The Doctor Rostering Problem - Asser Fahrenholz

Appendix B. GAMS Model 79
84 B0 no doctor should have both monday noon shifts and
friday afternoon shifts in the same week
85 B1 no doctor should have both friday afternoon shift
and the following monday noon shift
86 B2a shifts should be divided equally - the max var
87 B2b shifts should be divided equally - the min var
88 B3 no doctor should have a noon nor afternoon shifts
two days in a row
89 B4 no doctor should have the afternoon shift the day
after an evening shift
90 B5 no doctor should have the noon shift the same day
as an evening shift
91 B6a no doctor should have the noon shift the day after
an afternoon shift
92 B6b no doctor should have the afternoon shift the day
93
after a noon shift ;
94 VALUE .. z =e= sum (( workingdays ( day ),assignmentshifts ( shift
95
),doctor , index ),y(day , shift , doctor , index ))
+ dmax - dmin ;
96 H0a (day , shift , doctor ) .. x(day , shift , doctor
) + x(day , shift +1 , doctor ) =l= 1;
97 H0b (day , eveningshift ( shift ),doctor ).. x(day , shift -1 ,
doctor ) + b(day , shift , doctor ) =l= 1;
98 H0c (day , nightshift ( shift ),doctor ).. x(day , shift +1 ,
doctor ) + b(day , shift , doctor ) =l= 1;
99 H1(day , noonshift ( shift ),doctor ) .. b(day , shift +2 ,
doctor ) + x( day +1 , shift , doctor ) =l= 1;
100 H2(day , nightshift ( shift ),doctor ) .. b(day , shift , doctor
) + x(day , shift +1 , doctor ) + x(day , shift +2 ,
doctor ) =l= 1;
101 H3a (day , shift , doctor ) .. x(day , shift , doctor
) + b(day , shift , doctor ) =l= 1;
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G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m
C o m p i l a t i o n
102 H3b (day , shift , doctor ) .. x(day , shift , doctor
) + c(day , shift , doctor ) =l= 1;
103 H4( workingdays ( day ),assignmentshifts ( shift )) .. sum ( doctor ,x(day ,
shift , doctor )) =e= 1 + s(day , shift );
104 H5(day , nonshifts ( shift ),doctor ) .. x(
105
106
day , shift , doctor ) =e= 0;
107 B0( mondays ( day ),noonshift ( shift ),doctor , index0 ( index )) ..x(day , shift , doctor
) + x( day +4 , shift +1 , doctor ) =e=
108 1 + y(day ,
shift , doctor , index ) - k(day , shift , doctor ,in
dex );