final exam Flashcards
write down Xij set variables format. transportation
Xij = number of units sent from “i” to destribution center “J”
2 things to always remember on objective function for transportation
- put the costs of producing and the the costs of shipping for each variable. dont forget putting the cost!
- always put min or max Z
always say these 3 things for constraints in transportation
- Subject to:
- verbalize constraints
3, non negativity, binary or integer constraint
supply and demand. when one is bigger, another one is less and when they are equal to each other
When demand is greater : set supply constraints to =
when supply is greater: set demand constraints to =
when supply and demand are the same: demand and supply constraints set to =
LP relaxation BIP formulation
is when you relax the binary and integer constraints to obtain the relaxed (optimal) solution
a relax solution for BIP formulation will never be better solution than the actual binary or integer solution. true or false
false, relaxed solutions will be always optimal. making the the normal solution for BIP feasible
how to activate the variables for fixed costs on BIP problems
supply/capacity constraints 400 is example:
x1-400y1<= 0 or
x2<=400y2
xn<=400yn
mutually exclusive constraint where we cannot have both: x1 and x3
x1 + x3 <= 1
x1 and x3 muttually exclusive constraint where we need 1 but not more
x1 + x3 = 1
if project 4 is selected then project 2 must also be selected
x4<= x2
or
x2>=x4
project 1 must also be if 5 and vice versa.
x1=x5
if project 1 is selected, then projects 2 and 3 must also be selected
2X1<= x2 + x3
if project 1 is selected, then projects 2 or 3 must also be selected
X1<= x2 + x3
project 1 cannot be selected if both projects 2 and 3 are selected
x1 + x2 + x3 <=2
if projects 2 and 3 are selected, then project 1 must also be selected
x2 + x3 <= X1 + 1
optimistic approach for decision analysis
maximax approach. best of best
conservative approach for decision analysis
maximin approach. best of worst
minimize regret approach
minimax. minimizes regret
how to calculate regret table
best pay off of state of nature - pay off chosen
steps for minimax regret approach
calculate regrets for each cell. get maximum regret per row. choose the one with least regret
decision making approach called laplace
equally likely approach
decisi9on making approach called hurwicz
realism approach
equally likely approach
maximizes the average payoff per row
approach called realism hurwicz. Decision analysis
finds a compromise between the best and worst pay off
steps for realism approach
- multiply the best pay off from the row by alpha
- (1-alpha)(worst payoff of the row)
- add both values
- choose the one with highest value
expected value approach decision analysis
a weighted probability of the payoff*probability in a row. then choose the highest one
expected value of perfect information
maximum payment for additional information
formula for EVPI
EVPI = EVwPI - EVwoPI
how to calculate EVwPI
- choose the best payoff from each state of nature.
- multiply those values by the probability
- add all values
EOL approach
expected opportunity loss
EOL approach steps
- start with regret table
2.multiply by probability across SoN - choose with the min regret average
P(x | y). what is x and y for decision analysis 2
P(result of report | state of nature)
draw tables for posterior probabilities
prior. conditional. joint ….. marginal. posterior
how do you get marginal probabilities
add joint probabilities per table
how do you get joint probabilities
prior * conditional
how do you get posterior probabilities
joint probabilty / marginal probability
decision tree with sample information steps
start with decision node.
dont get sample information, or get sample information
- if getting, then results of sample. positive or negative or so
- paste original tree for each result
- change probabilities for posterior probabilities
- solve nodes
- solve decision
node for cpm showing ES EF LS LF
ES. # EF
LS. AT. LF
earliest start formula
earliest time = MAX EF of all immediate predecessors
earliest finish formula
Earliest finish = earliest start + activity time
latest finish formula
Min LS of all immediate following
latest start formula
=latest finish - activity time
or
=Lf - AT
slack in terms of CPM
LS - ES
or
LF - EF
how do you know if an activity is on the critical path
slack = 0
In project scheduling. When calculating Total variance, which variances are included in total variance
the variances of the activities that lie on the critical path
formula for expected time ET or TE (optimistic, most likely and pessimistic)
(O+4ML+P)/6
variance formula CPM ba
Variance = [ (p - o) / 6 ] ^2
formula for standard deviation
= Square root of total Variance
how to get the variance of an activity using standard deviation
standard deviation ^2
what is the definition of Z-score on project management/scheduling
how many standard deviations the project deadline is away from the mean (expected time of completion)
100% rule
what if you change more than one parameter at the time. will that change the solution? it will not change the optimal solution if the result of this formula is under 1: sum of : change in coefficient/allowable increase/decrease
