LP gone horribly wrong

[Patrizia]

Hi there!
I'm trying to solve the following problem: I've got five production
plants and numerous customers and I have to decide what amount of a
product should be produced by which plant to serve the needs of the
customers.

As I'm new to the XPress MP (Student version) I implemented that in
the
only way I could think of:

model test
uses "mmxprs"; !gain access kg the Xpress-Optimizer solver
!sample declarations section
declarations
a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, !variables for the amout
of products
b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, ! 1...10 --> customers
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, ! a...e --> plants
d1, d2, d3, d4, d5, d6, d7, d8, d9, d10,
e1, e2, e3, e4, e5, e6, e7, e8, e9, e10: mpvar

ka1=; ka2=; ka3=; ka4=; ka5=; ka6=; ka7=; ka8=; ka9=; ka10=; !costs
of production for each customer & plant
kb1=; kb2=; kb3=; kb4=; kb5=; kb6=; kb7=; kb8=; kb9=; kb10=;
kc1=; kc2=; kc3=; kc4=; kc5=; kc6=; kc7=; kc8=; kc9=; kc10=;
kd1=; kd2=; kd3=; kd4=; kd5=; kd6=; kd7=; kd8=; kd9=; kd10=;
ke1=; ke2=; ke3=; ke4=; ke5=; ke6=; ke7=; ke8=; ke9=; ke10=;


end-declarations
!the objective function consists of costs*amountvariables added up

Ziel:=ka1*a1+ka2*a2+ka3*a3+ka4*a4+ka5*a5+ka6*a6+ka7*a7+ka8*a8+ka9*a9+ka10*a10+
kb1*b1+kb2*b2+kb3*b3+kb4*b4+kb5*b5+kb6*b6+kb7*b7+kb8*b8+kb9*b9+kb10*b10+
kc1*c1+kc2*c2+kc3*c3+kc4*c4+kc5*c5+kc6*c6+kc7*c7+kc8*c8+kc9*c9+kc10*c10+
kd1*d1+kd2*d2+kd3*d3+kd4*d4+kd5*d5+kd6*d6+kd7*d7+kd8*d8+kd9*d9+kd10*d10+
ke1*e1+ke2*e2+ke3*e3+ke4*e4+ke5*e5+ke6*e6+ke7*e7+ke8*e8+ke9*e9+ke10*e10


a1+b1+c1+d1+e1= !constraint --> customers needs must be met
a2+b2+c2+d2+e2=
a3+b3+c3+d3+e3=
a4+b4+c4+d4+e4=
a5+b5+c5+d5+e5=
a6+b6+c6+d6+e6=
a7+b7+c7+d7+e7=
a8+b8+c8+d8+e8=
a9+b9+c9+d9+e9=
a10+b10+c10+d10+e10=

a1+a2+a3+a4+a5+a6+a7+a8+a9+a10= !production capacity constraints
for the plants
b1+b2+b3+b4+b5+b6+b7+b8+b9+b10=
c1+c2+c3+c4+c5+c6+c7+c8+c9+c10=
d1+d2+d3+d4+d5+d6+d7+d8+d9+d10=
e1+e2+e3+e4+e5+e6+e7+e8+e9+e10=

minimize(Ziel)


Unfortunately the result was quite frustrating, and even when I gave
the cheaper production plants significantly larger capacities it
didn't get a lot better.

I'm wondering now if that is because of my dilettantism or because of
the size of the problem ( 80 customers and five plants plus the
respective constraints)

I'd be grateful for your help!

thanks,

Patrizia

[Eelco Rietsema]

Hi Patrizia,

 

I think the studentversion of Xpress could deal with this size, but I am unsure. Please visit dashoptimization.com to find the dimensions of the student version.

 

Furthermore, it is unclear how many products can be produced by each factory. Is there only one product that each factory produces or are there more?

 

It is advised to use array constructions when a particular variable or parameter has more dimensions as one.

 

There are white papers available, as is the help function, where it is explained clearly how to implement these arrays.

 

Good luck!

--
Eelco Rietsema
van Woustraat 165-3
1074 AK Amsterdam
06-171 171 66