  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.
