Modeling if constraints with interger variable

Answered

Ray TAN

• November 19, 2020 15:13

I wanna write the constraint like

if x=K  (K is a constant )

then y=z

x,y,z are integer variables.

 

I scan the other related posts using big M method and I find it is unsuitable for my problem since this constraint is equal and I am looking forward to your help!

 

thanks a lot!

2

• Official comment

  

  Juan Orozco

  Gurobi Staff

  • November 25, 2020 17:56
  • Edited

  Dear Ray,

  I'd use two types of general constraints, namely model.addGenConstrAbs() and model.addGenConstrIndicator(), along with a few auxiliary variables. In Python, this would look as follows:

   

  import gurobipy as gp
  from gurobipy import GRB
  
  K = 5
  BigM = 15
  
  model = gp.Model("myModel")
  
  x = model.addVar(lb=-10, ub=10, vtype=GRB.INTEGER, name="x")
  y = model.addVar(vtype=GRB.INTEGER, name="y")
  z = model.addVar(vtype=GRB.INTEGER, name="z")
  
  temp = model.addVar(lb=-GRB.INFINITY, name="temp")
  abs_temp = model.addVar(name="abs_temp")
  flag = model.addVar(vtype=GRB.BINARY, name="flag")
  
  model.addConstr(temp == x - K, name="diff")
  model.addGenConstrAbs(abs_temp, temp, name="abs_diff")
  model.addConstr(abs_temp >= 1 - flag, name="aux_1")
  model.addConstr(abs_temp <= BigM*(1-flag), name="aux_2")
  model.addGenConstrIndicator(flag, True, y == z, name="indicator")
  
  
  model.setObjective(x, GRB.MAXIMIZE)

   

  Remark 1: For illustrative purposes, I chose an arbitrary objective function and constant K.

  Remark 2: The binary variable flag is equal to 1 if and only if abs_temp is equal to zero (i.e. it's equal to zero if abs_temp > 0).

  Remark 3: I bounded the general integer variable x, so that I could compute the minimum value for BigM. In fact, it's always a good idea to bound any general integer variable as much as possible. Therefore, it'd be wise to also bound y and z.

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