Vrptw mangsi1 pdf

1. Article Comparison of Symbiotic Organisms Search and Particle Swarm Optimization for sidering Investment Feasibility Prima Arinda Nurul Islami1, A.A.N. Perwira Redi Ngurah Agung Redioka4and Yogi Tri Prasetyo 1 Department of Logistics Engineering, Universitas Pe ; primaarinda29@gmail.com 2 Department of Industrial Engineering, Universitas Bina Nusantara, DKI J 3 Department of Information System, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia 4 Jurusan Sistem Informasi Akuntansi, STIMIK Primakara, Bali, Indonesia 5 School of Industrial Engineering and Intramuros, Manila 1002, Philippines; ytprasetyo@mapua.edu * Correspondence: Abstract: This study present a distribution method planning that is modeled as a vehicle routin problem with time windows (VRPTW). The model the cost of serve customers demands by taking accounts of vehicle capacity and time windows to serve each customer. The case study applied the model to select d tions of a central kitchen that needs to deliver daily raw materials for its outlet. The central kitchen is currently considering a milk words maximum. For strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight study; (2) Methods: briefly describe the main methods or treatments applied; (3) Results: su marize the article's main findings; (4) Conclusions: indicate the main conclus tions. The abstract should be an objective repr sults that are not presented and substantiated in the main text and should not exaggerate the main conclusions. Keywords: keyword 1; keyword 2; keyword 3 (List three to ten pertinent keywords article yet reasonably common within the subject discipline.) 1. Introduction In recent years the global market is becoming more competitive and challenging, especially in the food industry sector. Therefore, to be able survives and conquering the competition, companies need an appropriate business strategy. The implemented bus ness strategy should be able to maximize the profit by minimizing the expense cost. In implementing this strategy, logistic activities are one of the crucial things that need company concern. Because the average logistics cost contributes to 20 price formation, and 60% of the total logistic cost came from transportation activities [1]. One way to reduce total transportation cost is by efficiently running the system. PT XYZ is a company engaged in the food industry, i.e., restaurant and possesses outlets distributed in Bali, Indonesia. In fulfilling each outlet’s demands, PT XYZ has one Citation: Lastname, F.; Lastname, F.; Lastname, F. Title. J. Open Innov. Technol. Mark. Complex. 2021, 7, x. https://doi.org/10.3390/xxxxx Received: date Accepted: date Published: date Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and insti- tutional affiliations. Copyright: © 2021 by the authors. Submitted for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/license s/by/4.0/). Comparison of Symbiotic Organisms Search and Particle Swarm Optimization for Distribution Method Planning Co sidering Investment Feasibility A.A.N. Perwira Redi2,*, Nur Layli Rachmawati 1, Reny Nadlifatin Yogi Tri Prasetyo 5 Department of Logistics Engineering, Universitas Pertamina, DKI Jakarta, 12220, Indonesia primaarinda29@gmail.com (P.A.N.I); nl.rachmawati@universitaspertamina.ac.id (N.L.I) Department of Industrial Engineering, BINUS Graduate Program – Master of Industrial Engineering Universitas Bina Nusantara, DKI Jakarta, 11480, Indonesia; wira.redi@binus.edu Department of Information System, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia Jurusan Sistem Informasi Akuntansi, STIMIK Primakara, Bali, Indonesia School of Industrial Engineering and Engineering Management, Mapúa University, 658 Muralla St., Intramuros, Manila 1002, Philippines; ytprasetyo@mapua.edu Correspondence: wira.redi@binus.edu; This study present a distribution method planning that is modeled as a vehicle routin problem with time windows (VRPTW). The model aims to find a set of vehicle route that minimze the cost of serve customers demands by taking accounts of vehicle capacity and time windows to serve each customer. The case study applied the model to select distribution method in the oper tions of a central kitchen that needs to deliver daily raw materials for its outlet. The central kitchen is currently considering a milk-run type of distribution approach. A single paragraph of about 200 words maximum. For research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight ; (2) Methods: briefly describe the main methods or treatments applied; (3) Results: su marize the article's main findings; (4) Conclusions: indicate the main conclus stract should be an objective representation of the article and it must not contain r sults that are not presented and substantiated in the main text and should not exaggerate the main keyword 1; keyword 2; keyword 3 (List three to ten pertinent keywords reasonably common within the subject discipline.) 1. Introduction In recent years the global market is becoming more competitive and challenging, especially in the food industry sector. Therefore, to be able survives and conquering the competition, companies need an appropriate business strategy. The implemented bus ness strategy should be able to maximize the profit by minimizing the expense cost. In implementing this strategy, logistic activities are one of the crucial things that need company concern. Because the average logistics cost contributes to 20 price formation, and 60% of the total logistic cost came from transportation activities [1]. One way to reduce total transportation cost is by efficiently running the PT XYZ is a company engaged in the food industry, i.e., restaurant and possesses outlets distributed in Bali, Indonesia. In fulfilling each outlet’s demands, PT XYZ has one Comparison of Symbiotic Organisms Search and Particle Planning Con- , Reny Nadlifatin 3, Anak Agung rtamina, DKI Jakarta, 12220, Indonesia (P.A.N.I); nl.rachmawati@universitaspertamina.ac.id (N.L.I) Master of Industrial Engineering akarta, 11480, Indonesia; wira.redi@binus.edu Department of Information System, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia Engineering Management, Mapúa University, 658 Muralla St., This study present a distribution method planning that is modeled as a vehicle routing find a set of vehicle route that minimze the cost of serve customers demands by taking accounts of vehicle capacity and time windows to istribution method in the opera- tions of a central kitchen that needs to deliver daily raw materials for its outlet. The central kitchen A single paragraph of about 200 research articles, abstracts should give a pertinent overview of the work. We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight the purpose of the ; (2) Methods: briefly describe the main methods or treatments applied; (3) Results: sum- marize the article's main findings; (4) Conclusions: indicate the main conclusions or interpreta- esentation of the article and it must not contain results that are not presented and substantiated in the main text and should not exaggerate the main keyword 1; keyword 2; keyword 3 (List three to ten pertinent keywords specific to the In recent years the global market is becoming more competitive and challenging, especially in the food industry sector. Therefore, to be able survives and conquering the competition, companies need an appropriate business strategy. The implemented business strategy should be able to maximize the profit by minimizing the expense cost. In implementing this strategy, logistic activities are one of the crucial things that need company concern. Because the average logistics cost contributes to 20-25% of the selling price formation, and 60% of the total logistic cost came from transportation activities [1]. One way to reduce total transportation cost is by efficiently running the distribution PT XYZ is a company engaged in the food industry, i.e., restaurant and possesses outlets distributed in Bali, Indonesia. In fulfilling each outlet’s demands, PT XYZ has one

2. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 2 of 20 Central Kitchen (CK) used to store raw materials from suppliers and would be distributed to each outlet. The business process in PT XYZ is every night, each outlet sends a purchase order to CK, and on the next day they will send an employee to picks the raw materials up from the CK. The problem that PT XYZ have is inefficiency in the current distribution method. It contributes to the high distribution cost that the company should spend because each outlet conducts two to ten times of trip every day. Thus, PT XYZ wants to change the distribution method from each outlet to pick the raw materials from the CK (operator pickup) into the direct delivery method from CK to each outlet (direct shipping). By implementing the new distribution method, PT XYZ have to buy operational vehicles to distribute raw materials from the CK to each outlet. The new distribution method design will be influenced by operational vehicles’ efficiency, where they can distribute raw materials with minimal cost. Hence, PT XYZ needs to determine the most appropriate distribution route to minimize transportation costs expensed. In conducting the optimum route determination strategy in PT XYZ, a model for finding the most appropriate solution is needed. Vehicle Routing Problem (VRP) is the most appropriate model to use for problems related to route determination. VRP model can be defined as finding the optimal route from a depot to several customers in scattered areas and with different demand numbers. The VRP Model has several variations, which are grouped based on the limitations they have. The most appropriate completion model for the problem in PT XYZ where CK and outlets have their service time in delivery and receiving was the Vehicle Routing Problem with Time Windows (VRPTW). VRPTW model is used to schedule trips from a group of vehicles with limited capacity and travel time from the main depot to all customers in different locations, with demand and service time in particular (Nugraha and Mahmudy, 2015). Penentlitian sebelumnya terkait VRPTW for restaurant chain. Theoretically, VRPTW is an NP-hard problem, where solving the problem requires complex computational effort and long computation time [2]. So, one method that can be used to solve the NP-hard problem by using the metaheuristic method. The metaheuristic method was created to solve high-complexity problems and generate a near-optimum solution [2]. Solving optimization problem using metaheuristic algorithms tend to increase every year. One of the recent metaheuristic methods that many researchers developed is Sym- biotic Organisms Search (SOS) algorithm. Another metaheuristic algorithm commonly used to solve determination optimization problems is Particle Swarm Optimization (PSO). SOS and PSO have the same solution-seeking characteristics inspired by natural principles of living things and population-based approaches. Due to the same characteristics of SOS and PSO algorithms, many researchers evaluated and tested the solution quality generated from both algorithms. The comparison of performance evaluation between SOS and PSO algorithms was conducted by Yu et al. [3], which applied SOS and PSO algorithms on the CVRP problem. There was also research by Umam et al. [4] that modified the SOS algorithm for the TSP problem and compared the generated solution quality with the solution obtained from the PSO algorithm. Another research that tested both algorithms’ performance is by Pa- rayogo et al. [5] in their research regarding the layout determination of construction project facility based on working mileage. This research aimed to conduct performance quality testing between SOS and PSO algorithms in solving the VRPTW problem based on the research background. The algorithm with the best solution performance will be implemented in the company’s route determination. Besides, this research also conducted a feasibility analysis using the capital budgeting method to discover the feasibility of the new distribution method plan to be implemented in the company’s system. 2. Deskripsi Permasalahan

3. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW Metode pendistribusian bahan makanan dari Central Kitchen (CK) ke ma ing-masing outlet di PT XYZ yang kurang optimal menjadi sebuah permasalahan yang perlu diperbaiki. Permasalahan inefisiensi dalam metode pendistribusian di PT XYZ menyebabkan tingginya biaya distribusi yang perlu dikeluarkan. Hal ini dikarenakan dalam pengam melakukan dua sampai sepuluh kali perjalanan setiap harinya. Selain itu,terjadinya k terlambatan dalam pengambilan bahan makanan oleh pegawai dari masing outlet membuat kurang opti Permasalahan lain terkait metode distribusi yang saat ini diterapkan oleh PT XYZ yaitu ketidaksesuaian data barang yang ada dalam sistem inventory dengan barang yang disimpan. Hal ini terjadi dikarenakan, pe melebihi waktu pelayanan CK. han-permasalahan terkait sistem pendistribusian yang kurang optimal, PT XYZ ingin menerapakan sebuah kebijakan baru. Dimana kebijakan baru t pengiriman bahan makanan yang diambil oleh karyawan masing tor pickup) menjadi CK yang mengirimkan secara langsung bahan makanan ke ma ing-masing outlet (direct shipping). Dengan kebijakan yang baru tersebut, PT membeli kendaraan operasional perusahaan yang digunakan untuk mendistribusikan bahan makanan dari CK ke masing , x FOR PEER REVIEW Metode pendistribusian bahan makanan dari Central Kitchen (CK) ke ma masing outlet di PT XYZ yang kurang optimal menjadi sebuah permasalahan yang perlu diperbaiki. Permasalahan inefisiensi dalam metode pendistribusian di PT XYZ menyebabkan tingginya biaya distribusi yang perlu dikeluarkan. Hal ini dikarenakan dalam pengambilan bahan makanan dari CK ke masing-masing outlet, kendaraan harus melakukan dua sampai sepuluh kali perjalanan setiap harinya. Selain itu,terjadinya k terlambatan dalam pengambilan bahan makanan oleh pegawai dari masing outlet membuat kurang optimalnya waktu pegawai dalam bekerja satu harinya. Permasalahan lain terkait metode distribusi yang saat ini diterapkan oleh PT XYZ ketidaksesuaian data barang yang ada dalam sistem inventory dengan barang yang disimpan. Hal ini terjadi dikarenakan, pegawai dari masing-masing outlet datang ke CK melebihi waktu pelayanan CK. Oleh karena itu, untuk mengatasi permasal permasalahan terkait sistem pendistribusian yang kurang optimal, PT XYZ ingin menerapakan sebuah kebijakan baru. Dimana kebijakan baru tersebut mengganti metode pengiriman bahan makanan yang diambil oleh karyawan masing tor pickup) menjadi CK yang mengirimkan secara langsung bahan makanan ke ma masing outlet (direct shipping). Dengan kebijakan yang baru tersebut, PT membeli kendaraan operasional perusahaan yang digunakan untuk mendistribusikan bahan makanan dari CK ke masing-masing outlet. Illustrate Old Distribution Method 3 of 20 Metode pendistribusian bahan makanan dari Central Kitchen (CK) ke mas- masing outlet di PT XYZ yang kurang optimal menjadi sebuah permasalahan yang perlu diperbaiki. Permasalahan inefisiensi dalam metode pendistribusian di PT XYZ menyebabkan tingginya biaya distribusi yang perlu dikeluarkan. Hal ini dikarenakan masing outlet, kendaraan harus melakukan dua sampai sepuluh kali perjalanan setiap harinya. Selain itu,terjadinya ke- terlambatan dalam pengambilan bahan makanan oleh pegawai dari masing-masing malnya waktu pegawai dalam bekerja satu harinya. Permasalahan lain terkait metode distribusi yang saat ini diterapkan oleh PT XYZ ketidaksesuaian data barang yang ada dalam sistem inventory dengan barang yang masing outlet datang ke CK Oleh karena itu, untuk mengatasi permasala- permasalahan terkait sistem pendistribusian yang kurang optimal, PT XYZ ingin ersebut mengganti metode pengiriman bahan makanan yang diambil oleh karyawan masing-masing outlet (operator pickup) menjadi CK yang mengirimkan secara langsung bahan makanan ke mas- masing outlet (direct shipping). Dengan kebijakan yang baru tersebut, PT XYZ ingin membeli kendaraan operasional perusahaan yang digunakan untuk mendistribusikan

4. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW Dalam melakukan pembelian kendaraan makanan, PT XYZ memiliki beberapa faktor pertimbangan dalam memilih moda trasnsportasi yang paling tepat untuk diterapkan dalam operasional perusahaan. Faktor pertama yaitu total biaya investasi, perusahaan menetap vestasi yang dikeluarkan tidak lebih dari Rp 120.000.000. Faktor kedua yaitu fleksibilitas operasional kendaraan, perusahaan menginginkan moda trasnsportasi yang dapat be gerak dengan cepat dan dapat menyesuaikan dengan berbagai memiliki biaya bahan bakar yang rendah. Faktor yang terakhir yaitu penggunaan lahan parkir karena tidak semua outlet memiliki lahan parkir untuk kendaraan yang luas, s hingga hal ini yang menjadi salah satu faktor pertimbangan dala transportasi. Berdasarkan faktor transportasi yang tepat untuk digunakan yaitu kendaraan roda dua dengan box peng riman berkapasitas 50kg dan kendaraan roda tiga berkapasitas 250kg. Ba kendaraan yang nantinya digunakan juga mengikuti besarnya permintaan dari ma ing-masing outlet untuk tujuh hari pengiriman. Dimana besarnya permintaan outlet untuk tujuh hari pengiriman yaitu 207kg sampai dengan 295kg. Sehingga jumlah ke daraan yang akan dibeli untuk memenuhi permintaan semua outlet yaitu sebanyak enam kendaraan motor roda dua dan dua kendaraan motor roda tiga. Untuk meminimumkan biaya trannportasi yang nantinya dikeluarkan oleh PT XYZ, pada penelitian ini akan dilakukan den kan pendistribusian bahan makanan. Pencarian rute yang optimal nantinya akan menggunakan model Vehicle Routing Problem with Time Windows (VRPTW) dengan metode metaheuristik yaitu algoritma SOS dan PSO sebagai met Setalah mengetahui rute serta biaya transportasi yang paling optimal, penelitian ini juga akan membahas terkait analisis kelayakan investasi dari kendaraan operasional yang akan dibeli. Berdasarkan penjelasan di atas, untuk dapat menera yang baru di PT XYZ, maka dibuat dua skenario pengiriman bahan makanan dengan j nis kenadaraan yang berbeda. 1. Skenario Pengiriman Pertama , x FOR PEER REVIEW Illustrate New Distribution Method Dalam melakukan pembelian kendaraan operasional untuk mendistribusikan bahan makanan, PT XYZ memiliki beberapa faktor pertimbangan dalam memilih moda trasnsportasi yang paling tepat untuk diterapkan dalam operasional perusahaan. Faktor pertama yaitu total biaya investasi, perusahaan menetapkan bahwa besarnya biaya i vestasi yang dikeluarkan tidak lebih dari Rp 120.000.000. Faktor kedua yaitu fleksibilitas operasional kendaraan, perusahaan menginginkan moda trasnsportasi yang dapat be gerak dengan cepat dan dapat menyesuaikan dengan berbagai kondisi pengiriman serta memiliki biaya bahan bakar yang rendah. Faktor yang terakhir yaitu penggunaan lahan parkir karena tidak semua outlet memiliki lahan parkir untuk kendaraan yang luas, s hingga hal ini yang menjadi salah satu faktor pertimbangan dala Berdasarkan faktor-faktor yang dipertimbangkan oleh perusahaan, maka moda transportasi yang tepat untuk digunakan yaitu kendaraan roda dua dengan box peng riman berkapasitas 50kg dan kendaraan roda tiga berkapasitas 250kg. Ba kendaraan yang nantinya digunakan juga mengikuti besarnya permintaan dari ma masing outlet untuk tujuh hari pengiriman. Dimana besarnya permintaan outlet untuk tujuh hari pengiriman yaitu 207kg sampai dengan 295kg. Sehingga jumlah ke aan yang akan dibeli untuk memenuhi permintaan semua outlet yaitu sebanyak enam kendaraan motor roda dua dan dua kendaraan motor roda tiga. Untuk meminimumkan biaya trannportasi yang nantinya dikeluarkan oleh PT XYZ, pada penelitian ini akan dilakukan dengan pencarian rute yang optimal untuk melak kan pendistribusian bahan makanan. Pencarian rute yang optimal nantinya akan menggunakan model Vehicle Routing Problem with Time Windows (VRPTW) dengan metode metaheuristik yaitu algoritma SOS dan PSO sebagai met Setalah mengetahui rute serta biaya transportasi yang paling optimal, penelitian ini juga akan membahas terkait analisis kelayakan investasi dari kendaraan operasional yang Berdasarkan penjelasan di atas, untuk dapat menerapkan kebijakan pendistribusian yang baru di PT XYZ, maka dibuat dua skenario pengiriman bahan makanan dengan j nis kenadaraan yang berbeda. Skenario Pengiriman Pertama 4 of 20 operasional untuk mendistribusikan bahan makanan, PT XYZ memiliki beberapa faktor pertimbangan dalam memilih moda trasnsportasi yang paling tepat untuk diterapkan dalam operasional perusahaan. Faktor kan bahwa besarnya biaya investasi yang dikeluarkan tidak lebih dari Rp 120.000.000. Faktor kedua yaitu fleksibilitas operasional kendaraan, perusahaan menginginkan moda trasnsportasi yang dapat ber- kondisi pengiriman serta memiliki biaya bahan bakar yang rendah. Faktor yang terakhir yaitu penggunaan lahan parkir karena tidak semua outlet memiliki lahan parkir untuk kendaraan yang luas, sehingga hal ini yang menjadi salah satu faktor pertimbangan dalam pemilihan moda faktor yang dipertimbangkan oleh perusahaan, maka moda transportasi yang tepat untuk digunakan yaitu kendaraan roda dua dengan box pengiriman berkapasitas 50kg dan kendaraan roda tiga berkapasitas 250kg. Banyaknya jumlah kendaraan yang nantinya digunakan juga mengikuti besarnya permintaan dari mas- masing outlet untuk tujuh hari pengiriman. Dimana besarnya permintaan outlet untuk tujuh hari pengiriman yaitu 207kg sampai dengan 295kg. Sehingga jumlah ken- aan yang akan dibeli untuk memenuhi permintaan semua outlet yaitu sebanyak enam kendaraan motor roda dua dan dua kendaraan motor roda tiga. Untuk meminimumkan biaya trannportasi yang nantinya dikeluarkan oleh PT XYZ, gan pencarian rute yang optimal untuk melakukan pendistribusian bahan makanan. Pencarian rute yang optimal nantinya akan menggunakan model Vehicle Routing Problem with Time Windows (VRPTW) dengan metode metaheuristik yaitu algoritma SOS dan PSO sebagai metode pendekatannya. Setalah mengetahui rute serta biaya transportasi yang paling optimal, penelitian ini juga akan membahas terkait analisis kelayakan investasi dari kendaraan operasional yang pkan kebijakan pendistribusian yang baru di PT XYZ, maka dibuat dua skenario pengiriman bahan makanan dengan je-

5. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 5 of 20 Pada skenario pertama, pengiriman dilakukan dengan menggunakan kendaraan roda dua yaitu motor dengan tambahan tas box pengiriman sebagai media angkutnya. Skenario pengiriman pertama memiliki frekuensi pengiriman sebanyak enam kali dalam satu harinya. Jadwal pengiriman ini terbagi menjadi pengiriman pagi 1, pengiriman pagi 2, pengiriman siang 1, pengiriman siang 2, pengiriman sore 1, dan pengiriman sore 2. Data yang digunakan dalam skenario pengiriman pertama yaitu merupakan data large instance 50kg. Dimana pada data large instance 50kg, permintaan bahan makanan yang perlu dikirimkan oleh Central Kitchen ke masing-masing outlet akan dipecah berdasarkan waktu pengirimannya. Hal ini dilakukan karena dalam CK sendiri, tidak semua bahan makanan dapat dipersiapkan pada pengiriman pertama. Sehingga apabila pengiriman ke masing-masing outlet menunggu bahan makanan yang belum dipersiapkan, maka yang terjadi adalah terjadinya kekurangan bahan makanan lainnya yang dibu- tuhkan oleh masing-masing outlet. Oleh karena itulah dibuat sebuah jadwal pengiriman bahan makanan menjadi enam kali dalam seharinya agar bahan-bahan makanan yang tidak dapat dikirimkan pada pengiriman awal, dapat dikirimkan pada pengiriman selanjutnya. 2. Skenario Pengiriman Kedua Pada skenario kedua, pengiriman dilakukan dengan menggunakan kendaraan motor roda tiga dengan kapasitas angkut sebesar 250kg. Data yang digunakan dalam skenario pengiriman kedua yaitu data large instance 250kg. Skenario pengiriman kedua juga memiliki frekuensi pengiriman yang sama dengan pengiriman pertama, dimana terjadi dua kali pengiriman di setiap pagi, siang, dan sore. Hal yang membedakan skenario pengiriman pertama dan skenario pengiriman kedua yaitu dari sisi operasional bahan bakar dan besarnya biaya investasi yang perlu dikeluarkan. Dengan adanya dua skenario pengiriman yang ada, nantinya dapat dibandingkan skenario mana yang menghasilkan keuntungan yang lebih baik untuk PT XYZ dibandingkan dengan skenario lainnya. 3. Metodology Dalam melakukan penelitian ini, tahapan-tahapan yang dilakukan dimulai dengan mengidentifikasi permasalahan yang terjadi pada objek penelitian yaitu PT XYZ. Taha- pan selanjutnya yaitu menentukan tujuan penelitian yang ingin dicapai dari permasalahan yang terjadi. Setelah menentukan tujuan yang dicapai, selanjutnya melakukan studi pustaka pada penelitian sebelumnya terkait solusi apa saya yang bisa dilakukan untuk menyelesaikan permasalahan yang terjadi. Membangun model matematis matematis menjadi salah satu tahapan penting yang dilakukan pada penelitian ini. Hal ini dilakukan untuk memastikan, apakah model pe- nyelesaian yang digunakan yaitu VRPTW sudah sesuai dan merepresentasikan dengan permasalahan yang terjadi. Setelah model dinyatakan sesuai dengan permasalahan, maka sebelum XXXX 3.1. Vehicle Routing Problem with Time Windows Vehicle Routing Problem or commonly referred to as VRP, is a transportation model problem that aims to solve the problem of determining the route by using several vehicles and serving several customers in several different locations, where each customer has their demands, and the vehicles that used to transport has it is own the vehicle capacity. The VRP model has several development model variations that adjusted to the constraints and complexities of a problem. Vehicle Routing Problem with Time Windows (VRPTW) is one of the VRP variations that consider vehicle capacity limit and service time interval (time windows) in each customer. VRPTW aims to minimize the total transportation cost by considering the vehicle’s cost and traveling time matrixes. In the VRPTW model, there are two service time types to can be used, i.e., hard time windows and soft time windows. However, in this

6. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 6 of 20 research, the VRPTW model used was the hard time windows. In this model, when the vehicle comes after the service time, then customers cannot serve the vehicle. This VRPTW model fits with the problem in PT XYZ, because if the vehicle comes after the service time, there are no employees who were serving it. 3.2. Model Formulation The mathematical model formulation used in this research is the model of Vehicle Routing Problem with Time Windows (VRPTW) that developed by Kallehauge in 2001 [6]. This model has purpose to minimize the total transportation costs with time windows at each customer. The VRPTW mathematical model has a mathematical notation as follows: : a set of vehicles with the same capacity : a set of customers : a set of points consisting customers and depots : vehicle capacity k: vehicle i: customers demand Cij: transportation costs from nodes i to nodes j ij: travel timefrom nodes i to nodes j Sik: starting timeof service at customers i i: earliest time of service at customers i i: latest time of service at customers i The decision variable of the VRPTW mathematical model is:

7. 1, if there is a vehicle trip from i to j on route k 0, if there is no vehicle trip from i to j on route k $ Then the objective function is: min = '

8. ∈) ∈)

9. ∈* (1) With constraints:

10. = 1 ∈)

11. ∈* ∀. ∈ (2)

12. ≤ q ∀2 ∈ (3) ∈) ∈4 5

13. = 1 ∈) ∀2 ∈ (4) 7

14. − 7

15. ∈) = 0 ∈) ∀ℎ ∈ , ∀2 ∈ (5) ,;=,

16. = 1 ∀2 ∈ ∈) (6)

17. ?@

18. + − @

19. B ≤ 0 ∀., C ∈ , ∀2 ∈ (7) ≤ @

20. ≤ ∀. ∈ , ∀2 ∈ (8)

21. ∈ F0,1G ∀., C ∈ , ∀2 ∈ (9)

22. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 7 of 20 Based on the mathematical formulation above, equation 1 is an objective function of the model to minimize travel costs. Equation 2 stated that each customer is visited once. Equation 3 shows the limitation that a vehicle may not carry more than the vehicle's capacity. Equation 4 shows that each vehicle starts from a depot. Equation 5 shows that after visiting a customer, the vehicle will leave that customer and visit the next customer, and equation 6 states that each vehicle will end up at the depot.Equation 7 is used to express the relationship between the time of departure from customers and the time of travel to the next customer. Equation 8 ensures that the time windows limit of each customer is met and equation 9 states that the decision variable xijk is binary. Based on the mathematical model above it is known that equation 7 is nonlinear, therefore it needs to be changed to linear to verify the model. The linear equation is: @

23. + − I ?1 −

24. B ≤ @

25. ∀., C ∈ , ∀2 ∈ (10) Where constantan Mij can be derived tomax J + − K, (., C) ∈ L. 3.3. Metaheuristic Algorithm 3.3.1. SOS Algorithm The SOS algorithm is an optimization technique adopted from the inter-organism relationship pattern in its survival and proliferation [7]. Solution-seeking on the SOS algorithm begins with the initial population, the so-called ecosystem, consisting of several randomized individuals. These individuals will later pass three iterative seeking stages to generate an optimum solution variable. At each stage, each individual will interact randomly with one another to generate solutions. Interaction results on each stage will be evaluated for their objective value to obtain the best solution. The SOS algorithm’s seeking solution process will stop when the termination criteria are met. The pseudocode from the Symbiotic Organisms Search algorithm used in this research is presented in Figure X. BF= = (1 + round (rand(0,1)) Step 1: Ecosystem Initialization Step 2: For i = 1, 2, . . ., eco_size Evaluate f(Xi) Xbest = Minimum f(Xi) If Obj (Xi) Obj (Xbest) do Update Xbest = Xi End if Step 3: Whileiteration (iter) maximum iteration (max iter) do Fori = 1, 2, . . ., eco_size Mutualism Phase Select one organisme Xj randomly, where Xj ≠ Xi Calculate benefit vector and mutual vector BFQ = (1 + round (rand(0,1)) Mutual vector = STSU Q

26. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 8 of 20 Figure X Pseudocode SOS Figure X Cont. XWXYZ = XW + rand(0,1) ∗ (XY]^ − X_) X`aba]W^Y = rand (0,1) ∗ (UB − LB) + LB Comensalism Phase Select one organisme Xj randomly, where Xj ≠ Xi Calculate Xinew Decode Xinew Evaluate f(Xinew) If Obj Xinew Obj Xi do Update Xi = Xinew End If Parasitism Phase Select one organisme Xj randomly, where Xj ≠ Xi Generate Xparasite from organism Xi Generate r = random (0,1) r parasite_force Mutation Xi uses a random number with a range of [ub,lb] Decode Xparasite Xparasite dan Xj Evaluate f(Xparasite) and f(Xjnew) If Obj Xparasite Obj Xj do Update Xj = Xparasite End If End for End while

27. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 9 of 20 3.3.2. PSO Algorithm The solution-seeking procedure on PSO was conducted by a population comprised of several particles. Because PSO uses stochastics data, then the population within has to be raised using random numbers with the lowest value and highest value limitations. In seeking solutions, each particle conducts searching in the search space to find its particle's best position (local best) and the best position of all populations (global best). Moving particles will be searching in the search space using dynamic velocity that tends to move to the best searching area. Each particle executes the best position-seeking process in several determined particular iteration. On each iteration, solutions represented by the particle position were evaluated for their performance by entering the solution to the fitness function [8]. The pseudocode from the Particle Swarm Optimization algorithm in this research is presented in Figure X. Figure X Pseudocode PSO Algorithm e (f=) = e (f) + (f=) Step 1 : For each particle i : 1, 2, …N Random initialization Xi Random initialization Vi (or just set Vi to zero) Evaluate the fitness of particle i, f(xi) Evaluate Pbest and Gbest End For Step 2 : While iteration (iter) maximum iteration (max iter)do For each particle i : 1, 2, …N Update Velocities with (f=) = g (f) + h='=?ij@ (f) − e (f)B + hQ'Q?kj@ (f) − e (f)B Update Position with Evaluate the fitness of particle i, f(xi) If Pbest(t+1) Pbest(t) do Pbest(t) = Pbest(t+1) End If Gbest(t+1) = small value in Pbest If Gbest(t+1) Gbest(t) do Gbest(t) = Gbest(t+1) End For End While

28. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 3.4. Solution Representation Solution representation determination is an important process in implementing a metaheuristic algorithm. It is because the solution representation is the illustration r presentation of the generated creating a route to distribute raw materials from the CK to each outlet by not violating the vehicle capacity limit and service time on each outlet. The route began by vehicles departing from the nodes that have demand less than the vehicle capacity. Another limitation of vehicles’ starting time on each node is also mandatory besides the vehicle capacity. If the vehicle came after the outlet’s service time, the Therefore, the vehicle could not be served on that node and had to find another node or go back to the depot. One of the solution representation examples in this research is presented in Figure X. 3.5. Feasibility Study Analysis Feasibility study analysis is a procedure to assess, measure, and analyze the feas bility of a policy plan or project to be executed [10]. In conducting a feasibility study, there are three thin and capital budgeting analysis. There are three methods to evaluate an investment’s fe sibility in the capital budgeting analysis, namely NPV, PI, and PP. Solution represent tion determination is an important process in implementing a metaheuristic algorithm. It is because the solution representation is the illustration representation of the generated solution [9]. The solution raw materials from the CK to each outlet by not violating the vehicle capacity limit and service time on each outlet. 3.5.1. Net Present Value (NPV) Model It is a technique to estimate the company's generated profit in the future if we invest with t current monetary value. The NPV calculation is as follows: Where: NPV : Net Present Value Lf : Cash flow i : Interest rate used t : Project’s economist life, started from the initial stage to the end of n : Reviewed project’s life 3.5.2. Profitability Index (PI) Method It is a technique to estimate a project’s feasibility by comparing its net profit value with the initial investment value. The profitability index calculation is as , x FOR PEER REVIEW Solution Representation Solution representation determination is an important process in implementing a metaheuristic algorithm. It is because the solution representation is the illustration r presentation of the generated solution [9]. The solution-seeking in this research was by creating a route to distribute raw materials from the CK to each outlet by not violating the vehicle capacity limit and service time on each outlet. The route began by vehicles departing from the depot, and then each vehicle went to nodes that have demand less than the vehicle capacity. Another limitation of vehicles’ starting time on each node is also mandatory besides the vehicle capacity. If the vehicle came after the outlet’s service time, the nodes violated the service time limitation. Therefore, the vehicle could not be served on that node and had to find another node or go back to the depot. One of the solution representation examples in this research is presented in Figure X. Figure X Representation Solution VRPTW Model Feasibility Study Analysis Feasibility study analysis is a procedure to assess, measure, and analyze the feas bility of a policy plan or project to be executed [10]. In conducting a feasibility study, there are three things to be considered, i.e., financial analysis, perceived benefit analysis, and capital budgeting analysis. There are three methods to evaluate an investment’s fe sibility in the capital budgeting analysis, namely NPV, PI, and PP. Solution represent termination is an important process in implementing a metaheuristic algorithm. It is because the solution representation is the illustration representation of the generated solution [9]. The solution-seeking in this research was by creating a route to dist raw materials from the CK to each outlet by not violating the vehicle capacity limit and service time on each outlet. Net Present Value (NPV) Model It is a technique to estimate the company's generated profit in the future if we invest with t current monetary value. The NPV calculation is as follows: i = Lf (1 + .)f ; fl5 (11) Net Present Value Cash flow on period t : Interest rate used : Project’s economist life, started from the initial stage to the end of : Reviewed project’s life Profitability Index (PI) Method It is a technique to estimate a project’s feasibility by comparing its net profit value with the initial investment value. The profitability index calculation is as 10 of 20 Solution representation determination is an important process in implementing a metaheuristic algorithm. It is because the solution representation is the illustration re- seeking in this research was by creating a route to distribute raw materials from the CK to each outlet by not violating depot, and then each vehicle went to nodes that have demand less than the vehicle capacity. Another limitation of vehicles’ starting time on each node is also mandatory besides the vehicle capacity. If the vehicle nodes violated the service time limitation. Therefore, the vehicle could not be served on that node and had to find another node or go back to the depot. One of the solution representation examples in this research is entation Solution VRPTW Model Feasibility study analysis is a procedure to assess, measure, and analyze the feasibility of a policy plan or project to be executed [10]. In conducting a feasibility study, gs to be considered, i.e., financial analysis, perceived benefit analysis, and capital budgeting analysis. There are three methods to evaluate an investment’s feasibility in the capital budgeting analysis, namely NPV, PI, and PP. Solution representa- termination is an important process in implementing a metaheuristic algorithm. It is because the solution representation is the illustration representation of the generated seeking in this research was by creating a route to distribute raw materials from the CK to each outlet by not violating the vehicle capacity limit and It is a technique to estimate the company's generated profit in the future if we invest with the : Project’s economist life, started from the initial stage to the end of project’s life It is a technique to estimate a project’s feasibility by comparing its net profit value with the initial investment value. The profitability index calculation is as follows:

29. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 11 of 20 PI = PV of future cash plow PV of investment (12) Where: PI : Profitability index PV of future cash flow : Present value of future cash flow PV of investment : Initial Investment 3.5.3. Payback Period (PP) Method It is a technique used to assess the period of return on investment. The payback period calculation is as follows: PP = Cost of Investment Annual cashplow x 1 year (13) Where: PP : Payback period 4. Result and Discussion Data used in this research were divided into two, i.e., small instance and large instance data. The small instance data shows data for one-time delivery frequency, while the large instance data shows delivery scenario data in a day. The large instance data it- self is data processed following the delivery frequency to be implemented. This data was made by dividing each customer’s demand based on the delivery time and adjusted to vehicle capacity. In this research, the large instance data was categorized into two, i.e., large instance 50 kg and large instance 250 kg. The large instance 50 kg was the data used in the first delivery scenario using two-wheeled motor vehicles and a delivery box of 50 kg capacity. Meanwhile, the large instance 250 kg data was used in the second scenario using three-wheeled motor vehicles with a maximum capacity 250 kg. The data processing in this research used AMPL software with a GUROBI solver to verify the mathematical model. Meanwhile, for SOS and PSO metaheuristic methods program, Visual Studio of 2019 with C# programming language was used. Another software used was SPSS 16.0 to test statistical analysis. The computer used in this research was Lenovo C340 with specifications of intel core i3-10110U processor, RAM 8 GB, and system windows 10 64-bit. 4.1. Verification and Validation Model Model verification was conducted to ensure that the objective function and constraints of the model are mathematically accurate and logically consistent. Meanwhile, model validation was conducted to ensure that the mathematical model computation will generate the same output as manual calculation. Model verification and validation were conducted using the AMPL software, which declared that the model was verified and validated. The verification was proven by the absence of sub-routes or errors on the generated output. The model was also validated because it had the same value as the results of manual calculation. The verification and validation processes for the small instance data produce an optimum solution with an objective value of 4240. 4.2. Parameter Tuning Parameter tuning was conducted to discover the parameter combination that generates the best solution quality with short computation times. In this research, parameter value was determined before the algorithm was running, so-called off-line tuning. The parameter tuning method used in this research was the One Factor at A Time (OFAT), where one parameter will be tested for each value and assuming that other untested pa-

30. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 12 of 20 rameters have fixed values. Parameter value determination for both metaheuristic methods was adopted from a literature review of previous research. Parameter values used in this research are shown in Table 1. Table 1.Parameter Values of SOS and PSO Algo- rithms All parameter values in Table 1 were combined with each other to be analyzed for their parameter sensitivity. The parameter sensitivity analysis was made to discover the effect of a parameter on its solution quality and computation time length. The result of sensitivity analysis is discovering the best value of each parameter in solving the VRPTW problem. Based on the sensitivity analysis results, the best parameter value in the SOS algorithm for maxiter value is 1000, eco size 50, and parasite force (pf) 0.7. Meanwhile, the PSO algorithm has the best maxiter value 500, inertia weight (w) 1, swarm size (N) 20, and cognitive and social factors with the same value 2. 4.3. Verification and Validation Algorithm By using the best parameter value combination, the next step was to verify and va- lidate algorithms. Algorithm verification and validation were conducted by comparing the results of the objective values obtained from SOS and PSO algorithms with the objective values from the exact method. The verification and validation results are shown in Table 2. The table shows that SOS and PSO algorithms can generate the same objective values as a result of the exact method. Table 2.Computation Results of SOS and PSO Algorithms for the Small Instance Data Instance Exact Method SOS Algorithm PSO Algorithm Objective Value Objective Value Objective Value Small - 1 4240 4240 4240 Small - 2 4240 4240 4240 Small - 3 4240 4240 4240 Small - 4 4240 4240 4240 Small - 5 4240 4240 4240 Small - 6 4240 4240 4240 Small - 7 4240 4240 4240 Algorithm Parameter Value SOS Maxiter 500 1000 1500 Eco Size 25 50 75 Parasite Force (pf) 0.7 0.8 0.9 PSO Maxiter 500 1000 Inertia Weight (w) 0.25 0.5 1 Swarm Size (N) 20 40 80 Cognitive Factor 1 2 Social Factor 1 2

31. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 13 of 20 4.4. Computational Result Based on algorithm verification and validation results, it can be known that SOS and PSO algorithms can generate an optimum solution for the small instance data. Therefore, these two algorithms can be used to solve the VRPTW problem in the distribution problem of PT XYZ. The results of SOS and PSO algorithms using the best parameter combination are shown in Table 3 and Table 4. Table 3.Computational Result of SOS and PSO Algorithms for Large Instance 50 kg Instance SOS PSO Best Obj. Average Obj. CPU Time (s) Best Obj. Average Obj. CPU Time (s) Large 50 -1 7691 9639 4.82 10758 15032 1.35 Large 50 -2 13379 14470 2.67 10997 11144 1.42 Large 50 -3 12795 15129 2.77 11348 12654 1.72 Large 50 -4 13683 14943 2.46 11568 13384 1.80 Large 50 -5 11777 12620 2.41 12458 13882 1.39 Large 50 -6 11057 12643 2.63 11032 12548 1.63 Large 50 -7 12300 12913 2.75 11361 14478 2.05 Average 11812 13194 2.93 11360 13303 1.62 Table 4.Computational Result of SOS and PSO Algorithms for Large Instance 250 kg Instance SOS PSO Best Obj. Average Obj. CPU Time (s) Best Obj. Average Obj. CPU Time (s) Large 250 -1 19471 21035 2.28 14823 17822 1.86 Large 250 -2 17415 19664 2.41 18486 21756 1.26 Large 250 -3 20243 23442 4.17 17952 20787 1.88 Large 250 -4 19109 23085 4.99 21763 22756 1.87 Large 250 -5 17866 19529 5.22 17801 18793 1.73 Large 250 -6 21291 22028 4.68 20009 20643 1.25 Large 250 -7 17137 18529 2.67 19407 20907 2.16 Average 18933 21045 3.77 18606 20495 1.71 4.5. Statistical Analysis The statistical analysis test was conducted to measure the solution quality performance generated by each metaheuristic algorithm. The purpose of the statistical analysis test is to determine the difference in average objective values of each algorithm. Testing using statistical analysis began by conducting the normality test, homogeneity test, and paired t-test. 4.5.1. Normality Test The first testing was the normality test, where it was conducted to discover that the tested data are normally distributed. The hypothesis used in this testing were as follow:

32. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 14 of 20 H0 = Data are distributed normally H1 = Data are not distributed normally α = 0.05 The normality test results are shown in Table 5, showing all four tested data have a p-value (sig.) bigger than the value of α = 0.05. It is then concluded that H0 is accepted, or the data are distributed normally. Table 5.Results of Normality Test for the Large Instance 50 kg Data and Large Instance 250 kg Data Algorithm Shapiro - Wilk Statistic df Sig Objective SOS 50kg 0.882 7 0.235 PSO 50kg 0.976 7 0.939 SOS 250kg 0.934 7 0.588 PSO 250kg 0.944 7 0.680 4.5.2. Normality Test Homogeneity Test The second performance test was the homogeneity test, it was conducted to test the variance homogeneity of data. The hypothesis used in this test were as follow: H0 = Data variance are homogenous H1 = Data variance are not homogenous α = 0.05 The homogeneity test results are shown in Table 6 and Table 7, showing all four tested data have p-value (sig) bigger than the value of α = 0.05. The decision made is that H0 is accepted, or the data variance is homogenous. Table 6.Results of Homogeneity Tests of the Large Instance 50 kg Data Objective Levene Statistic Sig. Based on Mean 0.618 0.447 Based on Median 0.466 0.508 Based on Median and with adjusted df 0.466 0.511 Based on trimmed mean 0.678 0.426 Table 7.Results of Homogeneity Test of the Large Instance 250 kg Data Objective Levene Statistic Sig. Based on Mean 0.351 0.565 Based on Median 0.480 0.502 Based on Median and with adjusted df 0.480 0.503 Based on trimmed mean 0.371 0.554 4.5.3. Normality Test Paired T-test The last test was the paired t-test, where it was conducted to test the parametric difference on two paired data. The computational result of the SOS algorithm in large instance 50 kg was paired with the computational result of the PSO algorithm in large instance 50 kg. The paired t-test was also conducted for the computational result of the

33. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 15 of 20 large instance 250 kg SOS and the computational result of the large instance 250 kg PSO. The hypothesis used in this research were as follow: H0 = There is not a statistically significant difference H1 = There is a statistically significant difference α = 0.05 The results of the paired t-test are shown in Table 8, where pair 1, the relationship between the large instance 50 kg data of SOS and large instance 50 kg data of PSO, has a p-value = 0.925. Meanwhile, pair 2, the relationship between the large instance 250 kg data of SOS and large instance 250 kg data of PSO, has a p-value = 0.525. From both pairs, it is discovered that all p-values (sig.) are bigger than the value of α = 0.05. So it is concluded that H0 is accepted. It shows there is not a statistically significant difference between the results of the SOS and PSO algorithms for both data. Table 8.Results of Paired Samples Test for SOS and SPO Algorithms Pair t df Sig.(2-tailed) Pair 1 SOS 50kg - PSO 50kg -0.098 6 0.925 Pair 2 SOS 250kg - PSO 250kg 0.675 6 0.525 Based on the statistical analysis results, it can be concluded that even though there are differences between objective values generated by SOS and PSO algorithms, with the statistical analysis test shown, the differences are insignificant. Therefore, to discover which algorithm generates the best solution, it is necessary to conduct a test for the computation time. The computational time result can be seen in Table 3 and Table 4, where the PSO algorithm in Large Instance 50 kg and Large Instance 250 kg had shorter computational time than the SOS algorithm. So, it can be concluded that the PSO algorithm can get the solution that tends to optimal with short computational time. This research proves that the PSO algorithm to solve the Vehicle Routing Problem with Time Windows produces a better solution than the SOS algorithm. 4.6. Implementation of Metaheuristic Method Based on statistical analysis results, knowing that the PSO algorithm generates better objective values with a short computation time than the SOS algorithm. Hence, the PSO algorithm results to be used do represent the route determination result using metaheuristic methods. The results of PSO algorithm implementation on large instance 50 kg and large instance 250 kg data for 7-days delivery are shown in Table 9. Table 9.Results of PSO Algorithm for 7-Days Delivery Day Data Objec- tive Route 1 50 10758 26-21-20-19-22-24-23-29-6-5-18-13-14-8-9-30-25-27-28-15-16-1 2-11-10-7-4-3-2-17-1 250 14823 26-25-21-22-19-20-24-23-30-29-3-8-9-15-16-13-17-18-12-11-10- 7-6-5-4-2-27-28-14-1 2 50 10997 1-2-14-16-15-11-29-28-25-30-4-5-3-13-18-17-10-9-19-20-21-22-2 3-24-8-26-27-7-12-6 250 18486 2-26-20-19-24-23-30-9-8-7-13-18-17-16-14-15-25-27-28-21-22-2 9-12-11-10-6-5-4-3-1

34. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 16 of 20 3 50 11348 12-11-26-27-25-2-5-28-29-30-4-14-13-15-9-16-17-18-19-20-21-2 2-23-24-8-7-6-3-10-1 250 17952 4-1-25-19-22-21-20-27-29-3-2-13-14-15-16-17-18-28-26-30-11-1 2-10-9-8-7-23-24-6-5 4 50 11568 4-25-26-20-19-22-23-24-28-30-27-29-2-1-5-10-7-21-15-13-14-16- 17-18-12-11-9-8-6-3 250 21763 7-9-1-2-6-25-19-20-30-10-14-15-16-13-5-28-22-21-24-23-29-18-1 7-8-12-3-26-27-11-4 5 50 12458 2-3-28-22-23-24-25-26-27-29-1-9-12-15-14-19-21-20-30-13-16-1 7-18-11-10-8-7-6-5-4 250 17801 1-7-15-14-13-17-11-12-2-5-6-8-25-26-30-3-16-18-19-20-21-22-23 -24-10-9-27-28-29-4 6 50 11032 28-25-29-21-20-19-2-5-10-27-26-22-24-23-30-7-8-13-14-15-16-1 7-18-9-12-11-6-4-3-1 250 20009 7-9-25-29-3-4-16-14-17-2-1-28-26-27-30-6-13-15-8-10-12-11-18- 19-20-21-22-23-24-5 7 50 11361 27-26-25-29-11-12-2-10-7-9-30-19-22-23-24-13-14-15-16-17-18- 8-28-20-21-6-5-4-3-1 250 19407 2-20-19-27-30-12-13-14-15-16-17-25-28-26-29-6-3-1-10-9-21-22- 23-24-18-7-8-11-5-4 4.7. Comparison Total Cost of Existing and Solution Routes After obtaining the total cost for each delivery day and vehicle route to be taken, the next step was to compare the total cost generated by the proposed route versus the existing transportation cost. The comparison is shown in Table 10. Table 10.Comparison Total Cost of Existing and Solution Routes Day Total Cost Current Method Total Cost Scenario 1 Total Cost Scenario 2 50kg GAP (%) 250kg GAP (%) 1 Rp25.000 Rp10.758 56,97% Rp14.823 40,71% 2 Rp25.000 Rp10.997 56,01% Rp18.486 26,06% 3 Rp25.000 Rp11.348 54,61% Rp17.952 28,19% 4 Rp25.000 Rp11.568 53,73% Rp21.763 12,95% 5 Rp25.000 Rp12.458 50,17% Rp17.801 28,80% 6 Rp25.000 Rp11.032 55,87% Rp20.009 19,96% 7 Rp25.000 Rp11.361 54,56% Rp19.407 22,37% Based on Table 10, it can be seen that the proposed total cost is lower than the existing total cost. The gap between the first proposed scenario total cost with the existing total cost ranges from 50% to 56%. Meanwhile, it ranges from 12% to 40% for the second proposed scenario total cost compared to the existing total cost. Hence, route determination in the two proposed scenarios can minimize the transportation cost rather than the existing method.

35. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 17 of 20 4.8. Investment Feasibility Analysis The investment feasibility analysis was conducted to discover which scenario, first or second, that gives profit to the company, whether financial or benefit-wise. In conducting an investment feasibility analysis, the steps conducted are calculating investment feasibility based on financial analysis and capital budgeting. An analysis of perceived benefits from the investment plan was also conducted. 4.8.1. Cost Analysis Cost analysis was conducted to find out the cash flow in a company. There are four considerations in a company’s financial statements, i.e., investment cost, operational cost, revenue, and depreciation cost. These four costs are calculated during the vehicle’s eco- nomic life. The results of cost analysis are a financial statement and net cash flow of the company when executing the planned investment. 4.8.2. Capital Budgeting Analysis Capital budgeting was used to determine the acceptance or rejection of an investment plan to be executed. An investment plan’s feasibility is a consideration in determining a policy or plan to be carried out. In this research, the capital budgeting methods used were the net present value (NPV), profitability index (PI), and payback period (PP). The first and second scenarios calculation results using three capital budgeting methods are shown in Table 11. Table 11.Result of Investment Feasibility Analysis Indicator Criteria Scenario 1 Scenario 2 Value Decision Value Decision NPV NPV 0 (Rp 28.299.974) Not Feasible Rp9.149.022 Feasible Profitability Index PI 1 0,739 Not Feasible 1,112 Feasible Payback Period PP Useful Life 5 years Not Feasible 7,63 years Feasible Based on Table 11, it is discovered that the first scenario is not feasible to be implemented because the resulting calculation values are not fulfilling all criteria of capital budgeting calculation methods. In contrast, the second scenario is declared feasible because the resulting calculation values fulfill all criteria of capital budgeting methods. 4.8.3. Benefit Analysis A benefit analysis was conducted to discover the company’s perceived benefits by implementing the new distribution system. The perceived benefits are: 1. Saving in distribution costs By implementing the new distribution method, the company only spent a transportation cost of IDR 18,606. Cost is less than the current transportation cost of the company for IDR 25,000.

36. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 18 of 20 2. Delivery scheduling By determining a schedule, the delivery becomes six times per day. It makes the distribution system more organized and clearer. 3. Optimum operator working time By implementing the new policy, it will optimize each operator’s working time. The time can be maximized according to the determined operator’s working time. 4. Product delivery data With the new policy, delivery is entirely operated by the CK. It will avoid discre- pancy of inventory in CK. 5. Financial Statement Different from the current distribution method, this new distribution method has established the fuel and maintenance costs from the beginning. Thus, the monthly financial statement will be more organized and clearer. 5. Conclusions The solution quality resulted from the SOS algorithm has an insignificant difference with the solution quality PSO algorithm. However, in computation speed to reach the convergent point, the PSO algorithm has a relatively faster time than the SOS algorithm. Thus, the PSO algorithm will be implemented on the route determination problem of PT XYZ. By conducting route determination using metaheuristic approach methods, it saves daily distribution cost of 56% for the first scenario and 40% for the second scenario. Based on the feasibility analysis results, the second delivery scenario using three-wheeled motor vehicles is more feasible to be executed than the first scenario using motor vehicles with a delivery box. It is proven based on the calculation results using capital budgeting methods where resulting values fulfill are feasibility criteria in conducting an investment. Future research may apply and testing SOS and PSO algorithms performance in another optimization problem, especially in Vehicle Routing Problem (VRP) variations. Evaluating solution quality and computation times using both algorithms can be sup- ported by programming skills and better computer specifications. On the other hand, to get a better solution and computational times, future research may consider other parameter values or other parameter tuning methods.

37. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 19 of 20 6. Patents This section is not mandatory but may be added if there are patents resulting from the work reported in this manuscript. Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: title, Table S1: title, Video S1: title. Author Contributions: For research articles with several authors, a short paragraph specifying their individual contributions must be provided. The following statements should be used “Con- ceptualization, X.X. and Y.Y.; methodology, X.X.; software, X.X.; validation, X.X., Y.Y. and Z.Z.; formal analysis, X.X.; investigation, X.X.; resources, X.X.; data curation, X.X.; writing—original draft preparation, X.X.; writing—review and editing, X.X.; visualization, X.X.; supervision, X.X.; project administration, X.X.; funding acquisition, Y.Y. All authors have read and agreed to the published version of the manuscript.”Please turn to the CRediT taxonomy for the term explanation. Authorship must be limited to those who have contributed substantially to the work reported. Funding: Please add: “This research received no external funding” or “This research was funded by NAME OF FUNDER, grant number XXX” and “The APC was funded by XXX”. Check carefully that the details given are accurate and use the standard spelling of funding agency names at https://search.crossref.org/funding. Any errors may affect your future funding. Data Availability Statement: In this section, please provide details regarding where data sup- porting reported results can be found, including links to publicly archived datasets analyzed or generated during the study. Please refer to suggested Data Availability Statements in section “MDPI Research Data Policies” at https://www.mdpi.com/ethics. You might choose to exclude this statement if the study did not report any data. Acknowledgments:In this section, you can acknowledge any support given which is not covered by the author contribution or funding sections. This may include administrative and technical support, or donations in kind (e.g., materials used for experiments). Conflicts of Interest: Declare conflicts of interest or state “The authors declare no conflict of interest.” Authors must identify and declare any personal circumstances or interest that may be perceived as inappropriately influencing the representation or interpretation of reported research results. Any role of the funders in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript, or in the decision to publish the results must be declared in this section. If there is no role, please state “The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results”. Appendix A The appendix is an optional section that can contain details and data supplemental to the main text—for example, explanations of experimental details that would disrupt the flow of the main text but nonetheless remain crucial to understanding and repro- ducing the research shown; figures of replicates for experiments of which representative data is shown in the main text can be added here if brief, or as Supplementary data. Mathematical proofs of results not central to the paper can be added as an appendix. Appendix B All appendix sections must be cited in the main text. In the appendices, Figures, Tables, etc. should be labeled starting with “A”—e.g., Figure A1, Figure A2, etc. References References must be numbered in order of appearance in the text (including citations in tables and legends) and listed indivi- dually at the end of the manuscript. We recommend preparing the references with a bibliography software package, such as EndNote, ReferenceManager or Zotero to avoid typing mistakes and duplicated references. Include the digital object identifier (DOI) for all references where available.

38. J. Open Innov. Technol. Mark. Complex.2021, 7, x FOR PEER REVIEW 20 of 20 Citations and references in the Supplementary Materials are permitted provided that they also appear in the reference list here. In the text, reference numbers should be placed in square brackets [ ] and placed before the punctuation; for example [1], [1–3] or [1,3]. For embedded citations in the text with pagination, use both parentheses and brackets to indicate the reference number and page numbers; for example [5] (p. 10), or [6] (pp. 101–105). 1. Author 1, A.B.; Author 2, C.D. Title of the article. Abbreviated Journal NameYear, Volume, page range. 2. Author 1, A.; Author 2, B. Title of the chapter. In Book Title, 2nd ed.; Editor 1, A., Editor 2, B., Eds.; Publisher: Publisher Loca- tion, Country, 2007; Volume 3, pp. 154–196. 3. Author 1, A.; Author 2, B. Book Title, 3rd ed.; Publisher: Publisher Location, Country, 2008; pp. 154–196. 4. Author 1, A.B.; Author 2, C. Title of Unpublished Work. Abbreviated Journal Name stage of publication (under review; accepted; in press). 5. Author 1, A.B. (University, City, State, Country); Author 2, C. (Institute, City, State, Country). Personal communication, 2012. 6. Author 1, A.B.; Author 2, C.D.; Author 3, E.F. Title of Presentation. In Title of the Collected Work (if available), Proceedings of the Name of the Conference, Location of Conference, Country, Date of Conference; Editor 1, Editor 2, Eds. (if available); Pub- lisher: City, Country, Year (if available); Abstract Number (optional), Pagination (optional). 7. Author 1, A.B. Title of Thesis. Level of Thesis, Degree-Granting University, Location of University, Date of Completion. 8. Title of Site. Available online: URL (accessed on Day Month Year).

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