Prescriptive Analytics

Prescriptive Analysis – Assignment 7 Kavya Nagaraj, Udyan Sharma

Question 10) The decision variables are:

X - Distance of the motorist from X co-ordinate

Y - Distance of the motorist from Y co-ordinate

a) The objective function is:

MIN (SQRT((17 - X)2 + (34 - Y)2) – 29.5)2 + (SQRT((12 - X)2 + (5 - Y)2) – 4.0)2 + (SQRT((3 - X)2 + (23 - Y)2) – 17.5)2

The constraints are:

X, Y >=0

b) The model is the spreadsheet attached.

c) The location to which the rescue personnel should be dispatched is X = 8.037 and Y = 6.054

Question 29) The decision variables are:

Fij – Flow from station I to j

Pij = probability of failure of flow from station I to j (Values in excel – Computed as per the formula)

The objective function is: MAX : (1-P12)(1-P13)(1-P24)(1-P25)(1-P34)(1-P35)(1-P46)(1-P56)(1-P61)

Constraints are:

F12 <= 80

F13 <= 50

F24 <= 90

F25 <= 60

F34 <= 50

F35 <= 70

F46 <= 70

F56 <= 60

F12+F13+F24+F25+F34+F35+F46+F56 >= 110

Fij >= 0

Answer:

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Question 30) The decision variables are:

Xi, Yi = Location of warehouse 1, 2, 3 (I = 1,2 ,3)

Assignment Variables Aij = 30 variables ( I = warehouse, j = region name)

Objective Function: SUMPRODUCT (distance between warehouse1,2, 3: Assignment Variables)

The constraints are:

A1j +A2j+ A3j =1 ( j = 1 to 10)

Aij is binary

Answer in snapshot below:

Question 28) Decision Variables are: Pij = Probability of success of donation

Xij – assignment operator

Objective Function - MAX : (1-(1- P11)X11 (1-(1-P12)X12)………….(1-(1-P44)X44)

Constraints are: Summation Xij = 1 for each i

Summation Xij = 1 for each j

X ij are binary

Answer in snapshot:

Assign Sam to 4, Billie to 3, Sally to 2, Fred to 1

Prob. of receiving all donations = 0.15396

Sam to 4, Billie to 2, Sally to 1, Fred to 3,...