I am completely new to LINGO and I found this example in LINGO.
MODEL:
! A 6 Warehouse 8 Vendor Transportation Problem;
SETS:
WAREHOUSES / WH1 WH2 WH3 WH4 WH5 WH6/: CAPACITY;
VENDORS / V1 V2 V3 V4 V5 V6 V7 V8/ : DEMAND;
LINKS( WAREHOUSES, VENDORS): COST, VOLUME;
ENDSETS
! The objective;
MIN = #SUM( LINKS( I, J):
COST( I, J) * VOLUME( I, J));
! The demand constraints;
#FOR( VENDORS( J):
#SUM( WAREHOUSES( I): VOLUME( I, J)) =
DEMAND( J));
! The capacity constraints;
#FOR( WAREHOUSES( I):
#SUM( VENDORS( J): VOLUME( I, J)) <=
CAPACITY( I));
! Here is the data;
DATA:
CAPACITY = 60 55 51 43 41 52;
DEMAND = 35 37 22 32 41 32 43 38;
COST = 6 2 6 7 4 2 5 9
4 9 5 3 8 5 8 2
5 2 1 9 7 4 3 3
7 6 7 3 9 2 7 1
2 3 9 5 7 2 6 5
5 5 2 2 8 1 4 3;
ENDDATA
END
I have several things that I don't understand in this code.
In the derived set LINKS( WAREHOUSES, VENDORS): COST, VOLUME; how does it know that LINKS members should be as V1WH1,V1WH2,..,V1WH6,V2WH1,V2WH2,...,V6WH6,...,V8WH1,...,V8WH6.
That is how does it know that each vendor is connected to all the warehouses when it is specified by LINKS( WAREHOUSES, VENDORS): COST, VOLUME;
Is Volume data given in this?How has it obtained it?
I used to work a bit with Lingo long time ago. Things have changed since, but I have looked up their user manual (Lingo 14) - see page 31, it explains how the SETS definition works.
1) All the set members of the cartesian product WAREHOUSES x PRODUCTS are generated automatically (by concatenating the labels, considering all 'combinations').
Now, if certain pair warehouse-vendor should not be connected, its COST parameter should be left undefined. Look for 'Omitting Values in a Data Section' in the user manual, page 118. You need to use commas as separators in the COST matrix and use an empty field (e.g. 5, 5, , 6...).
2) VOLUME is a variable, not a parameter. The values of VOLUME are to be found by the solver - they will represent the optimal shipment volumes (where every vendor will get what he/she demands, and the total cost of the shipping will be minimal).
Related
I have more than 100,000 rows of training data with timestamps and would like to calculate a feature matrix for new test data, of which there are only 10 rows. Some of the features in the test data will end up aggregating some of the training data. I need the implementation to be fast since this is one step in a real-time inference pipeline.
I can think of two ways this can be implemented:
Concatenating the train and test entity sets and running DFS and then only using the last 10 rows and throwing away the rest. This is very time consuming. Is there a way to calculate a subset of an entity set while using data from the entire entity set?
Using the steps outlined in Calculating Feature Matrix for New Data section on the Featuretools Deployment page. However, as demonstrated below, this doesn't seem to work.
Create all/train/test entity sets:
import featuretools as ft
data = ft.demo.load_mock_customer(n_customers=3, n_sessions=15)
df_sessions = data['sessions']
# Create all/train/test entity sets.
all_es = ft.EntitySet(id='sessions')
train_es = ft.EntitySet(id='sessions')
test_es = ft.EntitySet(id='sessions')
all_es = all_es.entity_from_dataframe(
entity_id='sessions',
dataframe=df_sessions, # all sessions
index='session_id',
time_index='session_start',
)
train_es = train_es.entity_from_dataframe(
entity_id='sessions',
dataframe=df_sessions.iloc[:10], # first 10 sessions
index='session_id',
time_index='session_start',
)
test_es = test_es.entity_from_dataframe(
entity_id='sessions',
dataframe=df_sessions.iloc[10:], # last 5 sessions
index='session_id',
time_index='session_start',
)
# Normalise customer entities so we can group by customers.
all_es = all_es.normalize_entity(base_entity_id='sessions',
new_entity_id='customers',
index='customer_id')
train_es = train_es.normalize_entity(base_entity_id='sessions',
new_entity_id='customers',
index='customer_id')
test_es = test_es.normalize_entity(base_entity_id='sessions',
new_entity_id='customers',
index='customer_id')
Set cutoff_time since we are dealing with data with timestamps:
cutoff_time = (df_sessions
.filter(['session_id', 'session_start'])
.rename(columns={'session_id': 'instance_id',
'session_start': 'time'}))
Calculate feature matrix for all data:
feature_matrix, features_defs = ft.dfs(entityset=all_es,
cutoff_time=cutoff_time,
target_entity='sessions')
display(feature_matrix.filter(['customer_id', 'customers.COUNT(sessions)']))
session_id
customer_id
customers.COUNT(sessions)
1
3
1
2
3
2
3
1
1
4
2
1
5
2
2
6
2
3
7
2
4
8
1
2
9
2
5
10
1
3
11
1
4
12
2
6
13
3
3
14
1
5
15
3
4
Calculate feature matrix for train data:
feature_matrix, features_defs = ft.dfs(entityset=train_es,
cutoff_time=cutoff_time.iloc[:10],
target_entity='sessions')
display(feature_matrix.filter(['customer_id', 'customers.COUNT(sessions)']))
session_id
customer_id
customers.COUNT(sessions)
1
3
1
2
3
2
3
1
1
4
2
1
5
2
2
6
2
3
7
2
4
8
1
2
9
2
5
10
1
3
Calculate feature matrix for test data (using method shown in "Feature Matrix for New Data" on the Featuretools Deployment page):
feature_matrix = ft.calculate_feature_matrix(features=features_defs,
entityset=test_es,
cutoff_time=cutoff_time.iloc[10:])
display(feature_matrix.filter(['customer_id', 'customers.COUNT(sessions)']))
session_id
customer_id
customers.COUNT(sessions)
11
1
1
12
2
1
13
3
1
14
1
2
15
3
2
As you can see, the feature matrix generated from train_es matches the first 10 rows of the feature matrix generated from all_es. However, the feature matrix generated from test_es doesn't match the corresponding rows from the feature matrix generated from all_es.
You can control which instances you want to generate features for with the cutoff_time dataframe (or the instance_ids argument in DFS if the cutoff time is a single datetime). Featuretools will only generate features for instances whose IDs are in the cutoff time dataframe and will ignore all others:
feature_matrix, features_defs = ft.dfs(entityset=all_es,
cutoff_time=cutoff_time[10:],
target_entity='sessions')
display(feature_matrix.filter(['customer_id', 'customers.COUNT(sessions)']))
customer_id
customers.COUNT(sessions)
session_id
1
4
2
6
3
3
1
5
3
4
The method in "Feature Matrix for New Data" is useful when you want to calculate the same features but on entirely new data. All the same features will be created, but data isn't shared between the entitysets. That doesn't work in this case, since the goal is to use all the data but only generate features for certain instances.
I want to create an optimal meal plan with minimum sugar intake for
7 days but the everyday diet plan should include food from 3 different categories. How do I add constraint that I could get food from 3 different food categories and give meal plan for 7 days?
my dataframe is as follows:
id name energy sugar Food_Groups
1 4-Grain Flakes 140 58.8 Breakfast
2 Beef Mince, Fried 1443 8.0 Meat
3 Pork 1000 3.0 Meat
4 cake 1200 150 Sweet
5 cheese 1100 140 Sweet
6 Juice 700 85 Drink
7 cabbage 60 13 vegetarian
8 cucumber 10 10 vegetarian
9 eggs 45 30 Breakfast
I created a prob variable, formulated objective function, created dictionary variable, added constraints, and solved as follows
# Create the 'prob' variable to contain the problem data
prob = LpProblem("Simple Diet Problem",LpMinimize)
#create data variables and dictionary
food_items = list(df['name'])
calories = dict(zip(food_items,df['energy']))
sugars = dict(zip(food_items,df['sugar']))
food_vars =LpVariable.dicts("Food",food_items,lowBound=0,cat='Integer')
#Building the LP problem by adding the main objective function.
prob += lpSum([sugars[i]*food_vars[i] for i in food_items])
#adding calorie constraint
prob += lpSum([calories[f] * food_vars[f] for f in food_items]) >=
1800.0, "CalorieMinimum"
prob += lpSum([calories[f] * food_vars[f] for f in food_items]) <=
2200.0, "CalorieMaximum"
prob.writeLP("SimpleDietProblem.lp")
prob.solve()
print("Status:", LpStatus[prob.status])
I want to know how to make a menu for 7 days? I tried the following code but It repeats the same foods
days = ['Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday', 'Sunday']
for i in days:
print(days)
prob.writeLP("SimpleDietProblem.lp")
prob.solve(PULP_CBC_CMD())
print("Status:", LpStatus[prob.status])
print("Therefore, the optimal balanced diet consists of\n"+"-")
for v in prob.variables():
if v.varValue:
print(v.name , "=", v.varValue)
print("The total sugar of this balanced diet is: {}".format(round(value(prob.objective),2)))
I am trying to make an auctions system but can not figure out the logical conditions for doing so..
Lets say that I have 10 credit
$credit
I have already bet 5 credits on another auction... so I owe 5 from 10 $owe
I thus have 5 available... $available = $credit - $owe (=5)
I bet 3 from available (on a different item)...
I wish to bet again 4 (cancel 3, update to 4), but credit available is now $available - 3 (=2)
Can't find a logical solution.... written in code.
What is the condition for setting a bet???
Made up a matrix with the dependence between variables:
bet available owe lastbet
1 10 10 0
2 9 11 1
3 7 13 2
4 4 16 3
5 0 20 4
6 -5 25 5
7 -11 31 6
8 -18 38 7
9 -26 46 8
10 -35 55 9
11 -45 65 10
Need to translate it into a condition statement.... (the next row would not meet the conditions)
The condition should fail on the 11th row....
Based on the Matrix... I found out that the condition is:
if ($bet <= (($owe + $available) / 2)) {}
Not very intuitive......
I need to create a new transport ID based on the cumulative sum of the volume being transported. Let´s say that originally everything was transported in truck A with a capacity of 25. Now I want to assign these items to shipments with truck B (Capacity 15).
The only real constraint is amt shipped cannot exceed capacity.
I can´t post a picture because of the restrictions...but the overall set up would be like this:
Old Trans # Volume New Trans # Cumulative Volume for Trans
1 1
1 9
1 3
1 7
1 4
2 9
2 10
3 8
3 5
3 9
4 4
4 6
4 8
5 9
5 1
5 5
5 8
6 3
6 4
6 3
6 4
6 4
6 7
7 7
7 10
7 4
8 10
8 6
8 7
9 4
9 9
9 6
10 7
10 4
10 1
10 1
10 5
10 2
11 9
11 3
11 9
12 8
12 5
12 9
13 9
Expected output would be that the first three entries would result in a new shipment ID of 1;the next two entries would result in a new shipment ID of 2;and so on... I´ve tried everthing that I know(excluding VBA): Index/lookup/if functions. My VBA skills are very limited though.Any tips?? thanks!
I think I see what you're trying to do here, and just using an IF formula (and inserting a new column to keep track):
In the Columns C and D, insert these formulas in row 3 and copy down (changing 15 for whatever you want your new volume capacity to be):
Column C: =IF(B3+C2<15,B3+C2,B3)
Column D: =IF(B3+C2<15,D2,D2+1)
And for the cells C2 and D2:
C2: = B2
D2: = A2
Is this what you're looking to do?
A simple formula could be written that 'floats' the range totals for each successive load ID.
In the following, I've typed 25 and 15 in D1:E1 and used a custom number format of I\D 0. In this way, the column is identified and the cell can be referenced as a true number load limit. You can hard-code the limits into the formula if you prefer by overwriting D$1 but you will not have a one-size-fits-all formula that can be copied right for alternate load limits as I have in my example..
The formula in D2 is,
=IF(ROW()=2, 1, (SUM(INDEX($B:$B, MATCH(D1, D1:D$1, 0)):$B2)>D$1)+ D1)
Fill right to E2 then down as necessary.
I have an optimization exercise I am trying to work through and am stuck again on the syntax. Below is my attempt, and I'd really like a thorough explanation of the syntax in addition to the solution code. I think it's the specific index piece that I am having trouble with.
The problem:
I have an item that I wish to sell out of within ten weeks. I have a historical trend and wish to alter that trend by lowering price. I want maximum margin dollars. The below works, but I wish to add two constraints and can't sort out the syntax. I have spaces for these two constraints in the code, with my brief explanation of what I think they may look like. Here is a more detailed explanation of what I need each constraint to do.
inv_cap=There is only so much inventory available at each location. I wish to sell it all. For location 1 it is 800, location 2 it is 1200. The sum of the column FRC_UNITS should equal this amount, but cannot exceed it.
price_down_or_same=The price cannot bounce around, so it needs to always be less than or more than the previous week. So, price(i)<=price(i-1) where i=week.
Here is my attempt. Thank you in advance for assistance.
*read in data;
data opt_test_mkdown_raw;
input
ITM_NBR
ITM_DES_TXT $
LCT_NBR
WEEK
LY_UNITS
ELAST
COST
PRICE
TOTAL_INV;
cards;
1 stuff 1 1 300 1.2 6 10 800
1 stuff 1 2 150 1.2 6 10 800
1 stuff 1 3 100 1.2 6 10 800
1 stuff 1 4 60 1.2 6 10 800
1 stuff 1 5 40 1.2 6 10 800
1 stuff 1 6 20 1.2 6 10 800
1 stuff 1 7 10 1.2 6 10 800
1 stuff 1 8 10 1.2 6 10 800
1 stuff 1 9 5 1.2 6 10 800
1 stuff 1 10 1 1.2 6 10 800
1 stuff 2 1 400 1.1 6 9 1200
1 stuff 2 2 200 1.1 6 9 1200
1 stuff 2 3 100 1.1 6 9 1200
1 stuff 2 4 100 1.1 6 9 1200
1 stuff 2 5 100 1.1 6 9 1200
1 stuff 2 6 50 1.1 6 9 1200
1 stuff 2 7 20 1.1 6 9 1200
1 stuff 2 8 20 1.1 6 9 1200
1 stuff 2 9 5 1.1 6 9 1200
1 stuff 2 10 3 1.1 6 9 1200
;
run;
data opt_test_mkdown_raw;
set opt_test_mkdown_raw;
ITM_LCT_WK=cats(ITM_NBR, LCT_NBR, WEEK);
ITM_LCT=cats(ITM_NBR, LCT_NBR);
run;
proc optmodel;
*set variables and inputs;
set<string> ITM_LCT_WK;
number ITM_NBR{ITM_LCT_WK};
string ITM_DES_TXT{ITM_LCT_WK};
string ITM_LCT{ITM_LCT_WK};
number LCT_NBR{ITM_LCT_WK};
number WEEK{ITM_LCT_WK};
number LY_UNITS{ITM_LCT_WK};
number ELAST{ITM_LCT_WK};
number COST{ITM_LCT_WK};
number PRICE{ITM_LCT_WK};
number TOTAL_INV{ITM_LCT_WK};
*read data into procedure;
read data opt_test_mkdown_raw into
ITM_LCT_WK=[ITM_LCT_WK]
ITM_NBR
ITM_DES_TXT
ITM_LCT
LCT_NBR
WEEK
LY_UNITS
ELAST
COST
PRICE
TOTAL_INV;
var NEW_PRICE{i in ITM_LCT_WK};
impvar FRC_UNITS{i in ITM_LCT_WK}=(1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i])*LY_UNITS[i];
con ceiling_price {i in ITM_LCT_WK}: NEW_PRICE[i]<=PRICE[i];
/*con inv_cap {j in ITM_LCT}: sum{i in ITM_LCT_WK}=I want this to be 800 for location 1 and 1200 for location 2;*/
con supply_last {i in ITM_LCT_WK}: FRC_UNITS[i]>=LY_UNITS[i];
/*con price_down_or_same {j in ITM_LCT} : NEW_PRICE[week]<=NEW_PRICE[week-1];*/
*state function to optimize;
max margin=sum{i in ITM_LCT_WK}
(NEW_PRICE[i]-COST[i])*(1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i])*LY_UNITS[i];
/*expand;*/
solve;
*write output dataset;
create data results_MKD_maxmargin
from
[ITM_LCT_WK]={ITM_LCT_WK}
ITM_NBR
ITM_DES_TXT
LCT_NBR
WEEK
LY_UNITS
FRC_UNITS
ELAST
COST
PRICE
NEW_PRICE
TOTAL_INV;
*write results to window;
print
/*NEW_PRICE */
margin;
quit;
The main difficulty is that in your application, decisions are indexed by (Item,Location) pairs and Weeks, but in your code you have merged (Item,Location,Week) triplets. I rather like that use of the data step, but the result in this example is that your code is unable to refer to specific weeks and to specific pairs.
The fix that changes your code the least is to add these relationships by using defined sets and inputs that OPTMODEL can compute for you. Then you will know which triplets refer to each combination of (Item,Location) pair and week:
/* This code creates a set version of the Item x Location pairs
that you already have as strings */
set ITM_LCTS = setof{ilw in ITM_LCT_WK} itm_lct[ilw];
/* For each Item x Location pair, define a set of which
Item x Location x Week entries refer to that Item x Location */
set ILWperIL{il in ITM_LCTS} = {ilw in ITM_LCT_WK: itm_lct[ilw] = il};
With this relationship you can add the other two constraints.
I left your code as is, but applied to the new code a convention I find useful, especially when there are similar names like itm_lct and ITM_LCTS:
sets as all caps;
input parameters start with lowercase;
output (vars, impvars, and constraints) start with Uppercase */
Here is the new OPTMODEL code:
proc optmodel;
*set variables and inputs;
set<string> ITM_LCT_WK;
number ITM_NBR{ITM_LCT_WK};
string ITM_DES_TXT{ITM_LCT_WK};
string ITM_LCT{ITM_LCT_WK};
number LCT_NBR{ITM_LCT_WK};
number WEEK{ITM_LCT_WK};
number LY_UNITS{ITM_LCT_WK};
number ELAST{ITM_LCT_WK};
number COST{ITM_LCT_WK};
number PRICE{ITM_LCT_WK};
number TOTAL_INV{ITM_LCT_WK};
*read data into procedure;
read data opt_test_mkdown_raw into
ITM_LCT_WK=[ITM_LCT_WK]
ITM_NBR
ITM_DES_TXT
ITM_LCT
LCT_NBR
WEEK
LY_UNITS
ELAST
COST
PRICE
TOTAL_INV;
var NEW_PRICE{i in ITM_LCT_WK} <= price[i];
impvar FRC_UNITS{i in ITM_LCT_WK} =
(1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i]) * LY_UNITS[i];
* Moved to bound
con ceiling_price {i in ITM_LCT_WK}: NEW_PRICE[i] <= PRICE[i];
con supply_last{i in ITM_LCT_WK}: FRC_UNITS[i] >= LY_UNITS[i];
/* This code creates a set version of the Item x Location pairs
that you already have as strings */
set ITM_LCTS = setof{ilw in ITM_LCT_WK} itm_lct[ilw];
/* For each Item x Location pair, define a set of which
Item x Location x Week entries refer to that Item x Location */
set ILWperIL{il in ITM_LCTS} = {ilw in ITM_LCT_WK: itm_lct[ilw] = il};
/* I assume that for each item and location
the inventory is the same for all weeks for convenience,
i.e., that is not a coincidence */
num inventory{il in ITM_LCTS} = max{ilw in ILWperIL[il]} total_inv[ilw];
con inv_cap {il in ITM_LCTS}:
sum{ilw in ILWperIL[il]} Frc_Units[ilw] = inventory[il];
num lastWeek = max{ilw in ITM_LCT_WK} week[ilw];
/* Concatenating indexes is not the prettiest, but gets the job done here*/
con Price_down_or_same {il in ITM_LCTS, w in 2 .. lastWeek}:
New_Price[il || w] <= New_Price[il || w - 1];*/
*state function to optimize;
max margin=sum{i in ITM_LCT_WK}
(NEW_PRICE[i]-COST[i])*(1-(NEW_PRICE[i]-PRICE[i])*ELAST[i]/PRICE[i])*LY_UNITS[i];
expand;
solve;
*write output dataset;
create data results_MKD_maxmargin
from
[ITM_LCT_WK]={ITM_LCT_WK}
ITM_NBR
ITM_DES_TXT
LCT_NBR
WEEK
LY_UNITS
FRC_UNITS
ELAST
COST
PRICE
NEW_PRICE
TOTAL_INV;
*write results to window;
print
NEW_PRICE FRC_UNITS
margin
;
quit;