7/31/2019 Crew Assignment

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Crew Assignment

1. In the regular transport services as in bus, train, air services etc., the cost of the company increase withincrease of the number of hours spent by a crew actually on the vehicle and on the waiting time in the out

-stations between two subsequent trips between the two places of service. To minimize the cost, the time pe

spent by a crew in vehicles and out-stations is to be minimized by the proper adjustment of duty of a crew. Suproblem is called is called the crew assignment problem.

2. The restriction on the crew assignment may be of various types. One of them is to allow a minimum period o

time between two trips at the outstation. The other may be that a crew must be allotted at least one outward c

inward trip within the twenty four hours to run a regular daily service, and so on. In such assignments, there ineed of distinguishing between the capacities of the individual crews, i.e., any crew may be appointed in any

(unless otherwise required). However, a crew must be allotted his permanent residence at the place from whic

has to start his outward trip.3. In such a problem, a table is to be prepared which shows the smaller out-station time period spent by a

crew in his every outward-cum-inward trip. Then the optimal (minimal) solution corresponding to the

table is to be determined by the reduced matrix-method. In general, the time period of a trip between thetwo places of service is prescribed. Hence, only the out-station rest time of a crew is to be minimized.

Problem1.

A bus transport company runs five regular daily bus services between Calcutta(C) and Digha(D), a distance of six houbus journey. There are only five crews. The constraint is that a crew must have an outstation rest period of more than

hours but not more than twenty-four hours. There is no need of giving any preference to the efficiency of any crew . Tcompany has staff residence in both places. The time-table of the bus services is given below. Determine which crew

should be assigned to which outward trip and to which inward trip to minimize the out-station rest time. Also find thetotal minimum rest time.

Trip No C1 C2 C3 C4 C5

Departure hour from Calcutta 6.00 7.30 11.30 19.00 0.30

Arrival hour at Digha 12.00 13.30 17.30 1.00 6.30

Trip No D1 D2 D3 D4 D5Departure hour from Digha 5.30 9.00 15.00 18.30 0.00

Arrival hour at Calcutta 11.30 15.00 21.00 0.30 6.00

A small aero plane company operating seven days a week, serves the cities A and B, and also A and C according

To the schedule shown in the following table. The layover cost per stop is roughly proportional to the square of theLayover time. How should the planes be assigned to the flights so as to minimize the total layover cost.

Flight No. & Index Departure Place & Time Arrival Place & TimeA1B A, 9 a.m. B, noon.

A2 B A, 10 a.m. B, 1 p.m.A3B A, 3 p. m. B, 6 p.m.

A4C A, 8 p.m. C, midnight

A5C A, 10 p.m. C, 2 a.m.

B1A B, 4 a.m. A, 7 a.m.B2 A B,11 a.m. A, 2 p.m.

B3A B, 3 p.m. A, 6 p.m.

C1 A C, 7 a.m. A, 11 a.m.C2 A C, 3 p.m. A, 7 p.m.