Wagner Whitin Problem - Error in constraint: "contraint A cannot hold: body <= -20 cannot be >= 20, difference = -40"

[g.kus...@gmail.com]

Hello and a happy new year to everyone!

I´m trying to solve a Wagner Whiting Problem with the gurobi-solver, but unfortunately keep getting the same error message over and over again. I would love if someone of you could help me with this.

My model looks like this:

#Declaration of paramaters and sets

param t; 

set PERIODS = 1..t; 

set MIN = 2..t;

param d {i in PERIODS}; #demand in period i

param s; #setup cost

param h; #storage cost

param M; 

param I0; #inventory at the end of period 0

#Declaration of variables

var q {i in PERIODS}; #lot size in period i

var x {i in PERIODS} binary;

var I {i in PERIODS}; #inventory at the end of period i

#Objective Function

minimize costs: sum {i in PERIODS} (s * x[i] + h * I[i]); 

#Constraits

subject to A: I[1] = I0 + q[1] - d[1];

subject to B {i in MIN}: I[i-1] + q[i] - d[i] = I[i];

subject to C {i in PERIODS}: q[i] <= M * x[i];

subject to D {i in PERIODS}: q[i] >= 0;

subject to E {i in PERIODS}: I[i] >= 0;

My data file looks like this:

data;

param t:= 4;

param d:= 1 20 2 10 3 20 4 30;

param s:= 100;

param h:= 2;

param M:= 10;

param I0:= 0;

What I get from AMPL is the following:

sw: ampl

ampl: model serie1.mod;

ampl: data serie1a.dat;

ampl: option solver gurobi;

ampl: solve;

presolve: constraint A cannot hold:

body <= -20 cannot be >= 20; difference = -40

ampl: 

Thank you so much in advance.

Best regards

GK

[Robert Fourer]

The message

presolve: constraint A cannot hold:
body <= -20 cannot be >= 20; difference = -40

is telling you that AMPL's presolve phase has determined that no feasible solution to constraint A is possible, if all of the other constraints are satisfied. If you give the command "expand A;" you will see that after processing, AMPL converts constraint A as follows:

ampl: expand A;
subject to A:
-q[1] + I[1] = -20;

The "body" is the part "-q[1] + I[1]" (containing the variables) on the left. Clearly to satisfy the constraint, the body has to be <= -20 as given in the message. But the rest of the message is telling you that, based on the other constraints, AMPL's presolve has deduced that -q[1] + I[1] must be >= 20. This contradiction implies that no feasible solution is possible.

It may not be immediately obvious why the constraints imply -q[1] + I[1] >= 20, but if you examine the constraints closely you will be able to figure this out.

Bob Fourer
am...@googlegroups.com

=======

[Timo S.]

Your constraint C connects the q variables with the binary x variables, which means: You can only produce if the machine is set up and vice versa. Now take a look at your param M in the data, you set M := 10. But in your first period you have a demand of 20. So the constraint A cannot hold, because you cannot produce more than 10 per period and the problem becomes infeasible.
Suggestion 1: Set M to something big (M is called Big-M in literature) like 100000000000000 and your problem will become feasible.
Suggestion 2: Think about how big M at least really must be.

[Robert Fourer]

Setting M to something as large as 100000000000000 can cause other problems -- see my discussion of The Big M.  It's best to set M to a reasonably large value -- large enough to make the model valid, but not too much larger.

Bob Fourer
am...@googlegroups.com

From: am...@googlegroups.com [mailto:am...@googlegroups.com] On Behalf Of Timo S.

Sent: Tuesday, January 5, 2016 2:59 PM
To: AMPL Modeling Language

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[g.kus...@gmail.com]

Thank you both so much, your advices really helped me to figure it out!

[Amir Lm]

Hi Bob,

I have one small issue in my model that I was hoping to get some insight from you!

I developed a deterministic model which then being transferred to the stochastic form.

the deterministic model works perfectly fine, however, when I transfer it to stochastic programming form it gives me "Integer Infeasible" 

Attached please find the Deter. as well as Stoch. model

AMPL returns :

ampl: reset;

ampl: model FKS3.mod;

ampl: data FKS3.dat;

ampl: option solver cplex;

ampl: solve;

CPLEX 12.6.1.0: integer infeasible.

176 MIP simplex iterations

0 branch-and-bound nodes

No basis.

Thank you in advance for your time!