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All Journal JURNAL EKONOMI DAN KEBIJAKAN PEMBANGUNAN Jurnal Manajemen dan Agribisnis Jurnal Keuangan dan Perbankan TELKOMNIKA (Telecommunication Computing Electronics and Control) SEMIRATA 2015 BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics International Journal of Industrial Optimization (IJIO) Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Milang Journal of Mathematics and Its Applications Jurnal Matematika Integratif Jurnal Ekonomi dan Pembangunan Indonesia MILANG Journal of Mathematics and Its Applications
Toni Bakhtiar
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Transportation

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PERENCANAAN PRODUKSI MENGGUNAKAN FUZZY GOAL PROGRAMMING: STUDI KASUS PRODUKSI JILBAB PADA KONVEKSI RUMAHAN Rafif Suhairi; Prapto Tri Supriyo; Hidayatul Mayyani; Toni Bakhtiar; Mochamad Tito Julianto
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.43-53

Abstract

Perencanaan produksi adalah salah satu strategi untuk menghadapi berbagai permasalahan dalam proses produksi. Tujuan yang ingin dicapai dalam perencanaan produksi cukup bervariasi. Seringkali tujuan-tujuan tersebut bersifat samar sehingga mengandung ketidakpastian atau fuzzy. Penelitian ini bertujuan memodelkan masalah perencanaan produksi sebagai model fuzzy goal programming (FGP). Ketidakpastian pada fungsi tujuan diselesaikan menggunakan fungsi keanggotaan fuzzy. Fungsi keanggotaan fuzzy dibangun dengan refererensi batas optimal dari masing-masing fungsi tujuan dan batas toleransi yang diinginkan oleh pembuat keputusan. Model FGP diformulasikan dengan pendekatan max-min Bellman-Zadeh. Model diimplementasikan menggunakan bantuan software LINGO pada industri rumahan konveksi jilbab di Kebon Jeruk, Jakarta Barat dengan fungsi tujuan meminimumkan waktu produksi dan memaksimumkan keuntungan. Hasil implementasi menghasilkan tingkat produksi jilbab yang mengoptimalkan fungsi tujuan, yaitu meminimumkan waktu produksi dan memaksimumkan keuntungan. Minimum waktu produksi yang diperoleh 2105 menit, sedangkan maksimum keuntungan yang diperoleh yaitu Rp 3.460.295,68.
Investigating Farmers’ Preferences For Crop Insurance Product Attributes in Indonesia Using The Bayesian Best-Worst Method Rachman, Muhammad Ibrahim; Nuryartono, Nunung; Arifin, Bustanul; Bakhtiar, Toni
Jurnal Manajemen dan Agribisnis Vol. 21 No. 2 (2024): JMA Vol. 21 No. 2, July 2024
Publisher : School of Business, Bogor Agricultural University (SB-IPB)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17358/jma.21.2.261

Abstract

Background: In 2015, the government of Indonesia launched a crop insurance program to anticipate the economic impact of crop failure on farmers due to the climate crisis. Despite the government's high premium subsidy, farmers' participation rate in crop insurance remains very low. Therefore, a study is needed to determine which product attributes in an agricultural insurance product are important to farmers and can affect their participation rate. Purpose: This study aims to investigate the factors that farmers consider when selecting a crop insurance product. Design/methodology/approach: The study focuses on the features of the Rice Farm Insurance (AUTP) product: total sum insured, product type, premium, risk coverage, and claim. The research was conducted by sending questionnaires to 110 farmers in 15 villages in Sliyeg, Indramayu. The Bayesian Best-Worst Method was used to analyze the data. Using a scale from 1 to 9, the best and worst criteria are compared pairwise.Findings/Result: The findings indicated that the total sum insured is the most crucial consideration for farmers when choosing a crop insurance product, followed by the premium, risk coverage, terms of claims, and product type. The top two positions of the product attributes are finance-related, indicating a need for improved understanding of agricultural risk management among farmers, extending beyond dollar amount, through continuous education. With the findings in this study, the government and other stakeholders need to develop effective strategies to increase farmers' awareness of the importance of insurance in managing their business risks. This study's added value comes from convincingly showing that farmers prioritize the amount of sum insured over premiums and other aspects. Other researchers can use this research as a springboard to learn more about the importance of product attributes in creating crop insurance products.Conclusion: The top two positions of the product attributes are finance-related, indicating a need for improved understanding of agricultural risk management among farmers, extending beyond dollar amount, through continuous education. With the findings in this study, the government and other stakeholders need to develop effective strategies to increase farmers' awareness of the importance of insurance in managing their business risks.Originality/value (State of the art): This study's added value comes from its convincingly showing that farmers prioritize the amount of sum insured over premiums and other aspects. Other researchers can use this research as a springboard to learn more about the importance of product attributes in creating crop insurance products. Keywords: climate crisis, crop insurance, Bayesian best-worst method, multi-criteria decision making, farmer preference
EFFECT OF THE GOVERNMENT INTERVENTION PROGRAM TO THE CROP INSURANCE PARTICIPATION LEVEL Rachman, Muhammad Ibrahim; Nuryartono, Nunung; Arifin, Bustanul; Bakhtiar, Toni
Jurnal Manajemen dan Agribisnis Vol. 18 No. 1 (2021): JMA Vol. 18 No. 1, March 2021
Publisher : School of Business, Bogor Agricultural University (SB-IPB)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17358/jma.18.1.1

Abstract

In addition to premium subsidies, Indonesia's government implements other intervention programs as a stimulus to boost farmers’ participation in Rice Farmers Business Insurance (AUTP). Therefore, this study aimed to investigate the effect of the government intervention program in 2019 that requires participation in AUTP as a prerequisite for redeeming subsidized fertilizer. This study also aimed to ascertain the socioeconomic factors that influence farmers to participate. Meanwhile, primary data were obtained through questionnaires distributed from March 23 to April 6, 2020, and completed by 103 farmers in 14 villages in Sliyeg, Indramayu. The data were analyzed with McNemar Test to determine the effect of farmers’ participation in AUTP when the government intervention program was implemented and terminated. Furthermore, Logistic Regression Analysis is used to ascertain the socioeconomic factors that influence farmers to participate. The result showed that the program affects their participation in AUTP. This level is higher when the program is enforced and decreased when terminated. The socio-economics variables that influenced farmers to participate in AUTP when implemented in the government program are land ownership status and land size, while only land size influenced them when terminated. Keywords: agriculture risk, consumer behavior, government stimulus, participation rate, premium subsidy
A heterogeneous fleet electric vehicle routing model with soft time windows Kinanti, Yoanda Astri Ayu; Bakhtiar, Toni; Hanum, Farida
International Journal of Industrial Optimization Vol. 5 No. 2 (2024)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/ijio.v5i2.9014

Abstract

The emergence of electric vehicles in distribution and logistics activities has brought significant benefits due to their unique characteristics, such as energy-efficient and lower carbon emissions. In the perspective of vehicle routing problem, electric vehicles pose challenging constraints regarding the limited battery capacity, and thus their traveling ranges, and the availability of charging stations. In this paper, we propose a model of the fleet electric vehicle routing problem (EVRP) with soft time windows, where a mixed integer linear programming framework is implemented in model formulation. The objective of mathematical programming is to minimize the total operational cost, which consists of a fixed cost, a traveling cost, a battery charging cost, and probably a penalty cost due to time window violation. We implement our model in two simple cases, namely homogeneous and heterogeneous fleets EVRPs, characterized by loading and battery capacities. Each case consists of one depot, five customers, two electric vehicles, and two charging stations. Optimal routes are obtained using the well-known branch-and-bound method under Lingo 17.0. It is found that the existence of charging stations may affect the routes selection and the implementation of soft time windows rather than hard time windows has been proven to increase the feasibility of routing problem.
Control Strategies for HIV/AIDS-Hepatitis B Coinfection using Optimal Control Approach and Cost-Effectiveness Analysis Annisa, Winda Nur; Bakhtiar, Toni; Silalahi, Bib Paruhum
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29601

Abstract

HIV/AIDS and Hepatitis B are infectious diseases caused by viruses, sharing similar transmission mechanisms. This study seeks to determine the most effective and cost-efficient strategies for controlling the spread of these diseases by utilizing a modified HIV/AIDS-Hepatitis B coinfection model with various control variables. The model divides the total population into nine subpopulations, each representing a specific disease state. Based on these classifications, the model incorporates four key control variables, namely Hepatitis B vaccination program, Hepatitis B treatment, HIV/AIDS treatment, and public health education program. The research employs optimal control theory and the Pontryagin Maximum Principle to address the optimal control problem to minimize infection rates and implementation costs over a specific periode. The Hamilton function integritas the dynamic system and cost function. The model is analyzed through simulations using parameter values from previous studies, then optimizing control variables to generate a numerically solved system of differential equations that uses Scilab 2024 software. Simulation result show that the optimal combination of four control strategies reduces HIV/AIDS-Hepatitis B infection by 79,2% in under ten years. Furthermore, the cost-effectiveness of different strategies is evaluated using the Average Cost-Effectiveness Ratio (ACER) and Incremental Cost-Effectiveness Ratio (ICER) indicates that single control strategies are more cost-efficient, while combining all four strategies is more expensive. However, successful implementation depends on financial constraints (limited vaccination and ARV treatment), healthcare infrastructure (availability of testing facilities), and public compliance with health education programs. Consequently, the proposed strategies are recommended for policymakers, with consideration of associated costs to ensure feasibility.
Optimal Control Strategies for Syphilis and HIV/AIDS Coinfection Transmission with Cost-Effectiveness Analysis Cahyona, Dwizani Vinoma; Bakhtiar, Toni; Jaharuddin, Jaharuddin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.28571

Abstract

Syphilis and HIV/AIDS are global health problems with significant impacts on society. The combination of these two infections can worsen the prognosis of patients and increase the economic strain on the health system. This study aims to develop an optimal control model in managing the spread of syphilis and HIV/AIDS coinfection by considering HIV/AIDS treatment, syphilis treatment, and preventive measures through condom use as dynamic control variables. Pontryagin's maximum principle is used to derive the optimality conditions. To theoretically investigate the impact of the control measures, this study analyzed five strategies related to the implementation of these controls using Scilab-2024.0.0 for simulate and evaluate of their effectiveness. The simulation results show that the combination of three control interventions is more effective in decreasing the prevalence of syphilis and HIV/AIDS coinfection compared to the application of one type of control alone. This combination strategy significantly reduces the infection rate by up to 86.04%, emphasizing the importance of a multifaceted intervention approach rather than a single control measure. Furthermore, a cost-effectiveness analysis was conducted by comparing the costs and effectiveness of various control strategies to determine the most efficient and economically feasible option. The results of the comparison indicate that although integrated intervention is the most effective strategy in minimizing infection rates, a strategy that focuses only on preventive measures through the use of condoms is a more efficient option when considering the balance between budget limitations and control effectiveness.
Optimasi Penjadwalan Mata Pelajaran Berbasis Kurikulum Merdeka Menggunakan Integer Linear Programming Permana, Rendy Candra; Hanum, Farida; Bakhtiar, Toni; Supriyo, Prapto Tri
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 2 August 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i2.32513

Abstract

Scheduling subjects in secondary schools implementing the kurikulum merdeka presents a complex challenge. Kurikulum merdeka demands a high degree of flexibility, fulfillment of individual learning needs, and integration between mandatory and elective subjects. The complexity increases due to time constraints, uneven distribution of teaching loads, limited classroom availability, and potential schedule conflicts between teachers and students. The manual approach, which is still commonly used, is often inefficient, time-consuming, and results in suboptimal schedules. To address these challenges, this study proposes an automated scheduling model based on Integer Linear Programming (ILP), implemented using LINGO 19.0 software. The model considers various real-world constraints, such as the maximum number of study hours per day, designated days for mandatory and elective subjects, the requirement for two consecutive periods per subject, and teacher availability. A case study was conducted for Grade XI at SMAN 58 Jakarta, involving 9 classes, 32 teachers, and 18 subjects (9 mandatory and 9 elective). The experimental results show that the model can produce efficient, conflict-free schedules, accelerate the scheduling process, and support equitable teacher workload distribution.
OPTIMASI BIAYA OPERASIONAL PADA KRL COMMUTER LINE DENGAN PEMBERANGKATAN KERETA Luciana, Shelen; Aman, Amril; Bakhtiar, Toni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 1 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (863.533 KB) | DOI: 10.30598/barekengvol14iss1pp123-134

Abstract

Optimal trainset dispatching can reduce passenger build-up and optimize operational costs. This research aimed to create a model of trainset dispatching for each time slot with minimum operational costs so that passenger demand can be met. The parameters in this research are the number of passengers getting-on and getting-off, the availability of each type of train series, train capacity, operational costs, and time limits for using the training series during operational hours. The model was formed into integer linear programming and resolved with Lingo 11.0 software. This model is applied in one direction from Bogor station to the Jakarta Kota commuter line. Trainset dispatching is done by selecting the 8 SF, 10 SF, and 12 SF trainset types with minimum operational costs at each time slot. The optimum results obtained during operational hours need to dispatch 56 trainset trips. Due to the limitations of the study the optimum operational cost of trainset dispatched is obtained 302C.
OPTIMIZING THE PROCESS OF PICK-UP AND DELIVERY WITH TIME WINDOWS USING ANT COLONY AND TABU SEARCH ALGORITHMS Amalia, Imas Saumi; Bakhtiar, Toni; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (730.711 KB) | DOI: 10.30598/barekengvol16iss2pp651-662

Abstract

The provision of goods shuttle services sometimes faces several constraints, such as the limitation on the number of vehicles, vehicle capacity, and service time, or the vehicle used has single transport access. To avoid losses, a strategy is needed in determining the optimal route and policy for arranging goods in the vehicle especially if there are two types of goods involved. Traveling Salesman Problem and Pick-up and Delivery with Handling Costs and Time Windows (TSPPDHTW) is a model of an optimization problem that aims to minimize the total travel and goods handling costs in the goods pick-up and delivery with the constraints previously mentioned. Solving that model using the exact method requires a very long computation time so it’s not effective to be implemented in real-life. This study aims to develop a (meta)heuristic based on Ant Colony Optimization (ACO) and Tabu Search (TS) to be ACOTS to solve TSPPDHTW with reasonable computation time. The development is carried out by adding functions of clustering, evaluating constraints, cutting tours, arranging of goods, and evaluating moves on the TS, as well as modifying transition rules. The result has a deviation of about 22% and 99.99% less computational time than the exact method.
OPTIMIZATION MODEL FOR MULTI-DEPOT ELECTRIC VEHICLE ROUTING PROBLEM WITH SOFT TIME WINDOWS WITH SCENARIO-BASED ANALYSIS Tan, Elfina; Bakhtiar, Toni; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2751-2764

Abstract

The adoption of electric vehicles has increased due to their cost-efficiency and environmental impact. However, limited battery capacity requires careful route planning to ensure vehicles complete deliveries efficiently. This study focuses on the Multi-Depot Electric Vehicle Routing Problem with Soft Time Windows (MDEVRPSTW), where electric vehicles can depart from and return to multiple depots, while serving customers within predefined time windows that allow limited violations with penalty costs. The model is formulated using Mixed Integer Linear Programming (MILP) and solved using the exact branch-and-bound method in Lingo 20.0. Two operational scenarios are considered: (1) vehicles must return to their original depot, and (2) vehicles are allowed to return to any depot. Hypothetical data is used to simulate delivery routes with varied time windows and battery capacity constraints. Results show that both scenarios produce feasible, cost-minimizing solutions. Allowing flexible depot return (scenario 2) consistently reduces total travel cost, highlighting the practical benefit of depot flexibility in real-world logistics. This model contributes to the EV routing literature by integrating multiple depots—both fixed and flexible return options—soft time windows, and battery constraints into a single formulation. However, it assumes constant travel speeds and does not account for charging durations, which presents an opportunity for future research.
Co-Authors Amalia, Imas Saumi Amanatul Amriyah Amril Aman Amriyah, Amanatul Annisa, Winda Nur Bambang Juanda Bib Paruhum Silalahi Bustanul Arifin Cahyona, Dwizani Vinoma Dedi Budiman Hakim Endy Jeri Suswono Erliza Noor Farhana Zahrotunnisa Farida Hanum Farida Hanum Farida Hanum Ferry Syarifuddin JAENAL EFFENDI Jaharuddin Kinanti, Yoanda Astri Ayu Kurniawan, Benny Robby Lana Syakina Luciana, Shelen Maya Widyastiti Mayyani, Hidayatul Mochamad Tito Julianto Nunung Nuryartono Nur Azizah Paian Sianturi Permana, Rendy Candra Prapto Tri Supriyo Qomah, Yusti Rachman, Muhammad Ibrahim Rafif Suhairi Rahma Nurlailawati Salsabilla, Kamilia Sugema, Iman Suhairi, Rafif Syakina, Lana Tan, Elfina