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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Jambura Journal of Biomathematics (JJBM) Milang Journal of Mathematics and Its Applications Journal of Mathematics, Computation and Statistics (JMATHCOS)
Jaharuddin
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 Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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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.
THE EFFECT OF LONG-LASTING INSECTICIDAL NETS ON THE DYNAMICS OF MALARIA SPREAD IN INDONESIA Aprianti, Euis; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2443-2450

Abstract

Malaria is an infectious disease that can lead to death. Deaths from malaria globally have increased in 2020. So the spread of this disease is still a serious problem for society. The mathematical model used is the SIR-SI model, assuming that recovered individuals can be re-infected with malaria. Analysis was carried out on the effectiveness parameters of long-lasting insecticidal nets to determine their effect on the dynamics of the spread of malaria. The sensitivity analysis results showed that changes in the parameters of the effectiveness of long-lasting insecticidal nets had an inverse effect on the rate of spread of malaria. These results follow numerical simulations conducted using malaria case data in Indonesia (some assumptions). Thus, efforts can be made to suppress the spread of malaria by increasing the effectiveness of long-lasting insecticidal nets.
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.
NEW SCHEME OF MIGNOTTE (t,n) COLLABORATIVE SECRET SHARING ON CLOUD STORAGE Ekaputri, Dhea; Guritman, Sugi; 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/barekengvol19iss4pp2981-2992

Abstract

Cloud storage is an internet-based data storage service that allows users to collaborate to store, manage, and access data remotely. However, this collaborative characteristic creates challenges in security and privacy. One potential solution to these issues is implementing a collaborative secret sharing scheme. This research proposes a modified Mignotte collaborative secret sharing scheme by introducing a detector parameter to detect cheating. Additionally, the scheme is designed so that participants with multiple privileges only need to store a single share. The main contribution of this research is the integration of a cheating detection mechanism into the Mignotte collaborative secret sharing scheme while maintaining storage efficiency. Experimental results show that the scheme produces correct outputs across various test cases. The proposed modification enhances the security of the secret sharing scheme for cloud storage applications by protecting against cheating and unauthorized access. However, the current scheme is limited to detection without identifying the cheater. Future research can focus on developing mechanisms for further identifying cheaters to enhance overall security.
Robust Optimization of Vaccine Distribution Problem with Demand Uncertainty Fikri, Faiqul; Silalahi, Bib Paruhum; Jaharuddin, Jaharuddin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20035

Abstract

This study proposes a multi objective optimization model for vaccine distribution problems using the Maximum Covering Location Problem (MCLP) model. The objective function of the MCLP model in this study is to maximize the fulfillment of vaccine demand for each priority group at each demand point. In practice, the MCLP model requires data on the amount of demand at each demand point, which in reality can be influenced by many factors so that the value is uncertain. This problem makes the optimization model to be uncertain linear problem (ULP). The robust optimization approach converts ULP into a single deterministic problem called Robust Counterpart (RC) by assuming the demand quantity parameter in the constraint function is in the set of uncertainty boxes, so that a robust counterpart to the model is obtained. Numerical simulations are carried out using available data. It is found that the optimal value in the robust counterpart model is not better than the deterministic model but is more resistant to changes in parameter values. This causes the robust counterpart model to be more reliable in overcoming uncertain vaccine distribution problems in real life. This research is limited to solving the problem of vaccine distribution at a certain time and only assumes that the uncertainty of the number of requests is within a specified range so that it can be developed by assuming that the number of demand is dynamic.
Dynamics System in the SEIR-SI Model of the Spread of Malaria with Recurrence Ahkrizal, Afdhal; Jaharuddin, Jaharuddin; Nugrahani, Endar H.
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.18754

Abstract

Mathematical model is used to describe the dynamics of the spread of malaria in human and mosquito populations. The model used is the SEIR-SI model. This study discusses the stability of the equilibrium point, parameter sensitivity, and numerical simulation of the spread of malaria. The analysis shows that the model has two equilibrium points, namely the disease-free and endemic equilibrium points, each of which is locally asymptotically stable. Numerical simulations show that the occurrence of disease cure in exposed humans causes the rate of malaria spread to decrease. Meanwhile, the presence of disease recurrence causes the spread of malaria to increase.
The Effect of Susceptible Immigrants in a System Dynamic on the Spread of Malaria in Indonesia Aprianti, Euis; Jaharuddin, Jaharuddin; Nugrahani, Endar H.
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.v6i3.8630

Abstract

The spread of malaria is a serious public health problem, including in Indonesia. The mathematical model is formulated to describe the dynamic nature of the spread of malaria. The model used in this article is the SIR-SI model. This article discusses the stability of the fixed point analyzed using the Jacobian matrix and Routh-Hurwitz criteria, bifurcation analysis using the Castillo-Chaves and Song Theorem, and numerical simulation of the effect of the rate of susceptible immigrants on the dynamics of the malaria by using data on malaria cases in Indonesia. The results of the analysis show that the stability of the fixed point is related to the basic reproduction number determined by the next-generation matrix, and bifurcation occurs when the basic reproduction number is equal to one. The results of numerical simulations show that in order to suppress the spread of malaria, it is necessary to reduce the rate of susceptible immigrants. 
Optimal Control Model for The Spread of Respiratory Infectious Diseases Through Preventive and Treatment Measures Boby Rinaldi; Toni Bakhtiar; Jaharuddin Jaharuddin
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 11 No. 2 (2026): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v11i2.1135

Abstract

Respiratory infectious diseases, including acute respiratory infections, pneumonia, MERS-CoV, and COVID-19, remain major global health concerns due to their high transmission rates and significant health and socioeconomic impacts. However, most existing models do not explicitly distinguish population groups based on behavioral factors such as mask usage nor integrate multiple interventions within a unified optimal control and cost-effectiveness framework. This study develops a modified seven-compartment epidemiological model that differentiates susceptible and infected individuals based on mask usage and incorporates four control variables: mask usage, vaccination, quarantine, and treatment. The optimal control problem is formulated using the Pontryagin Maximum Principle and solved numerically using the fourth-order Runge-Kutta method combined with the Forward-Backward Sweep Method. The results indicate that treatment is the most effective single intervention in rapidly suppressing infection, while the combination of all control measures provides the fastest overall reduction in transmission. In terms of cost-effectiveness, the four-control combination yields the lowest Average Cost-Effectiveness Ratio (ACER), indicating the highest efficiency, whereas the combination of mask usage, quarantine, and treatment produces a negative Incremental Cost-Effectiveness Ratio (ICER), implying greater health benefits at a lower additional cost compared to alternative strategies. These findings emphasize the importance of distinguishing between effectiveness and cost-efficiency in determining optimal intervention strategies.
Explicit Determinant and Inverse Formulas of Skew Circulant Matrices with Alternating Fibonacci Numbers Sapto Mukti Handoyo; Sugi Guritman; Teduh Wulandari Mas'oed; Jaharuddin Jaharuddin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32358

Abstract

Skew circulant matrices have various applications such as cryptography, signal processing, and many more. Their structure can potentially simplify their determinant and inverse computations. This study presents explicit formulas for the determinant and inverse of skew circulant matrices with entries from the alternating Fibonacci sequence. Elementary row and column operations are used to derive simple explicit formulas for the determinant and inverse. Computational tests using Wolfram Mathematica show that the algorithm built from these explicit formulas performs with much faster execution time than the built-in functions, especially for large matrix size. The proposed approach offers a practical method for the numerical computation of the determinant and inverse of these matrices
Co-Authors A. KUSNANTO A. T. WIBOWO Ahkrizal, Afdhal Ali Kusnanto Amalia, Imas Saumi Bib Paruhum Silalahi Blante, Trianty Putri Boby Rinaldi Cahyona, Dwizani Vinoma D. NATALIA Darmawan, Azhar Janjang E. N. BANO Ekaputri, Dhea Endar Hasafah Nugrahani Eti Rohaeti Euis Aprianti F. FAHRURRAZI F. HANUM Fahri Novi Farida Hanum Farida Hanum Fikri, Faiqul H. HASANNUDIN H. HERMANSYAH Hadi Sumarno I. ALDILLA L. D. OKTAFIANI L. HAKIM Mirza Farhan Azhari N. AIN Nugrahani, Endar H. Nur Aziezah P. SIANTURI Paian Sianturi Rauf, Nurul Maqfirah Sahamony, Nur Fitriyani Sapto Mukti Handoyo Siswandi SISWANDI, S. Sugi Guritman T. BAKHTIAR Tan, Elfina TEDUH WULANDARI Teduh Wulandari Mas'oed Toni Bakhtiar