In a recent article in the Brifish Journal of Nutrition, Sklan & Dariel(1993) presented a method for diet planning employing a mixed-integer programming algorithm for meeting nutritional requirements at minimum costs for institutions or individuals. They recognized that most food items are generally consumed in whole units and as such they are represented as integer variables. However, as in most previous studies, they derived the minimum cost diets by optimizing over purchased food items. The present paper presents a computer-assisted, diet-planning modelling system for individuals by optimizing over recipes instead of food items. This is accomplished by restricting the integer programming solutions to those bundles of food that represent reasonably popular meal recipes. The modelling system is composed of three main components: recipe data entry, database management, and the model. The recipe data entry component creates and stores recipes. It also provides nutritional analysis of the recipes. The database management component creates and maintains several databases necessary to build the modelling data file. The modelling component solves the user-specified model. Currently, the model component can solve for the optimal diet by minimizing cost or minimizing cooking and preparation time. The optimal diet is prepared to satisfy the recommended nutritional guidelines for a predefined group of individuals for 1 week. The system currently has 895 popular recipes found in Hawaii. Diet plans generated using this modelling system with differing objectives are discussed and compared. Diet-planning model: Recipes: Minimum cost: Minimum time Minimum-cost diets have their origin in the seminal work of Nobel Laureate George Stigler (1945). Stigler (1945) formulated and provided an approximate solution to the now famous 'diet problem', which seeks the minimum cost of achieving the recommended daily allowances of nutrients known to be beneficial to humans. Since then the linear programming formulation of the classic diet problem has continued to evolve. Smith (1959), Prato (1973), Bassi (1976), Foytik (1981a and Silberberg (1985) have reestimated Stigler's (1945) original problem 'as is' or with minor changes. The common characteristic of all these studies is that they optimize over raw food materials subject to two sets of constraints. One set of constraints is used to specify the minimum nutritional requirements, and the other set is designed to raise the degree of palatability. Diets generated by these models are given in terms of raw food materials and ingredients rather than menus or recipes. Menu items are defined as mixtures of foods and ingredients, defined by recipes. While all these studies have demonstrated the surprisingly low cost of satisfying the purely nutritional needs, it remains up to the individual meal planner to construct meaningful meals from the selected raw food materials and ingredients. But in many cases there is no available technology (as represented by recipes) to convert the food materials a...
The implications on a minimum‐cost diet of introducing meal preparation time are explored using a multiple criteria framework. Using a bicriterion method, the tradeoff between the money cost of home‐cooked meals and the meal preparation time is empirically estimated with a set of 895 recipes popular in Hawaii. There is a clear tradeoff between cost and time in preparing home‐cooked meals, and it is found that the minimum‐cost diet is very sensitive to the meal pre‐parer's value of time.
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