A Mathematical Programming System for Food Management Applications

Abstract

A multistage multiple choice programming system was developed to reduce the food cost of institutional feeding programs by computer assisted menu planning and data control. Food management objectives were formulated as finding combinations of menu items for a sequence of days which satisfy desired nutritional, structural, compatibility and variety constraints at least cost, problems routinely faced by all volume feeding organizations and individuals. Solution was achieved by sequential solution of large integer programs with a specially developed truncated block enumeration algorithm. Programmed dialog made on-line postoptimal adjustments possible. A complete computerized food management information subsystem was also developed to support the matrix generator and provide a uniform file organization and data coding system applicable to any institution. System documentation, called S/360 CAMP, is available through the IBM Contributed Program Library. After initial implementation in four hospitals proved that mathematical optimization had indeed reduced the food service cost by 10–15 percent while maintaining prescribed nutritional and acceptability levels, two companies were formed to serve institutions in the application of CAMP and its derivatives. Published reports indicate successful applications in numerous hospitals, colleges, schools, and mental and penal institutions, realizing 5–34 percent cost savings. The number of applications in the United States and abroad has been increasing over the years with beneficial impact on food management and nutritional health. The results motivated a new approach to food price index theory since the applications provide a practical mechanism to optimally readjust food consumption in the face of price fluctuation.

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

“…This dynamic food menu environment must be tackled by caterers in the decision making process in order to satisfy all stakeholders. Thus, the proposed menu planning prototype is flexible in managing these changes in terms of the number of menu items involved, the price of menu items, the available budget and the caterer's cooking ability which was not taken into account by the previous studies which reported by 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), Fletcher et al (1994), Leung et al (1995), Gallenti (1997), Westrich et al (1998), Garille and Gass (2001) and Asyikin and Razali (2011). Based on the results, the process of generating the menu can take up to more than a week within seconds.…”

“…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.…”

A Review on Automated Menu Planning Approaches

“…Therefore, various optimization approaches have been applied by previous researchers to solve diet problem or menu planning problem, including linear programming (Smith, 1959;Bassi, 1976;Foytik, 1981;Silberberg, 1985;Westrich et al, 1998;Colavita and D'orsi, 1990;Fletcher et al, 1994), integer programming (Balintfy, 1964;Leung et al, 1995), multistage multiple-choice programming algorithm (Balintfy, 1975), mixed integer programming (Armstrong and Sinha, 1974), bi-criteria mathematical programming (Benson and Morin, 1987), mixed integer linear programming (Sklan and Dariel, 1993;Valdez-Peňa and Marĭnez-Alfaro, 2003) and goal programming (McCann-Rugg et al, 1983).…”

“…Several years later, Balintfy (1975) continued to upgrade the CAMP system by applying multistage multiple-choice programming algorithm for food management application. The food management such as in hospitals, colleges, schools and mental as well as penal institutions, were concerned more on food cost and budget.…”

Stigler's Diet Problem Revisited

“…In particular, pioneering work in menu planning, or computer-assisted menu planning, is described in Balintfy (1975). The history of this progress is reviewed in Lancaster (1992).…”