Stigler's Diet Problem Revisited

Abstract

We review Stigler's diet problem, its impact on linear programming and operations research, and we determine minimum cost diets using updated nutritional and cost data. We also discuss how Stigler's diet problem formulation and its extensions have, over the years, influenced dietitians and nutritionists in their search for more wholesome but cost-effective diets.

Planning a Nutritious and Healthy Menu For Malaysian School Children Aged 13-18 Using "Delete-reshuffle Algorithm" in Binary Integer Programming

“…This new algorithm has been categorically modified to suit the menu planning problem structure and has successfully improved the performance of generating feasible solutions and sensible menu lists with convincing reliability. It has been proven that the proposed approach has considerably outperformed the traditional method in terms of quality of solution and run time (Smith, 1959;Fletcher et al, 1994;Garille and Gass, 2001;Sidik and Ahmad, 2004;Asyikin and Razali, 2011). This dynamic food menu environment must be tackled by caterers in the decision making process in order to satisfy all stakeholders.…”

“…Planning for adequate menus faces many economic and psychological constraints. It involves simultaneous consideration of several types of constraints; the desired nutritional content, the likes and dislikes of the person that it is being planned for the amount (volume or weight) of food to be consumed and the expected form and content of different kinds of meals (Garille and Gass, 2001;Sidik and Ahmad, 2004). …”

“…This model, as in most operation research models have been set up on the traditional fundamental assumption that the decision maker seeks to optimize a single objective function. The problem has continued to be investigated by scientists and nutritionists (Smith, 1959;Armstrong and Sinha, 1974;Balintfy, 1975;Bassi, 1976;Foytik, 1981;McCann-Rugg et al, 1983;Silberberg, 1985;Benson and Morin, 1987;Lancaster, 1992;Sklan and Dariel, 1993;Leung et al, 1995;Gallenti, 1997;Westrich et al, 1998;Garille and Gass, 2001;Martinez-Alfaro, 2003;Cadenas et al, 2004). Therefore in this study, the main studies are to expend the current knowledge in menu planning and diet problems focusing on Malaysian recipes, minimizing the cost, fulfill the nutritional requirements and serve variety of food serve each day.…”

Cost-minimizing food budgets in Ghana

“…Garille and Gass (2001) illustrates that economic literature credits Stigler's (1945) diet problem for its role in present linear programming applications. Stigler's interest was to find how much of his chosen 77 foods would be consumed by a man weighing 154 pounds so that his intake of nine nutrients would be at least equal to the recommended dietary intake (as suggested by the National Research Council) while maintaining minimum costs.…”

“…His diet consisted of varying amounts of wheat flour, cornmeal, evaporated milk, peanut butter, lard, beef liver, potatoes, spinach and dried navy beans. Garille and Gass (2001) points out the inadequacies of Stigler's minimal subsistence diet in terms of palatability, variety, and overall adequacy. In her article describing the evolution of the diet model into a more acceptable menu-planning approach, Lancaster (1992) observes that "the solution to the least cost diet is the equivalent of the human dog biscuit."…”