**Article 1**

**Least Cost Diet for Children 2 to 3 Years in Malaysia Using Linear Programming Approach**

Nor Hayati Shafii\*, Rohana Alias, Noradilla Radzuan

Faculty of Computer and Mathematical Sciences,

Universiti Teknologi MARA, Malaysia  
  
<norhayatishafii@perlis.uitm.edu.my>, <annna@perlis.uitm.edu.my>, <dradzuan@gmail.com>

*Abstract*

*The early period of life, namely from birth to 2 years of age is critical for the promotion of optimal growth , brain development as well as health and behavioral development* *(Committee & Ministry, 2013). Thus, attaining the daily required nutrition during this stage of life is very crucial because nutrition is strongly associated with the children’s development at the very young age* *(Poh et al., 2018). It is a major challenge in Malaysia to ensure children get proper* *balance diet, especially* *for families with low socioeconomic status. As reported in the “Edge Weekly”, the review concomitantly found that 24.9% or nearly one in four children in Malaysia experienced moderate or severe food insecurity due to financial constraints* (Ho, n.d.)*.* *Wong et al. emphasized the three main factors associated with child malnutrition, which include low socioeconomic status and household food insecurity which are strongly associated with the financial background of a family* *(Wong, Moy, & Nair, 2014).* *Therefore,* *in this study, a linear programming diet model is used to determine* *an affordable cheapest basket of food items that satisfy* *the daily recommended nutritional requirements for children between 2-3 years old in Malaysia. POM-QM for Windows Version 5.2 by Howard J. Weiss is used. Initial finding shows that the* *average costs are* *RM2.69. This food basket consists of 474g of egg, 55g of tofu, 29g of papaya, 5g of spinach and 201g of potato. With this food basket and the estimated food expenditure, the parents can save about 40% of their child’s daily food expenditure.* *Sensitivity analyses are also performed to test the robustness of the findings.*

*Keywords:* *Food Items, Nutrition, Low Cost, Linear Programming Model, Optimization*

**Introduction**

Malnutrition is associated with about half of all child deaths worldwide (Mj, Cheah, & Lee, 2014). One of the explanations for this, addressed by Schönfeldt et al. (2010) is an inefficient education about eating healthily and lack of ability to gain the necessary education due to economic constraints.

Socioeconomic background is the main factor for parents, whether they could afford to buy food with sufficient nutrient or not (GL et al., 2012). In Malaysia, the prevalence of underweight and stunting persist among young children from poor rural areas (Khor & Sharif, 2003). According to Temim et al. (2010), the problem could be addressed by initiating low cost changes in the health system which would make the entire sector more responsive to the targeted people’s requirements.

Linear programming has been utilized in various different applications for the purpose of explaining diet related problems. Okubo et al., 2015 has used Linear Programming to determine the pattern of food intake in fulfilling the recommendation of nutrient by Dietary Reference Intake (DRIs) and numerous researches have been done with different purposes such as by Briend et al., 2008 and Van der Merwe et al., (2014).

This study uses Linear Programming approach to determine the minimum food budget that satisfies the nutritional requirements for Malaysian children aged between 2 to 3 years old. Secondary data is used for the input dietary data. Since this study focuses on diet optimization, the data on nutritional contents are obtained from SELF Nutrition Data of Standard Tables Food Composition at nutritiondata.self.com and data on caloric needs for age group of 2 to 3 years was taken from Malaysian Dietary Guidelines for Children and Adolescents Summary.

The food items considered in this study were collected based on high recommendations by other researchers which also satisfy the suggestion from the Ministry of Health (2013). The prices of the respective food item were taken from Giant Hypermarket Kangar on March 26, 2017 and the prices were normal prices without promotion or discount. The daily minimum amount of each required nutrient refers to the dietary Reference Intake for an average Malaysian child of 2 to 3 years old.

**Method of Data Analysis**

The best and effective method in solving linear programming is the Simplex Method. George Dantzig developed a general step to apply the Simplex Method manually by incorporating both optimality and feasibility test to find the optimal solution to a linear programming (Giordano et al., 2014) as shown in Figure 1.

***The Simplex Method and Shadow Price Analysis in Formulating the Model of Least Cost Diet***

The objective is to minimize the food budget. According to Malaysian Dietary Guidelines for Children and Adolescents Summary, Malaysian favourite food items are milk, yoghurt-plain, chicken, egg, mackerel, tofu, banana, papaya, carrot, spinach, white rice, white bread, potato, plain biscuits and also noodles. All these food items were considered as the independent variables.

The constraints in this model were labelled as follows: Carbohydrates as , calcium as Ca, iron as Fe, magnesium as Mg, potassium as K, sodium as Na, vitamin A, C, E, K as Vit.A, Vit.C, Vit.E, Vit.K, respectively. Labels for energy, protein and fats remain the same.

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| ![](91--181-1-5-20180918_media/media/image17.png) |

Figure 1: Steps in the Formulation of Optimal Linear Programming Model using Simplex Method

The formulation of the model is given by equation (1) and (2).

Minimize cost:

(1)

Subject to:

(2)

Z = The minimum food budget for children (RM), = The quantity (100g) of the food item *j*, = The cost of (100g) of food item *j*, = The amount of nutrient *i* in food item *j*, = Minimum daily requirement of nutrient *i*.

Incorporating the prices of 15 food items (RM), the amount and the minimum daily requirement of nutrient for the model of least cost basket results in the following formulation:

Table 1: Price and Nutritional Content of 100 grams of Food Items

![](91--181-1-5-20180918_media/media/image24.PNG)

Model of minimum cost:

(4)

Subject to all the constraints such as Energy , Fat etc.;

(5)

***Formatting Surplus Variables and Artificial Variables***

The Simplex Method requires that constraints be written as equalities. Specifically, in this study all inequality signs for all the constraints were identified with the sign more than and equal (). Therefore, these models involved surplus and artificial variables to make it equal.

For example, the inequality for energy constraints in equation (5) is written as an equal in equation (6). This is done by subtracting a value of surplus variable , .

(6)

An artificial variable in equation (6) is a variable introduced into each equation that has a surplus variable. An artificial variable is required to satisfy the nonnegative constraint to ensure that the only basic feasible solution is considered. Next, the data is analysed using POM-QM software.

**Results and Discussion**

The LP solution is shown in Table 2 and the results were summarized in Table 3 and Table 4 respectively. The result shows that RM2.68 was the minimum amount per day that parents need to spend on food for children of 2 to 3 years old, to meet the necessary nutritional requirements. The food basket must consist of 4.69g of egg, 0.53g of tofu, 0.05g of spinach, 1.86g of potato and 0.68g of noodle.

If parents want to add food items other than the food items suggested in the Model, the parents need to increase food expenditure following the value in the “Reduced” column shown in Table 3. The “Reduced” column in Table 3 shows that consumption of 100 grams of milk will increase food expenditure by RM0.34, consumption of chicken and rice will increase costs by RM0.46 and RM0.21 per 100g of chicken and rice, respectively. For both yoghurt and mackerel, 100 grams consumption of each will increase food expenditure by RM0.61.

Table 3: Optimal Values of Food Items

![](91--181-1-5-20180918_media/media/image33.PNG)

Table 2: Optimal Solution of Food Basket

![](91--181-1-5-20180918_media/media/image34.PNG)

All Papaya, Carrot and Bread are quite insignificant with prices RM0.05 and RM0.04 for every 100grams of its consumptions. These values are too small or unimportant to be worth consideration.

| Table 4: (i) Constraints Ranging Result (ii) Optimal values of nutrient requirement for the model |                                                   |
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| ![](91--181-1-5-20180918_media/media/image35.png)                                                 | ![](91--181-1-5-20180918_media/media/image36.png) |

Table 4 shows that the value of surplus variable obtained from “surplus” column can also be written as follows:

4991.108, 72.47541, 74.54718, 74.61584, 926.0453, 3.462236, 0, 0, 0, 8.754319, 122.6744, 992.8777, 0, 0.

Vitamin E, vitamin K, calcium, potassium and sodium have zero value for surplus variable which the resources are fully utilized. Thus, these 5 nutrients are binding constraints. Although these constraints are binding, a unit increase in the right-hand side of any of these nutrients will not increase food expenditure significantly.

Meanwhile, the constraints of the energy, carbohydrates, fats, protein, vitamin A, vitamin C, iron, magnesium and phosphorus are not binding in the Model because the value of the surplus is not equal to zero. This indicates that there has an excess amount of resources utilized. Therefore, a new column is created known as “level” column as shown in Table 4 as new limitations for the constraints. These values are from the original values plus the surplus value for each constraint.

**Conclusion and Recommendation**

This study aimed to find the least cost food basket while satisfying nutritional requirements for children between 2 to 3 years old in Malaysia. The Simplex method used in this study was successful in providing a systematic tool for designing least cost nutritious food basket. The least cost diet model proposed is also significant for parents from low income household as it provides information on proper balance diet for their children with affordable food items. Furthermore, all the suggested food items such as egg, tofu, papaya, spinach, potato and noodle are widely available in Malaysia. This study only considered children of low household income from the Malay ethnic in Malaysia; not for any other specific cultural groups or races. It would be interesting if we can consider the food consumption patterns of specific cultural groups or races such as Chinese, Indian or other races in Sabah and Sarawak.

**References**

Committee, N. C., & Ministry, N. (2013). Malaysian Dietary Guidelines for Children and Adolescents.GL, K., ZM, S., S, S., SLM, H., M, M., YM, C., … BNM, Y. (2012). Milk Drinking Patterns among Malaysian Urban Children of Different Household Income Status. *Journal of Nutrition and Health Sciences*, *1*(4). https://doi.org/10.15744/2393-9060.1.401Ho, S. (n.d.). Special Report: Childhood stunting - A silent crisis in Putrajaya | The Edge Markets. Retrieved July 26, 2018, from http://www.theedgemarkets.com/article/special-report-childhood-stunting-silent-crisis-putrajayaKhor, G. L., & Sharif, Z. M. (2003). Dual forms of malnutrition in the same households in Malaysia--a case study among Malay rural households. *Asia Pacific Journal of Clinical Nutrition*, *12*(4), 427–437. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/14672867Mj, E., Cheah, W. L., & Lee, P. Y. (2014). Factors Influencing Malnutrition among Young Children in a Rural Community of Sarawak, *20*(2).Poh, B. K., Ng, B. K., Din, M., Haslinda, S., Shanita, S. N., Wong, J. E., … Norimah, A. K. (2018). Nutritional status and dietary intakes of children aged 6 months to 12 years : findings of the Nutrition Survey of Malaysian Children ( SEANUTS Malaysia ) British Journal of Nutrition. *British Journal of Nutrition*, *110*(2013), S21–S35. https://doi.org/10.1017/S0007114513002092Schönfeldt, H. C., Gibson, N., & Vermeulen, H. (2010). NEWS AND VIEWS: The possible impact of inflation on nutritionally vulnerable households in a developing country using South Africa as a case study. *Nutrition Bulletin*, *35*(3), 254–267. https://doi.org/10.1111/j.1467-3010.2010.01837.xWong, H. J., Moy, F. M., & Nair, S. (2014). Risk factors of malnutrition among preschool children in Terengganu , Malaysia : a case control study, 1–10.