## Problem with writing equation Topic is solved

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canycetin
User Posts: 1
Joined: 7 months ago

### Problem with writing equation

Dear all,
I am having a problem with Equation part of my gams code. If you check initial_balance and balance equations , you'll see what is my problem and what I want to do.
For initial_balance equation I want to assign Jun for t and for balance eq. I want to assign t-1 for store variable.
I would be glad if you help me .
Sets
t 'Months' /Jan,Feb,Mar,Apr,May,Jun/
p 'Products' /1,2,3,4,5,6,7/
m 'Machines' /Gr,VD,HD,Br,Pl/ ;

Parameters
profit(p) 'Profit of product p'
/1 10
2 6
3 8
4 4
5 11
6 9
7 3/
installed(m) ' Number of machines of type m installed in the factory'
/Gr 4
VD 2
HD 3
Br 1
Pl 1/;

Table
down(t,m) 'Number of machines of type m scheduled for maintenance at month t'
Gr VD HD Br Pl
Jan 1 0 0 0 0
Feb 0 0 2 0 0
Mar 0 0 0 1 0
Apr 0 1 0 0 0
May 1 1 0 0 0
Jun 0 0 1 0 0

Table
time_req(m,p) 'Time (in hours/unit) needed on machine m to manufacture one unit of product p'

1 2 3 4 5 6 7
Gr 0.5 0.7 0 0 0.3 0.2 0.5
VD 0.1 0.2 0 0.3 0 0.6 0
HD 0.2 0 0.8 0 0 0 0.6
Br 0.05 0.03 0 0.07 0.1 0 0.08
Pl 0 0 0.01 0 0.05 0 0.05 ;
Table
max_sales(t,p) 'Maximum number of units of product p that can be sold at month t'
1 2 3 4 5 6 7
Jan 500 1000 300 300 800 200 100
Feb 600 500 200 0 400 300 150
Mar 300 600 0 0 500 400 100
Apr 200 300 400 500 200 0 100
May 0 100 500 100 1000 300 0
Jun 500 500 100 300 1100 500 60 ;
Parameter
holding_cost 'Monthly cost (in USD/unit/month) of keeping in inventory a unit of any product type'
store_target 'Number of units of each product type to keep in inventory at the end of the planning horizon'
hours_per_month 'Time (in hours/month) available at any machine on a monthly basis'
max_inventory 'Maximum number of units of a single product type that can be stored in inventory at any given month ';
holding_cost=0.5;
hours_per_month=2*8*24 ;
max_inventory=100;
Variables
make(t,p) ' Number of units of product p to manufacture at month t'
store(t,p) 'Number of units of product p to store at month t'
sell(t,p) 'Number of units of product p to sell at month t'
z 'The total profit of the planning horizon' ;
Positive Variables
make
store
sell;
Equations
initial_balance(t,p) 'For each product p, the number of units produced should be equal to the number of units sold plus the number stored'
balance(t-1,p) 'For each product p, the number of units produced should be equal to the number of units sold plus the number stored'
machine_cap(m,t) 'Total time used to manufacture any product at machine type m cannot exceed its monthly capacity'
store_cap(t,p) 'Quantity of product p that stored must be lower or equal to 100'
sell_cap(t,p) 'Max sell must be equal or lower than'
maxprofit 'obj function' ;

maxprofit.. z=e=sum(t,sum(p,profit(p)*make(t,p)-holding_cost*store(t,p)));
initial_balance(Jun,p).. make(Jun,p)=e=sell(Jun,p)+store(Jun,p);
balance(t-1,p).. store(t-1,p)+make(t,p)=e=sell(t,p)+store(t,p);
machine_cap(m,t).. sum(p,time_req(m,p)*make(t,p))=l=hours_per_month*(installed(m)-down(t,m));
store_cap(t,p).. store(t,p)=l=max_inventory ;
sell_cap(t,p).. sell(t,p)=l=max_sales(t,p);
Model Untitled_2 /all/;
Solve Untitled_2 using LP maximizing z;

abhosekar
Moderator Posts: 190
Joined: 10 months ago

### Re: Problem with writing equation

you should use 'Jun' instead of Jun and remove it from equation index as follows:
initial_balance(p).. make('Jun',p)=e=sell('Jun',p)+store('Jun',p);

You can write balance equation as follows:
balance(t,p)\$(ord(t) ne 1).. store(t-1,p)+make(t,p)=e=sell(t,p)+store(t,p);

This will include the equation starting from Feb and you will not face error because of t-1.
If there is some initial store, you can do the following:

balance(t,p).. store(t-1,p)\$(ord(t) ne 1)+ initial_store(p)\$(ord(t) eq 1) + make(t,p)=e=sell(t,p)+store(t,p);

Hope this helps.

- Atharv