ED 067 748

AUTHORTITLE

DOCUMENT RESUME

24 EA 004 600

Findorff, Irene K.A Study on Linear Programming Applications for theOptimization of School Lunch Menus. SummationReport.

INSTITUTION Tulane Univ., New Orleans, La.SPONS AGENCY National Center for Educational Research and

Development (DHEW/OE) , Washington, D.C.BUREAU NO BR-0-G-024PUB DATE Jul 72GRANT OEG -7 -70 -0165 (509)

NOTE 16p.

EDRS PRICE MF-$0.65 HC-$3.29DESCRIPTORS *Computer Programs; *Cost Effectiveness; Data Bases;

Food; Food Service; Foods Instruction; *LinearPrograming; *Lunch Programs; *Nutrition; Planning

IDENTIFIERS Louisiana; New Orleans; *New Orleans PublicSchools

ABSTRACTThis document summarizes the results of a project at

Tulane University that was designed to adapt, test, and evaluate acomputerized information and menu planning system utilizing linearprograming techniques for use in school lunch food serviceoperations. The objectives of the menu planning were to formulatemenu items into a palatable, nutritionally adequate combination atminimum cost. The author did an empirical study of menu planning inthe New Orleans Public Schools and found that the use of linearprograming reduced raw food expenditures 13 percent over manualplanning methods. (Author/DN)

U.S. DEPARTMENT OF HEALTH,EDUCATION & WELFAREOFFICE OF EDUCATION

THIS DOCUMENT HAS BEEN REPRO.DUCED EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIGINATING IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILYREPRESENT OFFICIAL OFFICE OF EDU-CATION POSITION OR POLICY.

SUMMATION REPORTProject No. 0G024

Grant No. OEG-7-70-0165-(509)

A STUDY ON LINEAR PROGRAMMING. APPLICATIONS FOR THEOPTIMIZATION OF SCHOOL LUNCH MENUS

FILMED FROM BEST AVAILABLE COPY

Irene K. Findorff

Tulane University6823 St. Charles Avenue

New Orleans, Louisiana 70113

July, 1972

SUMMATION REPORT

Project No. OG024Grant No. OEG-7-70-0165-(509)

A STUDY ON LINEAR PROGRAMMING APPLICATIONS FOR THEOPTIMIZATION OF SCHOOL'LUNCH MENUS

Irene K. Findorff

Tulane University

New Orleans, Louisiana

July 24, 1972,

The research reported herein was performed pursuant to agrant with the Office of Education; U.S. Department ofHealth, Education, and Welfare. Contractors undertakingsuch projects under Government sponsorship are encouragedto express freely their professional judgment in theconduct of the project. Points of view or opinionsstated do not, therefore, necessarily represent officialOffice of Education position or policy.

r 6

11

OE Bureau of Research No. Grant No.: OEG-7-70-0165-(509)

Period: 4/1/70 - 5/31/71 Date of subMission: 7/24/72

Name of institution: Tulane University

Title of project: A Study on Linear Programming Applicationsfor the Optimization of School LunchMenus

Project director: Irene K. Findorff U.S. Office ofEducation

DREWRegion VIIDallas, Texas

Description of. Problem

Due to the need for demonstrating to school lunchprofessionals the superiority of menu planning throughlinear programming techniques in order to provide mealsto the participants at lower cost while satisfyingnutritional requirements with greater precision than hasbeen evidenced with manual procedures, a project wascompleted at Tulane University to adapt, test, andevaluate a computerized inforMation and menu planningsystem for use in school lunch food service operations.Menu planning as a decision process affects the nutritionaland palatability qualities.as well as the cost of foodserved in institutions. The well-known objectivesinvolved in the menu planning process are to formulatemenu items into a palatable, nutritionally adequate,economical combination, that is, to satisfy a large setof simultaneous requirements for which the determinationof the optimum condition has long been identified as alinear programming problem.

Scope of the Study

From both nutritional and financial viewpoints,it appeared worthwhile to explore the experimentaldevelopment of a computer-assisted menu planning systemfor the school lunch program to provide optimum menuswhich would be more economical and possess greatersatisfaction of exact nutrient constraints than has beenfeasible with the use of manual menu planning tools.

.

A data bank was created which contained nutrit,cost, and menu item information in computerized format.

These data were used to evaluate a 30-day cycle schoollunch. menu planned by conventional methods and to testa linear programming model used to plan menus withcomputer assistance. Menus planned by the manual andcomputerized procedures were compared with respect tototal raw food cost and fulfillment of nutrient require-ments.

Objectives Pursued

The overall objectives of the study included:(1) 'to build and test a linear programming model

suitable for planning menus on computer for the schoollunch program which incorporated price, nutrient, andmenu item frequency constraints derived from.lconyen-tionally planned school lunch menus to formulate afeasible solution.

(2) to use the linear programming iidel tocomputerplan a 30-day school lunch menu containingnutrient constraints based on one-third of the Recom-mended Dietary Allowances for the 10-12 year old child(1).

(3) to evaluate the computer-planned menus interms of indicated raw food cost savings and satisfactionof nutrient and menu item frequency constraints.

(4) to disseminate the research. findings obtainedfrom the investigation to school lunch professionals sothat

(a) the superiority of linear programmingas a menu planning tool could be demonstrated.

(b) the demand for advanced educationalprograms necessary for the understanding of a computerassisted menu planning system could be realized.

(c) the possibility of initiating a futurepilot study within a school lunch feeding program toimplement the computeized menu planning process couldbe entertained.

Methods Used

Coding procedures to formulate data for theIBM-CAMP system (2) were followed which involved thecollection of quantitative nutrient, food item, and recipeinformation to create a school lunch data base.

A manually-planned 30-day cycle menu as used inthe New Orleans Public Schools was obtained (3). Eachitem that appeared on this plan as coded to create amenu item master file which stored all pertinent inform-ation about a menu item including the ingredient list,

ingredient purchase quantities, required weight and costof each ingredient, recipe yield, portion size, cost perserving, physical attributes, dominant characteristics,and nutrient composition of a single serving of the recipe.In addition, recipes recommended by the. U.S. Departmentof Agriculture for preparation of school lunches (4) wereobtained and coded for inclusion in the menu item masterfile.

Price and purchase information for each recipeingredient obtained from the Food Service Department ofthe New Orleans Public Schools (3) were coded and storedin a food item data file. Price data were updated priorto the evaluation of conventional menus and held constantfor the computer assisted menu planning processes.

A computerized file of nutrient data based primarilyon information found in.U.S. Department of Agriculture,Handbook Number 8, Table 1 (5) was obtained and revised'to include values for magnesium (5) and for vitamins B6and B12 derived from USDA Home Economics Research ReportNumber 36 (6).

A nutrient tally computer program (2) wasemployed to calculate the raw food cost and nutrientcontent of the 30 menus planned by manual methods.

A menu planning model (7,8) was adapted foruse to computer-plan the school lunch menus utilizingdata generated from the aforementioned files. Thislinear programmingmodel with upper bounds can providefor 35 constraints'subdivided as attribute, structural,nutrient, and special constraints, and for 400 menu` itemsclassified into nine categories. The program runs. throughoff-line batch processing and produces a sequence ofmenus with desired variety while satisfying nutritionalspecifications on the average at minimum cost. Theprogram is a chain.of linked subroutines containing:

(1) a matrix generator program(2) a linear programming code with implicit

upper bounds(3) optional subroutines for indifference and

feasibility ranges(4) a listing subroutine.

Three matrices were developed and employed totest the application of the linear procxamming approachto school lunch menu planning. These matrices representeddata sub-sets of the menu item file information with theaddition of separation ratings (i.e. the number of daysthat must elapse before the item may recur in a menu

-3-

5

plan) and served to define the nutrient and structuralrequirements for the menu planning program.

Conventional- and computer-planned menus werecompared with respect to total raw food cost andfulfillment of stipulated nutrient constraints.

Results Obtained

Traditionally, school lunch menus have beenmanually planned with respect to Federal reimbursementstandards to fulfill requirements known as the Type Apattern. The Type A lunch provided minimally toparticipants a two-ounce serving of lean meat, poultry,fish or equivalent of such, a threefourths cup servingof two or more vegetables or fruits, one slice of wholegrain or enriched bread or suitable equivalent, oneteaspoon of butter or fortified margarine; and one halfpint of whole, fluid milk, This pattern was designed asa tool to assist school lunchroom managers in theformulation of palatable, nutritious meals and providedfor the development of a monitoring system to determineFederal and Stte reimbursement for the meal served.For example, if it could be shown that the daily schoollunch menu met the Type.A requirements, subsidy wasautomatic

It was anticipated but never stated as a regulationthat judicious use of the Type A pattern would result inmenu plans that would contain one-third of the RecommendedDietary Allowances (1) for each respective age-group ofschool children. Guidelines were.published*anddistributed !eo school lunch managers to encourage theachievement of this secondary nutrient goal throughincorporation of selected nutrient-endwed foods inthe weekly menu plan, Similarly, it was hoped thatnutritional needs for different age-sex groups of childrenwould be fulfilled by the expansion and/or contractionof portion sizes of food offered.

Current technology permits the rapid computationof nutrients contained in a meal or menu providing thataccurate nutrient data are available_ Consequently,consideration has been given to the possibility ofplanning school lunch menus .according to a nutrientstandard rather than attempting to select foods to fillout the former Type pattern. Use of such a standard

awould permit exact achievement of nutrient.eoalsparticularly if computer* assisted menu planning teciqueswere employed since the computer method allows the userto stipulate definite nutrient constraints,

Data obtained from the nutrient tally programincluded the daily raw food cost and daily nutrientcomposition of the 30-day conventional menu plan. Thenutrient data represented values for food energy (calories),protein, fat, saturated and unsaturated*fatty acids,magnesium, calcium, iron, vitamins A, B6, B12, C, thiamine,riboflavin, and niacin (Appendix, Table 1). The resultsof the present investigation demonstrate the ineffective-ness of the use of the manual tool, the Type A pattern,for planning school lunch menus to meet a nutrient standard.The conventionally planned 30-day Orleans Parish schoollunch menu contained inadequate quantities of foodenergy (calories), iron and thiamine and excessiveamounts of protein, calcium, vitamin A, riboflavin,niacin equivalents, and vitamin C when the daily averagenutrient content of the menus was compared to theone-third value of the National Research Councilrecommendations (1) for. .the 10-12 year old child asstipulated.by USDA to comprise a nutrient standard forschool lunches (9)

A menu planning matrix was Constructed whichspecified as constraints the exact nutrients as werefound in,the conventional school lunch Type A pattern'meals served to participants in Orleans Parish. Also,the frequency of service of various menu items wasparalleled to that observed in the New Orleans schools,Only menu items which appeared in the 30 day conventionalcycle were included in the matrix. This matrix informationwas utilized to computer-plan a 30-day menu. The linearprogramming solution using identical menu item data aswere found in the manual Type A plan satisfied allnutrient constraints at a lesser raw food cost. Theaverage daily cost of the manual plan was 20.43 centsand of the computer menu plan, 17.70 cents (Appendix,Table 2).

A second computer menu plan was obtained usingmatrix data which specified one-third of the RecommendedDietary Allowanese(1) for the 10-12 year old child asnutrient constraints with the eNception of protein; theprotein requirement was entered as one-half of therespective allowances. The nutrients stipulated for thissecond matrix represented increases in the quantitiesof calories, iron, and thiamine and decreases in thelevels of protein, calcium, vitamin A, and riboflavinwhen the values were compared to data contained in thefirst matrix. This ,second matrix also.included menuitems from the USDA recipe file (144) as well as the

original Orlea»s Parini) items derived from the conven-tionz.:1 menu plan. The a.verage daily raw food cost ofthis computer menu j)lan was :i7.91 cents reflecting a2.52 cent savincTs when compared to the conventionalplan (Appendix, Table 2 ). It is interesting to notethat even though the protein constraint was lower,the cost of this computer menu plan increased due to thesatisfaction of the increased iron requirement. Thestipulation for protein, and in fact all nutrients, wasexpressed as a greater than or equal to inequality.This second computer menu plan actually contained moreprotein than obtained when only the conventional dataand requirements were used (Plans 1 and 2, Appendix,Table 2). Iron was shown to be a binding nutrientconstraint when the menu plan. solution was evaluated.

The data were manipulated in an effort to obtaina third menu plan soltuion which would possibly showadditional raw food cost savings. The structure ofthe third matrix differed from the second in thefollowing .,.Yays:

(1) the caloric thiamine', and riboflavinnutrient constraints were decreased to represent recentrecommendations from USDA (9).

(2) the protein' constraint was decreased toxeflect one-third of the Recommended Dietary Z- llowances(1) for the 10-12 year oldechi:10..

(3) requirements for dominant items werechanged to increase menu variety. For example, theconstraint for potato-containing 'items was changedfrom less than or equal to one to greater than orequal to five occurrences permitted to enter intothe 30-day menu solution.

(4) upper bounds for all menu items were increasedby one, a procedure which relaxes restrictions imposedon the data.

(5) a dominant characteristic code was attachedto all bread-contributing entrees which by nature ofits incompatability action would force more plain breaditems into the computer solution.

The menu plan obtained from this third datasub-set shoi.;ed a daily raw food cost of 17.74 centswhich represented a. 2.69 cent cost saving from theoriginal conventional plan (Appendix, Table 2 ).

Results obtained from the three linear progrnmmingsolutions indicate that there. is a potential for atleast. a thirteen percent savings in raw food cost ':tsimultaneous satisfaction of nutrient and palatabilityconstraints if the corriputer assisted technique forschool lunch menu planning would he implemented,

-6-

Dissemination of the findings of this investigationwas achieved through formal presentations at the followingprofessional meetings:

(1) Third International Congress of Food Scienceand Technology, Washington, D.C. , August 141 1970.

(2) ORSA Annual Meeting, New Orleans, Louisiana,April, 1972,

(3) Louisiana School Food Service Association,Baton Rouge, Louisiana, June 14 1972.

The need to provide advanced educational andtraining programs to prepare school lunch professionalsfor utilization of computer assisted menu planningsystems was emphasized as part of the following programswhich were not supported by this grant:

(1) USDA-Training Course, Dade County PublicSchools, Miami, Florida, January 31 - February 11, 1972.

( 2 ) USDA-Training Course , Memphis city Schools ,Memphis, Tennessee, April 17 28, 1972.

(3) Computer Applications in Food ServiceManagement and Dietetics Tulane University, New Orleans,Louisiana, June 9, 1972.

Future dissemination activities emanating fromthis work include two presentations scheduled for theEast Baton Rouge School*Lunch Board, Baton Rouge,Louisiana, November 21, 1972.

Highlights of Findings

In 1967, the U.S. Department of Agricultureinitiated a study to test the interpretation of theType A pattern to evaluate whether the basic lunch asserved did provide adequate quantities of nutrients tosatisfy the one-third Recommended Dietary Allowancevalues (1) for 10-12 year old children (10,11) . Thesurvey encompassed 300 schools from 19 states selectedto represent the United States as a whole. Six-thousandlunches as served were analyzed for calorie and nutrientcontent and the results were compared with both one-thirdand one-fourth of the 19 68 recommended allowances.

The lunches from the 300 schools on the averagemet or exceeded the nutritional goal of one-third ofthe recommended allowance for all nutrients except ironand magnesium and tended to fall below the goal infood energy (calories). When the results were appraisedby districts - lunches from a number of schools fail:?.:71to provide sufficient nutriment to meet the requirci,i:...ts

. for food energy and for certain vitamins and mine ral:particularly vitamin A, vitamin 136, iron and magnesium.

-7-

9

Since only ccnventional menu planning tools wereavailable, the De::artment of 14.griculture couldonly recommt-md that foods Considered rich sources ofvitamin A and iron be served to :school lunch participantsmore frequently than suggested previously; additionalquantitice of vitamins i and D were provided by fo-tifyingcommodity dry milk solids with these nutrients; alsoschool lunch managers were advised to serve recommendedportion sizes of items in an attempt to alleviate thecaloric deficit revealed from the analysis of thelunches.

The results of the USDA study and of the currentinvestigation do indeed confirm the suspicion that mealpatterns and guidelines cannot be used effectively toachieve precise satisfaction of nutrient stipulations.School lunch menu items carry a designation thatcategorize the individual recipe according to theparticular meal pattern component provided. For example,a single portion of the USDA recipe for Braised Beefreferred to as a "proteinrich food with vegetable" furnishesthe equivalent of -two ounces of cooked, edible meat, andonefourth cup of vegetable; nutrient calculations forthis serving of the Braised Beef are not included.The process of insertion of items into meal patternsto construct menus has at least two shortcomings inasmuchas neither the complete nutritional analysis of the totalrecipe or its respective single portion nor the mathematicalsolution of equations is utilized. The methodology ofconventional menu planning possibly hinges upon the humaningenuity of balancing sets of random variables by trialand error methods. Balancing meals for more than onenutrient is a problem of solving simultaneous systemsof equations which may involve dozens of constraintsand hundreds of variables, so that this strictlymathematical problem can be solved accurately only bycomputer. The methodology applied to the computer-plannedmenus, therefore, sets the absolute standard of thecomputation subject to the accuracy of specifying anygiven set of nutritional data and constraints.

Since linear programming is a mathematical'optimization technique concerned-with the most efficientallocation of limited resources to merit given objectives:'maximum qu:-..'ntities of government distributed commodityfood items appeared in the solution of the computerizedmenu plrmning problem. With the provision of improvedsatisfaction of exact nutrient Constraints at a relativelylesser cost, it can be predicted that despite continually'rising food prices 7 more 'meals can be served, particularly

-8-

the reduced.- or non-costmeals that are needed to fosterthe improvement of nutritional status among 'childrenof poverty, without increasing the total budget of theschool lunch operation.

Significance and Implications

The results obtaiiled from the present studyshow the potential for a thirteen pRront savings inschool lunch expenditures for raw food :if computerassisted menu planning techniques were to be employed.Estimates obtained from the American school Food ServiceAssocj.ation reporting financial needs for the. 1970school year indicated that 807.8 million dollarswere requested and yet only 504 million dollars wereappropriated by the Congress of the United Statesfor the National School Lunch Program (12). The program,thus, had to operate at a deficit, If computer assisted;menu planning systems had been implemented at this time,the financial deficit could have been reduced, Theraw food cost of the conventional menu plan used inOrleans Parish was 20.43 cents per day; the averagecost savings achieved with the computer menu planswas 2. 65 cents per day. Extending this savings to the25 million school children reached daily by the NationalSchool Lunch Program would save the operation 662.5thousand dollars per day or 1.3 million dollars fora. two-day period, The computer assisted approachto school lunch menu planning goes beyond raw foodcost savings with improved nutritional control andchild satisfaction to provide an efficient tool forthe management ofchild feeding programs (13 ).

Recommendation s

Results of the present study served as a basisfor development of additional programs. The followingrecommendations emanating from this work are elicitedeven though it is realized that some of these. suggestionsare currently in effect:

(.1) use of a nutrient standard along withcomputer assisted menu planning procedures to formulateschool lunch menus

(2) develop a national data bank which wouldcontain the basic information required for the computerassisted menu planning program

(3) crc.--:ate a c learing center where ..new andrevised nutrient information can be evaluated tomaintain an accurate, and reliable nutrient data file

(4) implement the reported computerized systemin an operating school food service operation on atrial basis to demonstrate the effectiveness in actualpractice

(5) offer training programs to educate theschool lunch professionals concerning the use of thiscomputerized menu planning methodology.

dr

low

References

(1) National Academy of Sciences - National ResearchCouncil, Recommended Dietary Allov,?ance.s, Revised1968. Publ. No. 1694: Washington, D.C. 1968.

(2) IBM Corporation: Contributed Program Library.System/360. Computer Assisted Menu Planning,360D-15.2.013. Date of submittal: September 23,1969.

(3) Personal communications: Food Service Department ,New Orleans Public Schools, Mrs. Mary C. Sherwood,Director, New Orleans, Louisiana. August, 1970through February, 1971.

(4) U.S. Department of Agriculture. Quantity Recipesfor Type A School Lunches. Program Aid 631.U.B. Government Printing Office: Washington,D.C. 1971.

(5)

(6)

Watt 13,K, and Merr i 11, A. L. 1963. Compositionof Foods, Raw, Processed, Prepared. AgricultureHandbook No. 8, U.5, Department of Agriculture.U.S. Government Printing Office: Washington,D.C.

Orr, M. L. 1969, Pantothenic Acid, Vitamin B6,and Vitamin B12 in Foods, Home Economics ResearchReport No. 36, U.S. Department of Agriculture.U.S. Government Printing Off ice: Washington,DI CO

(7) Dennis, L.C. and Balintfy, J.L. ComputerizedDietary Information System. Volume V. SingleStage Menu Planning Program. To be published.

(8) Personal communications: Lyman C. Dennis II,President, Management Optimization Systems, Inc.Suite 13.36, National Bank of Commerce, New Orleans,Louisiana. April, 1970 through July, 1972.

(9) Food and Nutrition Service, U.S. Department ofAgriculture. Meal Standard for School Lunches(Preliminary for Review). February, 1971.

(10) U.S. Department of Agriculture, AgriculturalResearch Service and the Consumer a.nd MarketingService. Nutrients in.Type A School Lunches. 1969.

11-

(11) Murphy E.V7. Grossman, $ and Forz iati$ F. H.The nutritive contont of Type 21 lunches, SchoolLunch Journal 22:11-18, 1968.

(12) Personal communication: Louise A.K. Frolich,Field Coordinator, American School Food ServiceAssociation, Denver, Colorado. May, 1971.

(13) Gelpi Balintly j. L. Dennis andFindorff: C.K.: Integrated nutrition and foodcost control by computer. J. Am. Dietet. Assn.(to be published, Fall, 1972 ).

Appendix Table 1

Nutrient Content and Raw Food Cost of a 307EDay ConventionallyPlanned School Lunch Menu Cycle'

Nutrient Valueper clay

Calories 786.

Protein (gm) 27.8

Fat (gm) 38.6

Saturated Fatty Acids (gm) 14.5

Unsaturated Fatty Acids 1 (gm.) 12.4

Unsaturated Fatty Acids 2 (gm) 2.7

Magnesium (mg) 67.5

Calcium (mg) 472.5

Iron (mg) 3.8

Vitamin B6 (mg) 2.725

Vitamin B12 (mcg) 1.274

Vitamin A (T. U., ) 2385.

Thiamine (rag) .387

Riboflavin (mg) .792

Niacin (mg equiv) 8.465

Vitamin C (mg) 20.0

Raw Food Cost (cents) 20.43

"'Conventional menu plans were obtained from the New OrleansPublic Schools as served to participants September c3 ,

October 16, 1970.

Appendix Table 2

Nutrient Content and Raw Food Cost of Three Computer Menu Plans*

Nutrient Constraint

Plan I

Plan 2**

Plan 3

Required

Actual

Required

Actual

Rr---ql,ired

Actual

per day

per day

per day

Calories

Protein (am)

Calcium (mg)

> 786,

> 27.8

> 472,

788.

27.8

496,

> 835.

>22.5

> 400.

879,

29.2

479.

> 800.

>17.0

> 400.

867.

29.1

491

Iron (mg)

>3.8

_3.8.

>.

5.0

5.0

>5.0

.....

5.0

Vitamin A (I.U.)

>2385.

2693.

>1500.

4521.

>1500.

4649.

Thiamine (mg)

>.387

.39

>.43

.43

..

.41

.42

Riboflavin (mg)

_.792

.80

>.43

.90

>.41

.90

Cos

t***

Raw Food Cost (cents)

17.70

17.9

117

.74

Cost Savings (cents)

2.73

2.52

2.69

Cost Savings (percent)

13.36

12.33

13,17

*Menus were planned for a 30-day period.

**Requirement based on one-third of the Recommended Dietary Allowances

(1) for the

10-12 year old school child with the exception of protein; the protein recuireent

represented one-half of the respective allowance.

**Cost saving values based on difference between cost of computer menu

plan and the

conventional menu clan (20.43 cents per day).

"ood price information was held

constant for the evaluation of conl;cntional menus and the planning of computer me:ius,