LINGO Sets&Basic parts

Problem

Sailing company SAILCO need to decide how many sailboats to produce per quarter in the next four quarters. The next four quarters’ demand for vessels is 40，60，75 and 25. These demand must be met in time. Normal production capacity of each quarter is 40 sailboat， and the production cost for each sailboat is $400. The production cost per vessel is $450 if you work overtime . At the end of each quarter, the inventory fee for each ship is $20. Assuming the production time is 0 and the initial stock is 10 ships. How to schedule production can minimize the total cost?

Solution

It is important for us to understand the concept of

Set

and

Attribute

in LINGO13 before we solve this problem.

Let us use

DEM

,

NP

,

OP

and

INV

to represent the demand, normal production, overtime production and inventory respectively. The

DEM

is known while

NP

,

OP

and

INV

are unknown.

The objective function is the sum of all costs：

MIN=∑400∗NP(I)+450∗OP(I)+20∗INV(I)

The constraints are:

1) Constraint of productivity:

NP(I)<40，I=1,2,3,4

2) Product quantity balance:

INV(I)=INV(n−1)+NP(I)+OP(I)−DEM(I),I=1,2,3,4;INV(0)=10

3)Sign restrains (as all variables should be non negative).

Code

MODEL:
SETS:
    QUARTERS/,,,/:DEM,NP,OP,INV;
ENDSETS
DATA:
    DEM=,,,;
ENDDATA
MIN=@SUM(QUARTERS(I):400*NP(I)+450*OP(I)+20*INV(I));
@FOR(QUARTERS(I):NP(I)<40);
@FOR(QUARTERS(I)|I#GT#1：
    INV(I)=INV(N-)+NP(I)+OP(I)-DEM(I););
INV()=+NP(）+OP()-DEM();
END
           

Summary

The basic parts of a LINGO program:

1. SET-ENDSETS

   part:

   You can create some sets in this part, and if there are too many elements in one set to list, you can use

   ...

   to omit some subscripts, like

   QUARTERS/1...1000/: DEM, NP, OP, INV;

2. objective function and constraints part:

   This is the only part which has no special mark. In fact, any thing outside other four parts belongs to this part.

3. DATA-ENDDATA

   part:

   In this part, you can input the basic information for the sets defined before. And usually we use

   attribute=value_list(constant)

   to assign values to elements. If there are some variables which you don’t want to assign until running the program, you can use

   variable=?

   to do it.

4. INIT-ENDINIT

   part:

   This part is similar with the

   DATA-ENDDATA

   part, and you can use

   attribute=value_list(constant)

   to assign initial values to elements. But these values just help computer to reduce calculation time and may help you get a better answer, yet they can be changed during the iteration.

5. CALC-ENDCALC

   part:

   Some basic calculation can be done in this part. As the raw data may can’t be used in the model, they can be pretreated before they are used in objective function and constraints part.

End of 2

I’m too busy these day, and this tutorial may be refreshed a little slow. Hope you like it :-)