye;
  3. A Financial Model for an Apartment Building, Hao Troeung;
  4. Simulation for Optimal Capacity to Maximize Profits at JPR Shipping Corporation, Yang Tang, Zuotao Liu, Chih-Yuan Kang;
  5. Baseball Simulation, Tang Liu, Christopher Lossett;
  6. Bank of America Lobby System, Hui-Chung Huang, Phoebe Pahng, Hsiao-En Tsai;
4. Project final report due on Friday, June 5 (both hard copy and iLearn);

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MGT 239, SPRING 2009

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