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;
