# Linear JUMP model violates constraint

**URL:** <https://discourse.julialang.org/t/linear-jump-model-violates-constraint/2749>\
**Category:** General Usage\
**Created:** [March 18, 2017, 1:49pm UTC](https://discourse.julialang.org/t/linear-jump-model-violates-constraint/2749 "2017-03-18T13:49:18Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![ozgutr](https://avatars.discourse-cdn.com/v4/letter/o/df705f/32.png) [@ozgutr](https://discourse.julialang.org/u/ozgutr)\
**Post date:** [March 18, 2017, 1:49pm UTC](https://discourse.julialang.org/t/linear-jump-model-violates-constraint/2749/1 "2017-03-18T13:49:18Z")

</div>

Hi, I have JuMP model which violates following set of constraints(from .lp output)

```
Line 35: c32: 1 Weeks_1_1_3_2_1 - 0.03898471331421523 ThputM_1_1_3_2_1 = 0
Line 107: c104: 1 Weeks_1_1_3_2_1 <= 28.3
Line 179: c176: 1 Weeks_1_1_3_2_1 >= 2.3000000000000007
Line 251: c248: 1 Final_Weeks_1_1_3_2 - 1 Weeks_1_1_3_2_1 >= 0
Line 323: c320: -1 XW_p_1_1_3_2_1 + 1 Weeks_1_1_3_2_1 <= 18.3
Line 395: c392: 1 XW_n_1_1_3_2_1 + 1 Weeks_1_1_3_2_1 >= 18.3
Line 684: 0 <= Weeks_1_1_3_2_1 <= +inf

```

**When I print out the value of decision variable array after optimizing, value of corresponding variable ( Weeks\_1\_1\_3\_2\_1 above) is 33.6. What might be the reason for this?**

Here is full code:

```julia
using JuMP
using DataFrames
using Gurobi

# Penalty cost of laying off a crew
# pset = ["packaging1", "packaging2"]
root="C:/Users/.../v4"
filename=string(root,"/Manufacturing Sites.csv")
mset = readtable(filename)
a_mset= convert(Matrix,mset)
size_mset = length(a_mset)
filename=string(root,"/Period List.csv")
timeset = readtable(filename)
a_timeset= convert(Matrix,timeset)
size_timeset = length(a_timeset)
filename=string(root,"/API List.csv")
apiset = readtable(filename)
a_apiset= convert(Matrix,apiset)
size_apiset = length(a_apiset)
demandsizeset = [1,2,3]
size_demandlevels=length(demandsizeset)
scenarioset = ["1"]
#,"s2","s3","s4","s5","s6","s7","s8","s9","s10","s11","s12","s13","s14","s15","s16"
size_scenarioset = length(scenarioset)
filename=string(root,"/BaseUsage.csv")
BaseUsage_raw = readtable(filename)
a_BaseUsage= convert(Array,BaseUsage_raw[:,3])
BaseUsage= Array(Float64, size_timeset, size_mset)
count=1
for m = 1:size_mset
  for t = 1:size_timeset
    BaseUsage[t,m]=a_BaseUsage[count]
    count=count+1

  end
end
SR = ones(Float64,size_apiset,size_timeset,size_mset,size_demandlevels,size_scenarioset)
RW = ones(Float64,size_apiset,size_timeset,size_mset,size_demandlevels,size_scenarioset )
KGS = ones(Float64,size_apiset,size_timeset,size_mset,size_demandlevels,size_scenarioset)
DEMAND= ones(Float64,size_apiset,size_timeset,size_mset,size_demandlevels,size_scenarioset)
for s = 1:size_scenarioset
  for d = 1:3
    if d == 1 mid_name="BaseDemand" end
    if d == 2 mid_name="HighDemand" end
    if d == 3 mid_name="LowDemand" end
    filename=string(root,"/SR Scenario",mid_name,scenarioset[s],".csv")
    scenario_input=readtable(filename)
    SR_raw=convert(Array,scenario_input[:,4])
    DEMAND_raw= convert(Array,scenario_input[:,8])
    KGS_raw= convert(Array,scenario_input[:,12])
    RW_raw= convert(Array,scenario_input[:,16])
    count=2
    for a = 1:size_apiset
      for m = 1:size_mset
        for t = 1:size_timeset
          SR[a,t,m,d,s]=parse(Float64,SR_raw[count])
          RW[a,t,m,d,s]=parse(Float64,RW_raw[count])
          KGS[a,t,m,d,s]=parse(Float64,KGS_raw[count])
          DEMAND[a,t,m,d,s]=parse(Float64,DEMAND_raw[count])
          count=count+1

        end
      end
    end
  end
end

print("Size of manufacturing set:")
println(size_mset)
print("Size of API set:")
println(size_apiset)
print("Size of time set:")
println(size_timeset)

prod = Model(solver=GurobiSolver())

### VARIABLES ###
@variable(prod, ThputM[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset] >= 0) 

@variable(prod, 0 <= Weeks[1:size_apiset, 1:size_timeset, 1:size_mset, d=1:size_demandlevels, 1:size_scenarioset] <= 52)
@variable(prod, 0 <= Final_Weeks[1:size_apiset, 1:size_timeset, 1:size_mset, d=1:size_demandlevels] <= 52)
@variable(prod, XW_p[1:size_apiset, 1:size_timeset, 1:size_mset, d=1:size_demandlevels, 1:size_scenarioset] >= 0)
@variable(prod, XW_n[1:size_apiset, 1:size_timeset, 1:size_mset, d=1:size_demandlevels, 1:size_scenarioset] >= 0)

### CONSTRAINTS ###

#relate to the total demand
@constraint(prod,linear_pos_abs_D[a=1:size_apiset, t=1:size_timeset, d=1:size_demandlevels, s=1:size_scenarioset], sum(ThputM[a,t,m,d,s] for m=1:size_mset) >= DEMAND[a,t,d,s])

#calculate the number of weeks
@constraint(prod, thput_relate_Total_API_to_weeks[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset], Weeks[a,t,m,d,s] - (ThputM[a,t,m,d,s]/(SR[a,t,m,d,s]*RW[a,t,m,d,s]*KGS[a,t,d,s])) == 0)

#restrict the number of weeks using available capacity
@constraint(prod, restrict_weeks_ub[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset], Weeks[a,t,m,d,s] <= 52-BaseUsage[t,m])

#restrict the number of weeks using lower bound
@constraint(prod, restrict_weeks_lb[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset], Weeks[a,t,m,d,s] >= 26-BaseUsage[t,m])

#find the maximum of all the number of weeks' production over all scenarios
@constraint(prod, final_thput_relateF[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset], Final_Weeks[a,t,m,d]-Weeks[a,t,m,d,s] >=0 )

#find the deviation from 42 weeks
@constraint(prod,linear_pos_abs_P[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset], (-1*XW_p[a,t,m,d,s])+Weeks[a,t,m,d,s]+BaseUsage[t,m] <= 42)

@constraint(prod,linear_neg_abs_P[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset], XW_n[a,t,m,d,s]+Weeks[a,t,m,d,s]+BaseUsage[t,m] >= 42)

#restrict the number of final weeks using available capacity
@constraint(prod, restrict_final_weeks_ub[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels], Final_Weeks[a,t,m,d] <= 52-BaseUsage[t,m])

#restrict the number of final weeks using lower bound
@constraint(prod, restrict_final_weeks_lb[a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels], Final_Weeks[a,t,m,d] >= 26-BaseUsage[t,m])

@objective(prod, Min,sum(XW_p[a,t,m,d,s]+XW_n[a,t,m,d,s] for a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels, s=1:size_scenarioset)+
  sum(Final_Weeks[a,t,m,d] for a=1:size_apiset, t=1:size_timeset, m=1:size_mset, d=1:size_demandlevels))

filename=string(root,"/Gene.lp")
writeLP(prod, filename, genericnames=false)
print(prod)
production = solve(prod)

```

---

<div class="post-metadata">

**Author:** ![joehuchette](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/joehuchette/32/32_2.png) [@joehuchette](https://discourse.julialang.org/u/joehuchette)\
**Post date:** [March 18, 2017, 5:50pm UTC](https://discourse.julialang.org/t/linear-jump-model-violates-constraint/2749/2 "2017-03-18T17:50:23Z")

</div>

Without seeing the model, it’s impossible to diagnose.

-Joey

---

<div class="post-metadata">

**Author:** ![ozgutr](https://avatars.discourse-cdn.com/v4/letter/o/df705f/32.png) [@ozgutr](https://discourse.julialang.org/u/ozgutr)\
**Post date:** [March 18, 2017, 6:32pm UTC](https://discourse.julialang.org/t/linear-jump-model-violates-constraint/2749/3 "2017-03-18T18:32:52Z")

</div>

I have added the model

---

<div class="post-metadata">

**Author:** ![joehuchette](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/joehuchette/32/32_2.png) [@joehuchette](https://discourse.julialang.org/u/joehuchette)\
**Post date:** [March 18, 2017, 6:41pm UTC](https://discourse.julialang.org/t/linear-jump-model-violates-constraint/2749/4 "2017-03-18T18:41:30Z")

</div>

Can’t say for sure but your values in `BaseUsage` may not be what you intend (if the `restrict_weeks_ub` constraints are the ones that you believe are not being satisfied).

---

<div class="post-metadata">

**Author:** ![ozgutr](https://avatars.discourse-cdn.com/v4/letter/o/df705f/32.png) [@ozgutr](https://discourse.julialang.org/u/ozgutr)\
**Post date:** [March 19, 2017, 1:23am UTC](https://discourse.julialang.org/t/linear-jump-model-violates-constraint/2749/5 "2017-03-19T01:23:26Z")

</div>

![](https://global.discourse-cdn.com/julialang/original/3X/4/8/4846cf11681b700f13a94806aa3e071244f86e98.png)

That was the first thing I suspected it does not seem so in the input file (Attached file). I also checked the order of indices in my outputting routine with the constraint right hand side and indices of the variable in that constraint. They all seem to match.

**Can there be a limitation on the number of constraints that Gurobi reads with JuMP? I realized there are more bound violations than I pointed above !!!**