Family-Personalized Dietary Planning with Temporal Dynamics

TL;DR

This paper introduces a new dietary planning model that accounts for ingredient perishability and preparation time, providing a computational approach to optimize family diets within temporal constraints.

Contribution

It formulates a novel integer programming model for diet planning with temporal dynamics and develops a deterministic approximation algorithm for efficient solutions.

Findings

The approximation algorithm performs well in numerical experiments.

The model effectively balances diet quality with temporal constraints.

Experimental results demonstrate the approach's practicality and efficiency.

Abstract

Poor diet and nutrition in the United States has immense financial and health costs, and development of new tools for diet planning could help families better balance their financial and temporal constraints with the quality of their diet and meals. This paper formulates a novel model for dietary planning that incorporates two types of temporal constraints (i.e., dynamics on the perishability of raw ingredients over time, and constraints on the time required to prepare meals) by explicitly incorporating the relationship between raw ingredients and selected food recipes. Our formulation is a diet planning model with integer-valued decision variables, and so we study the problem of designing approximation algorithms (i.e, algorithms with polynomial-time computation and guarantees on the quality of the computed solution) for our dietary model. We develop a deterministic approximation algorithm that is based on a deterministic variant of randomized rounding, and then evaluate our deterministic approximation algorithm with numerical experiments of dietary planning using a database of about 2000 food recipes and 150 raw ingredients.