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. 2022 Feb 9;25(2):311–332. doi: 10.1007/s10729-021-09588-8
Index set Description
cC Specialties
rR OT-Rooms
tT Days in the planning horizon
tO Days without elective surgery,OT
iI Block or Patient type (Ward block = 0 or ICU block = 1)
sS Shifts in a day (early, late, night)
Parameters
Lc,tICU Probability that a patient from specialty c stays at least t days in the ICU
Ec,tICU Probability that a patient from specialty c stays exactly t days in the ICU
Lc,t,iWard Probability that a patient from specialty c stays at least t days in the ward with prior transfer from the ICU (i=1) or OT (i=0)
Ec,t,iWard Probability that a patient from specialty c stays exactly t days in the ward with prior transfer from the ICU (i=1) or OT (i=0)
BcMax Maximum number of daily MSS blocks for specialty c
BcTotal Required number of MSS blocks in the planning horizon for specialty c
Pc# Average number of patients in each block for specialty c
PcShare Target ICU share for specialty c over the planning horizon
NsICU Patient-to-nurse ratio in the ICU in shift s
Nc,sWard Patient-to-nurse ratio in ward c in shift s
AsICU Physician time associated with an ICU admission in shift s
Rt,sICU Physician time associated with ICU daily routine for each patient on day t in shift s
DsICU Physician time associated with a discharge from the ICU in shift s
Ac,sWard Physician time associated with a patient admission in a ward with specialty c in shift s
Rc,t,sWard Physician time associated with daily ward routine for each patient in time slot t for specialty c in shift s
Dc,sWard Physician time associated with a discharge from a ward with specialty c in shift s
Ht,s Shift length for ICU and ward stations on day t in shift s
M¯c,r,t Preexisting MSS assignments (if necessary); 1 if specialty c has room r on day t, 0 otherwise
α Penalty weight for the maximum nurse workload in the ICU and wards
β Penalty weight for the maximum physician workload in the ICU and wards
γ Penalty weight for the number of ICU blocks
Decision variables
mc,r,t,i 1 if specialty c has room r on day t with block type i, 0 otherwise
bc,r,tShare ICU share in a block of specialty c in room r on day t
nt,sICU FTE of ICU nurses required on day t in shift s
nsICUMax Maximum FTE of ICU nurses in shift s within the planning horizon
pt,sICU FTE of ICU physicians required on day t in shift s
psICUMax Maximum FTE of ICU physicians in shift s within the planning horizon
nc,t,sWard FTE of ward nurses required for specialty c on day t in shift s
nc,sWardMax Maximum FTE of ward nurses for specialty c in shift s within the planning horizon
pc,t,sWard FTE of ward physicians for specialty c on day t in shift s
pc,sWardMax Maximum FTE of ward physicians for specialty c in shift s within the planning horizon
yc,t,i Auxiliary variable for the ward admissions of patient type i specialty c on day t
zc,r,t   Auxiliary variable for linearization