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All Journal Media Statistika Jurnal Ilmu Dasar CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society Dharmakarya : Jurnal Aplikasi Ipteks Untuk Masyarakat Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri IJEBD (International Journal Of Entrepreneurship And Business Development) JTAM (Jurnal Teori dan Aplikasi Matematika) Agrisocionomics: Jurnal Sosial Ekonomi Pertanian Jambura Journal of Mathematics International Journal of Global Operations Research Jurnal Matematika Integratif
Diah Chaerani
Departemen Matematika, Fakultas MIPA, Universitas Padjadjaran
Agriculture, Biological Sciences & Forestry Arts Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Public Health Transportation

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Systematic Literature Review: Optimal Stopping and Investment Optimization for Bankruptcy Risk Management in Sharia Insurance Okta Yohandoko, Setyo Luthfi; Chaerani, Diah; Sukono, F
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.35523

Abstract

The increasing demand for Sharia-compliant financial services in Muslim-majority countries such as Indonesia has driven the rapid development of Sharia insurance (Takaful). Despite its growth, the Sharia insurance sector faces significant challenges in managing investment portfolios and mitigating bankruptcy risks. Addressing these challenges requires a comprehensive understanding of the existing mathematical and financial models configured according to Islamic principles. Several studies have introduced stochastic approaches to model surplus processes, investment returns, and risk probabilities in insurance operations. Among these, the Cramér–Lundberg model has been widely used to estimate surplus dynamics and bankruptcy risks, while the Vasicek model provides a stochastic framework for modeling investment returns. Quadratic programming has also been applied to optimize asset allocation under specific constraints. However, these methodologies have typically been explored in isolation, which limits their ability to provide an integrated and effective framework for simultaneous bankruptcy risk mitigation and Sharia-compliant investment optimization. This methodological gap constrains the advancement of comprehensive, practically applicable, and theoretically sound solutions that are specifically designed to address the distinctive operational characteristics of Shariainsurance. The objective of this systematic review of the literature is to synthesize and critically analyze the methods used in previous research and to explore how they can be systematically integrated to form a comprehensive risk and investment management framework for Sharia insurance. The review identifies the strengths, limitations, and potential for combining optimal stopping theory, stochastic surplus modeling, and investment optimization to support robust financial decision making. This review contributes by offering a structured research agenda for the development of integrated models that simultaneously address the complexities of bankruptcy risk and Sharia-compliant investment strategies. Furthermore, this study provides valuable information for academics and practitioners seeking to improve the financial sustainability of the Islamic Insurance industry.
A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications Haq, Fadiah Hasna Nadiatul; Chaerani, Diah; Triska, Anita
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29398

Abstract

This paper comprehensively explains how to solve mixed-integer nonlinear programming (MINLP) models using the generalized benders decomposition (GBD) method. The MINLP problem is an optimization model in which some variables must be integers and the objective function or constraints are nonlinear.  The GBD method is an extension of the Benders Decomposition (BD) method, effectively handles the characteristics of the MINLP  model, where the model has nonlinear properties and involves two types of variables, namely continuous variables and integer variables. The GBD method decomposes the problem into primal and master problems that are solved alternately until the optimal solution is found. The main difference between the GBD and BD methods is that GBD uses nonlinear duality in the main problem so that GBD can solve the nonlinear problem, whereas BD applies linear duality. This paper also presents some theorem proofs related to GBD that were not presented in detail in the previous literature. The application of the GBD method is also presented to demonstrate how the method can be effectively used to solve real-world MINLP problems.
Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems Haq, Fadiah Hasna Nadiatul; Chaerani, Diah; Triska, Anita
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.31539

Abstract

The robust Mixed-Integer Linear Programming (MILP) model is an approach to address uncertainty in linear optimization involving integer and continuous variables, which can be solved using the Benders Decomposition method. One of its applications is facility location problems, which often face demand, costs, and capacity uncertainties. This article presents a systematic literature review (SLR) on solving robust MILP models using the Benders Decomposition method and its application to facility location problems. The objectives are to explore the state-of-the-art and research trends, identify issues modeled as robust MILP and solved using Benders Decomposition, and determine the most frequently used uncertainty sets. SLR was conducted using the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) method on the Scopus, Science Direct, and Dimensions databases for the last five years of publication, with bibliometric analysis using VOSviewer and RStudio. The results show that there are limited articles that discuss the solution of the robust MILP model on the problem of facility location with the ellipsoidal uncertainty set. In addition, the Benders Decomposition method is widely used to solve robust MILP problems in energy, logistics, supply chains, and scheduling, with interval uncertainty sets being the most common. This topic is an influential theme and has the potential to be explored further.
Systematic Literature Review Robust Graph Coloring on Electric Circuit Problems Balqis, Viona Prisyella; Chaerani, Diah; Napitupulu, Herlina
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 4 (2022): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i4.9446

Abstract

Graph Coloring Problem (GCP) is the assignment of colors to certain elements in a graph based on certain constraints. GCP is used by assigning a color label to each node with neighboring nodes assigned a different color and the minimum number of colors used. Based on this, GCP can be drawn into an optimization problem that is to minimize the colors used. Optimization problems in graph coloring can occur due to uncertainty in the use of colors to be used, so it can be assumed that there is an uncertainty in the number of colored vertices. One of the mathematical optimization methods in the presence of uncertainty is Robust Optimization (RO). RO is a modeling methodology combined with computational tools to process optimization problems with uncertain data and only some data for which certainty is known. This paper will review research on Robust GCP with model validation to be applied to electrical circuit problems using a systematic review of the literature. A systematic literature review was carried out using the Preferred Reporting Items for Systematic reviews and Meta Analysis (PRISMA) method. The keywords used in this study were used to search for articles related to this research using a database. Based on the results of the search for articles obtained from PRISMA and Bibliometric R Software, it was found that there was a relationship between the keywords Robust Optimization and Graph Coloring, this means that at least there is at least one researcher who has studied the problem. However, the Electricity keyword has no relation to the other two keywords, so that a gap is obtained and it is possible if the research has not been studied and discussed by other researchers. Based on the results of this study, it is hoped that it can be used as a consideration and a better solution to solve optimization problems.
A Systematic Review on Integer Multi-objective Adjustable Robust Counterpart Optimization Model Using Benders Decomposition Irmansyah, Athaya Zahrani; Chaerani, Diah; Rusyaman, Endang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8578

Abstract

Multi-objective integer optimization model that contain uncertain parameter can be handled using the Adjustable Robust Counterpart (ARC) methodology with Polyhedral Uncertainty Set. The ARC method has two stages of completion, so completing the second stage can be assisted by the Benders Decomposition. This paper discusses the systematic review on this topic using the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA). PRISMA presents a database mining algorithm for previous articles and related topics sourced from Scopus, Science Direct, Dimensions, and Google Scholar. Four stages of the algorithm are used, namely Identification, Screening, Eligibility, and Included. In the Eligibility stage, 16 articles obtained and called Dataset 1, used for bibliometric mapping and evolutionary analysis. Moreover, in the Included stage, six final databases obtained and called Dataset 2, which was used to analyze research gaps and novelty. The analysis was carried out on two datasets, assisted by the output visualisation using RStudio software with the " bibliometrix" package, then we use the command 'biblioshiny()' to create a link to the “shiny web interface”. At the final stage of the article using six articles analysis, it is concluded that there is no research on the ARC multi-objective integer optimization model with Polyhedral Uncertainty Sets using the Benders Decomposition Method, which focuses on discussing the general model and its mathematical analysis. Moreover, this research topic is open and becomes the primary references for further research in connection.  
Robust Optimization Model for Twitter Sentiment Analysis of PeduliLindungi Application Fatimathuzahra, Alfia Azizah; Chaerani, Diah; Firdaniza, Firdaniza
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8624

Abstract

Technological advances during the COVID-19 pandemic in Indonesia gave rise to the PeduliLindungi application which is developed by the government to prevent the spread of COVID-19. The advantages and disadvantages of developing PeduliLindungi can be seen from the responses and opinions from users, one of which is through the Twitter. A person's opinion about PeduliLindungi based on the tweet can be classified into positive, negative, or neutral categories using a Machine Learning approach with the Support Vector Machine (SVM) algorithm. In this paper, multiobjective optimization modeling is used to maximize the performance metrics, which are the value of Accuracy, Precision, Recall, and F1-Score. The value of the performance metrics is considered to contain uncertainty factors. Therefore, the optimization problem is solved by using Robust Optimization to handle the uncertainty factor. The data uncertainty is assumed to be belongs to polyhedral uncertainty set thus the resulted robust is computationally tractable. Numerical experiment is presented to complete the discussion.
Systematic Literature Review of GPS-based Multi-Objective Environmentally Friendly Shortest Path with a Proposed Lexicographic Framework Salsabila, Thania Nur; Chaerani, Diah; Napitupulu, Herlina
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40489

Abstract

Environmentally friendly path planning has become an important topic in transportation research as concerns about carbon emissions continue to grow. This study aims to review existing research on environmentally friendly shortest path problems and to identify the current state of the art in green shortest path optimization. A Systematic Literature Review is conducted using the PRISMA guideline and supported by bibliometric analysis to examine research trends and optimization methods discussed in the literature. The review indicates that most studies focus on metaheuristic and artificial intelligence–based approaches, while deterministic methods with explicit objective prioritization receive less attention. Based on the synthesis of previous studies, this paper discusses emerging research directions and outlines a conceptual framework for priority-based multi-objective shortest path optimization. The results of this review provide a clear overview of current methods and can support future research on eco-friendly shortest path models.
Optimization Model for Agricultural Processed Products Supply Chain Problem in Bandung During Covid-19 Period Zahrani Irmansyah, Athaya; Chaerani, Diah; Rusyaman, Endang
Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri Vol. 23 No. 2 (2021): Dec 2021
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.9744/jti.23.2.83-92

Abstract

Coronavirus disease, commonly called Covid-19, is a virus that causes a pandemic in almost every country globally. One of those countries is Indonesia, which has many big cities with dense populations. This study was conducted in Bandung, the capital of West Java, Indonesia. As a result of the Covid-19 pandemic, Bandung was seriously affected in various ways. One was the disruption in the distribution of the agricultural processed products supply chain, which changes producers and consumers' behaviour. Furthermore, as an effort by the government to break the spread of the virus, health protocols limit the distribution. The purpose of this study is to design an optimization model for the supply chain problem of agricultural processed products in Bandung during the Covid-19 period with the objective function is maximizing product suppliers so that all demands on consumers are fulfilled. The use of Local Food Hub (LFH) is a help in this research as a distribution centre point between the producer zone and the consumer zone. Finally, numerical experiments were carried out in two scenarios, namely Large-scale Social Distancing (LSD) and Partial Social Distancing (PSD). It was found that the optimal distribution solution was obtained if the PSD scenario was applied.
Co-Authors Al Fataa Waliyyul Haq Alit Kartiwa Andika, Alif Anita Triska Ashgi, Rizky Azis, Chusnul Chatimah Balqis, Viona P Balqis, Viona Prisyella Betty Subartini Budi Nurani Ruchjana Cornelis Roos Cornelis Roos D -, Kurnia, D Devi Munandar, Devi Elis Hertini Eman Lesmana Endang Rusyaman Erick Paulus Erna Erna Erna Erna, Erna Fadillah, Ghiffaniaz Zahra Fahmi Candra Permana Fatimathuzahra, Alfia Azizah Fauziyah, Wida Nurul Firdaniza Firdaniza Ghiffaniaz Zahra Fadillah Ghiffari, Alif Muhamad Haq, Fadiah Hasna Nadiatul Heri setiawan Herlina Napitupulu Hesty Nurul Utami Ija Royana Irmansyah, Athaya Zahrani Johar, Dwindi Agryanti Juli Rejito Julita Nahar, Julita Kankan Parmikanti Mahrudinda, Mahrudinda Marisa Yulistiana Marisa Yulistiana, Marisa Melda Noereast Talytha Munadi Munadi Muslihin, Khoirunnisa R A Naufal Badruzzaman Naufal Badruzzaman Nurul Gusriani, Nurul Okta Yohandoko, Setyo Luthfi Olivia Anjanette Poppy Amriyati Poppy Amriyati, Poppy Rani Darmayanti Robbi, Muttaqien Rodhiya Royana, Ija S.S.A.S. Putri Salsabila, Thania Nur Siti Rabiatul Adawiyah Siti Rabiatul Adawiyah, Siti Rabiatul Stanley P. Dewanto Stanley P. Dewanto, Stanley P. Sudradjat Supian Sukono Sukono Sunarta Susanto Supian, Sudradjat Tegar Bratasena WKM Tomy Perdana Viona Prisyella Balqis Vionanda, Aurellya Vivian Wilhelmina Vivian Wilhelmina Wida Nurul Fauziyah WKM, Tegar Bratasena Zahrani Irmansyah, Athaya