E3, Ch 13: Linear Optimization

Question 1

optimization

Answer 1

process of selecting values of decision variables that minimize or maximize a quantity

Question 2

using optimization in Transportation (airlines)

Answer 2

maximizing profit according to different seat prices and customer demand, aka yield management

Question 3

using optimization in Manufacturing

Answer 3

max. profit by assigning diff. products to diff. factories

Question 4

using optimization in the Energy Industry

Answer 4

max. profits by mixing outputs from coal/nuclear/oil/etc. w/ diff. prices and matching it to demand for electricity

Question 5

linear programming is a “____ ____” application where inputs and outputs can be explained, and the process of input → output _______ be easily explained

Answer 5

black box
cannot

Question 6

building Iinear optimization model process (4)

Answer 6

1. Identify decision variables – unknown values model seeks to determine
2. Identify objective function – quantity we seek to minimize/maximize
3. Identify appropriate constraints
4. Write objective function and constraints as mathematical expressions

Question 7

“Cannot exceed” →
‘At least’ →
“Must contain exactly’ →

Answer 7

less than or equal to
greater than or equal to
equal to

Question 8

constraint function

Answer 8

left-hand side of the constraint/equation

Question 9

a LP has 2 basic properties:

Answer 9

1. Objective function and constraints are linear functions of the decision variables, meaning each function is simply a sum of terms with each constant multiplied by a decision variable
2. All variables are continuous, assuming any real value but typically nonnegative

Question 10

implementing LP on a spreadsheet (3)

Answer 10

1. Put objective function, constraints, and right-hand values in a logical format
2. Define a set of cells for the values of the decision variables
3. Define separate cells for objective function and each constraint

Question 11

SUMPRODUCT

Answer 11

can compute a pairwise sum of products; simplifies the model building process when many variables are involved

Question 12

use SUMPRODUCT:
B9B14+C9C14 →

Answer 12

=SUMPRODUCT(B9:C9, B14:C14)

Question 13

Some common functions can cause difficulty when solving LPs using Solver as they are discontinuous/nonsmooth. Some of these include…

Answer 13

IF
MAX, MIN
INT
ROUND, COUNT
VLOOKUP

Question 14

feasible solution

Answer 14

any solution satisfying all constraints, all feasible solutions are in the Feasible Region

Question 15

feasible region

Answer 15

can be drawn on a coordinate plane; the nonnegativity constraints are the max of each of the variables (refer to slide 44)

Question 16

optimal solution

Answer 16

best of the feasible solutions

alternative/multiple optimal solutions are a coincidence

Question 17

Solver

Answer 17

free add-in to Excel for optimization problems
Data → Analysis → Solver, use Solver Parameters dialog to define objective, variables, constraints

Question 18

Premium Solver

Answer 18

part of Analytic Solver Platform with better functionality, accuracy, reporting, etc.

Question 19

Solver Answer Report provides info about the optimal solution including (3)

Answer 19

• original and final values of objective functions and decision variables
• constraints
• other stats

Question 20

binding constraint

Answer 20

cell value is equal to right-hand side of constraint

Question 21

Status Column

Answer 21

tells whether each constraint is binding or not

Question 22

slack

Answer 22

diff. b/w left and right hand sides of constraints

Question 23

corner points

Answer 23

points at which constraint lines intersect along feasible region. This is where an optimal solution will occur

Question 24

Solver uses a mathematical algorithm called the _______ _______, which characterizes feasible solutions algebraically, moves systematically from one corner point to another to improve the objective function until an optimal solution is found

Answer 24

Simplex Method

Question 25

Solver assigns names to.. (3)

Answer 25

target cells
changing cells
constraint function cells

Question 26

Names are formed by…

Answer 26

concatenating first cell w/ text, to the left of the cell, and above the cell

Question 27

unbounded solution

Answer 27

objective can be in/decreased without bound – missing a constraint

Question 28

infeasibility

Answer 28

no solution exists – you but in a bad constraint

Question 29

solver sensitivity report

Answer 29

allows us to understand the impact of changes in decision variables, constraints, etc.

Question 30

interpreting sensitivity information:
final value
objective coefficient
allowable in/decrease

Answer 30

optimal values of objective function

original values of objective function

ranges for which objective coefficients can vary without changing optimal values

Question 31

reduced cost

Answer 31

amount an objective function coefficient needs to improve before a variable can have a positive optimal solution

Question 32

Nothing can be truly __________, even if the price is 0 _________ will always be a constraint (duck duck go, firefox)

Answer 32

unbounded
demand

Question 33

shadow price

Answer 33

how much the optimal objective function value will change per unit increase in a constraint’s right-hand side value

Question 34

whenever a constraint has positive slack, the shadow price is

Answer 34

zero