Transcript
CREW SCHEDULINGCREW SCHEDULING
İ.HAKAN KARAÇİZMELİİ.HAKAN KARAÇİZMELİ
GENERAL VIEWGENERAL VIEW
• CREW SCHEDULING TYPESCREW SCHEDULING TYPES
• FLEXIBLE MANAGEMENT STRATEGIESFLEXIBLE MANAGEMENT STRATEGIES
• DESCRIPTION OF PROBLEMDESCRIPTION OF PROBLEM
• FORMULATION OF PROBLEMFORMULATION OF PROBLEM
• MODEL IN LINGOMODEL IN LINGO
• SOLUTION & ANALYSISSOLUTION & ANALYSIS
CREW SCHEDULINGCREW SCHEDULING
• Airline Crew SchedulingAirline Crew Scheduling1.1.The most appropriate pairings.The most appropriate pairings.
2.Equal workloads.2.Equal workloads. 3.Minimum crew COSTS.3.Minimum crew COSTS.
• Mass Transit Crew SchedulingMass Transit Crew Scheduling 1.1.Railway track maintenance problems.Railway track maintenance problems. 2.Mathematical program. 2.Mathematical program. 3.Tabu search.3.Tabu search.
• Generic Crew SchedulingGeneric Crew Scheduling
1.1.Manpower scheduling problems.Manpower scheduling problems.
2.Mixed integer program.2.Mixed integer program.
3.Mimimum manpower.3.Mimimum manpower.
4.Package programs(CPLEX..).4.Package programs(CPLEX..).
FLEXIBLE MANAGEMENT FLEXIBLE MANAGEMENT STRATEGIESSTRATEGIES
• Functional FlexibilityFunctional Flexibility
--Deployment on different tasks.Deployment on different tasks.
• Numerical FlexibilityNumerical Flexibility
--Variable working hours.Variable working hours.
• Temporal FlexibilityTemporal Flexibility
--Career breaks,job sharing,term-time works..Career breaks,job sharing,term-time works..
• Wage FlexibilityWage Flexibility
--Performance related pays.Performance related pays.
DESCRIPTION OF PROBLEMDESCRIPTION OF PROBLEM
-Algorithm of Problem:-Algorithm of Problem:SOFTWARE COMPANYSOFTWARE COMPANY CUSTOMERCALL OF CUSTOMER
CALL OF CUSTOMER
ASSIGN SERVICE ENGINEER
Informations about problemInformations about problem
• Service engineering is not different job . All Service engineering is not different job . All of Software engineers may go services .of Software engineers may go services .
• Service time includes times which pass on Service time includes times which pass on the way too .the way too .
• We see that service times did not pass We see that service times did not pass over 2 hours according to old datas .over 2 hours according to old datas .
• This problem include assignments only for This problem include assignments only for an afternoon .an afternoon .
Customer NumberCustomer Number Time of AppointmentTime of Appointment
11 13:0013:00
22 13:0013:00
33 14:0014:00
44 14:0014:00
55 14:3014:30
66 15:0015:00
77 15:0015:00
88 16:0016:00
99 16:0016:00
1010 16:0016:00
1111 17:0017:00
# of Services in one # of Services in one tourtour
Costs($)Costs($)
11 1010
22 1818
33 2525
44 3030
Tour NumberTour Number Customer Customer NumberNumber
Cost1Cost1
11 11 1010
22 22 1010
33 33 1010
44 44 1010
55 55 1010
66 66 1010
77 77 1010
88 88 1010
99 99 1010
1010 1010 1010
1111 1111 1010
Tour NumberTour Number Customer NumberCustomer Number Cost2Cost2
12(1)12(1) 1,61,6 1818
13(2)13(2) 1,71,7 1818
14(3)14(3) 1,81,8 1818
15(4)15(4) 1,91,9 1818
16(5)16(5) 1,101,10 1818
17(6)17(6) 1,111,11 1818
18(7)18(7) 2,62,6 1818
19(8)19(8) 2,72,7 1818
20(9)20(9) 2,82,8 1818
21(10)21(10) 2,92,9 1818
22(11)22(11) 2,102,10 1818
23(12)23(12) 2,112,11 1818
24(13)24(13) 3,83,8 1818
25(14)25(14) 3,93,9 1818
26(15)26(15) 3,103,10 1818
27(16)27(16) 3,113,11 1818
28(17)28(17) 4,84,8 1818
29(18)29(18) 4,94,9 1818
30(19)30(19) 4,104,10 1818
31(20)31(20) 4,114,11 1818
32(21)32(21) 5,115,11 1818
Tour NumberTour Number Customer Customer NumberNumber
Cost3Cost3
33(1)33(1) 1,6,111,6,11 2525
34(2)34(2) 1,7,111,7,11 2525
35(3)35(3) 2,6,112,6,11 2525
36(4)36(4) 2,7,112,7,11 2525
After these informations we describe After these informations we describe our mathematical model:our mathematical model:
• Decison Variables :Decison Variables :
-X : Number of 1 Customer Service in -X : Number of 1 Customer Service in One Tour ( X=1..11 )One Tour ( X=1..11 )
-Y : Number of 2 Customer Services -Y : Number of 2 Customer Services in One Tour ( Y=1..21 )in One Tour ( Y=1..21 )
-Z : Number of 3 Customer Services -Z : Number of 3 Customer Services in One Tour ( Z=1..4 )in One Tour ( Z=1..4 )
• Objective Function:Objective Function:
-Zmin=∑(X*Cost1) + ∑(Y*Cost2) + -Zmin=∑(X*Cost1) + ∑(Y*Cost2) + ∑(Z*Cost3)∑(Z*Cost3)
• Constraints:Constraints:– For customer 1 : X1 + Y1 + Y2 + Y3 + Y4 +Y5 + Y6 + Z1 + Z2 = 1 For customer 1 : X1 + Y1 + Y2 + Y3 + Y4 +Y5 + Y6 + Z1 + Z2 = 1 – For customer 2 : X2 + Y7 + Y8 + Y9 + Y10 + Y11 + Y12 + Z3 + Z4 For customer 2 : X2 + Y7 + Y8 + Y9 + Y10 + Y11 + Y12 + Z3 + Z4
= 1 = 1 – For customer 3 : X3 + Y13 + Y14 + Y15 + Y16 = 1 For customer 3 : X3 + Y13 + Y14 + Y15 + Y16 = 1 – For customer 4 : X4 + Y17 + Y18 + Y19 + Y20 = 1 For customer 4 : X4 + Y17 + Y18 + Y19 + Y20 = 1 – For customer 5 : X5 + Y21 = 1 For customer 5 : X5 + Y21 = 1 – For customer 6 : X6 + Y1 + Y7 + Z1 + Z3 = 1 For customer 6 : X6 + Y1 + Y7 + Z1 + Z3 = 1 – For customer 7 : X7 + Y2 + Y8 + Z2 + Z4 = 1 For customer 7 : X7 + Y2 + Y8 + Z2 + Z4 = 1 – For customer 8 : X8 + Y3 + Y9 + Y13 + Y17 = 1 For customer 8 : X8 + Y3 + Y9 + Y13 + Y17 = 1 – For customer 9 : X9 + Y4 + Y10 + Y14 + Y18 = 1 For customer 9 : X9 + Y4 + Y10 + Y14 + Y18 = 1 – For customer10: X10 + Y5 + Y11 + Y15 + Y19 = 1 For customer10: X10 + Y5 + Y11 + Y15 + Y19 = 1 – For customer11: X11 + Y6 + Y12 + Y16 + Y20 + Y21 + Z1 + Z2 + For customer11: X11 + Y6 + Y12 + Y16 + Y20 + Y21 + Z1 + Z2 +
Z3 + Z4=1 Z3 + Z4=1
MODEL IN LINGOMODEL IN LINGO
SETS:SETS:
SERVICE/1..11/:COST1,X;SERVICE/1..11/:COST1,X;
SERVICE2/1..21/:COST2,Y;SERVICE2/1..21/:COST2,Y;
LOOK(SERVICE,SERVICE2):MATRIX1;LOOK(SERVICE,SERVICE2):MATRIX1;
SERVICE3/1..4/:COST3,Z;SERVICE3/1..4/:COST3,Z;
LOOK2(SERVICE,SERVICE3):MATRIX2;LOOK2(SERVICE,SERVICE3):MATRIX2;
ENDSETSENDSETS
DATA:DATA:COST1=10 10 10 10 10 10 10 10 10 10 10;COST1=10 10 10 10 10 10 10 10 10 10 10;MATRIX1=1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0MATRIX1=1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1;0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1;
COST2=18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 COST2=18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18;18 18;
MATRIX2=1 1 0 0MATRIX2=1 1 0 0 0 0 1 10 0 1 1 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 1 0 1 01 0 1 0 0 1 0 10 1 0 1 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 1 1 1 1;1 1 1 1;COST3=25 25 25 25;COST3=25 25 25 25;ENDDATAENDDATA
@FOR(SERVICE:@BIN(X));@FOR(SERVICE:@BIN(X));@FOR(SERVICE2:@BIN(Y));@FOR(SERVICE2:@BIN(Y));@FOR(SERVICE3:@BIN(Z));@FOR(SERVICE3:@BIN(Z));MINMIN=@SUM(SERVICE:X*COST1)+@SUM(SERVI=@SUM(SERVICE:X*COST1)+@SUM(SERVI
CE2:Y*COST2)+@SUM (SERVICE3:Z*COST3);CE2:Y*COST2)+@SUM (SERVICE3:Z*COST3);@FOR(SERVICE(I):X(I)@FOR(SERVICE(I):X(I)
+@SUM(SERVICE2(J):MATRIX1(I,J)*Y(J))+@SUM(SERVICE2(J):MATRIX1(I,J)*Y(J))+@SUM(SERVICE3(K):MATRIX2(I,K)*Z(K)) = +@SUM(SERVICE3(K):MATRIX2(I,K)*Z(K)) = 1);1);
ENDEND
SOLUTION & ANALYSISSOLUTION & ANALYSIS
• Objective Value = 99 $ Objective Value = 99 $
• X5 = 1X5 = 1
• X10 = 1X10 = 1
• Y1 = 1Y1 = 1
• Y14 = 1Y14 = 1
• Y17 = 1Y17 = 1
• Z4 = 1Z4 = 1
• X5 CUSTOMER5 at 14:30X5 CUSTOMER5 at 14:30
• X10 CUSTOMER10 at 16:00X10 CUSTOMER10 at 16:00
• Y1 CUSTOMER1 at 13:00Y1 CUSTOMER1 at 13:00
CUSTOMER6 at 15:00CUSTOMER6 at 15:00
• Y14 CUSTOMER3 at 14:00Y14 CUSTOMER3 at 14:00
CUSTOMER9 at 16:00CUSTOMER9 at 16:00
• Y17 CUSTOMER4 at 14:00Y17 CUSTOMER4 at 14:00
CUSTOMER8 at 16:00CUSTOMER8 at 16:00
• Z4 CUSTOMER2 at 13:00Z4 CUSTOMER2 at 13:00
CUSTOMER7 at 15:00CUSTOMER7 at 15:00
CUSTOMER11 at CUSTOMER11 at 17:0017:00
• Objective Objective Value=1*10+1*10+1*18+1*18+1*18+1*25=99Value=1*10+1*10+1*18+1*18+1*18+1*25=99
Row Row Slack or Surplus Slack or Surplus Dual Price Dual Price
11 99.00000 99.00000 1.000000 1.000000
22 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
33 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
44 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
55 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
66 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
77 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
88 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
99 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
1010 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
1111 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
1212 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
THANK YOUTHANK YOU
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