Cplex: cannot get value for decision variables

Question

I'm solving a hospital staff scheduling problem in Cplex and I'm new for Cplex.

But Cplex cannot configure answers of decision variables.

I think maybe it's about my model design problem.

It's a long model.

Very appreciate if I can get help.

++Model

--Sets:

{string} E=...; // set of experience levels (Senior , Rookie)

{string} I=...; // set of all physicians

{string} Is=...; //set of physicians with experience level S

{string} Ir=...;//set of physicians with experience level R

{string} K=...; //type of shifts (o & t)

{string} A1=...; //set of shift o work (Day, evening, night)

{string} A2=...; //set of shift t work (Day, evening, night 1, night 2)

--Parameters

int D=...;

range Day=1..D;//range of planning horizon

int Co[Is]=...; //hiring cost for physician i with senior experience level

int Ct[Ir]=...; //hiring cost for physician i with rookie experience level

int Pku=...; //max. days for physician to perform shift o

int Pkd=...; //min. days for physician to perform shift o

int Pkuh=...;//max. days for physician to perform shift t

int Pkdh=...;//min. days for physician to perform shift t

int s=...; //max. consecutive working days

int dosd=...; //shift o day work demand for "senior"physician

int dose=...; //shift o evening work demand for "senior"physician

int dosn=...; //shift o night work demand for "senior"physician

int dord=...; //shift o day work demand for "rookie"physician

int dore=...; //shift o evening work demand for "rookie"physician

int dorn=...; //shift o night work demand for "rookie"physician

int dtsd=...; //shift t day work demand for "senior"physician

int dtse=...; //shift t evening work demand for "senior"physician

int dtsn1=...; //shift t night1 work demand for "senior"physician

int dtsn2=...; //shift t night2 work demand for "senior"physician

int dtrd=...; //shift t day work demand for "rookie"physician

int dtre=...; //shift t evening work demand for "rookie"physician

int dtrn1=...; //shift t night1 work demand for "rookie"physician

int dtrn2=...; //shift t night2 work demand for "rookie"physician

--Binary decicion variable

dvar int x1[I][Day][A1] in 0..1; //1, if senior+ shift o+ one of the work

dvar int x2[I][Day][A2] in 0..1; //1, if senior+ shift t+ one of the work

dvar int y1[I][Day][A1] in 0..1; //1, if rookie+ shift o+ one of the work

dvar int y2[I][Day][A2] in 0..1; //1, if rookie+ shift t+ one of the work

--Expression of Desicion Variables

dexpr float cost =sum(i in Is,  d in Day, a in A1)Co[i]*x1[i][d][a]  

+ sum(i in Is,  d in Day, a in A2)Co[i]*x2[i][d][a]

+ sum(i in Ir,  d in Day, a in A1)Ct[i]*y1[i][d][a] 

+ sum(i in Ir,  d in Day, a in A2)Ct[i]*y2[i][d][a] ;

--Objective function

minimize cost;

--Constraints

subject to

{

forall(d in Day, Day in A1)

{

sum(i in Is) x1[i, d ,"Day"] == dosd; //Daily demand:Senior+shift o+day work 

}

forall(d in Day, Evening in A1)

{

sum(i in Is ) x1[i, d, "Evening"] == dose; //Daily demand:Senior+shift o+evening work 

}

forall(d in Day, Night in A1)

{

sum(i in Is ) x1[i, d, "Night"] == dosn; //Daily demand:Senior+shift o+night work 

}

forall(d in Day, Day in A2)

{

sum(i in Is) x2[i, d, "Day"] == dtsd; //Daily demand:Senior+ shift t +day work 

}

forall(d in Day, Evening in A2)

{

sum(i in Is) x2[i, d, "Evening"] == dtse; //Daily demand:Senior+shift t+evening work 

}

forall(d in Day, Night1 in A2)

{

sum(i in Is) x2[i, d, "Night1"] == dtsn1; //Daily demand:Senior+shift t+night1 work 

}

forall(d in Day, Night2 in A2)

{

sum(i in Is) x2[i, d, "Night2"] == dtsn2; //Daily demand:Senior+shift t+night2 work 

}

forall(d in Day, Day in A1)

{

sum(i in Ir) y1[i, d, "Day"] == dord; //Daily demand:Rookie+shift o+day work 

}

forall(d in Day, Evening in A1)

{

sum(i in Ir) y1[i, d, "Evening"] == dore; //Daily demand:Rookie+shift o+evening work 

}

forall(d in Day, Night in A1)

{

sum(i in Ir) y1[i, d, "Night"] == dorn; //Daily demand:Rookie+shift o+night work 

}

forall(d in Day, Day in A2)

{

sum(i in Ir) y2[i, d, "Day"] == dtrd; //Daily demand:Rookie+shift t+day work 

}

forall(d in Day, Evening in A2)

{

sum(i in Ir) y2[i, d, "Evening"] == dtre; //Daily demand:Rookie+shift t+evening work 

}

forall(d in Day, Night1 in A2)

{

sum(i in Ir) y2[i, d, "Night1"] == dtrn1; //Daily demand:Rookier+shift t+night1 work 

}

forall(d in Day, Night2 in A2)

{

sum(i in Ir) y2[i, d, "Night2"] == dtrn2; //Daily demand:Rookie+shift t+night2 work 

}

forall(i in Is, d in Day:d<D, Evening in A1)

{    

x1[i, d, "Evening"]+ x1[i,(d+1), "Day"]<=1; //(Senior)For shift type o,if previous day is evening 

work, can't have day work the following day'    

}

forall(i in Is, d in Day:d<D, Evening in A2)

{

x2[i, d, "Evening"]+ x2[i,(d+1), "Day"]<=1; //(Senior)For shift type t,if previous day is evening 

work, can't have day work the following day'

}

forall(i in Ir, d in Day:d<D, Evening in A1)

{    

y1[i, d, "Evening"]+ y1[i,(d+1), "Day"]<=1; //(Rookie)For shift type o,if previous day is evening 

work, can't have day work the following day'  

}

forall(i in Ir, d in Day:d<D, Evening in A2)

{    

y2[i, d, "Evening"]+ y2[i,(d+1), "Day"]<=1; //(Rookie)For shift type t,if previous day is evening 

work, can't have day work the following day'

}  

forall(i in Is, d in Day:d<D, Night in A1)

{  

  x1[i, d,"Night"]+ x1[i,(d+1),"Day"]<=1; //(Senior)For shift type o,if previous day is night work, 

can't have day work the following day'    

}

forall(i in Is, d in Day:d<D, Night1 in A2)

{

x2[i, d,"Night1"]+ x2[i,(d+1),"Day"]<=1;  //(Senior)For shift type t,if previous day is night1 work, 

can't have day work the following day'

}

forall(i in Is, d in Day:d<D, Night2 in A2)

{

x2[i, d,"Night2"]+ x2[i,(d+1),"Day"]<=1;  //(Senior)For shift type t,if previous day is night2 work, 

can't have day work the following day'

} 

forall(i in Ir, d in Day:d<D, Night in A1)

 {    

y1[i, d,"Night"]+ y1[i,(d+1),"Day"]<=1; //(Rookie)For shift type o,if previous day is night work, 

can't have day work the following day'    

}

forall(i in Ir, d in Day:d<D, Night1 in A2)

{

y2[i, d,"Night1"]+ y2[i,(d+1),"Day"]<=1;  //(Rookie)For shift type t,if previous day is night1 work, 

can't have day work the following day'

}

forall(i in Ir, d in Day:d<D, Night2 in A2)

{

y2[i, d,"Night2"]+ y2[i,(d+1),"Day"]<=1;  //(Rookie)For shift type t,if previous day is night2 work, 

can't have day work the following day'

} 

forall (i in Is, d in Day)

{

sum(a in A1)x1[i,d,a] + sum(a in A2)x2[i,d,a] <=1;  //(Senior)each day can only have one work with 

one shift

}

forall (i in Ir, d in Day)

{

sum(a in A1)y1[i,d,a] + sum(a in A2)y2[i,d,a] <=1;  //(Rookie)each day can only have one work with 

one shift
  }

forall(i in Is, a in A1)

{

sum(d in Day)x1[i,d,a] <=Pku; //(Senior) can’t have shift type o that more than upper bound. (in 

days)

}

forall(i in Ir, a in A1)

{

sum(d in Day)y1[i,d,a] <=Pku; //(Rookie) can’t have shift type o that more than upper bound. (in 

days)

}

forall(i in Is, a in A1)

{

sum(d in Day)x1[i,d,a]>=Pkd; //(Senior) can’t have shift type o that less than lower bound. (in 

days)

}

forall(i in Ir, a in A1)

{

sum(d in Day)y1[i,d,a]>=Pkd; //(Rookie) can’t have shift type o that less than lower bound. (in 

days)

}


forall(i in Is, a in A2)

{

sum(d in Day)x2[i,d,a]<=Pkuh; //(Senior) can’t have shift type t that more than upper bound. (in 

days)

}

forall(i in Ir, a in A2)

{

sum(d in Day)y2[i,d,a]<=Pkuh; //(Rookie) can’t have shift type t that more than upper bound. (in 

days)

}

forall(i in Is, a in A2)

{

sum(d in Day)x2[i,d,a]>=Pkdh; //(Senior) can’t have shift type t that less than lower bound. (in 

days)

}

forall(i in Ir, a in A2)

{

sum(d in Day)y2[i,d,a]>=Pkdh; //(Rookie) can’t have shift type t that less than lower bound. (in 

days)

}

forall(i in Is)

{

sum(d in Day:d<=(D-s), a in A1)x1[i,d,a]+sum(d in Day:d<=(D-s), a in A2)x2[i,d,a]<=s; //(Senior) 

can’t have consecutive working days (regardless of shift type) that more than upper bound. (in days)

}

forall(i in Ir)

{

sum(d in Day:d<=(D-s), a in A1)y1[i,d,a]+sum(d in Day:d<=(D-s), a in A2)y2[i,d,a]<=s; //(Rookie) 

can’t have consecutive working days (regardless of shift type) that more than upper bound. (in days)

}

++Data

E={"Senior","Rookie"};

I={"A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S","T","W","X","Y","Z"};

Is={"A","B","C","D","E","F","G","H"};

Ir={"I","J","K","L","M","N","O","P","Q","R","S","T","W","X","Y","Z"};

K={"o","t"};

A1={"Day","Evening","Night"};

A2={"Day","Evening","Night1","Night2"};

D=7;

Co=[1200,1150,1100,1050,1000,950,900,850];

Ct=[800,750,750,750,700,700,700,700,700,700,650,650,650,650,650,650];

Pku=10;

Pkd=5;

Pkuh=8;

Pkdh=4;

s=5;

Answer 1

Your model is probably not feasible. If you label your constraints then CPLEX will give you some relaxation and conflicts that will help you understand why. My suggestion is to label all your constraints.

For instance you can change

forall(d in Day, Day in A1)

{

sum(i in Is) x1[i, d ,"Day"] == dosd; //Daily demand:Senior+shift o+day work 

}

into

forall(d in Day, Day in A1)

    ct1:sum(i in Is) x1[i, d ,"Day"] == dosd; //Daily demand:Senior+shift o+day work