Or Case 5

CASE – 05

Title: PROJECT PICKING

Submitted To: Submitted By:

Group Capt. D.P.Apte

ISBJ (DIV - D)

INTRODUCTION :

Tazer, is a pharmaceutical manufacturing company in the market for the past 12 years. It has been producing six drugs, out of that five are substitutes of existing drugs and not giving profit. Sixth drug is a patent product (hypertension drug) and was a huge success. Company was never interested in R&D. Profit was coming from the sixth drug which was making Tazer successful in the market. And that’s why company never felt about finding new drug which give it some extra edge.

But now its patent is going to expire in 5 years, and so it is in fear of losing of the profit getting from the market till now and fear of competition from the generic drug manufacturing companies. So Tazer’s management feels that if extensive R&D is done now it may find a successful drug like the sixth one. So, five projects are taken into consideration and for that five senior scientists are consulted. 1000 bid points have been given to each scientist to give their preference of choice. And there are some constraints which are considered to find the solution in every aspect (Experience, Knowledge, No preference etc.).

PROBLEM:

The problem is which Project should be assigned to whom. This is basically an Assignment problem which is to be solved using various angles such as what if a scientist is not interested in the project or scientist having different field experience ( prohibited route problem etc.)

Solution:

Table Provided is: (a)

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dr. RollinsProject Up 100 0 100 267 100Project Stable 400 200 100 153 33Project Choice 200 800 100 99 33Project Hope 200 0 100 451 34Project Release 100 0 600 30 800

As this is maximization problem first we have to convert it into Minimization problem and that is done by subtracting all the matrix values from the largest value in the matrix i.e., 800. So the Table will be :


Now, Using HAM method in first step subtract the elements in each row with the element having least value in that row.

Reduced Table 1


In second step subtract the elements in each column with the element having least value in that column.

Reduced Table 2

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dr. RollinsProject Up 167 267 [0] 0 167Project Stable [0] 200 133 247 367Project Choice 600 [0] 533 701 767Project Hope 251 451 184 [0] 417Project Release 700 800 33 770 [0]

Thus, the Project will be allocated as:

Project Up – Dr. Tsai (400)Project Stable – Dr. Kvaai (800)Project Choice – Dr. Zuner (100)Project Hope – Dr. Mickey (451)Project Release – Dr. Rollins (800)

Total Preference = 2551

(b)

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dummy Var.Project Up 100 0 100 267 0Project Stable 400 200 100 153 0Project Choice 200 800 100 99 0Project Hope 200 0 100 451 0Project Release 100 0 600 30 0

Dummy variables are added to make this matrix balanced.




Reduced Table 1



Reduced Table 2


In this Number of lines = 4 ≠ n, so we have to choose the least value element from the uncovered one and subtract it from all uncovered element and add it to those which are on the intersection.

Reduced Table 3

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dummy Var.Project Up 167 200 167 0 [0]Project Stable [0] 133 300 247 133Project Choice 67 [0] 167 168 0Project Hope 251 384 351 [0] 184Project Release 500 533 [0] 570 333

Thus, the Project will be allocated as:

Project Up – Dummy Var. (0)Project Stable – Dr. Kvaai (400)Project Choice – Dr. Zuner (800)Project Release – Dr. Tsai (600)Project Hope – Dr. Mickey (451)

Total preference = 2251

The Project which is not to be done is Project Up.

(c)

From part b, We will take third Reduced Table

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dr. RollinsProject Up 167 200 167 [0] 0Project Stable [0] 133 300 247 133Project Choice 67 [0] 167 168 0Project Hope 251 384 351 0 184Project Release 500 533 [0] 570 333

Only the column for Dr. Micky has the zero for Project Hope so the scientist who can take two project is Dr. Mickey.

Total Preference:

Project Up – Dr. Mickey (267)Project Stable – Dr. Kvaai (400)Project Choice – Dr. Zuner (800)Project Hope – Dr. Mickey(451)Project Release – Dr. Tsai (600)

Total Preference = 2518

(d)

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dummy VarProject Up 100 20 100 267 0Project Stable 400 450 100 153 0Project Choice 200 451 100 99 0Project Hope 200 39 100 451 0Project Release 100 40 600 30 0

Dummy Variables are added to balance the problem.




Reduced Table 1



Reduced Table 2

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dummy VarProject Up 117 247 167 0 [0]Project Stable [0] 0 350 297 183Project Choice 201 [0] 351 352 184Project Hope 201 352 351 [0] 184Project Release 450 560 [0] 570 333

Thus, Total Preference

Project Up – Dummy Var (0)Project Stable – Dr. Kvaai (400)Project Choice – Dr. Zuner (451)Project Hope – Dr. Mickey(451)Project Release – Dr. Tsai (600)


Here, Dr. Mickey is to be given two projects as per the last Reduced Table.

(e)

Yes, I support this assignment as all project’s are considered via balancing the matrix and using the HAM method .

(f)

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dr. RollinsProject Up 86 0 100 300 -MProject Stable 343 200 100 -M 50Project Choice 171 800 100 125 50Project Hope -M 0 100 -M 100Project Release -M 0 600 175 600


Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dr. RollinsProject Up 714 800 700 500 MProject Stable 457 600 700 M 750Project Choice 629 0 700 675 750Project Hope M 800 700 M 700Project Release M 800 200 625 200


Reduced Table 1

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dr. RollinsProject Up 214 300 200 0 MProject Stable 0 143 243 M 293Project Choice 629 0 700 675 750Project Hope M 100 0 M 0Project Release M 600 0 425 0

In second step subtract the elements in each column with the element having least value in that column. But here table remains same, So :

Reduced Table 2

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mickey Dr. RollinsProject Up 214 300 200 [0] MProject Stable [0] 143 243 M 293Project Choice 629 [0] 700 675 750Project Hope M 100 [0] M 0Project Release M 600 0 425 [0]


Project Up – Dr. Mickey (300)Project Stable – Dr. Kvaai (343)Project Choice – Dr. Zuner (800)Project Hope – Dr. Tsai(100)Project Release – Dr. Rollins (600)


(g)

Project Dr. Kvaai Dr. Zuner Dr. Tsai Dr. Mick. Dr. Rolli. Dr. Arria. Dr. Sant.Project Up

86 0 100 300 -M 250 111

Project Stable

343 200 100 -M 50 250 1

Project Choice

171 800 100 125 50 -M -M

Project Hope

-M 0 100 -M 100 250 333

Project Release

-M 0 600 175 600 250 555

Dummy Rows

0 0 0 0 0 0 0

Dummy Rows

0 0 0 0 0 0 0



714 800 700 500 M 550 689

Project Stable

457 600 700 M 750 550 799

Project Choice

629 0 700 675 750 M M

Project Hope

M 800 700 M 700 550 467

Project Release

M 800 200 625 200 550 245

Dummy Rows

800 800 800 800 800 800 800

Dummy Rows

800 800 800 800 800 800 800


Reduced Table 1


214 300 200 [0] M 50 189

Project Stable

[0] 143 243 M 293 93 342

Project Choice

629 [0] 700 675 750 M M

Project Hope

M 333 233 M 233 83 [0]

Project Release

M 600 [0] 425 0 350 45

Dummy Rows

0 0 0 0 [0] 0 0

Dummy Rows

0 0 0 0 0 [0] 0

As there are zero in each and every row we don’t have to do the second step of HAM method. That’s why we have drawn the lines to see the assignement.


Project Up – Dr. Mickey (300)Project Stable – Dr. Kvaai (343)Project Choice – Dr. Zuner (800)Project Hope – Dr. Santos(333)Project Release – Dr. Tsai (600)


Documents

Or Case 5