Constraint Modelling

回答済み

Salma Dessouki

2023年12月16日 03:38

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Yes it worked, thank you!

I would like to add a constraint to my model: w_ij = min(1, sum over k of R_ijk) for every i, j

w = model.addVars(I, J, vtype=GRB.BINARY, name="w") #:if clinic i is assigned to timeslot j

R = model.addVars(I, J, K, vtype=GRB.INTEGER, name="R") # Number of rooms assigned to clinic i assigned to a timeslot j and location K

Number of clinics (I): 205 Number of timeslots (J): 10 Number of locations (K): 16

 

I have tried the following:

1) model.addConstrs((w[i, j] == min_(R.sum(i, j, '*'), constant=1) for i in range(I) for j in range(J)), name="w_ij_constraint") but I get the error "GurobiError: Invalid data in vars array"

2) NotImplementedError: 

# Constraint: If sum(R_ijk) > 0, then w_ij = 1

model.addConstrs((gp.quicksum(R[i, j, k] for k in range(K)) > 0) >> (w[i, j] == 1) for i in range(I) for j in range(J))

# Constraint: If sum(R_ijk) = 0, then w_ij = 0

model.addConstrs((gp.quicksum(R[i, j, k] for k in range(K)) == 0) >> (w[i, j] == 0) for i in range(I) for j in range(J))

Any idea how to fix this and correctly code this constraint?

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• 

  Riley Clement

  • Gurobi Staff

  2023年12月16日 05:04

  Hi Salma,

  These issues are related in that they can all be resolved by closely followed the API documentation.

  The documentation for min_ indicates the arguments (except for the constant) must be "Var, or list of Var, or tupledict of Var values", but in your code you are trying to use R.sum(i, j, '*') which is a sum of variables.  In order to resolve you will need to create another family of variables to equal R.sum(i, j, '*'), eg

  w = model.addVars(I, J, vtype=GRB.BINARY, name="w") #:if clinic i is assigned to timeslot j
  R = model.addVars(I, J, K, vtype=GRB.INTEGER, name="R") # Number of rooms assigned to clinic i assigned to a timeslot j and location K
  R_ij_sum = model.addVars(I, J, name="R_ij_sum")
  
  model.addConstrs((R_ij_sum[i, j] == R.sum(i, j, '*') for i in range(I) for j in range(J)), name="R_ij_sum_constraint")
  model.addConstrs((w[i, j] == min_(R_ij_sum[i,j], constant=1) for i in range(I) for j in range(J)), name="w_ij_constraint")
  

  It is also worth considering whether the following would also be enough to model what you need to

  w = model.addVars(I, J, vtype=GRB.BINARY, name="w") #:if clinic i is assigned to timeslot j
  R = model.addVars(I, J, K, vtype=GRB.INTEGER, name="R") # Number of rooms assigned to clinic i assigned to a timeslot j and location K
  
  model.addConstrs((w[i, j] <= R.sum(i, j, '*')) for i in range(I) for j in range(J)), name="w_ij_constraint")

   

  As for the indicator constraints the documentation states

  An INDICATOR constraint \( z = f \rightarrow a^T x \leq b \) states that if the binary indicator variable \( z \) is equal to \( f \), where \( f \in \{0,1\} \), then the linear constraint \( a^T x \leq b \) should hold. 

  The following

  If sum(R_ijk) > 0, then w_ij = 1

  cannot be directly modeled with an indicator constraint because it does not fit the requirements:

  * sum(R_ijk)  is not a binary variable
  * the relation is >, and not =

  In order to achieve what you want you will need to form the contrapositive of your expression, eg "if w = 0 then sum(R_ijk) = 0" and model that instead.

  - Riley

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