How to constrain an integer variable using a binary variable?

[firas...@gmail.com]

Hello everyone!!

I have a set of integer variables Xpdt that represents the number of units produced of product p using die d at time t. (To be determined by the solver)

Example: X111 represents the number of units produced of product 1 using die 1 at time period 1.

Each die can make one type of products per time period. (i.e. if X111 > 0, then X211 = 0 & X311 = 0)

The question is: How can I code the above condition?

The logic I have is as follows: (I hope my handwriting is readable)

Based on the logic shown in the picture above, I thought of creating a binary variable s[d,t] which will have a value of 1 if False & a value of 0 if True. Then, I will penalize s in the objective function.

I have wrote the below code in AMPL, but I am getting a message that says: Logical constraint is not an indicator constraint.

subject to c1{d in 1..Dies, t in 1..Time}:

s[d,t] = 1 ==>

(if

sum{p in 1..Parts}x[p,d,t] <= x[1,d,t] or

sum{p in 1..Parts}x[p,d,t] <= x[2,d,t] or

sum{p in 1..Parts}x[p,d,t] <= x[3,d,t] then 1) >= 1;

subject to c2{d in 1..Dies, t in 1..Time}:

s[d,t] = 0 ==>

(if

sum{p in 1..Parts}x[p,d,t] <= x[1,d,t] or

sum{p in 1..Parts}x[p,d,t] <= x[2,d,t] or

sum{p in 1..Parts}x[p,d,t] <= x[3,d,t] then 1) >= 1;

Any help in solving this issue would be highly appreciated!!

[AMPL Google Group]

There is a standard way to do this. For each X[p,d,t] define also a binary variable Z[p,d,t]. Then the constraints are

Z[p,d,t] = 0 ==> X[p,d,t] = 0
sum {p in 1..Parts} Z[p,d,t] <= 1

You'll have to add "subject to" and the appropriate indexing to each constraint. The first one is a valid indicator constraint accepted by CPLEX, Gurobi, or Xpress.

--
Robert Fourer
am...@googlegroups.com

{#HS:834846086-41884#}

[Firas Abdo]

Your efforts are highly appreciated Mr. Robert !!!

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