CREW SCHEDULING

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





• Z4 CUSTOMER2 at 13:00Z4 CUSTOMER2 at 13:00


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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CREW SCHEDULING