Menu scheduling for high blood pressure patient with optimization method through Integer Programming
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Journal of Physics: Conference Series
PAPER • OPEN ACCESS
Menu scheduling for high blood pressure patient with optimization
method through Integer Programming
To cite this article: Liew Su Hui et al 2021 J. Phys.: Conf. Ser. 1874 012088
View the article online for updates and enhancements.
This content was downloaded from IP address 46.4.80.155 on 22/09/2021 at 23:45RETREAT 2020 IOP Publishing
Journal of Physics: Conference Series 1874 (2021) 012088 doi:10.1088/1742-6596/1874/1/012088
Menu scheduling for high blood pressure patient with
optimization method through Integer Programming
Liew Su Hui1, Suliadi Firdaus Sufahani1,*, Kamil Khalid1, Mohd Helmy Abd
Wahab2, Syed Zulkarnain Syed Idrus3, Asmala Ahmad4 and Tamil Selvan
Subramaniam5
1
Department of Mathematics and Statistics, Faculty of Applied Sciences and
Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, 84600 Pagoh,
Johor, Malaysia.
2
Faculty of Electrical and Electronic Engineering, Universiti Tun Hussein Onn
Malaysia, 86400 Parit Raja, Batu Pahat Johor, Malaysia
3
Faculty of Applied and Human Sciences, Universiti Malaysia Perlis (UniMAP), Perlis,
Malaysia
4
Faculty of Information and Communication Technology, Universiti Teknikal
Malaysia Melaka, Jalan Hang Tuah Jaya, 75300, Melaka, Malaysia
5
Department of Skills and Professionals, Faculty of Technical and Vocational
Education, Universiti Tun Hussein Onn Malaysia, Parit Raja, 86400 Batu Pahat, Johor,
Malaysia
Corresponding Author Email: suliadi@uthm.edu.my
Abstract. High blood pressure or hypertension is a global public health issue. High blood
pressure can lead to cardiovascular disease, stroke, diabetes and others. The diet problem of
high blood pressure patients has always been concerned by the field of operational research.
Some previous and recent research have proposed that diet plays an important role in affecting
the condition of high blood pressure. A balanced diet will provide essential nutrients for high
blood pressure patients that help to control and lower blood pressure. The purpose of this study
is to construct a diet menu that meet the nutritional requirements of high blood pressure patient
as well as minimize the food cost by developing a mathematical model using linear and integer
programming approaches. The model of this study involved 10 type of food groups with 413
types of food variables based on the Malaysian recipes. The findings show that integer
programming is a good alternative for linear programming. Integer programming leads to an
optimal and effective solutions for the diet problem of high blood pressure patients.
Keywords: High Blood Pressure, Diet Problems, Mathematical Programming, Optimal
Solution
1. Introduction
High blood pressure is a global public health issue. In medical term, High blood pressure known as
hypertension [1]. It happened when the blood pressure in the arteries increases as the blood vessels
become narrow, the blood pressure level excess 140 over 90 mmHg (millimeter of mercury) [2].
Globally, the high blood pressure cases increase from year 1980 to 2008, there are approximately 40%
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd 1RETREAT 2020 IOP Publishing
Journal of Physics: Conference Series 1874 (2021) 012088 doi:10.1088/1742-6596/1874/1/012088
of adults aged 25 and above suffered from high blood pressure [3]. In Malaysia, the prevalence of
hypertension has growing rapidly among the younger and adults. High blood pressure also affects the
elderly in Malaysia [4].
A balanced diet is a key to healthy lifestyle. Taking a diet with balanced nutrient intake is not
only to prevent and manage chronic diseases, yet also basic for children and adolescents to ensure their
healthy growth [5]. A well-balanced diet is vital for every people especially those people who suffers
from diseases. In addition, a balanced diet plays an important role in treating high blood pressure. In
general, most of the high blood pressure patients are lack of knowledge about nutrition need and this
reason had become one the factor that affecting hypertension [6]. Thus, a menu that meet the nutrients
requirement of high blood pressure patient is needed to control the prevalence of high blood pressure.
Previously high blood pressure patient was referring to Dash diet, it is a dietary pattern developed by
an initiative of the National Heart, Lung, and Blood Institute (NHLBI) to examine dietary factors that
affect blood pressure [7]. The pattern of dash diet refers to an eating plan to control blood pressure [8].
However, in this case, the patient may refer to the diet menu which solved by using mathematical
programming model. Foods that recommended in Dash diet will be added into Malaysia food menu,
since, Dash diet only involved general type of foods. Then, a new diet menu is produced based on the
Malaysian style of recipes and the recommended nutrient intake (RNI) of Malaysian which is easier
for the people to follow.
In this study, menu that meet the nutritional requirements of high blood pressure patient will
be developed by applying mathematical programming techniques. In order to prepared menu which are
suitable for high blood pressure patient, the range of each nutrients that required by high blood
pressure patient should be discovered according to the age, gender and health status of patient. The
menu produced must be low cost so that high blood pressure patients are able to consume. Besides, the
menu should prepare for more than one day if possible, let the high blood pressure patient to have
more choices.
2. Methodology
There are two programming techniques being used in this study which are linear programming and
integer programming. The menu is generated using the two techniques by developing the mathematical
model along with 413 food data.
2.1 Data Descriptions
The recommended nutrients intake for high blood pressure patients were obtained from some previous
research done by [9, 10, 11, 12]. While, the requirement of each nutrients was obtained from the book
of Recommended Nutrient Intakes for Malaysia (RNI) 2017. The nutrients requirements of patient are
varied according to their age, gender, health status and others. The information were then verified by
nutritionist. The menu is prepared based on the 413 types of Malaysia foods which provided in the
book of Nutrient Composition of Malaysia Food [13]. Moreover, there are some considerations such as
the price of the food items, the nutrient compositions of each food item and recommended nutrient
intake (RNI) for Malaysian should be taken when developing the model to construct a menu.
In this study, the one-day diet menu designed involved six nutrients, including sodium, protein,
potassium, calcium, Vitamin B2 and Vitamin C and consists of total 18 dishes from ten food groups as
shown in Table 1. Sodium intake is the essential component when preparing menu for high blood
pressure patient, since the reduction of daily sodium intake will help to lower the blood pressure [14].
In addition, the menu designed are classified into six types of meals in one day as shown in Table 2.
Table 1: Food requirement per day
2RETREAT 2020 IOP Publishing
Journal of Physics: Conference Series 1874 (2021) 012088 doi:10.1088/1742-6596/1874/1/012088
Type of Food No. of requirement per day (n)
Beverage ( ) 6* including 2 plain water ( )
Cereal Flour Based ( ) 1
Rice Flour Based ( ) 1
Cereal Based Meal ( ) 2* including 1 plain rice ( )
Meat Dishes ( ) 1
Vegetables ( , ) 2
Fruits ( ) 2
Wheat Flour Based ( ) 1
Seafood ( ) 1
Miscellaneous ( ) 1
Total Dished per Day 18
Table 2: The menu planning of food item per day
Meal Type of Food Group Amount
Beverage 1
Breakfast
Cereal Flour Based 1
Beverages 1
Morning Tea
Rice Flour Based 1
Beverages 1
Cereal Based Meal 1
Lunch Vegetables 1
Fruits 1
Meat / Seafood 1
Beverages 1
Evening Tea
Wheat Flour Based 1
Beverages 1
Cereal Based Meal 1
Dinner Vegetables 1
Fruits 1
Meat / Seafood 1
Beverages 1
Supper
Miscellaneous 1
Total 18
There are some differences between a high blood pressure diet and normal diet. Thus, there is a high
blood pressure patient being considered in this study as an example in panning menu. The patient is a
female who aged 54 with 80kg. She is an inactive person but she does not have any other disease or
allergy. Table 3 show the range of each nutrients of the patient which depend on her age and gender.
Table 3: Lower and upper bound values of the 5 nutrients (female patient)
3RETREAT 2020 IOP Publishing
Journal of Physics: Conference Series 1874 (2021) 012088 doi:10.1088/1742-6596/1874/1/012088
Nutrients Lower Bound (LB) Upper Bound (UB)
Sodium (mg) - 1500
Protein (g) 52 -
Potassium (mg) 4700 -
Vitamin B2 (mg) 1.1 -
Calcium (mg) 1200 2000
Vitamin C (mg) 70 2000
2.2 Model Description and Development
There are two programming techniques: linear programming and integer programming used construct
a diet menu by developing a mathematical model with 413 food data. There are three main
components included in the mathematical model which are objective function, decision variables and
constraints. The objective function of this study is to minimize the total food cost which written as [15]:
N P Q
c x
i 1 j 1 k 1
i ijk (1)
Minimize total cost =
where is decision variable of food items, for 10 food groups, and 6 meals, , is the cost for
each food items , is the number of meal per day and is the number of food groups.
Furthermore, the constraints have divided into two parts which are the general nutritional requirements
and the food group requirements [15]. The constraints of 6 nutrients based on Table 3 is computed as
follows:
N 10 6
LowerBoundi wi xijk UpperBoundi (2)
i 1 j 1 k 1
where is the weight of nutrient for the food. This study had six nutrients constraints with lower and
upper bound values except for sodium, protein and Vitamin B2. The sodium only has an upper bound
value while the other two nutrients only have the lower bound values. Meanwhile, the food
requirements based on Table 1 are obtained as follows:
10
Type of
i 1 food groups( xi ) n
(3)
The variables involved in the model should be binary. If the foods appear in the menu, the decision
variables (Xi) will only be 1 or 2, each food could only be served once or twice in a day, otherwise is
zero. Besides, the coding is programmed by using the computer program, LPSolve IDE. When the user
key in the data, an automated system will be built up to generate a list of menus for one day as an
output.
3. Results and Discussions
The diet menu is designed according to the constraints and requirements mentioned in Section 2.1 by
using linear and integer programming approaches along with 413 food variables. In this study, the
linear programming approach is used to check the validity of the diet menu produced. The results
obtained will be shown table below:
4RETREAT 2020 IOP Publishing
Journal of Physics: Conference Series 1874 (2021) 012088 doi:10.1088/1742-6596/1874/1/012088
Table 4: Comparison on one-day menu for case 1 using LP and IP (big data set)
Big model LP IP
Meals Food items Amount Amount Food items
Milo 1.1163 1 Plain water
Breakfast
Biscuit soda/plain 1 1 Biscuit soda/plain
Yogurt orange 0.8837 1 Yogurt orange
Morning tea
Kuih kasui 1 1 Kuih kasui
Coconut water 1
1 Coconut water
Noodle, rice 0.6802
1 Rice, cooked
Rice, fried 0.3198
Lunch 1 Celery (daun seleri)
Mustard leaves, chinese 1
1 Jackfruit
Jackfruit (Nangka) 1
1 Chicken, satay
Chicken satay 1
Plain water 1 1 Coconut water
Evening tea
Doughnut 1 1 Doughnut
Coconut water 1
1 Sugar cane juice
Rice, cooked 1
1 Noodle, rice
Mustard leaves, chinese 1
Dinner 1 Mustard leaves, chinese
Jackfruit (Nangka) 1
1 Jackfruit
Indian mackerel, fried in 1
1 Fish crackers, fried
chilli
Plain water 1 Plain water
1
Supper Candy, coconut 0.9634 Pengat keledek, gula
1
Pengat keledek, gula merah 0.0366 merah
Total number of
20 18 18 18
dishes per day
Total food cost RM 6.10 RM 6.20
Table 4 shows the comparison result with both linear and integer programming approach. The result
obtained using both programming approaches have meet all the constraints for one day diet menu of
high blood pressure. However, there is some differences on number of dishes per day and total food
cost. The cost of one-day diet menu which generated by linear and integer programming approaches
are RM6.10 and RM6.20 respectively. The total food cost for integer programming (IR) approach is
slightly higher than linear programming (LP) approach. However, the amount of foods produced by
LP approach is impossible to be considered since the foods are served in real numbers with decimal
place. Besides, the number of dishes per day which produced by LP approach does not achieve the
constraints of food group, it produced more than 18 foods per day. Hence, the IP approach is preferred
to be considered and served by patient, since the amount of food produced is expressed in whole unit
and it has achieved the constraints of nutrients of the female patient and food groups which is 18 foods
per day.
Compared with the LP method, the IP method provides the optimal solution for the diet
problems of high blood pressure. Hence, it will be used to produce more than one day menus with
different food combination and minimizing the total food cost while fulfilling all the constraints and
requirements of nutrients and food groups. The process need to eliminate foods that have been served
on the previous day’s menu and consider the remaining foods that are still available for the next day’s
menu. So that, the foods in previous day menu will not repeat in the next day menu. The looping
process will be continued to produce the several days of diet menu.
5RETREAT 2020 IOP Publishing
Journal of Physics: Conference Series 1874 (2021) 012088 doi:10.1088/1742-6596/1874/1/012088
Table 5: Menu structure for the subsequent 5 days using IP (case 1).
Day 2 Day 3 Day 4 Day 5 Day 6
Meals Food items
Orange Milk, UHT, Milk, UHT, full
Milk, cow,
flavoured low-fat, cream,
Milo fresh
Breakfast drink, powder recombined recombined
Putu bambu Cookies,
Biscuit, Biscuit Biscuit, green
peanut
coconut savoury gram
Yogurt Plain water Malted milk
Plain water Plain water
Morning tea strawberry Kuih koci drink, packet
Bidaran Kuih seri muka
Kuih lompang pulut putih Wajik
Plain water Plain water Plain water
Plain water
Rice, coconut Rice, “dagang” Rice, cooked
Chicken rice Syrup rose
milk2 Spinach (bayam Spinach, red
Fern shoots (Sirap ros)
Mengkudu pasir) (bayam
Kismis Rice, cooked
Lunch Banana Banana (pisang merah)
(Raisin) Cekur manis
(pisang brangan) Avocado
Indian Durian belanda
tanduk) Beef, fried pear
mackerel, Beef satay
Quail egg, (Daging lembu Hairtail scad,
fried
whole goreng) fried in chilli
Malted milk
Yogurt Yogurt Tea & milk
Plain water drink, packet
Evening tea banana strawberry Curry puff
Kuih keria Curry puff
Kuih kapit Kuih ketayap twisted
only
Orange juice Plain water
Lime juice Rice, cooked Rice
Syrup rose
Rice, cooked Grass jelly Spinach (bayam porridge,
(Sirap ros)
Mengkudu (Lengkong) pasir) fish, instant
Brown rice
Banana Rice, cooked Banana (pisang Spinach, red
Peanut
Dinner (pisang Fern shoots brangan) (bayam
Cempedak
tanduk) Kismis Hairtail scad, merah)
Indian
Indian (Raisin) cooked in Avocado
mackerel, in
mackerel, Maw satay vinegar (Ikan pear
soya sauce
fried in chilli cencaru masak Hen egg,
cuka) whole
Milk, UHT,
Yogurt Plain water Milk, UHT,
chocolate Milk, cow,
banana Jelly crystals, low-fat,
Supper flavoured fresh
Candy, strawberry recombined
Pengat keledek, Chicken soto
coconut flavoured Rojak
gula putih
Total
number of 18 18 18 18 18
dishes
Total food
RM 6.80 RM 7.20 RM 7.77 RM 8.70 RM 9.95
cost
Table 5 shows the results of diet menu for Day 2 until Day 6 using IP approach (as result for Day 1 is
already shown in Table 4). Due to limitations of nutrients and food groups, the IP approach only able
6RETREAT 2020 IOP Publishing
Journal of Physics: Conference Series 1874 (2021) 012088 doi:10.1088/1742-6596/1874/1/012088
to produce a six-day diet menu for the female patient. The results show the total food cost increases
slightly higher from Day 2 (RM6.80) to Day 6 (RM9.95). However, the number of dishes is still the
same for every day which is 18. The menus are served with variety of food items in each day while
fulfilling the requirements of nutrient intake and food groups.
4. Conclusion
A menu which meet the nutrients requirements of high blood pressure is needed to manage or lower
the blood pressure. Different patients will have different requirement of nutrients according to their
age, gender and health status. The mathematical programming techniques were applied to generate the
optimal solutions to solve the diet problem of high blood pressure patient. Based on the findings, the
integer programming approach has developed menus with minimum food cost and the amount of food
that are possible to be served, while fulfilling the constraints and requirements of nutrients and food
groups. Thus, IP approach is a good alternative compare to the LP approach. It is a good approach to
construct a diet menu that satisfy all the constraints with minimum food cost by developing a
mathematical model.
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