[2022] Numerical Optimization - Group Assignment

Summary

The presentation explores the application of the Simplex method to minimize total costs, including goods and delivery fees, in an online grocery store setting amidst the COVID-19 pandemic. It provides an overview of the shift to e-commerce and focuses on optimizing consumer purchases across four major Malaysian grocery stores. The study formulates an objective function, applies the Simplex method to determine optimal store selections, and calculates the minimum total cost, concluding that a combination of items from selected stores yields significant savings compared to single-store purchases.

Takeaways

• 📈 The Simplex method is used to minimize the total cost of goods and delivery fees in an online grocery store setting.
• 🌐 The COVID-19 pandemic led to a significant increase in e-commerce sales, including a 14.8% rise for non-store retailers as reported by the OECD.
• 🛒 The Malaysian government initiated a movement control order (MCO) on March 18, 2020, which increased the preference for online grocery shopping among Malaysians.
• 🏪 The study focuses on four major online grocery stores in Malaysia: Lotus, Giant, Grocer Migosa, and Shopping Supermarket.
• 🔢 The Simplex method is chosen for its popularity and success in solving linear programming problems, including maximization and minimization with a set of linear constraints.
• 📚 A previous study by Angora et al. in 2019 applied the Simplex method for profit optimization in the home industry, demonstrating its applicability.
• 📊 The dataset used in this study is small, simplifying the computation process for the optimization problem.
• 🛍️ The study aims to help consumers find the best deals when purchasing multiple items from different online grocery stores based on price and delivery fees.
• 💰 The objectives of the study are to formulate a minimum objective function for total cost, apply the Simplex method to determine the best store for each item, and calculate the total minimum cost for consumers.
• 📈 The Simplex method was implemented using Octave, an open-source programming language, to solve the optimization problem.
• 📊 The results show that purchasing a combination of items from selected stores can lead to lower costs compared to buying from a single store, with a total minimum cost of 139.56 Ringgit.
• 🚀 The presentation suggests potential enhancements, such as building a robust recommendation system and incorporating delivery time, discounts, and minimum spend for free delivery into the model.

Q & A

What is the main focus of the presentation by Juan Amira Valkis?

The presentation focuses on the use of the Simplex method to minimize the total cost of goods and delivery fees in an online grocery store setting, particularly in the context of the shift to e-commerce during the COVID-19 pandemic.

What impact did the COVID-19 pandemic have on retail sales according to the OECD report mentioned in the script?

The OECD reported that sales increased for non-store retailers by 14.8 percent during the pandemic, indicating a significant shift in consumer behavior towards online shopping.

What was the government's response in Malaysia to slow down the transmission rate of COVID-19?

The Malaysian government initiated a movement control order (MCO) on March 18th, 2020, to control the spread of the virus.

How many online grocery delivery services are there in Malaysia according to the cloak report?

According to the cloak report, there are 14 online grocery delivery services in Malaysia.

Which four online grocery stores were selected for the study presented in the script?

The four online grocery stores selected for the study are Lotus, Giant, Grocer Migosa, and Shopping Supermarket.

What is the Simplex method and why was it chosen for this study?

The Simplex method is a popular and successful mathematical optimization technique used for solving linear programs, specifically for maximization and minimization problems with a set of linear equalities and inequalities. It was chosen for this study due to its effectiveness in handling such problems.

What are the two perspectives from which the problem statement is viewed in the script?

The problem statement is viewed from both the consumer's point of view, who wants the cheapest and highest quality goods with the lowest delivery fee, and the business owner's perspective, who aims to maximize revenue by encouraging more purchases, potentially through lowering prices and adjusting delivery fees.

What are the three objectives of the study as outlined in the script?

The three objectives are: 1) to formulate the minimum objective function for the total cost of goods and delivery fees, 2) to apply the optimization method to determine which store should be chosen for purchasing items, and 3) to calculate the total minimum cost for the best combination of goods and delivery fees for a consumer.

What assumptions were made regarding the stability of the cost of goods and delivery fees in the study?

The assumptions made were that the cost of goods and delivery fees are stable over time and that the uncertainty in these costs is low.

How was the data for the study collected and what does it include?

The data was collected through market research conducted on May 22nd, focusing on four famous online grocery stores and scoping out seven items with their respective prices and delivery fees.

What software was used to apply the Simplex method in the project, and how was the data inputted?

Octave was used to apply the Simplex method. The coefficients of the objective function were inputted into 'c', the coefficients of constraints into 'a', the right-hand side of constraints into 'b', and the lower and upper bounds of the variables into 'lb' and 'ub', respectively. The 'c-type' and 'v-type' were set according to the constraints and variable types, and 'sense' was set to one for minimization.

What was the outcome of applying the Simplex method to the optimization problem presented in the script?

The outcome showed that the total minimum cost for the consumer, based on the optimization, was 139.56 Ringgit, which was lower than purchasing all items from a single store. It also identified which items should be purchased from which stores to achieve this minimum cost.

What suggestions were made for future enhancements of the study?

Suggestions for future enhancements include building a robust recommendation system with more selection of items and stores, and factoring in delivery time, discount vouchers, and minimum spend for free delivery to reflect realistic logistical arrangements in stores.

Outlines

00:00

🛒 Introduction to the Simplex Method for Online Grocery Shopping

The video introduces the application of the Simplex method to minimize the total cost of goods and delivery fees in an online grocery store setting. The presenter, Juan Amira Valkis, sets the context by discussing the impact of the COVID-19 pandemic on the shift from physical to online retail, with a specific focus on Malaysia's movement control order. The study examines four prominent online grocery stores: Lotus, Giant, Grocer Migosa, and Shopping Supermarket. The Simplex method is chosen for its effectiveness in solving linear programming problems, including maximization and minimization with linear constraints. The goal is to find the optimal combination of purchases across these stores to minimize costs for consumers. The video outlines the objectives of the study, which include formulating a minimum cost function, applying the Simplex method to determine the best purchasing strategy, and calculating the total minimum cost for consumers.

05:03

📊 Data Collection and Model Assumptions

This paragraph delves into the data collection process and the assumptions made for the study. Market research was conducted on four renowned online grocery stores and seven items, with their respective prices and delivery fees listed. The assumptions include the stability of goods and delivery fees, the limitation of purchasing one unique item per store, and logistical factors such as delivery radius and time. The system diagram is introduced to visualize the decision-making process, with binary variables representing whether an item is chosen from a particular store and delivery cost incurred. The objective function is defined to minimize the total cost of goods and delivery fees, with constraints ensuring that only one unique item is purchased from each store and that at least one item is chosen from a particular store.

10:03

🔢 Application of the Simplex Method and Optimization Results

The presenter, Alan, explains the application of the Simplex method to solve the minimization problem using Octave software. The coefficients of the objective function and constraints are inputted, along with the bounds and types of constraints. The method is applied to determine the optimal purchasing strategy from the selected online stores. The results show that only two stores, Lotus and Shopping Supermarket, are chosen for purchasing all specified items, incurring two delivery costs. The comparison of total costs reveals that the optimized combination yields a lower cost than purchasing from a single store. The study successfully achieves its objectives by formulating the objective function, applying the Simplex method to determine the best store for each item, and obtaining a total minimum cost of 139.56 Ringgit for the consumer. The video concludes with suggestions for future enhancements, such as developing a robust recommendation system and incorporating additional logistical factors into the model.

Keywords

💡Simplex method

The Simplex method is a popular mathematical programming technique used for solving linear programming problems, particularly those involving the maximization or minimization of a function subject to constraints. In the context of the video, it is utilized to minimize the total cost of goods and delivery fees for consumers shopping at online grocery stores. The method is highlighted as one of the most successful due to its ability to handle a set of linear equalities and inequalities, as mentioned when discussing its application in profit optimization for a bakery industry.

💡Online grocery store

An online grocery store is a virtual marketplace where consumers can purchase groceries and have them delivered to their homes. The video discusses the shift in consumer behavior towards online grocery shopping due to the COVID-19 pandemic, leading to an increase in demand for e-commerce platforms. The study focuses on optimizing the cost of shopping at such stores, with specific examples given from four Malaysian online grocery stores: Lotus, Giant, Grocer Migosa, and Shopping Supermarket.

💡COVID-19

COVID-19, also known as coronavirus 19, is the disease caused by the SARS-CoV-2 virus. The pandemic has had a significant impact on consumer behavior, as referenced in the video, leading to a surge in online shopping, including online grocery stores. The shift to online platforms was a response to the movement control order (MCO) implemented by the Malaysian government to slow down the virus transmission.

💡E-commerce

E-commerce refers to the buying and selling of goods or services using the internet, and the transfer of money and data to execute these transactions. The video mentions a report by the Organization for Economic Cooperation and Development (OECD) indicating a 14.8 percent increase in sales for non-store retailers during the pandemic, underscoring the importance of e-commerce in the new retail landscape.

💡Optimization

Optimization in this context refers to the process of making the best or most effective use of a situation or resource. The video's main theme revolves around using the Simplex method to optimize the cost for consumers when purchasing from multiple online grocery stores. The goal is to determine the most cost-effective combination of goods and delivery fees, ensuring consumers get the lowest combined costs.

💡Linear programming

Linear programming is a mathematical technique used to determine the best outcome in a given mathematical model whose requirements are represented by linear relationships. The video discusses the Simplex method as a popular approach within linear programming for solving problems with a set of linear constraints, such as finding the minimum total cost in an online grocery shopping scenario.

💡Consumer perspective

The consumer perspective is the viewpoint of the end-user in any business or economic activity. In the video, the problem is examined from the consumer's point of view, where the aim is to buy the cheapest, highest-quality goods with the lowest delivery fees. This perspective is crucial for formulating the objective function that seeks to minimize the total cost for consumers.

💡Business owner's perspective

The business owner's perspective focuses on the goals and strategies of the sellers or service providers. In the context of the video, the business owner's goal is to maximize revenue by encouraging more consumers to purchase more items, which may involve adjusting prices and delivery fees. This perspective is considered when developing a model to balance consumer savings with business revenue.

💡Objective function

An objective function is a mathematical expression that an optimization problem aims to either maximize or minimize. In the video, the objective function is formulated to represent the total cost of goods and delivery fees that need to be minimized. The function guides the application of the Simplex method to find the optimal solution for the consumer.

💡Constraints

Constraints in optimization problems are limitations or conditions that must be satisfied by the solution. The video mentions constraints such as the consumer being able to purchase only one unique item from each of the four online stores and the binary nature of decision variables (0 or 1), which represent whether an item is chosen from a particular store.

💡Delivery fee

A delivery fee is a charge made by a seller for the shipping and delivery of goods to the buyer. The video discusses the importance of minimizing not only the cost of goods but also the delivery fees in the total cost optimization process. The study aims to find the optimal combination of items and stores that results in the lowest delivery fees, in addition to the cost of the items themselves.

Highlights

Introduction to the Simplex method for minimizing total cost in online grocery shopping.

Shift in consumer demand from physical stores to e-commerce due to COVID-19.

OECD reports a 14.8% increase in sales for non-store retailers during the pandemic.

Malaysian government's implementation of Movement Control Order (MCO) on March 18, 2020.

Study focuses on four major online grocery stores in Malaysia: Lotus, Giant, Grocer Migosa, and Shopping Supermarket.

Utilization of the Simplex method for numerical optimization to determine the best deal for consumers.

Previous application of Simplex method in profit optimization for the home industry bakery.

Data set for the study is small to simplify computation in solving the optimization problem.

Problem statement from both consumer and business owner perspectives.

Objective to formulate a minimum objective function for total cost of goods and delivery fees.

Application of the Simplex method to determine the best store for purchasing items.

Calculation of the total minimum cost for consumers combining goods and delivery fees.

Market research conducted on four online grocery stores and seven items with their respective prices and delivery fees.

Assumptions made for the study regarding the stability of goods and delivery fees, and consumer purchasing behavior.

System diagram visualization of the model with decision variables for purchasing and delivery costs.

Use of Octave for inputting coefficients and constraints to apply the Simplex method.

Optimization outcome showing the value of each variable and the minimum of the objective function.

Comparison of total cost for purchasing all items in a single store versus a combination of selected stores.

Achievement of the study's objectives: formulating the objective function, applying the Simplex method, and obtaining the total minimum cost.

Recommendation for future enhancements including a robust recommendation system and factoring in logistical arrangements.

Transcripts

greetings Dr Lim today group view of

seven is excited to bring you on a

journey in discovering more on the usage

of Simplex method to minimize the total

cost of goods and delivery fee in an

online grocery store setting so stay

tuned for more stories

hi everyone my name is Juan Amira valkis

and I will be presenting the

introduction problem statement and

objectives in early 2019 the entire

world came into a home due to the

emergence of an outbreak known as

coronavirus 19 or covet 19. this caused

a shift in demand from brick and mortar

retail to e-commerce websites the

organization for economic cooperation

and development or oecd reported that

sales have increased for non-store

retailers by 14.8 percent during this

time

in Malaysia the government initiated a

movement control order MCO on the 18th

of March 2020 to slow down transmission

rate of covet 19. however Malaysians

preferred to do grocery shopping online

compared to in-store the online travel

booking website cloak reported that

there are 14 online grocery grocery

delivery services in Malaysia and for

the purpose of this study we will focus

on four stars which are Lotus Giant

grocer migosa and shopping Supermarket

with numerical optimization we could

figure out the best deal for consumers

that are purchasing several items from

different online grocery stores at the

same time based on its price and

delivery fee for this study we will

utilize the Simplex method reason being

Simplex method is one of the most

popular and successful method in solving

linear programs specifically

maximization and minimization of a

problem with a set of linear equalities

and inequalities constraints a sample

case of simplest method is a study by

Angora at Al in 2019 where they applied

Simplex method for profit optimization

on the home industry Bakery in sukharama

Banda lampong

the data set utilized for this study

will be small which means it will make

computation less complex in solving the

optimization problem

for the problem statement we can look at

it in two perspectives which is in the

consumer's point of view and the

business owner's perspective

as the consumer they would want to buy

the cheapest but highest quality Goods

along with having the lowest fee for

delivery but if you're the business

owner the goal is to ensure that more

items are purchased by more consumers

which would sometimes lead to the

potential of lowering of prices

of the items add delivery fee to

maximize the revenue instead therefore a

stable model is needed to represent the

minimization of total cost from both

costs of goods and delivery fee so that

we can allow the consumer to get the

lowest combined costs across the four

stores mentioned before in the

introduction

the objectives of this study are as

below number one to formulate the

minimum objective function for total

cost of goods and delivery fees we need

to get the minimum objective function

before we can move to objective 2 which

is to apply optimization method in

determining which store should the items

be purchased from so we will apply the

Simplex method to determine which store

provides the best price for the items

next the third objective is to calculate

the total minimum cost from both cost of

goods and delivery fees for a consumer

we need to get the total minimum cost

for the best combination of cost of

goods and delivery fees for a consumer

hello again doctor

as I didn't get the chance to introduce

myself earlier here goes my name is anik

and I will briefly describe about the

data we acquired to ensure consistency

we decided to do a market research

together on May the 22nd we scoped out

four Famous online grocery stores which

is lotus Jaya grocer my grocer and

shopping Supermarket along with it will

be the scoping of seven items as you see

on the left side of the table with their

respective prices on the right as well

as the delivery fees at the most bottom

of the table the next sections will

further describe on the usage of this

sample data to help a consumer make

smarter decisions which is to save his

or her total spending via cost

optimization

the obsessing function is to minimize

the cost of the goods and minimize the

total delivery fee so in the

formula the formal part is to minimizing

the total cost of the food based on

seven items across four online grocery

store and the later part is to remind

the total delivery fee for four online

grocery store so

formula p i then is the price of the

item from store j and x i j is the

binary relation variable on whether I

thought I will be chosen from store J

meaning the binary decision variable on

whether the university is in code or at

storage

the assumptions are as below first the

uncertainty of the cause of goods and

delivery fee is more meaning the cost of

goods and they will see are quite stable

across the time and the uncertainty of

the four online grocery store is more

also

the consumer can only purchase one

unique item each from a list of four

stores meaning if I want to buy 30X I

just only can buy the ads or

in one of the four shots so next the

distance from each grocery store to a

consumable destination is the middle not

sure the radius 15 5 km and the time

also delivery is within 90 hours no free

shipping conditions for minimal spend in

these problems and no delivery discount

voucher apply

the system diagram of the model was

visualized so the y1 is the decision

variable whether the consumers will buy

in this store

or the Y2 y314 apply the same whether

the consumer should buy in the store and

X is a decision about whether he needs

or he will buy the item in this shop or

item in this shop item in this shop so

s114 only uh equal to one meaning

the consumer only can buy the item in

one of the four shops

the goal is to minimize the objective

function as follow so we plug in the

price into this minimization p i j s i j

plus djyj so I think

90 is the price for the item one in shop

1 and 299 D is the item one in Shop 2 29

19 is uh item one in stock 3 and Etc so

uh and here over here the Y one is the

very cost for the short one and this is

the world course for the shop to

delivery cost for shop 3 and it will

cost for shop for so this minimize the

objecting function is subtract to four

constraints

first a consumer only can purchase one

unique item each from a list of four

online for free store so summation of

the division variable

of

the four four one item or four online

grocery store equal to one only so I

thought this wearable will be one and

other will be zero and this apply to

other

item and next topic you will receive

will be encouraged in at least one item

is chosen from a particular store

if I choose a item a short one so we

will see will be just about short one

well I chose the item to shop so the

very thing from the white so the shop

two will be cut also

next stop

x i j is a digital variable whether I

choose the item so sij is either 0 or 1

0 is when the item is not chosen well

one is running the item is chosen

last but not least YJ is study whether

the delivery cost incurred in the shop

what shop J and also zero meaning the

delivery cost is not incurred and one is

meaning that the very cost of the stock

is incurred so where I equal to one to

seven means foreign

hi doctor and all my friends I'm calling

you may call me Alan I'll take over the

presentation with the topic of Simplex

method so since we are dealing with

constraint problem we would like to

apply Simplex method to solve the

problem above in minimizing the cost

based on objective function instead of

using manual calculation octave is used

in this project

in this case we will input the

coefficients of the objective function

to C then the coefficients of

constraints are input into a and the

right hand side of the constraints which

is the bound are input into B

next since there is either value 0 or 1

for all the variables zero is input into

lb which is a lower bound and one is

input into u b which is the upper bound

of the variable

c-type indicates whether the constraint

is upper bound lower bound or equality

since the first five constraints are

equality and last four constraints are

up amount hence we input 5s and 4u for C

type we input 32 I into V type since all

the 32 variables are integers lastly we

set sense as one since we are doing

minimization after this we run glpt with

all Dimension parameters we can observe

in the outcome the value of each

variable in xopt after optimization and

the minimum of objective function is

139.56

this table contains the value of each

variable in xopt shown in the last slide

it shows the online store to be chosen

to purchase the specified item after

optimization the value 1 indicates that

the item is purchased in particular

store while value 0 means the opposite

we can see from the table there there

are only two online store chosen in

total to purchase all the specified

items which are Lotus and shopping

market as a result there are two

delivery costs incurred in this grocery

purchase

this table illustrates the comparison

between total cost of purchasing all

items in single store and combination of

items purchased from selected stores

it can be observed that delivery costs

with two or nice or Lotus and shopping

Supermarket are incurred if you purchase

combination of item based on the

optimization outcome they are eight

Ringgit and 450 which is 1250 in total

after summing up the total item cost at

income delivery cost uh the lower score

for the lowest cost of purchasing

139 Ringgit 56 Cent is obtained compared

to purchasing all specified items in

each single store on the contrary buying

all items in my grocer will incur

highest purchasing cost which is 179

Ringgit and 65

in a nutshell we fulfill our three

objectives firstly to formulate the

objective function in minimizing the

total cost of goods and delivery fee

based on this formula secondly with all

valid assumptions made an identification

of constraints we used Simplex method to

determine which store should items be

purchased from and lastly via

optimization we managed to obtain a

total minimum cost of 139 Ringgit and 56

cents for the consumer even lower than

purchasing all items from a single store

hands down Simplex method is the best

optimization method due to its

Simplicity and cost efficiency because

every penny matters to a consumer

however point to be noted in every study

there's always room for enhancement

firstly we could consider extending our

work to build a robust recommendation

system for consumers with more selection

of items and stores the lowest possible

combination of prices when increase in

demand for online grocery shopping will

provide a win-win situation for both

consumers and business owners also apart

from just a big standard delivery fee

delivery time discount vouchers and

minimum amount spent for free delivery

should also be factored into the

optimization model to reflect realistic

logistical Arrangements in stores

that is all for the presentation once

again my name is anik together with

Amira xiaohan and Ellen

signing off