Well done company case final [compatibility mode]

CASE STUDY ON ASSIGNMENT PROBLEM

1

Prepared By:

HARSH VYAS - 212011

RESHMI RAVEENDRAN - 212027

Well-Done Company has taken the third floor of a building for rent with a view to locate one of their zonal offices. There are five main rooms in this to be assigned to five managers. Each room has its own advantages and disadvantages.

Some have windows, some are closer to the washroom or to the canteen or secretarial pool. The rooms are of all different sizes and shapes. Each of the five managers were asked to rank their room preferences amongst the rooms 301, 302, 303, 304 and 305. Their preferences were recorded in a table as indicated below:

MANAGERS

M1 M2 M3 M4 M5

302 302 303 302 301

Most of the managers did not list all the five rooms since they were not satisfied with some of these rooms and they have left these from the list. Assuming that their preferences can be quantified by numbers, find out as to which manager should be assigned to which room so that their total preference ranking is a minimum.

302 302 303 302 301

303 304 301 305 302

304 305 304 304 304

301 305 303

302

CASE STUDY ON ASSIGNMENT PROBLEM

� Maximization Or Minimization Problem

� Check whether the problem is Balanced

� If there are any prohibit assignments, then assign ‘∞’

� Proceed with Hungarian Method : Subtract the Minimum from each row

� Subtract the minimum from each column

� Find the row with single zero & assign that zero

� Find the column with single zero & assign

� Cancel all zero in the corresponding row & coloumn of the assigned � Cancel all zero in the corresponding row & coloumn of the assigned zero

� Draw Minimum no. of Lines to cover all zeros

� Select the minimum (lets say Ө) uncrossed element and subtract it from rest uncrossed elements. In case of row/coloumn elements crossed by lines write the elements as it is & in case of elements intersected by 2 lines add Ө

� Proceed with the new matrix as in step 4 until all rows and coloums have a ‘0’ assigned to the corresponding parameters.

CASE STUDY ON ASSIGNMENT PROBLEM

Solution :

MANAGERS

M1 M2 M3 M4 M5

302 302 303 302 301

303 304 301 305 302

304 305 304 304 304

301 305 303

302

Step1: Rewrite as per the priority and assign ∞ in prohibited areas

M1 M2 M3 M4 M5

301 ∞ 4 2 ∞ 1

302 1 1 5 1 2

303 2 ∞ 1 4 ∞

304 3 2 3 3 3

305 ∞ 3 4 2 ∞

Step1: Rewrite as per the priority and assign ∞ in prohibited areas

CASE STUDY ON ASSIGNMENT PROBLEM

M1 M2 M3 M4 M5

301 ∞ 4 2 ∞ 1

302 1 1 5 1 2

303 2 ∞ 1 4 ∞

304 3 2 3 3 3

305 ∞ 3 4 2 ∞

Step 2: Reduce row and column by subtracting the minimum elements from row & Column

M1 M2 M3 M4 M5

301 ∞ 3 1 ∞ 0

302 0 0 4 0 1

303 1 ∞ 0 3 ∞

304 1 0 1 1 1

305 ∞ 1 2 0 ∞

CASE STUDY ON ASSIGNMENT PROBLEM

Step 3: Assign row/ column with single 0 and cross the zeros in corresponding row/ column

M1 M2 M3 M4 M5

301 ∞ 3 1 ∞

302 0 0 4 0 1

303 1 ∞ 3 ∞

304 1 1 1 1

0

0

0

0

6

304 1 1 1 1

305 ∞ 1 2 ∞0

CASE STUDY ON ASSIGNMENT PROBLEM

M1 M2 M3 M4 M5

301 ∞ 3 1 ∞

302 0 4 0 1

303 1 ∞ 3 ∞

304 1 1 1 1

305 ∞ 1 2 ∞

0

0

0

0

0

M1 M2 M3 M4 M5

7

M1 – 302 M2- 304 M3 – 303 M4 – 305 M5 – 301

Total minimum ranking – 1 + 1 + 1 + 2 + 2 = 7CASE STUDY ON ASSIGNMENT PROBLEM

M1 M2 M3 M4 M5

301 ∞ 4 2 ∞ 1

302 1 1 5 1 2

303 2 ∞ 1 4 ∞

304 3 2 3 3 3

305 ∞ 3 4 2 ∞

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