Problems in aimms modeling of vehicle routing problem

[Wingkins]

Hello,
I am currently building a model involving the vehicle routing problem
about distribution center distribute goods to different districts and
so to analyze the minimum cost. After I had amlost finish the model,
there are no optimal result came out. I doubt that it may be related
to the binary variable setting condition, but I am not sure. I would
be greatly appreciate for your help as this model is very essential to
me! Below are the describtion of the problem and the system that we
did.

Indices
i index of plant ( i = 1,2...m)
j index of warehouse( j = 1,2,..n)

Parameters

SupplyAi = number of units available at plant i
DemandBj= number of units demanded at warehouse j
unitcostCij= the cost of shipping one unit from plants i to warehouse
j
routinecostDij = fixed cost asociated with route ( i,j)

Decision variable

transportunitXij = the unknown quantity to be transproted on route
( i,j )
totaltransportcostfij(x) = total transportation cost for shipping per
unit from plant i to warehouse j in which fij(x) = Cij * Xij will be a
cost function if it is linear

The usual objective function is to minimiz the total variable cost
and fixed costs from the allocation. it is one of the combinatorial
problem invovlving constraints. This fcTP with m plants and n
warehouse can be formulated as follows:

min f(x) = summation( Fij(x) + Dij * Gij (x)) , i from
1 to n , j from 1 to m

Such that summation (Xij) <= Ai i = 1,2,...m
summation (Xij) >= Bj j = 1,2,....n

Xij >= 0 , for all i,j

wit BInaryGij ( x) = if Xij>0 then equal to 1
otherwise equal to 0


Here is our model file

[Marcel Hunting]

Hi,

I seems that you intended to include an AIMMS model but none is there.

Marcel Hunting
AIMMS Software Developer

[Wingkins]

http://www.sendspace.com/file/rr5ejz

[Wingkins So]

Sorry, Sir

I forgot to check whether post the link in the message

here is the link
http://www.sendspace.com/file/rr5ejz

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[Guido Diepen]

Hi,

I am not sure if you are intentionally modeling this as a Mixed Integer Non Linear Program (MINLP).

The problem is that in the definition of the BinaryG variable, you are using the following definition:
if (transportunitX(i,j)>0)
then 1
else 0
endif

which is not linear. Is it the goal to create a linear program, or a non-linear program? If you need to create a linear program, you will have to remove the above definition and use additional constraints.

Guido Diepen
AIMMS Specialist.

[Wingkins]

Sorry, Sir

I forgot to check whether post the link in the message

here is the link
http://www.sendspace.com/file/rr5ejz

Thank you

> > Here is our model file- 隱藏被引用文字 -
>
> - 顯示被引用文字 -

[Marcel Roelofs]

Not to be picky, but maybe it's a good idea to stop using a service
for sending files, where all directly visible download buttons link to
virus-infected files, and one needs to scroll down to find the link to
the actual file you want us to look at.

For formulating fixed costs in a linear fashion, you can take a look
at the modeling guide.

Cheers,
Marcel