Assignment Problem

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Home > Operation Research calculators > Assignment Problem

Assignment Problem

1. Assignment problem
1.1 Assignment problem (Using Hungarian method-2)
1.2 Assignment problem (Using Hungarian method-1)
2.1 Travelling salesman problem using hungarian method
2.2 Travelling salesman problem using branch and bound (penalty) method
2.3 Travelling salesman problem using branch and bound method
2.4 Travelling salesman problem using nearest neighbor method
2.5 Travelling salesman problem using diagonal completion method
3. Assignment problem using LP Model Formulation
4. Crew Assignment Problem

Operation Research with example

1. Assignment Problem

1.1 Balanced Assignment Problem (Using Hungarian method)

1. A department has five employess with five jobs to be permormed. The time (in hours) each men will take to perform each job is given in the effectiveness matrix.

		Employees
		I	II	III	IV	V
Jobs	A	10	5	113	15	16
	B	3	9	18	13	6
	C	10	7	2	2	2
	D	7	11	9	7	12
	E	7	9	10	4	12

How should the jobs be allocated, one per employee, so as to minimize the total man-hours?

1.2 Unbalanced Assignment Problem (Using Hungarian method)

2. In the modification of a plant layout of a factory four new machines M1, M2, M3 and M4 are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M2 cannot be placed at C and M3 cannot be placed at A. The cost of locating a machine at a place (in hundred rupess) is as follows.

		Location
		A	B	C	D	E
Machine	M1	9	11	15	10	11
	M2	12	9	--	10	9
	M3	--	11	14	11	7
	M4	14	8	12	7	8

Find the optimal assignment schedule.

2. Travelling salesman problem
2.1 using hungarian method
2.2 using branch and bound (penalty) method
2.3 using branch and bound method
2.4 Travelling salesman problem using nearest neighbor method
2.5 Travelling salesman problem using diagonal completion method

1. A travelling salesman has to visit five cities. He wishes to start from a particular city, visit each city only once and then return to his starting point. The travelling cost of each city from a particular city is given below.

		To city
		A	B	C	D	E
From city	A	x	2	5	7	1
	B	6	x	3	8	2
	C	8	7	x	4	7
	D	12	4	6	x	5
	E	1	3	2	8	x

How should the jobs be allocated, one per employee, so as to minimize the total man-hours?

3 Crew Assignment Problem

1. Best-ride airlines that operates seven days a week has the following time-table.

Delhi - Mumbai

Mumbai - Delhi

Flight No	Departure	Arrival
1	7.00	8.00
2	8.00	9.00
3	13.00	14.00
4	18.00	19.00

Flight No	Departure	Arrival
101	8.00	9.00
102	9.00	10.00
103	12.00	13.00
104	17.00	18.00

Crews must have a minimum layover of 5 hours between flights. Obtain the pairing of flights that minimizes layover time away from home. For any given pairing, the crew will be based at the city that results in the smaller layover. For each pair also mention the city where crew should be based.