Announcements
1.
2.
3.
4.
5.
Midterm during lecture hours (12:30-1:50pm) on Thu, Mar 17
Review problems posted in compass2g
Topics will include everything covered until (including)
the Assignment Problem
No cheat sheets allowed during the midterm
Seating

Plan for today
If no entering variable, optimum
reached
If no leaving variable, unbounded.
Recap: Transportation Problem, Solution method: Stage 1
Basic Feasible Solution for the Transportation Problem
Stage 2: Iterate to optimal solution
Unbalanced

Topic for the week
Dynamic Programming
Example 2: Project Assistant Allocation
Example 3: Employment Scheduling
Announcement
Homeworks are due on
Tuesdays henceforth
(Continuous decisions and states)
Example 4: Reject Allowance
(Decision dependent pro

Plan for the day
Announcement
Submit your homework
Dynamic Programming
Example 3: Employment Scheduling
before this slide disappears
(Continuous decisions and states)
Example 4: Reject Allowance
(Decision dependent probabilistic state transitions)
Exa

Topic for the week
Dynamic Programming
Example 1: Stagecoach
Terminologies
Announcement
Homeworks are due on
Tuesdays henceforth
Example 2: Project Assistant Allocation
Example 3: Employment Scheduling
(Continuous decisions and states)
Example 4: Re

INTRODUCTION
What is Operations Research
Operations Research (OR)
scientific approach to decision making
seeks to determine how best to design and operate a system
under conditions requiring the allocation of scarce resources
Provides a set of algori

Plan for today: Simplex Method
Example
Limitations
Simplex Method in Algebraic Form
Simplex Method in Tabular Form
Recap
Simplex Method: overview
Initialization
transform the original LP into the augmented LP, determine basic and non-basic variables

Topic for this week: Duality
Recap
SHADOW PRICES
Recap
Example
Example (from first lecture)
Company makes two products: glass door sells for $3 per batch, window sells for $5 per batch.
Working hours needed and the total hours available are given below:
d

Plan for today
Assignment Problem, Hungarian Algorithm
Network Optimization Models
Terminologies
Minimum Spanning Tree Problem
Announcements
3.
Midterm during lecture hours (12:30-1:50pm) on Thu, Mar 17
Review problems posted in compass2g
Topics will

Announcements
1.
Submit your homework before the beginning of the lecture
before this slide disappears
2.
Midterm during lecture hours (12:30-1:50pm) on Thu, Mar 17
Review problems posted in compass2g
Topics will include everything covered until
3.
4.
R

Plan for today
Dual Optimal Solution from the Simplex Tableau
Dual Simplex Method
Example
Recap
SHADOW PRICES
Shadow price of a constraint is the rate of objective
increase when the constraint is relaxed/tightened
Recap
Example
Primal Dual Connection
P