Originally posted by: user1234567

Hello, i'm using a mathematical model (milp model) to solve Flexible Jobshop Problem. I get results out of the upper and the lower bounds. For example, in the following data (donnees.DAT) i should get a value between 133, and 157. (LB, UB) = (133, 157). I get the value 198 !!

Please can you help me to know the reason why i get unreasonable objective functions ? Can anyone check my model if it is working correctly ? Thank you in advance.

 

My model:

 

decision variables:

X i,j,k = {1 if machine k is selceted for operation Oij, 0 otherwise}

Y i,j,i',j',k = {1 if operation Oij precedes operation Oi'j' on machine k, 0 otherwise}.

 

The mathematical model:

 

Minimize (x i,j,k , y i,j,i',j',k): Cmax

sum (k∈Mj) X i,j,k = 1, i∈J, j∈Oi (1)

sum (i=1,..n, j=1..rj) X i,j,k <= e i,j,k; k∈Mj (2)

where, for given {x i,j,k}, {y i,j,i',j',k} solves:

 

Minimize (y i,j,i',j',k) Cmax 

sum (i in 1,..,n, j=1,..,rj) y i,j,i',j',k <= 1; i'∈J, j'∈Oi', k∈Mj∩Mj', (3)

sum (i in 1,..,n, j=1,..,rj) y i,j,0,1,k <= 1; k∈Mj∩Mj', (4)

sum (i in 1,..,n, j=1,..,rj) y i,j,i',j',k <= sum (i in 0,..,n, j=1,..,rj) y i',j',i,j,k; i'∈J, j'∈Oi', k∈Mj∩Mj', (5)

 

C i,j,k >= C i',j' + y i,j,i',j',k * (p i,j,k + s i,i',k) - L * (1-sum(k=1,..,m) y i,j,i',j',k); i,i' ∈ J, j,j' ∈ Oi', k∈Mj∩Mj', (6)

C i,j,k >= sum (k∈Mj) C i,j-1,k + sum(i=1,..,n, j=1,..,rj, k=1,..,m) y i,j,i',j',k * (p i,j,k + s i',j',k); i ∈ J, j ∈ Oi, (7)

Ci >= sum (k∈Mj) C i,j,k;  i ∈ J, j' ∈ Oi', k∈Mj∩Mj', (8)

Cmax >= Ci;  i ∈ J, (9)

C i,j,k >= 0;  i ∈ J, j ∈ Oi, k∈Mj. (10)

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You are using CP. Please post this question in one of the CP related forums.

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Originally posted by: user1234567

I asked in the CP related forums, and they suggested that i ask in a mathematical programming forum. I just used CP because it makes sens to use it. when i use cp it's easier. 

Also when i delete using cp; and the corresponding commands (endbeforestart, nooverlap, alternative...). I get no result.

Do u have an example of mathematical model (MILP) for the same problem (FJSP) or similar to my mathematical model, so that i can compare it with my model and see if there are some mistakes in the formulation of the problem ?

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#MathematicalProgramming-General

Originally posted by: user1234567

Okay. Normally i should use MILP model without using CP Optimizer.

Now, i'm using CPLEX instead of CP to solve the MILP. So, my model now is correct ?

But, actually i'm facing some problems here: 1) How can i change the structure of Ops in the data or in the.mod. The structure is actually incorrect and i don't know how to write it correctly. 

Second, i want that my problem is a flexible jobshop; so that cplex can choose one machine out of a set of the eligible machines.and this is made by the constraint sum (i in Jobs, j in Oper) X[i][j][k] <= e[i][j][k]; k ∈ Mj. I wrote this constraint in my code. But, i'm not sure if it's correct and works well ! 

Third, are all the constraints in my program work well ?

Thank you.

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