Page 177 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Avg. time on machines
Machine Operators 1 2 3 4 5 6 New
A 10 12 8 10 8 12 11
B 9 10 8 7 8 9 10
C 8 7 8 8 8 6 8
D 12 13 14 14 15 14 11
E 9 9 9 8 8 10 9
F 7 8 9 9 9 8 8

12. A section head has five stenotypists and five jobs to complete. The stenos differ in their
efficiency and the jobs differ in their intrinsic complexity. The estimate of the time (in
hours) each steno would take to perform the task is given in the effectiveness matrix
below. How should tasks be allocated, one to a person, so as to maximize the total time
taken to complete all the jobs?
Tasks Steno-typists
A B C D E
I 10 17 15 11 14
II 18 22 14 16 12
III 29 20 12 18 22
IV 14 19 7 17 16
V 9 17 14 12 15

13. A tourist car rental agency has a surplus car in each of the cities A, B, C, D, E and F, and a
deficit of one car in each of the cities AA, BB, CC, DD, EE, and FF. The distances between
cities with a surplus car and cities with a deficit car are given in the following matrix. How
should the cars be dispatched so as to maximize the total distance covered?
From To
AA BB CC DD EE FF
A 28 39 47 51 36 42
B 44 49 38 25 29 32
C 59 50 31 31 21 28
D 48 64 80 49 26 38
E 40 71 38 51 50 29
F 39 39 80 59 40 71

14. A domestic airline which operates seven days a week has a time table between two
airports as shown below. Crew must have a minimum layover of 2 hours between any
two flights. Obtain an optimal pairing of flights to minimize layover time away from HQ.
For any given pairing, the crew will be based at the city that results in the smaller layover.
Chennai-Bangalore Bangalore-Chennai
Ft. no. Departure Arrival Ft. no. Departure Arrival
185 6.30 a.m 7.00 a.m 186 8.00 a.m 8.30 a.m
255 8.00 a.m 8.30 a.m 256 10.00 a.m 10.00 a.m
275 2.00 a.m 2.30 a.m 286 7.00 a.m 1.30 a.m
285 6.00 p.m 6.30 a.m 286 7.00 a.m 7.30 a.m

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