Operation Research Project Work

Topic: Planning the Product Mix at Panchtantra Corporation

Introduction

• Mr. Ganesh had to prepare a production plan of Intensive Handloom Development project for the next month.

• Types of handloom to be produced :• Lungi (60sx40s)• Shirting (40sx40s)

• The main objective of Mr. Ganesh was to decide over how many metres of Lungi and shirting should be produced in order to maximize the profit satisfying the various constraints.

Exihibit 1S. No. Parameter Lungi Shirting

1 Selling Price (Rs. Per metre) 10.9 6.6

2 Variable Cost

2.a. Wages paid to weavers (Rs. Per metre) 4.5 1.5

2.b. Yarn Cost (Rs. Per metre) 5.5 4.5

3 Contribution (Rs. Per metre) 0.9 0.6

4 Production Rate (No. of metre per loom day) 5 12

5 Yarn Consumption (grams per metre)

5.a. 40s yarn 60 100

5.b. 60s yarn 40 0

Decision Variables

• Mr. Ganesh had to decide over the product Mix i.e. how many metres of Lungi and Shirting should be produced.

Therefore Decision Variable are : Length of Lungi to be produced (in metres) = X1Length of Shirting to be produced (in metres) = X2

Objective Function

• Maximizing the Total Sales Profit

Profit per metre of Lungi = Rs. 0.9Profit per metre of Shirting = Rs. 0.6

Therefore, Objective Function is :

Max (0.9 X1 + 0.6 X2)

Constraints

• Various constraints that affect the production and the decision variables are listed in following slides

1. Maximum number of Loom Days available are 3000Loom Days <= 3000

» (X1/5)+(X2/12) <= 3000» 12X1 + 5X2 <= 3000 x 60» 12X1 + 5X2 <= 180000 --(1)

Constraints (contd.)

2. 60s Yarn available was 480 Kgs. 60s yarn <= 480 kgs.

60s yarn is used only for Lungi at the rate of 40 grams per metre.

» 40X1 <= 480x1000 --(2)

3. 40s Yarn available was 2400 Kgs. 40s yarn <= 2400 kgs.

40s yarn is used in Lungi at the rate of 60 grams per metre and in Shirting at the rate of 100 grams per metre

» 60X1 + 100X2 <= 240x1000 --(3)

Constraints (contd.)

4. As per sales department, due to piled up stocks in inventory, production of Shirting should not be more than 22000 metres.

Sales level of Shirting <= 22000 metres

» X2 <= 22000 --(4)5. As per sales department, due to piled up stocks in

inventory, production of Lungi should not be more than 11000 metres.

Sales level of Lungi <= 11000 metres

» X1 <= 11000 --(5)

Problem #1 - Analysis• Mr. Ganesh wanted to produce as much of lungi as

possible, therefore he would want to use the entire sales limit of 11000 mts.Therefore, the constraint #5 would be as :

X1 = 11000 --(5.a)

• Mr. Ganphathy was however in favor of producing only the optimal level of Lungi so that the rest of the resources can be used for maximizing the profit.Therefore, the constraint #5 would be as :

X1 <= 11000 --(5.b)

Problem #1 - Solution

As per Mr. Ganesh's plan

As per Mr. Ganphathy's plan

X1 = Length of Lungi to be produced (in metres) 11000 6666.67

X2 = Length of Shirting to be produced (in metres) 9600 20000

Total Profit 15660 18000

• Refer “Model_Question1” sheet in the attached Solver Model excel file.

• Hence To optimize the profit, following should be the production plan for the next month (we should go with Mr. Ganphaty's Plan):

• Length of Lungi to be produced = 6666.67 metres• Length of Shirting to be produced = 20000 metres

• Increase in profit in this way will be Rs. 2340 with optimal profit of Rs. 18000

Problem #2 – Additional Constraint

• Additional constraint added to ensure that on an average, the production paid as wages to the weavers at least Rs. 20.5 per loom day.

• Total wages for the production could be given by

4.5X1 + 1.5X2• Total number of loom days used could be given by

(X1/5) + (X2/12)• Therefore

4.5X1 + 1.5X2 >= 20.5 x [(X1/5) + (X2/12)]» (4.5-20.5/5)X1 + (1.5 - 20.5/12)X2 >= 0

» 0.4X1 – 0.2083X2 >= 0 -- (6)

Problem #2 - Solution• Refer “Model_Question2” sheet in the attached Solver Model excel file.

• Hence to satisfy the minimum wage constraint for weavers, following should be the production plan for next month:

• Length of Lungi to be produced = 8333.33 metres• Length of Shirting to be produced = 16000 metres

• Increase in wages paid to weavers in this way would be Rs. 0.5 per loom day

  Plan suggested in Q.1For wages >=

Rs.20.5/loom day

X1 = Length of Lungi to be produced (in meters) 6666.67 8333.33

X2 = Length of Shirting to be produced (in meters) 20000 16000

Wages to weavers per loom day 20 20.5

Total Profit 18000 17100

Problem #3 – Additional Constraint

• As informed by Finance Manager, Cash available with Panchtantra Corporation is Rs. 1.50 Lakhs

• Variable (Wages and Yarn cost) were paid in cash. Therefore, total variable cost during production will be :

(4.5+5.5)X1 + (1.5+4.5)X2• Hence, the additional constraint :

(4.5+5.5)X1 + (1.5+4.5)X2 <= 150000 --(7)

Problem #3 – Solution

• Refer “Model_Question3” sheet in the attached Solver Model excel file.

• Hence, by taking the cash constraint into the consideration, following should be the production plan for next month:

X1 = Length of Lungi to be produced (in metres) 6970.26

X2 = Length of Shirting to be produced (in metres) 13382.90

Optimal Profit 14302.97

Solver Answer Report• Wages and Cash constraints are binding constraints that limit the

optimal profit.• All the other constraints are having slack which indicates the

possibilities of increased profit if wage or cash constraints are eased.

Solver Sensitivity Report

End of slides