(Solved) : Assignment Solve Online Allocation Problem Seen Class Using Duality Problem Following M Re Q30657527 . . .
In this assignment, you will solve the online allocation problemthat you have seen in class by using duality. The problem is thefollowing:
· There are m resources, x1 , …, xm with fixedcapacities b1, …, bm
Demand requests arrive sequentially, noted j = 1…N, withrequirements ai, i=1…m and profit p
We want to make accept/reject decisions without knowing futuredemands
We have the historical data of N demands in the file“demand.csv”:
Part A:
In this question, you will formulate the problem as a linearprogram. To do so, you will transform the LP to standard form:
max cTx
Ax <= b
x >= 0
while cT represents the profit of accepting each demand, Arepresents the number of required resources, and b represents theupper bound limit for each resources.
You will take m=4, N=100, b0=125, b1=130, b2=118, b3=137 and usethe data in the file “data_online_allocation.csv” whichsimulates the demand for N=100. Return A as a matrix, b asa list, and c as a list.
Note: When you construct the matrix A (lists within list),the first 4 rows will correspond to the capacity constraints andthe following 100 rows will correspond to the upper bound of xi fori=1…100
Part B:
In this question, you will use the standard form that you haveset up in the previous question. Write the dual and solve it usingGurobi. As a reminder, the dual is:
min bTy
ATy >= c
y >= 0
Return the optimal objective value, and the optimal values ofthe variables in one list.
Note: The list of the optimal values of the variables shouldcontain the dual of the capacity constraints in the first 4position
Part C:
Use the shadow prices you fund in the previous questions tocreate a static policy to make the accept/reject decisions. Applythat policy to the products in the file “new_data.csv” and returnthe list of the products you reject (this list is called“reject_list”).
The list should be of the form: [2,7,38…] (i.e. it shouldcontain the index of the product, which goes from 1 to 100)
(Hint) Accept if:
Pj – sum(lambdai * aij , i=1..m) >= 0
where lambdai are the values youcalculated when solving the dual in question 2.
The demand forcast file is as follows:
a1,a2,a3,a4,p
5,1,3,1,3
4,2,3,2,16
3,1,2,1,8
0,1,2,0,9
3,2,3,3,16
4,1,2,3,13
2,0,1,1,5
3,1,3,3,8
4,3,0,2,9
3,1,1,1,5
2,1,1,2,3
1,3,2,1,6
0,1,2,0,3
2,2,2,1,6
6,1,0,2,11
6,2,2,2,4
2,3,2,2,12
0,2,2,2,13
4,1,3,2,3
1,1,1,2,11
5,1,2,2,1
1,1,0,1,13
3,2,3,1,4
2,1,0,2,7
2,1,1,1,6
3,2,2,1,13
1,0,2,1,6
0,1,0,1,4
2,3,1,2,16
1,2,1,3,13
2,1,1,0,4
5,2,2,2,13
0,3,2,1,7
5,1,0,3,14
4,2,2,0,14
0,1,0,3,12
4,2,1,0,15
0,2,2,0,7
3,0,0,1,2
1,3,3,2,4
4,2,2,1,5
5,1,0,0,3
2,2,2,3,11
6,1,0,1,4
3,3,2,2,4
5,2,0,3,9
6,3,2,1,6
2,2,3,3,7
1,0,2,1,11
3,1,2,1,13
6,0,1,3,9
5,2,0,3,11
5,1,3,1,5
3,2,0,3,12
2,1,3,2,5
5,2,1,1,9
5,2,1,0,6
1,1,1,1,1
6,2,2,2,12
3,3,3,1,7
6,0,0,2,7
1,2,2,3,3
4,0,1,3,8
5,0,0,2,4
5,3,1,2,1
4,2,1,2,5
1,1,0,2,8
0,2,1,0,9
1,2,2,0,3
3,0,3,2,12
4,2,1,3,3
4,2,2,2,9
5,1,2,1,7
3,2,1,0,16
2,2,2,1,15
1,0,2,2,5
4,2,1,2,5
0,2,2,0,15
2,1,3,1,10
2,3,1,3,4
5,2,2,3,7
2,1,3,1,10
3,2,0,2,1
1,1,1,0,10
3,1,0,2,4
5,3,1,3,14
4,0,3,1,8
4,3,1,0,10
6,2,0,2,9
0,1,0,3,9
2,2,2,1,6
1,0,0,1,10
2,0,0,0,3
0,3,1,1,10
2,1,2,1,11
5,2,0,1,2
3,1,3,2,14
4,1,2,3,12
5,2,3,1,2
1,2,1,1,4
There is also a file new_data as follows:
a1,a2,a3,a4,p
1,2,2,1,10
0,2,3,2,5
0,1,1,2,15
0,0,3,2,2
0,3,2,3,12
2,1,3,2,7
2,2,1,1,4
2,1,3,2,15
1,1,2,1,9
1,0,2,1,9
0,1,2,3,10
3,2,0,3,4
3,2,1,0,1
1,1,2,1,15
0,2,2,1,2
1,2,2,1,2
2,1,2,1,7
1,0,1,2,15
1,0,3,1,9
1,3,2,1,15
2,2,3,3,5
2,3,1,2,2
3,3,3,0,13
3,1,2,3,12
0,1,3,1,9
0,2,3,3,8
2,1,2,3,11
3,2,1,2,13
0,2,1,2,10
1,2,2,2,5
2,0,1,1,11
2,0,3,2,15
1,0,1,0,10
1,3,2,1,7
3,2,1,1,14
2,3,2,0,1
1,1,3,0,14
1,2,3,1,1
3,2,1,2,13
1,2,2,2,7
1,3,2,0,1
2,3,1,1,7
1,0,1,0,1
3,3,3,2,7
1,3,1,1,14
0,2,0,2,11
2,1,0,2,10
2,3,3,3,9
1,1,1,0,14
2,0,2,0,1
2,1,0,3,15
1,1,1,1,16
1,1,1,1,6
1,1,0,2,8
0,3,3,1,6
0,2,3,3,4
0,2,1,2,11
2,2,2,1,7
1,1,2,2,14
3,3,2,2,15
2,2,1,1,7
2,2,1,3,4
2,0,2,1,3
3,2,1,2,13
0,0,1,1,12
1,1,1,1,15
1,1,1,1,11
2,2,1,2,13
2,1,2,3,2
3,0,1,1,11
3,1,2,1,13
2,2,1,2,12
1,2,0,1,4
2,1,1,1,4
2,0,1,1,7
1,2,1,0,9
0,2,1,2,11
1,1,1,2,14
2,1,2,1,14
1,2,1,2,12
2,1,1,2,14
1,2,1,3,7
0,3,1,3,11
2,0,2,1,3
0,2,0,1,7
0,2,1,3,1
0,2,2,2,11
1,1,1,2,4
1,2,1,1,3
1,1,0,0,11
3,1,2,1,12
2,0,1,1,13
0,3,3,2,9
2,1,2,2,12
3,2,1,1,12
1,2,3,0,12
3,0,3,2,4
1,2,1,3,11
3,0,3,0,14
5,1,2,2,13
Expert Answer
Answer to Assignment Solve Online Allocation Problem Seen Class Using Duality Problem Following M Re Q30657527 . . .
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