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ITOM 6/10: Exam Notes

On Chance Notes

  • Consecutive chance notes are technically possible but rare.

  • Multiple chance notes are often integrated into one.

ITOM Courses Recommendation

  • ITOM 6214 (Spring Month A) by John Sample:

    • Advanced optimization and simulation models.

    • Solves more challenging problems.

  • ITOM 6220 by Tom Pan:

    • Data analytics.

  • ITOM 6219 (Web and Social Media Analytics) by Instructor:

    • Analytics course.

    • Six weeks long.

    • Week 1: AI application development.

      • Basics of large language models.

      • Web development.

      • Prompt engineering.

    • Week 2: Google Analytics and campaign.

      • Python basics.

    • Week 3: Social media analytics.

      • Data collection from Twitter.

      • Topic models generation from textual data.

      • Linear regression with topic data as input.

    • Week 4: Social network analysis.

      • Representation of unstructured data by networks.

      • Centrality measures for nodes.

      • Linear regression with network measures.

    • Week 5: A/B testing.

      • Implementation of A/B testing.

      • Examples of implementations.

    • Week 6: Search engine optimization (SEO).

      • SEO principles.

      • Implementation of SEO on apps.

    • Example Projects:

      • Wine recommendation system.

      • AI investor advisor.

      • Foodie finder.

    • Workload:

      • 3 hours a week for homework and learning.

      • coding template based learning.

      • Students modify provided templates; they don't need to start from scratch.

Final Exam Preparation

  • Exam Structure: Four questions, each worth 25 points.

    • Sensitivity analysis is part of problem one (5 points).

  • Resources Available:

    • All slides in PDF.

    • All Excel files.

    • Notes in Word.

    • Homework solutions.

    • Practice exam and solutions.

    • Lecture and office hour recordings.

    • Video recordings for fixed cost and business threshold problems.

  • Exam Format: Paper submission with Excel and other files submitted via Canvas. Two submission boxes: one for simulation problems, one for linear programming problems.

Linear Programming

  • Three models: allocation, covering, and blending.

  • Allocation Model:

    • Time constraints: derived from production rate (e.g., production rate 150 per hour implies \frac{1}{150} hours per unit).

  • Covering Problem:

    • Demand consideration: must produce equal to or greater than the demand (left-hand side \geq right-hand side when a contract is signed).

    • Maximum homes to be sold: can produce less if no contract exists.

  • Yield Rate Consideration:

    • When logs turning into the woods, use the yield rate to represent the wood produce

  • Blending Model:

    • Nonlinear constraints transformed into linear ones.

Sensitivity Analysis

  • Review Farmer Moore's problem.

Integer Linear Programming

  • Capital Budgeting Problem Example:

    • Division A of Mar Corporation has \$160,000,000 for capital projects.

    • Five projects proposed:

      • P1: New information systems.

      • P2: License new technology.

      • P3: Recycling facility.

      • P4: Automated machine center.

      • P5: Move receiving department.

    • Data (in millions of dollars):

      • Project NPV Expenditure

      • 1 10 48

      • 2 17 96

      • 3 16 80

      • 4 8 32

      • 5 14 84

    • Maximize total NPV subject to budget limit.

    • Decision Variables: Binary variables y_i (1 if project i is selected, 0 otherwise).

    • Objective Function: Maximize 10y1 + 17y2 + 16y3 + 8y4 + 14y_5

    • Budget Constraint: 48y1 + 96y2 + 80y3 + 32y4 + 84y_5 \leq 160

*Application of Binary Variables for Logical Conditions:
* At least m projects selected: \sum{i=1}^{5} yi \geq m
* At most n projects selected: \sum{i=1}^{5} yi \leq n
* Exactly k projects selected: \sum{i=1}^{5} yi = k
* Mutually exclusive projects (e.g., P1 and P2): y1 + y2 \leq 1
* Contingency (P5 requires P3): y3 \geq y5
* Rearranged: y3 - y5 \geq 0

  • Scheduling problem

    • The most hard part is to come up with the decision variables
      *The decision variables was

    • the number of people who work on Sunday
      *the number of people who work on Monday

    • the number of people who work on Tuesday
      *and so on

Fixed Cost Problem

  • Inequality: x \leq My (x is units to produce, y is decision to start production line, M is a large number).

  • Cost Function: f \cdot y + c \cdot x (f is fixed cost, c is variable cost).

Minimum Threshold Model

  • Two inequalities:

    • x - m\cdot y \geq 0

    • x - M \cdot y \leq 0

    • (m is minimum feasible value if x is nonzero, M is a sufficiently large number).

  • Need to consider both inequalities for every pair of decision variables x and y.

  • Avoid very large numbers for M.

Structured Decision Tree

  • Basics:

    • Time proceeds from left to right.

    • Branches leaving chance nodes represent states of nature (with probabilities).

    • Branches leaving decision nodes represent decision alternatives.

    • End of each limb: payoffs.

    • Decision strategy: a sequence of decisions based on chance outcomes.

  • Using Nested IF for Probability Mass Function
    *When Random variable between 0 and 22%, the number of the failure is 0
    *When Random variable between 22% and 76%, the number of the failure is 1
    *When Random variable between 76% and 99%, the number of the failure is 2
    *When Random variable between 99% and 100%, the number of the failure is 3

Monte Carlo Simulation

  • Minkl's Copy Example (Service Contract Options):

    • Rinkles copy has two service contract options for its xRock's photocopy machines

    • Option a, they pay 1,000 for each failure

    • Option two, they prepay \$800 for the failure with no refund
      *they pay \$500 for each additional failure

    • Contracts:

      • A: \$1,000 per failure.

      • B: \$800 prepay + \$500 per additional failure.

    • Relative Frequency of Failures:

      • Failures Frequency

      • 0 22%

      • 1 54%

      • 2 23%

      • 3 1%

  • Use inverse CDF to solve the function. Create the CDF manually, instead of leveraging a function
    The whole process is to construct the inverse CDF manually

  • Most Critical Part: Modeling the random variable (number of failures).

    • Need to use a nested IF, this one only requires you know it and understands the logic.

Airline Overbooking Problem Extensions (Week 5 Excel File):

  • Inverse Normal Distribution

    • Use random inverse normal distribution to recover the random variable that follows a normal distribution

    • add Max function that and allow your demand to be the maximum between the random variable following normal distribution and the zero.

  • Notes in Updated Excel File:
    Ticket revenue

  • Accounting practice: revenue will be recognized in the next flight, so use the number of filed Seats multiply \$400
    *If use of all the revenue: Use the number that shows multiply \$400
    Link Demand with the price alpha-B price epsilon
    *D the demand is equal to Alpha is a perimeter minus Beta, which is the perimeter that controls the sensitivity of price times price plus Epsilon

  • Epsilon:error term,which usually follows a normal distribution with mean zero and a certain standard deviation