Exam 1

Question 1

Optimistic method

Answer 1

pick the best number to represent an option and choose the the best option based on those numbers

Question 2

Pessimistic method

Answer 2

pick the worst number to represent an option and choose the best option based on those numbers

Question 3

Harwitz method

Answer 3

alpha x (best) + (1 - alpha) x worst
use equation for each option and chose option with best outcome based on the equation

Question 4

Minimax Regret

Answer 4

create a table based on original table given, find the best option per situation not option assign a value of 0, calculate difference between value of best situation and the other situations, choose the option that presents the least amount of regret

Question 5

Equal likelyhood

Answer 5

Find the average of the outcomes for each option. Choose the option with the highest average.

Question 6

Decision Tree

Answer 6

composed of two nodes: Decision nodes and Chance nodes. When evaluating always start at the end and work back ward. Final answer should be the option not the expected value

Question 7

Decision node

Answer 7

choices of options

Question 8

Chance node

Answer 8

probability

Question 9

Expected value of Perfect Information

Answer 9

EV(w/ PI) - EV(w/o PI)

• Note: the quality of decision with PI should be better or equal to never worse than decision w/o PI

Question 10

Discrete problem

Answer 10

The choice of locations are pre determined

Question 11

Continuous problem

Answer 11

Infinite possible locations to choose from. 2 options Minisum and minimax

Question 12

Minisum discrete problems

Answer 12

Minimize total travel time. Sum of demand x distance for each option. Must check each quantity of possibilities. Ex copier example, have to check 1 copier vs 2 copiers vs 3 copiers…etc. The number of options for each number of copiers is:
x! / (y! * (x - y)!)

Question 13

Minimax discrete problems

Answer 13

Minimize the maximum travel time. This is more related to service like fire stations

Question 14

straight line distance equation

Answer 14

sqrt((x1 - x)^2 + (y1 - y)^2)

Question 15

rectilinear distance equation

Answer 15

x1 - x | + | y1 - y |

Question 16

Minisum straight line distance

Answer 16

Objective Function: Min ∑ wi * di^2
di = sqrt((x1 - x)^2 + (y1 - y)^2)
x* = ( ∑ xi * wi ) / ( ∑ wi )
y* = ( ∑ yi * wi ) / ( ∑ wi )
best location: (x*, y*)

Question 17

Minisum rectilinear distance

Answer 17

Objective Function: Min ∑ wi * di
di = | x1 - x | + | y1 - y |
• find 1/2 ∑ wi
• create a number line for x and y coordinate sorting from left to right in increasing order
• assign weights below each location
• choose x or y coordinate where to sum of weights to the left and right of the chosen coordinate are less than 1/2 ∑ wi
best location: (x, y)

Question 18

Minimax rectilinear distance (algorithm)

Answer 18

• Note: no demand information is needed
• Create table with xi, yi, xi + yi, and -xi + yi columns
• find the following
C1 = min (xi + yi)
C2 = max (xi + yi)
C3 = min (-xi + yi)