Nutrition-Optimized-Menu-Planning

This GitHub repository provides tools and data for optimizing menu planning across different age groups. The focus is on maximizing nutrition and cost efficiency in meal plans tailored to diverse demographic needs.

Table of Contents

• Relevance of the problem
• Problem Description
• Model Formulation
  • Decision Variables
  • Objective Function
  • Constraints
• Numerical Analysis
  • Comparative Analysis of Combined vs. Individual Optimization
  • Impact of Relaxing Diversity Constraints
  • Price Sensitivity Analysis
• Conclusion

Relevance of the problem

Problem Description

Model Formulation

Model data

The model includes nutritional requirements and item information for various demographic groups:

1. Nutritional Requirements by Demographic Group

This data was gathered from the U.S. Department of Health and Human Services. The data contains nutritional goals for each age/sex group used in assessing the adequacy of USDA Food Patterns at various calorie levels - Link

Age Group	Calories	Sodium	Carbohydrates	Dietary Fiber	Protein	Total Fat
Male Child	1400	2050	130	19.6	26.5	30
Female Child	1600	2050	130	22.4	26.5	30
Male Teenager	2800	2300	130	30.8	52	30
...	...	...	...	...	...	...
Female Adult	1800	2300	130	25.2	46	30
Male Adult	2200	2300	130	30.8	56	30

2. Nutritional Information by Menu Item

Item	Calories	Sodium	Carbohydrates	Dietary Fiber	Protein	Total Fat
Egg McMuffin	300	750	31	4	17	13
Egg White Delight	250	770	30	4	18	8
...	...	...	...	...	...	...
McFlurry ... (Medium)	810	400	114	2	21	32
McFlurry ... (Snack)	410	200	57	1	10	16

3. Cost Per Item

The original dataset did not contain this information. This data was appended to the original dataset that contained only the nutritional information.

Item	Cost
Egg McMuffin	$2.50
Egg White Delight	$2.50
...	...
McFlurry ... (Medium)	$2.25
McFlurry ... (Small)	$1.85

Decision Variables

Objective Function

The objective function aims to minimize the total cost by optimizing menu choices for different demographic groups:

$$ min \ Z = \sum_{i} \sum_{j} c_i \cdot x_{ij} $$

where:

• $c_i$ is the cost of item $i$.
• $x_{ij}$ is the number of units of item $i$ consumed by demographic group $j$.

Constraints

The model includes several constraints to ensure nutritional needs and item selection diversity:

• Nutrition Needs Constraint:
  Ensures nutritional requirements are met for each demographic group based on selected menu items.

• Category Constraint:
  Ensures a minimum number of items are chosen from specific menu categories (e.g., breakfast, chicken and fish, beef and pork).

For specific categories:

• Breakfasts (Items 1-42):

$$ \sum_{i=1}^{42} u_{ij} $$

• Chicken and Fish (Items 43-57):

$$ \sum_{i=43}^{57} u_{ij} \geq 3 $$

• Beef and Pork (Items 58-84):

$$ \sum_{i=58}^{84} u_{ij} \geq 3 $$

• Salads (Items 85-90):

$$ \sum_{i=85}^{90} u_{ij} \geq 3 $$

• Snack and Sides (Items 91-103):

$$ \sum_{i=91}^{103} u_{ij} \geq 3 $$

• Dessert (Items 104-110):

$$ \sum_{i=104}^{110} u_{ij} \geq 3 $$

• Beverages (Items 111-137):

$$ \sum_{i=111}^{137} u_{ij} \geq 3 $$

• Coffee and Tea (Items 138-232):

$$ \sum_{i=138}^{232} u_{ij}$$

$$ \ . \ . \ . $$

$$ \sum_{i=233}^{260} u_{ij} $$

• Diversity Constraint:
  Limits the number of units of each item consumed by a demographic group to ensure variety in the diet.

• Lower Bound Constraint:
  Ensures that the decision variable is binary, indicating whether an item is chosen for a demographic group.

Numerical Analysis

Comparative Analysis of Combined vs. Individual Optimization

This study compares two optimization approaches for meeting nutritional needs across different age groups. By evaluating concurrent optimization of menu schedules for all age groups versus individual optimization for each group, the research aims to determine the most effective method in fulfilling dietary requirements while respecting specific constraints and guidelines for each demographic category. Two menu designs were created: one aimed at meeting overall nutritional needs for all demographics at a minimal cost, and another tailored to the unique nutritional requirements of each demographic group.

Impact of Relaxing Diversity Constraints

In this experiment, we adjusted the Diversity Constraint to observe its impact on optimized menus. Surprisingly, even with a significantly looser constraint, the results remained similar to more constrained settings. This suggests that menu diversity was inherently limited, aligning with the unique dietary needs of each group while optimizing cost efficiency.

Price Sensitivity Analysis

This analysis examines the impact of item price variations on menu composition, essential for business profitability and consumer satisfaction. To maintain profitability and customer appeal, businesses like McDonald’s must understand how price adjustments affect menu choices. Similarly, consumers' purchasing decisions are influenced by price changes, emphasizing affordability and value. We conduct two experiments from these dual perspectives: one focused on inflation-based scenarios, and the other on market disruptions affecting item prices.

Conclusion

Future Work

• Adding an interface to turn this model into a web application
• Add an efficient implementation of the Simplex algorithm - Python
• Try changing the model to get more insights from the business perspective.
  • Changing the objective to maximize the cost(Selling Price)
  • Products that need improvement/boost in marketing