Acme

Acme Employee Scheduling Model with Three Scheduled Meals per Shift - LINDO Comments: E10:E11:E12 are the full-time Early shift (7 am - 4 pm) workers with lunch at 10 am, 11 am & 12 noon L5:L6:L7 are the fukk-time Late shift (2 - 11 pm) workers with dinner at 5, 6 & 7 pm P7-P19 are the part-time workers starting at 7 am ... 7 pm PTH is the total part time hours worked, FTH is the total full-time hours worked and TOTH is the total hours worked LINDO input follows: Min 750E10+750E11+750E12+750L5+750L6+750L7+300P7+300P8+300P9+300P10+300P11+300P12+300P13+300P14 +300P15+300P16+300P17+300P18+300P19 ST 7AM) E10+E11+E12 +P7 >= 15 8AM) E10+E11+E12 +P7+P8 >= 15 9AM) E10+E11+E12 +P7+P8+P9 >= 15 10AM) E11+E12 +P7+P8+P9+P10 >= 20 11AM) E10 +E12 +P8+P9+P10+P11 >= 20 12PM) E10+E11 +P9+P10+P11+P12 >= 20 1PM) E10+E11+E12 +P10+P11+P12+P13 >= 20 2PM) E10+E11+E12 +L5+L6+L7 +P11+P12+P13+P14 >= 20 3PM) E10+E11+E12 +L5+L6+L7 +P12+P13+P14+P15 >= 25 4PM) +L5+L6+L7 +P13+P14+P15+P16 >= 25 5PM) +L6+L7 +P14+P15+P16+P17 >= 25 6PM) +L5 +L7 +P15+P16+P17+P18 >= 20 7PM) +L5+L6 +P16+P17+P18+P19 >= 20 8PM) +L5+L6+L7 +P17+P18+P19 >= 15 9PM) +L5+L6+L7 + P18+P19 >= 15 10PM) +L5+L6+L7 +P19 >= 15 PTHrs) PTH-4P7-4P8-4P9-4P10-4P11-4P12-4P13-4P14-4P15-4P16-4P17-4P18-4P19 = 0 FTHrs) FTH-8E10-8E11-8E12-8L5-8L6-8L7 = 0 TotHrs) TOTH-PTH-FTH = 0 PTHrsLmt) PTH-0.5TOTH <= 0 E10 >= 0 E11 >= 0 E12 >= 0 L5 >= 0 L6 >= 0 L7 >= 0 P7 >= 0 P8 >= 0 P9 >= 0 P10 >= 0 P11 >= 0 P12 >= 0 P13 >= 0 P14 >= 0 P15 >= 0 P16 >= 0 P17 >= 0 P18 >= 0 P19 >= 0 End GIN 19 LINDO output follows: LP OPTIMUM FOUND AT STEP 20 OBJECTIVE VALUE = 25875.0000 SET E11 TO <= 0 AT 1, BND= -0.2588E+05 TWIN=-0.2588E+05 22 SET E10 TO >= 8 AT 2, BND= -0.2610E+05 TWIN=-0.2590E+05 33 SET L5 TO >= 2 AT 3, BND= -0.2632E+05 TWIN=-0.2616E+05 36 SET L6 TO >= 5 AT 4, BND= -0.2632E+05 TWIN=-0.2642E+05 41 SET L7 TO >= 5 AT 5, BND= -0.2640E+05 TWIN=-0.2632E+05 45 NEW INTEGER SOLUTION OF 26400.0000 AT BRANCH 5 PIVOT 45 BOUND ON OPTIMUM: 25875.00 DELETE L7 AT LEVEL 5 DELETE L6 AT LEVEL 4 FLIP L5 TO <= 1 AT 3 WITH BND= -26156.250 SET E10 TO <= 8 AT 4, BND= -0.2616E+05 TWIN=-0.1000E+31 45 SET L5 TO >= 1 AT 5, BND= -0.2616E+05 TWIN=-0.1000E+31 45 SET P11 TO <= 0 AT 6, BND= -0.2616E+05 TWIN=-0.1000E+31 45 SET L7 TO <= 4 AT 7, BND= -0.2632E+05 TWIN=-0.2632E+05 50 DELETE L7 AT LEVEL 7 DELETE P11 AT LEVEL 6 DELETE L5 AT LEVEL 5 DELETE E10 AT LEVEL 4 DELETE L5 AT LEVEL 3 FLIP E10 TO <= 7 AT 2 WITH BND= -25895.455 SET L5 TO >= 2 AT 3, BND= -0.2599E+05 TWIN=-0.2590E+05 52 SET E12 TO <= 0 AT 4, BND= -0.2599E+05 TWIN=-0.1000E+31 52 SET L5 TO <= 2 AT 5, BND= -0.2599E+05 TWIN=-0.1000E+31 52 SET P13 TO <= 0 AT 6, BND= -0.2599E+05 TWIN=-0.1000E+31 52 SET P18 TO <= 0 AT 7, BND= -0.2599E+05 TWIN=-0.1000E+31 52 SET P15 TO <= 6 AT 8, BND= -0.2599E+05 TWIN=-0.2610E+05 61 SET L7 TO >= 4 AT 9, BND= -0.2599E+05 TWIN=-0.2610E+05 64 SET L6 TO >= 7 AT 10, BND= -0.2610E+05 TWIN=-0.2610E+05 74 NEW INTEGER SOLUTION OF 26100.0000 AT BRANCH 10 PIVOT 74 BOUND ON OPTIMUM: 25875.00 DELETE L6 AT LEVEL 10 DELETE L7 AT LEVEL 9 DELETE P15 AT LEVEL 8 DELETE P18 AT LEVEL 7 DELETE P13 AT LEVEL 6 DELETE L5 AT LEVEL 5 DELETE E12 AT LEVEL 4 FLIP L5 TO <= 1 AT 3 WITH BND= -25895.455 SET E10 TO >= 7 AT 4, BND= -0.2590E+05 TWIN=-0.1000E+31 74 SET P13 TO <= 0 AT 5, BND= -0.2590E+05 TWIN=-0.1000E+31 74 SET P14 TO <= 0 AT 6, BND= -0.2590E+05 TWIN=-0.1000E+31 74 SET P18 TO <= 0 AT 7, BND= -0.2590E+05 TWIN=-0.1000E+31 74 SET L7 TO <= 4 AT 8, BND= -0.2610E+05 TWIN=-0.2599E+05 83 DELETE L7 AT LEVEL 8 DELETE P18 AT LEVEL 7 DELETE P14 AT LEVEL 6 DELETE P13 AT LEVEL 5 DELETE E10 AT LEVEL 4 DELETE L5 AT LEVEL 3 DELETE E10 AT LEVEL 2 FLIP E11 TO >= 1 AT 1 WITH BND= -25875.000 SET P13 TO <= 0 AT 2, BND= -0.2588E+05 TWIN=-0.1000E+31 90 SET E10 TO >= 7 AT 3, BND= -0.2588E+05 TWIN=-0.2592E+05 97 SET L5 TO >= 1 AT 4, BND= -0.2599E+05 TWIN=-0.2599E+05 103 DELETE L5 AT LEVEL 4 FLIP E10 TO <= 6 AT 3 WITH BND= -25920.000 SET E10 TO >= 6 AT 4, BND= -0.2592E+05 TWIN=-0.1000E+31 103 SET L5 TO <= 0 AT 5, BND= -0.2592E+05 TWIN=-0.1000E+31 103 SET P12 TO <= 0 AT 6, BND= -0.2592E+05 TWIN=-0.1000E+31 103 SET P14 TO <= 0 AT 7, BND= -0.2592E+05 TWIN=-0.1000E+31 103 SET L7 TO >= 5 AT 8, BND= -0.2599E+05 TWIN=-0.2604E+05 105 DELETE L7 AT LEVEL 8 DELETE P14 AT LEVEL 7 DELETE P12 AT LEVEL 6 DELETE L5 AT LEVEL 5 DELETE E10 AT LEVEL 4 DELETE E10 AT LEVEL 3 DELETE P13 AT LEVEL 2 DELETE E11 AT LEVEL 1 ENUMERATION COMPLETE. BRANCHES= 14 PIVOTS= 105 LAST INTEGER SOLUTION IS THE BEST FOUND RE-INSTALLING BEST SOLUTION... OBJECTIVE FUNCTION VALUE 1) 26100.00 VARIABLE VALUE REDUCED COST E10 7.000000 750.000000 E11 0.000000 750.000000 E12 0.000000 750.000000 L5 2.000000 750.000000 L6 7.000000 750.000000 L7 4.000000 750.000000 P7 8.000000 300.000000 P8 0.000000 300.000000 P9 0.000000 300.000000 P10 12.000000 300.000000 P11 1.000000 300.000000 P12 0.000000 300.000000 P13 0.000000 300.000000 P14 0.000000 300.000000 P15 5.000000 300.000000 P16 7.000000 300.000000 P17 2.000000 300.000000 P18 0.000000 300.000000 P19 2.000000 300.000000 PTH 148.000000 0.000000 FTH 160.000000 0.000000 TOTH 308.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 7AM) 0.000000 0.000000 8AM) 0.000000 0.000000 9AM) 0.000000 0.000000 10AM) 0.000000 0.000000 11AM) 0.000000 0.000000 12PM) 0.000000 0.000000 1PM) 0.000000 0.000000 2PM) 1.000000 0.000000 3PM) 0.000000 0.000000 4PM) 0.000000 0.000000 5PM) 0.000000 0.000000 6PM) 0.000000 0.000000 7PM) 0.000000 0.000000 8PM) 2.000000 0.000000 9PM) 0.000000 0.000000 10PM) 0.000000 0.000000 PTHRS) 0.000000 0.000000 FTHRS) 0.000000 0.000000 TOTHRS) 0.000000 0.000000 PTHRSLMT) 6.000000 0.000000 22) 7.000000 0.000000 23) 0.000000 0.000000 24) 0.000000 0.000000 25) 2.000000 0.000000 26) 7.000000 0.000000 27) 4.000000 0.000000 28) 8.000000 0.000000 29) 0.000000 0.000000 30) 0.000000 0.000000 31) 12.000000 0.000000 32) 1.000000 0.000000 33) 0.000000 0.000000 34) 0.000000 0.000000 35) 0.000000 0.000000 36) 5.000000 0.000000 37) 7.000000 0.000000 38) 2.000000 0.000000 39) 0.000000 0.000000 40) 2.000000 0.000000 NO. ITERATIONS= 105 BRANCHES= 14 DETERM.= 1.000E 0