**************************************************** * RARDIN, OPTIMIZATION IN O.R., P.131-153 * * SHIFT SCHEDULING & STAFF PLANNING MODELS * * EXAMPLE 4.5 - OHIO NATIONAL BANK PROBLEM * * [this problem has multiple optimal solutions] * * * * DSN = R148.SAS * ****************************************************; DATA NEW; INPUT _TYPE_ $ _ROW_ $ _COL_ $ _COEF_; CARDS; MIN COST . . . COST X11 90.0 . COST X12 91.0 . COST X13 92.0 . COST Y11 18.0 . COST Y12 18.0 . COST Z11 28.0 . COST Z12 28.0 . COST Z13 28.0 . COST Z14 28.0 . COST Z15 29.0 . COST Z16 30.0 . COST Z17 31.0 . COST Z18 32.0 LE MACH-11 X11 1.0 . MACH-11 Z11 1.0 . MACH-11 _RHS_ 35.0 LE MACH-12 X11 1.0 . MACH-12 X12 1.0 . MACH-12 Z11 1.0 . MACH-12 Z12 1.0 . MACH-12 _RHS_ 35.0 LE MACH-13 X11 1.0 . MACH-13 X12 1.0 . MACH-13 X13 1.0 . MACH-13 Z11 1.0 . MACH-13 Z12 1.0 . MACH-13 Z13 1.0 . MACH-13 _RHS_ 35.0 LE MACH-14 X11 1.0 . MACH-14 X12 1.0 . MACH-14 X13 1.0 . MACH-14 Z11 1.0 . MACH-14 Z12 1.0 . MACH-14 Z13 1.0 . MACH-14 Z14 1.0 . MACH-14 _RHS_ 35.0 LE MACH-15 X12 1.0 . MACH-15 X13 1.0 . MACH-15 Z12 1.0 . MACH-15 Z13 1.0 . MACH-15 Z14 1.0 . MACH-15 Z15 1.0 . MACH-15 _RHS_ 35.0 LE MACH-16 X11 1.0 . MACH-16 X13 1.0 . MACH-16 Z13 1.0 . MACH-16 Z14 1.0 . MACH-16 Z15 1.0 . MACH-16 Z16 1.0 . MACH-16 _RHS_ 35.0 LE MACH-17 X11 1.0 . MACH-17 X12 1.0 . MACH-17 Z14 1.0 . MACH-17 Z15 1.0 . MACH-17 Z16 1.0 . MACH-17 Z17 1.0 . MACH-17 _RHS_ 35.0 LE MACH-18 X11 1.0 . MACH-18 X12 1.0 . MACH-18 X13 1.0 . MACH-18 Z15 1.0 . MACH-18 Z16 1.0 . MACH-18 Z17 1.0 . MACH-18 Z18 1.0 . MACH-18 _RHS_ 35.0 LE MACH-19 X11 1.0 . MACH-19 X12 1.0 . MACH-19 X13 1.0 . MACH-19 Z16 1.0 . MACH-19 Z17 1.0 . MACH-19 Z18 1.0 . MACH-19 _RHS_ 35.0 LE MACH-20 Y11 1.0 . MACH-20 X12 1.0 . MACH-20 X13 1.0 . MACH-20 Z17 1.0 . MACH-20 Z18 1.0 . MACH-20 _RHS_ 35.0 LE MACH-21 Y12 1.0 . MACH-21 X13 1.0 . MACH-21 Z18 1.0 . MACH-21 _RHS_ 35.0 LE OVTM-11 X11 -0.5 . OVTM-11 Y11 1.0 . OVTM-11 _RHS_ 0.0 LE OVTM-12 X12 -0.5 . OVTM-12 Y12 1.0 . OVTM-12 _RHS_ 0.0 LE TOTOVTM Y11 1.0 . TOTOVTM Y12 1.0 . TOTOVTM _RHS_ 20.0 GE COVER-11 X11 1.0 . COVER-11 Z11 0.8 . COVER-11 W12 1.0 . COVER-11 _RHS_ 10.0 GE COVER-12 X11 1.0 . COVER-12 X12 1.0 . COVER-12 Z11 0.8 . COVER-12 Z12 0.8 . COVER-12 W12 -1.0 . COVER-12 W13 1.0 . COVER-12 _RHS_ 11.0 GE COVER-13 X11 1.0 . COVER-13 X12 1.0 . COVER-13 X13 1.0 . COVER-13 Z11 0.8 . COVER-13 Z12 0.8 . COVER-13 Z13 0.8 . COVER-13 W13 -1.0 . COVER-13 W14 1.0 . COVER-13 _RHS_ 15.0 GE COVER-14 X11 1.0 . COVER-14 X12 1.0 . COVER-14 X13 1.0 . COVER-14 Z11 0.8 . COVER-14 Z12 0.8 . COVER-14 Z13 0.8 . COVER-14 Z14 0.8 . COVER-14 W14 -1.0 . COVER-14 W15 1.0 . COVER-14 _RHS_ 20.0 GE COVER-15 X12 1.0 . COVER-15 X13 1.0 . COVER-15 Z12 0.8 . COVER-15 Z13 0.8 . COVER-15 Z14 0.8 . COVER-15 Z15 0.8 . COVER-15 W15 -1.0 . COVER-15 W16 1.0 . COVER-15 _RHS_ 25.0 GE COVER-16 X11 1.0 . COVER-16 X13 1.0 . COVER-16 Z13 0.8 . COVER-16 Z14 0.8 . COVER-16 Z15 0.8 . COVER-16 Z16 0.8 . COVER-16 W16 -1.0 . COVER-16 W17 1.0 . COVER-16 _RHS_ 28.0 GE COVER-17 X11 1.0 . COVER-17 X12 1.0 . COVER-17 Z14 0.8 . COVER-17 Z15 0.8 . COVER-17 Z16 0.8 . COVER-17 Z17 0.8 . COVER-17 W17 -1.0 . COVER-17 W18 1.0 . COVER-17 _RHS_ 32.0 GE COVER-18 X11 1.0 . COVER-18 X12 1.0 . COVER-18 X13 1.0 . COVER-18 Z15 0.8 . COVER-18 Z16 0.8 . COVER-18 Z17 0.8 . COVER-18 Z18 0.8 . COVER-18 W18 -1.0 . COVER-18 W19 1.0 . COVER-18 _RHS_ 50.0 GE COVER-19 X11 1.0 . COVER-19 X12 1.0 . COVER-19 X13 1.0 . COVER-19 Z16 0.8 . COVER-19 Z17 0.8 . COVER-19 Z18 0.8 . COVER-19 W19 -1.0 . COVER-19 W20 1.0 . COVER-19 _RHS_ 29.994 GE COVER-20 Y11 1.0 . COVER-20 X12 1.0 . COVER-20 X13 1.0 . COVER-20 Z17 0.8 . COVER-20 Z18 0.8 . COVER-20 W20 -1.0 . COVER-20 W21 1.0 . COVER-20 _RHS_ 20.0 GE COVER-21 Y12 1.0 . COVER-21 X13 1.0 . COVER-21 Z18 0.8 . COVER-21 W21 -1.0 . COVER-21 _RHS_ 8.0 LE W12-MAX W12 1.0 . W12-MAX _RHS_ 20.0 LE W13-MAX W13 1.0 . W13-MAX _RHS_ 20.0 LE W14-MAX W14 1.0 . W14-MAX _RHS_ 20.0 LE W15-MAX W15 1.0 . W15-MAX _RHS_ 20.0 LE W16-MAX W16 1.0 . W16-MAX _RHS_ 20.0 LE W17-MAX W17 1.0 . W17-MAX _RHS_ 20.0 LE W18-MAX W18 1.0 . W18-MAX _RHS_ 20.0 LE W19-MAX W19 1.0 . W19-MAX _RHS_ 20.0 LE W20-MAX W20 1.0 . W20-MAX _RHS_ 20.0 LE W21-MAX W21 1.0 . W21-MAX _RHS_ 20.0 . W12-MAX _RHS_ 20.0 ; PROC LP SPARSEDATA ; TITLE 'ONB SHIFT SCHEDULING PROBLEM'; RUN;