Is there a unique model for each probelm?

no, the same real-worlds can be often modeled in different but equivalent ways

What is often better than writting x(i,j)>=0 as non-negativity condition

x(i,j) ∈Z+ only if only whole number are acceptable

What is the main difference between Minimum Cost Flow Problem and Transpoertation Problem

Transportation problem is special case of minimum cost flow with only supply and demand nodes MCFP also has transshipment nodes

What is notation for Integers in Mixed Integer Programming Problems

yi ∈ Z xi ∈ R (is for continuous variables)

What is general objective of Mixed Integer Problems

zMIP = max ∑c(i)*x(i) + ∑h(j)*y(j)

What are four basic types of number

N (natural numbers) = {1,2,..} Z (Integers) = {..-1,0,1...} Q (rational numbers) = {2/9 , 3/9, ..} "can be express as ratio of integers R (real numbers) = {e, pi}

What is the notation in The Knapsack Problem (4)

j ... Experiment that is or isnt taken w(j) .. weight of experiment j p(j) .. profit of experiment j C ... capacity of the knapsack

What are the decision variables in The Knapsack Problem

x(j) ∈ { 1, if j is taken 0, otherwise }

What are constrains in The Knapsack Problem (3)

x(j) ∈ {0;1} j ∈ {1; .. n of experiments} ∑ w(j) * x(j) <= C

What is objective function in The Knapsack Problem

z(x) = S⊆{j;..n} ∑p(j) z* = max z(x)

What is our goal in The Knapsack Problem

to get into our "bag" item combination with the highest profit possible

What is our goal in Bin Packing Problem

to get all the requiered item into as few bins as possible

How many bins do we have in a problem

number of bins = number of items

What are decision variables in Bin Packing Problem (2)

1,(do we use bin j) yj = {1 if used , 0 otherwise } 2, (do we pack items i into bin j > xij = { 1 if packed, 0 otherwise}

What are 2 constrains in Bin Packing Problem

1, Capacity constrains ∑w(i)*x(i,j) <= C(y(j)) capacity of bin j is not exeeded 2, Assigment constrains ∑ x(i,j) = 1 each item is exactly once given into a bin

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PDS #3

Question	Answer
Is there a unique model for each probelm?	no, the same real-worlds can be often modeled in different but equivalent ways
What is the sum of each column in incidence matrix	it is 0
What is often better than writting x(i,j)>=0 as non-negativity condition	x(i,j) ∈Z+ only if only whole number are acceptable
What is the main difference between Minimum Cost Flow Problem and Transpoertation Problem	Transportation problem is special case of minimum cost flow with only supply and demand nodes MCFP also has transshipment nodes
What is notation for Integers in Mixed Integer Programming Problems	yi ∈ Z xi ∈ R (is for continuous variables)
What is general objective of Mixed Integer Problems	zMIP = max ∑c(i)x(i) + ∑h(j)y(j)
What are four basic types of number	N (natural numbers) = {1,2,..} Z (Integers) = {..-1,0,1...} Q (rational numbers) = {2/9 , 3/9, ..} "can be express as ratio of integers R (real numbers) = {e, pi}
What is the notation in The Knapsack Problem (4)	j ... Experiment that is or isnt taken w(j) .. weight of experiment j p(j) .. profit of experiment j C ... capacity of the knapsack
What are the decision variables in The Knapsack Problem	x(j) ∈ { 1, if j is taken 0, otherwise }
What are constrains in The Knapsack Problem (3)	x(j) ∈ {0;1} j ∈ {1; .. n of experiments} ∑ w(j) * x(j) <= C
What is objective function in The Knapsack Problem	z(x) = S⊆{j;..n} ∑p(j) z* = max z(x)
What is our goal in The Knapsack Problem	to get into our "bag" item combination with the highest profit possible
What is our goal in Bin Packing Problem	to get all the requiered item into as few bins as possible
How many bins do we have in a problem	number of bins = number of items
What are decision variables in Bin Packing Problem (2)	1,(do we use bin j) yj = {1 if used , 0 otherwise } 2, (do we pack items i into bin j > xij = { 1 if packed, 0 otherwise}
What are 2 constrains in Bin Packing Problem	1, Capacity constrains ∑w(i)*x(i,j) <= C(y(j)) capacity of bin j is not exeeded 2, Assigment constrains ∑ x(i,j) = 1 each item is exactly once given into a bin
What is objective function in Bin Packing Problem	min ∑y(j)

Created by: semester1.IBWL

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