How to get the square root(sum of binary decission variable)

Answered

Mohd Munasib

• November 29, 2023 11:36

Hi Team,

Hope you are doing well.

In this df i have defined the decission binary variable 

origin	fixed_cost	var_cost	cap	open
chennai	$    50,000	$        2.23	400,000	<gurobi.Var *Awaiting Model Update*>
bhopal	$    56,000	$        2.32	240,000	<gurobi.Var *Awaiting Model Update*>
jaipur	$    65,000	$        2.25	300,000	<gurobi.Var *Awaiting Model Update*>
kolkata	$    65,000	$        2.45	200,000	<gurobi.Var *Awaiting Model Update*>
nasik	$    55,000	$        2.21	300,000	<gurobi.Var *Awaiting Model Update*>
pune	$    89,000	$        2.56	300,000	<gurobi.Var *Awaiting Model Update*>
sonipat	$    95,000	$        2.78	240,000	<gurobi.Var *Awaiting Model Update*>

My goal is  to get the square root of (sum of "open") variable (√(∑(open)) )

I am looking forward to get resolved this shortly 

Thanks 

Munasib

0

• 

  Riley Clement

  Gurobi Staff

  • November 30, 2023 04:16

  Hi Mohd,

  You can decompose √(∑(open)) into two constraints:

  sum_open = model.addVar(ub=ub1, vtype="I")
  sqrt_sum_open = model.addVar(ub=ub2)
  
  model.addConstr(sum_open == df["open"].sum())
  model.addConstr(sum_open == sqrt_sum_open**2)

  Note that if there is a limit to how many "open" binary variables can be 1 in an optimal solution then you should use this value for ub1, and sqrt(ub1) for ub2.

  Note, if your objective function is simply sqrt_sum_open then you don't actually need the square root, you can use sum_open instead.

  - Riley

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