CPlex coding logic - optimization

The professor in charge of an industrial engineering design course is faced with the problem of assigning 28 students to 8 projects. Each student must be assigned to one project and each project group must have 3 or 4 students. The students have been asked to rank the projects, with 1 being the best ranking and higher numbers representing lower rankings.
a) Formulate an OPL model for this problem.
b) Solve the assignment problem for the following table of assignments:
A ED EZ G H1 H2 RB SC
Allen 1 3 4 7 7 5 2 6
Black 6 4 2 5 5 7 1 3
Chung 6 2 3 1 1 7 5 4
Clark 7 6 1 2 2 3 5 4
Conners 7 6 1 3 3 4 5 2
Cumming 6 7 4 2 2 3 5 1
Demming 2 5 4 6 6 1 3 7
Eng 4 7 2 1 1 6 3 5
Farmer 7 6 5 2 2 1 3 4
Forest 6 7 2 5 5 1 3 4
Goodman 7 6 2 4 4 5 1 3
Harris 4 7 5 3 3 1 2 6
Holmes 6 7 4 2 2 3 5 1
Johnson 2 2 4 6 6 5 3 1
Knorr 7 4 1 2 2 5 6 3
Manheim 4 7 2 1 1 3 6 5
Morris 7 5 4 6 6 3 1 2
Nathan 4 7 5 6 6 3 1 2
Neuman 7 5 4 6 6 3 1 2
Patrick 1 7 5 4 4 2 3 6
Rollins 6 2 3 1 1 7 5 4
Schuman 4 7 3 5 5 1 2 6
Silver 4 7 3 1 1 2 5 6
Stein 6 4 2 5 5 7 1 3
Stock 5 2 1 6 6 7 4 3
Truman 6 3 2 7 7 5 1 4
Wolman 6 7 4 2 2 3 5 1
Young 1 3 4 7 7 6 2 5
How many students are assigned their second or third choice?
c) Some of the projects are harder than others to reach without a car. Thus, it is desirable that at least a certain number of students assigned to each project must have a car; the numbers vary by project as follows:
A ED EZ G H1 H2 RB SC
1 0 0 2 2 2 1 1
The students who have cars are Chung, Demming, Eng, Holmes, Manheim, Morris, Nathan, Patrick, Rollins and Young.
Modify the model to add this car constraint and solve the problem again. How many more students than before must be assigned second or third choices?
I coded the file for a) & b) but i am getting stuck at c).
can anyone help pls with the logic? even ampl wil suffice


Let C_i be the indicator matrix (input): C_i = 1 if student i has a car and 0 otherwise. I'll assume you have the following decision variables:
x_ij = 1 if student i is assigned to project j; 0 otherwise
then c) constraint can me modeled as follows
sum_i C_i * x_ij >= b_j for all j
where b_j is
j A ED EZ G H1 H2 RB SC
b_j 1 0 0 2 2 2 1 1

Related

SQL append data based on multiple dates

I have two tables; one contains encounter dates and the other order dates. They look like this:
id enc_id enc_dt
1 5 06/11/20
1 6 07/21/21
1 7 09/15/21
2 2 04/21/20
2 5 05/05/20
id enc_id ord_dt
1 1 03/7/20
1 2 04/14/20
1 3 05/15/20
1 4 05/30/20
1 5 06/12/20
1 6 07/21/21
1 7 09/16/21
1 8 10/20/21
1 9 10/31/21
2 1 04/15/20
2 2 04/21/20
2 3 04/30/20
2 4 05/02/20
2 5 05/05/20
2 6 05/10/20
The order and encounter date can be the same, or differ slightly for the same encounter ID. I'm trying to get a table that contains all order dates before each encounter date. So the data would like this:
id enc_id enc_dt enc_key
1 1 03/7/20 5
1 2 04/14/20 5
1 3 05/15/20 5
1 4 05/30/20 5
1 5 06/11/20 5
1 1 03/7/20 6
1 2 04/14/20 6
1 3 05/15/20 6
1 4 05/30/20 6
1 5 06/12/20 6
1 6 07/21/21 6
1 1 03/7/20 7
1 2 04/14/20 7
1 3 05/15/20 7
1 4 05/30/20 7
1 5 06/12/20 7
1 6 07/21/21 7
1 7 09/15/21 7
2 1 04/15/20 2
2 2 04/21/20 2
2 1 04/15/20 5
2 2 04/21/20 5
2 3 04/30/20 5
2 4 05/02/20 5
2 5 05/05/20 5
Is there a way to do this? I am having trouble figuring out how to append the orders and encounter table for each encounter based on orders that occur before a certain date.

You may join the two tables as the following:
SELECT O.id, O.enc_id, O.ord_dt, E.enc_id
FROM
order_tbl O
JOIN encounter_tbl E
ON O.ord_dt <= E.enc_dt AND
O.id = E.id
See a demo from db<>fiddle.

pandas dataframe enforce monotically per row

I have a dataframe:
df = 0 1 2 3 4
1 1 3 2 5
4 1 5 7 8
7 1 2 3 9
I want to enforce monotonically per row, to get:
df = 0 1 2 3 4
1 1 3 3 5
4 4 5 7 8
7 7 7 7 9
What is the best way to do so?

Try cummax
out = df.cummax(1)
Out[80]:
0 1 2 3 4
0 1 1 3 3 5
1 4 4 5 7 8
2 7 7 7 7 9

Group counts in new column

I want a new column "group_count". This shows me in how many groups in total the attribute occurs.
Group Attribute group_count
0 1 10 4
1 1 10 4
2 1 10 4
3 2 10 4
4 2 20 1
5 3 30 1
6 3 10 4
7 4 10 4
I tried to groupby Group and attributes and then transform by using count
df["group_count"] = df.groupby(["Group", "Attributes"])["Attributes"].transform("count")
Group Attribute group_count
0 1 10 3
1 1 10 3
2 1 10 3
3 2 10 1
4 2 20 1
5 3 30 1
6 3 10 1
7 4 10 1
But it doesnt work

Use df.drop_duplicates(['Group','Attribute']) to get unique Attribute per group , then groupby on Atttribute to get count of Group, finally map with original Attribute column.
m=df.drop_duplicates(['Group','Attribute'])
df['group_count']=df['Attribute'].map(m.groupby('Attribute')['Group'].count())
print(df)
Group Attribute group_count
0 1 10 4
1 1 10 4
2 1 10 4
3 2 10 4
4 2 20 1
5 3 30 1
6 3 10 4
7 4 10 4

Use DataFrameGroupBy.nunique with transform:
df['group_count1'] = df.groupby('Attribute')['Group'].transform('nunique')
print (df)
Group Attribute group_count group_count1
0 1 10 4 4
1 1 10 4 4
2 1 10 4 4
3 2 10 4 4
4 2 20 1 1
5 3 30 1 1
6 3 10 4 4
7 4 10 4 4

Comparing two dataframe and output the index of the duplicated row once

I need help with comparing two dataframes. For example:
The first dataframe is
df_1 =
0 1 2 3 4 5
0 1 1 1 1 1 1
1 2 2 2 2 2 2
2 3 3 3 3 3 3
3 4 4 4 4 4 4
4 2 2 2 2 2 2
5 5 5 5 5 5 5
6 1 1 1 1 1 1
7 6 6 6 6 6 6
The second dataframe is
df_2 =
0 1 2 3 4 5
0 1 1 1 1 1 1
1 2 2 2 2 2 2
2 3 3 3 3 3 3
3 4 4 4 4 4 4
4 5 5 5 5 5 5
5 6 6 6 6 6 6
May I know if there is a way (without using for loop) to find the index of the rows of df_1 that have the same row values of df_2. In the example above, my expected output is below
index =
0
1
2
3
5
7
The size of the column of the "index" variable above should have the same column size of df_2.
If the same row of df_2 repeated in df_1 more than once, I only need the index of the first appearance, thats why I don't need the index 4 and 6.
Please help. Thank you so much!
Tommy

Use DataFrame.merge with DataFrame.drop_duplicates and DataFrame.reset_index for convert index to column for avoid lost index values, last select column called index:
s = df_2.merge(df_1.drop_duplicates().reset_index())['index']
print (s)
0 0
1 1
2 2
3 3
4 5
5 7
Name: index, dtype: int64
Detail:
print (df_2.merge(df_1.drop_duplicates().reset_index()))
0 1 2 3 4 5 index
0 1 1 1 1 1 1 0
1 2 2 2 2 2 2 1
2 3 3 3 3 3 3 2
3 4 4 4 4 4 4 3
4 5 5 5 5 5 5 5
5 6 6 6 6 6 6 7

Check the solution
df1=pd.DataFrame({'0':[1,2,3,4,2,5,1,6],
'1':[1,2,3,4,2,5,1,6],
'2':[1,2,3,4,2,5,1,6],
'3':[1,2,3,4,2,5,1,6],
'4':[1,2,3,4,2,5,1,6],
'5':[1,2,3,4,2,5,1,6]})
df1=pd.DataFrame({'0':[1,2,3,4,5,6],
'1':[1,2,3,4,5,66],
'2':[1,2,3,4,5,6],
'3':[1,2,3,4,5,66],
'4':[1,2,3,4,5,6],
'5':[1,2,3,4,5,6]})
df1[df1.isin(df2)].index.values.tolist()
### Output
[0, 1, 2, 3, 4, 5, 6, 7]

pandas drop duplicate row value from a specific column

I want to remove the duplicate row value from a specific column - in this case the column name is "number".
Before:
number qty status
0 10 2 go
1 10 5 nogo
2 4 6 yes
3 3 1 no
4 2 7 go
5 5 2 nah
6 5 6 go
7 5 3 nogo
8 1 10 yes
9 1 10 go
10 5 2 nah
After:
number qty status
0 10 2 go
5 nogo
1 4 6 yes
2 3 1 no
3 2 7 go
4 5 2 nah
6 go
3 nogo
5 1 10 yes
10 go
6 5 2 nah

It is possible replace values to empty string or NaNs by mask with duplicated by new Series a created by comparing column with shifted column with cumsum:
a = df['number'].ne(df['number'].shift()).cumsum()
#for replace ''
df['number'] = df['number'].mask(a.duplicated(), '')
#for replace NaNs
#df['number'] = df['number'].mask(a.duplicated())
print (df)
number qty status
0 10 2 go
1 5 nogo
2 4 6 yes
3 3 1 no
4 2 7 go
5 5 2 nah
6 6 go
7 3 nogo
8 1 10 yes
9 10 go
10 5 2 nah
Detail:
a = df['number'].ne(df['number'].shift()).cumsum()
print (a)
0 1
1 1
2 2
3 3
4 4
5 5
6 5
7 5
8 6
9 6
10 7
Name: number, dtype: int32