project report optimization model for building shelters in responding to flood in tuy phuoc district binh dinh province

Optimizing costs include construction and maintenance costs; expenses for the construction of public places such as toilets, bathrooms, and canteens; the cost of hiring staff to rescue a

VIETNAM NATIONAL UNIVERSITY - HO CHI MINH CITY

SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

PROJECT REPORT

OPTIMIZATION MODEL FOR BUILDING SHELTERS IN RESPONDING TO FLOOD IN TUY PHUOC DISTRICT

BINH DINH PROVINCE Course Name: Deterministic Models in OR

Group 05

3 Trần Ngọc Hi n Chi ề IELSIU20010 100%

5 Nguy n Tr n Thúy Vy ễ ầ IELSIU20468 100%

Module code: IS020IU Lecturer: Hà Th Xuân Chi ị

TABLE OF CONTENT

I INTRODUCTION 1

1 Background 1

1.1 Background study 1

1.2 CPLEX 1

2 Problem statement 2

3 Objective 3

II MATHEMATICAL MODEL 3

1 Parameter 3

1.1 Indice 3

1.2 Parameter: 3

2 Decision variables 4

3 Objective function 4

4 Constraint 4

5 Assumption 5

III CASE STUDY APPLICATION 5

IV RESULT ANALYSIS AND DISCUSSION 8

1 Result 8

2 Sensitivity analysis 9

3 Solution discussion 10

3.1 Strength 10

3.2 Weakness 11

3.3 Recommendation 11

4 Future direction 11

5 Question analysis 12

APPENDIX 13

1 CPLEX code 13

1.1 File mod 13

1.2 File dat 14

2 Input data 14

3 Output data 16

4 MAP 17

REFERENCE 18

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I INTRODUCTION

1 Background

1.1 Background study

According to a UNDP study and statistics, torrential rains and floods in five central provinces in Viet Nam, especially Tuy Phuoc Binh Dinh Province, caused more than 37,000 – houses to be damaged or destroyed between October 21 and October 23 Eventually, flood water ruined and washed away household things such as blankets, curtains, and kitchen utensils, then families with damaged homes, flooded residences, and damaged or lost household possessions will not be able to return to normal life totally within the next 3-5 weeks Since these are impoverished families, they lose everything and are unable to invest in home repairs or new purchases Therefore, current priority needs are addressing the shelter needs of evacuees and setting up and building appropriate shelter and evacuation centers - to enhance preparedness for emergencies The problem

in this project is to locate shelters in a reasonable location that allows people to move swiftly while minimizing the expense of relief boats

The remainder of the paper is broken into four major sections, which are as follows Part 1 introduces the background, CPLEX method, problem statement, and objective of our project Part

2 will include a more thorough and detailed approach and mathematical modeling details Part 3 will run the code, display the results, and give sensitivity analysis so that they can be compared and new suggestions for this problem can be made The last section is the application problem

1.2 CPLEX

CPLEX Optimizer is also a tool for determining the

(maximum/minimum) value based on a model that includes

constraints, variables, and parameters It can solve a wide range

of problems in linear programming, mixed integer programming,

quadratic programming, and other fields with ease and

professionalism CPLEX Optimizer allows users to make

smarter decisions after discovering the optimal solution for their

projects or challenges

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2 Problem statement

Hurricanes severely impacted Tuy Phuoc district annually, threatening residents' lives and properties Because of that, a charity fund would be raised to assist them during the flood period

by specific actions namely investment in recovery from flood, donating money or essential commodities, and building shelters In the long-term aspect, however, they would be a temporary solution since they waste time, money, and human resources to go door- -door and replenish each to household Additionally, the residents may not have a safe place to stay during the flood Therefore, in this project, a model will be built to establish shelter points to have an effective place for people to stay and have enough essential equipment in the impacted region More specifically, the staff can promptly rescue victims as well as have available accommodation, thus people can come when the flood is forecasted

Some factors influence how to build a suitable shelter They are to optimize distance, optimize time and optimize cost In this article, optimizing cost would be performed to solve the problem Optimizing costs include construction and maintenance costs; expenses for the construction of public places such as toilets, bathrooms, and canteens; the cost of hiring staff to rescue and care for victims affected by floods; transportation costs to rescue victims; the cost of buying essentials

There is a single issue in response to humanitarian relief logistics the variation in the location-allocation problem The given region Tuy Phuoc would be divided into flood-affected i areas, then, the shelters would be built with reasonable distance from shelter to There would j d i

be fixed cost for opening a shelter added to the decision k

In this paper, the basic goal is to determine the optimal number of shelters with the minimum opening shelter cost at an acceptable distance from the affected area Additionally, victims from each flooded area could only be assigned one shelter When it comes to location-allocation problems, in this case study, algorithms relating to relevant input requirements such as the number of available facilities, the operation cost, and other specific elements would be primarily established to select the new location

This study will be based on some problem concepts would be described as follows:

• Shelter: a temporary place that protects to avoid the hurricane The shelter in this case study will be built on an available substructure and equipped with basic furniture

• Area: the determined space which is flood-affected

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• Distance: the length of transport movement is estimated by the euclidean method between the affected areas and shelters

• Fixed cost: the amount of money includes the cost of installing furniture, equipment; staff’s salary

3 Objective

This paper is a deterministic model in the operations research topic In more detail, we would divide the flooded region into 10 affected areas with 20-underexamined-shelter There would be 2 players: the candidate shelter and the affected area With the help of CPLEX, the goal

is to find the solution to optimize the number of shelters in flood-affected areas by determining the appropriate distance from the affected area to shelters, as well as the optimal cost for opening shelters, when one flooded area could be assigned to one shelter only

II MATHEMATICAL MODEL

1 Parameter

1.1 Indice

I Set of affected areas

J Set of candidate shelters

1.2 Parameter:

dij Distance between affected area i and candidate shelter j

cj Capacity of the candidate shelter j

hi Number of victims in area i

fj Fixed cost for opening the shelter j

M Maximum acceptable distance between affected area and shelter

𝜶 Constant coefficient of transportation cost per kilometer per person per trip

𝜷 Wage per person per day for hiring staff to work in the shelter

𝜸 Ratio of the required staff per victim

T Duration of the disaster occurrence

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2 Decision variables

X 1, if candidate shelter j is selected; otherwise, 0 j

Y 1, if affected area i is assigned to shelter j; otherwise, 0 ij

Z Number of victims in area i that are assigned to shelter j ij

3 Objective function

𝑀𝑖𝑛 𝑓1= ∑ 𝑋𝑗

𝑗 ∈ 𝐽

𝑓𝑗+ 𝛼 ∑ ∑ 𝑑ijYij hi+ 𝛽𝑇 ∑Zij 𝛾

𝑖 ∈ 𝐼

𝑗 ∈ 𝐽

𝑖 ∈ 𝐼 This objective function aims to reduce the overall cost, which is comprised of three terms

• The first term refers to the fixed cost of opening the shelters, where f could be stated as j cost for household appliances, temporary kitchens, portable toilets, etc

• The second component would be transportation cost, which is determined by the distance and number of victims transported from the afflicted location I to the specified shelter j

• The third is the service cost, which is estimated by the required number of staff working in shelters during a disaster

4 Constraint

∑𝑗 ∈ 𝐽Yij = 1, ∀i ∈ I (1)

Constraint (1) restricts that an affected area i must be entirely assigned to only single shelter j Yij ≤ Xj, ∀i ∈ I,j J ∈ (2)

Constraint (2) stipulates that affected area i must be assigned to only open shelters j

d Y ij ij≤ M, ∀i ∈ ∈ I,j J (3)

According to constraint (3), the distance between affected area I and allocated shelter j must be less than or equal to the maximum acceptable distance between affected area and shelter

∑ Zij ≤ cj𝑋i ∈ I 𝑗, ∀j ∈ J (4)

Constraint (4) restricts the number of assigned victims to within the capacity of selected shelter j

∑𝑖 ∈ 𝑗𝑍𝑖𝑗 = ℎ𝑖, i I ∀ ∈ (5)

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Constraint (5) assures that the number of victims assigned is equal to the number of victims in each affected area i

Zij =ℎ𝑖 Y , ij ∀ i ∈ I, j J ∈ (6)

Constraint (6) assures that the number of victims assigned is equal to the number of victims in each affected area i

𝑋𝑗 ∈ {0, 1}, ∀j ∈ J (7)

Constraint (7) is a binary variable: X is 1 if candidate shelter is selected to open; otherwise, 0 j 𝑌𝑖𝑗 ∈ {0, 1}, ∀i ∈ ∈ I,j J (8)

Constraint (8), which is a binary variable, is as follows: If affected area I is assigned to candidate shelter j, Y is 1; otherwise, 0 ij

5 Assumption

In this model, we would concern with some assumptions would be listed below:

• The identified and unchanged number of victims in each affected area

• All affected regions and possible shelters are pinpointed

• The traffic conditions are ignored

• All staff has the same working ability and salary

• The fuel consumption rate is constant

III CASE STUDY APPLICATION

The applicability of the proposed model is demonstrated through a case study of shelter location-allocation in responding to floods in Tuy Phuoc District, Binh Dinh province Initially, there are a total of 5012 victims residing in the 10 most-affected areas as follows:

Area Number of

victims

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In Tuy Phuoc district, floods will leave heavy impacts on most of the areas located near the Con River and its tributaries Unfortunately, all the affected areas are densely populated, especially in Phuoc Thuan and Phuoc Hoa communes With an aim to promptly respond to these affected areas, we have proposed a decentralized shelter location-allocation model which is assigned based on multiple criteria to cover all the affected areas There are 20 candidate shelters shown in the following figure

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The distance among 20 shelters is calculated by the Euclidean method, which is taking the skyway from one place to another Besides, five of the candidates are public schools with an available capacity of 1200 and 1000, while the remaining shelters are expected to identically hold

500 victims

5 Phuoc Hiep No 2 elementary school 1000

17 Phuoc Thuan No 1 elementary school 1200

Due to the impact of the flood that the water level rose above human head everywhere, and road vehicles are incapably utilized to evacuate the unfortunate victims Hence, other alternatives, specifically the canoe in this project, would be used instead There canoes’ capacity can cover 12 people and the fuel consumption rate is 8 km/liter and each liter of fuel costs 28,000 VND The constant alpha (α) is 18,667 (by taking fuel cost multiplied by the fuel consumption rate and divided by the vehicle’s capacity) Additionally, each staff working in the shelter is paid 250,000

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VND per day (β) The number of staff required is 1 member of staff taking care of 50 victims (γ) Based on the historical data, the average duration of flood occurrence is approximately one week Each shelter has different fixed costs, resulting from the difference in building materials, construction scale, housing cost, and many other expenses

Shelter Fixed cost (VND) Shelter Fixed cost (VND)

IV RESULT ANALYSIS AND DISCUSSION

1 Result

Shelter Area Victim

17

Total cost 2,674,958,637.67

By running the CPLEX code, we have come up with 5 selected shelters 1, 4, 5, 17, and –

18 with a total cost of 2,674,958,637.67 VND These shelters take capacity limitations into account, and the maximum acceptable distance does not exceed 9 kilometers The proposed shelter

location-9

allocation model is decentralized, and all the shelters are schools with large capacities that can cover entire victims in an area The following figure visualizes the outcome

2 Sensitivity analysis

The sensitivity analysis is conducted to demonstrate how parameters influence the objective function and the model In this part, the maximum acceptable distance is considered to vary by about 1km to see if the change in the distance leads to a change in the results Because shelters are not centrally distributed, changing M will limit the distance between shelters and the affected area to select qualified shelters

Change M greater than or equal to 10: The result when running the model does not change when M = 9km This is explained as follows, when M = 9 km, this is the maximum distance that shelters can meet the safe distance from other affected areas

M is less than or equal to 7 km: When running the model, there is no value This is because when reducing M is less than or equal to 7 km, the distance limit is minor compared to the general distance of shelters and affected areas Therefore, no shelter meets the conditions

When M is changed by 8 km, the limited distance between the shelter and the affected area will be narrowed The results demonstrate that 6 selected shelters meet the requirements As a

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result, fixed costs and transportation costs rise The cost of services will not be affected by physical separation since the constraint assures that all victims are well served

The limit distance will be increased when M = 9 km: More shelters will meet the distance criteria, while low-cost shelters that meet the requirements will be prioritized Therefore, 5 shelters have been chosen, resulting in lower fixed expenses and lower moving costs

To summarize, when the maximum permissible distance is 9 km, the cost-effectiveness is maximized

3 Solution discussion

3.1 Strength

The above-mentioned results highlight one of th commendable features of this model, e particularly providing a suggestion for decision-makers illustrate the appropriate strategies for to the shelter location-allocation problem Furthermore, it can recognize the relationship among features included in the problem, which supports future appropriate adjustments Finally, limiting the maximum acceptable distance from the flood center helps decision-makers identify and eliminate remote shelters Therefore, we can figure out prominent shelters that minimize the distance and time to evacuate the victims