Journal of Mathematical Sciences and Optimization

Hamilton Cycle on the Wheel Graph

Fadhila Anggraini — 2024-07-31

This article discusses the existence of the Hamilton cycle in the wheel graph by constructing steps to find the existence of the Hamilton cycle. A graph that has a Hamilton cycle is called a Hamilton graph, A circle graph is a graph where each vertex has a degree of two, denoted by C_n. A graph obtained by adding a central vertex to a circle graph and connecting it to all the vertices of the circle graph is called a wheel graph, denoted by W_n . If the wheel graph W_n has m where m is the number of that replaces each point in W_n then it can be denoted by W^m_n . Then, in the wheel graph W^m_n is the number of outermost points of W^m_n added to 1 point located in the center. Based on the construction, it is found that there is a Hamilton cycle in the wheel graph. In the wheel graph W_n contains Hamilton cycle for n>=3. Furthermore, the wheel graph W^m_n also contains Hamilton cycle for n>=3 and m>=1, but the image of the wheel graph W^m_n is only perfectly drawn for n=2k where k is an integer. This is because there are colliding edges in the wheel graph for n=2k-1 where k is an integer.

The Stability Results for a Singular System of Generalized p-Fisher-Kolmogoroff Steady State Type

Salah Khafagy — 2024-07-31

In the present paper, we are interested in the study of the stability results of nontrivial positive weak solutions for the generalized p-Fisher-Kolmogoroff nonlinear steady state problem involving the singular p-Laplacian operator. We provide a simple proof to establish that every positive solution is stable (unstable) under some certain conditions.

Use of the Discrete Facility Location Model in Optimizing the Number and Location of Fire Stations: A Case Study

Erfa Julia — 2024-07-31

This article discusses the application of discrete facility location model in optimizing the number and location of fire stations in Pekanbaru City. This quantitative model uses three basic discrete facility location models: the location set covering problem (LSCP), maximum covering location problem and the p-median problem. The mathematical model in this problem is solved using the LINGO 18.0. Computational results show that this discrete facility location model can determine the minimum number of fire stations, location of fire stations, maximum fire stations services and the allocation of each subdistrict to the fire stations

Distribution Cost Optimization Using Average Opportunity Cost Method and Average Total Opportunity Cost Method

Lisa Harianto — 2024-07-31

Every company carries out distribution activities to distribute goods to consumers. PT Petrokimia Gresik is one of the providers of organic fertilizer called petragonik fertilizer. They must ensure that distribution from source to destinations does not occur scarcity of organic fertilizers. Selection of inappropriate distribution channels, very high transportation costs and to meet the number of different requests for each detination are factors that can hinder the process of distributing goods. The main aim of this research is to help PT Petrokimia Gresik in solving cost optimization problems related to the distribution of goods. The methods used in this research are Average Opportunity Cost Method (AOCM) and Average Total Opportunity Cost Method (ATOCM), then continued using Modified Distribution (MODI) for optimization test. Based on the research results, it is found that the initial cost of distribution using AOCM is smaller than ATOCM. So for the case of PT Petrokimia Gresik, the AOCM method is better than ATOCM. While the optimization test results get the minimum distribution cost of IDR194.350.000.

SEPIR Model of Skin Cancer Caused by Exposure to Ultraviolet Light

Devi Yanti — 2024-07-31

Skin cancer is a disease that occurs due to a change in the nature of normal skin cells into abnormal skin cells, where these cells will divide into abnormal forms in an unconditioned manner due to DNA damage. This research explains the stability of the SEPIR model in skin cancer caused by exposure to ultraviolet light. The population is divided into five subpopulations, namely, susceptible (S), latent period with early symptoms (E), pre-cancer (P), infected (I), and recovered from skin cancer (R). Based on the model analysis using Jacobian matrix and eigen value, there is one equilibrium point free and one endemic equilibrium point for skin cancer and the basic reproduction number R0. The results of the stability test of the equilibrium test using basic reproduction number (R0) showed that if R0<1, then the equilibrium point free from skin cancer is asymptotically stable and if R0>1 the equilibrium point endemic to skin cancer is asymptotically stable.