Application of Decision Modeling Techniques to Diet Optimization & Mess Menu Management @ IMT, Ghaziabad

Group IIIANOOP CHAND CHETNA SINGHALEASWARAMURTHI PSHUBHAM SAMDANI SUTAPA MISHRAVAIBHAV GARGV S R PRAVEEN

AGENDA

Problem Formulation

Optimum Solution (Cost)

Interpretation of the results

Sensitivity Analysis

What-If-Analysis

IMT MESS MENU

Variables

Major Ingredients of a Meal

• Potato (grams) - P• Dal (grams) - D• Rice (grams) - R• Chapati (count) - C• Milk (ml) - M

Objective Function

Total Cost of Major Ingredients• Price of potato - 1000 Rs per quintal• Price of rice - 1720 Rs per quintal• Price of dal - 6160 Rs per quintal• Price of wheat flour - 1750 Rs per quintal• Price of milk - 40 Rs per litre

Per Unit Cost of Major Ingredients(1 quintal = 10^5 grams)

• Price of potato - .01 Rs per gram• Price of rice - .0172 Rs per gram• Price of dal - .0616 Rs per gram• Price of 1 chapati - .47 Rs per count• Price of milk - .04 Rs per ml

• Total Cost –

0.01P + 0.0616D + 0.0172R + 0.47C + 0.04M

Constraints

Calories Content of Major Ingredients

100 gm potato - 75 cal100 gm rice - 126 cal100 gm dal - 116 cal100 gm wheat flour - 337 cal250 ml milk - 155 cal1 medium roti - 90 cal

Nutritional Diet

As per the Indian Dietetic Association (IDA), the daily calories required for a sedentary lifestyle during the age of 20-30 years are as follows –

For Males - 2400 caloriesFor Females - 2000 calories

Daily Calories Requirement

• 900 males and 300 females

• Total minimum calories(900 *2400) + (300*2000) = 2760000

• 70% (rice, dal, potato, roti and milk/curd) of the total0.70*2760000 = 1932000

(1) 0.75P + 1.16D + 1.26R + 90C + 0.62M >= 1932000

Basic Nutrients

Per person –

• Min. potato - 200 gm (carbohydrates)• Min. dal - 100 gm (proteins)• Min. rice - 250 gm (carbohydrates, fiber,

minerals and vitamins)

• Min. roti - 4 (all major nutrients)• Min. milk - 500 ml (calcium)

Calories Requirement

For 1200 people –

(2) 0.75P + 0D + 0R + 0C + 0M >= 180000

(3) 0P + 1.16D + 0R + 0C + 0M >= 139200

(4) 0P + 0D + 1.26R + 0C + 0M >= 378000

(5) 0P + 0D + 0R + 90.0C + 0M >= 432000

(6) 0P + 0D + 0R + 0C + 0.62M >= 372000

Optimized Solution

Interpretation of the results

Sensitivity Analysis

Question 1

• There is some uncertainty in the cost of chapati. How sensitive is the current optimal solution to the cost?

Allowable Increase = 0.7326Allowable Decrease = 0.4674

Range = (0.4674 - 0.4674) to (0.4674+0.7326) = 0 to 1.2

Question 2

• What do the shadow prices for carbohydrates and proteins calories imply in this problem?

• Carbohydrates calories - 0.00814For range = (0,610800)

• Proteins calories - 0.04791For range = (0,570000)

What-If Analysis

Question

• Since both potato and rice contains good amount of carbohydrates, some dieticians suggest that the total calories of potato can be reduced by 50000, provided that the total calories of rice are increased by 50000.

Is this new diet plan cost-effective for the IMT mess to implement?

100% Rule

• Sum of ratios = (50000/180000) + (50000/430800) = 0.394

< 1

Reduction in total cost = 50000* 0.00814 = Rs 407

Increase in total cost = 50000* 0.00846= Rs 423

Net Impact = Increase in the cost by Rs 16 (423 - 407)

New Diet Plan

• Since there is a net increase in the cost, so this diet plan is not cost-effective for the IMT mess.

• But the difference in the overall daily cost due to this new diet plan is just Rs 16, hence it may be implemented.

References

• www.idaindia.com• www.indicat.com/Market-Rates/Commodity-Rates• www.indiatoday.intoday.in• www.fatsecret.com• www.myfitnesspal.com• www.positivehealthsteps.com• www.wikipedia.org