International conference on mathematics and mathematics education 2025

Permanent URI for this collectionhttps://ir.lib.pdn.ac.lk/handle/20.500.14444/5977

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A Case study on replacement theory to estimate the economic lifetime of an offset printing machine
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07) Gunasekara, A.D.A.I.; Daundasekera, W.B.
Replacement Theory, which is a branch of Operations Research, deals with determining the optimal time to replace equipment, assets, or components to minimize their operational and maintenance costs, and maximize operational efficiency. For industries that depend on machine intensive processes, identifying the optimal time to replace the machine is essential to maintain cost-effective operations. This study proposes a mathematical model to find the economic life of an offset printing machine which enables efficient cost management. In this study, Heidelberg SM74-4 offset printing machine is considered as a case study to demonstrate the model. The factors considered in the development of the model are operational costs, maintenance costs, depreciation, electricity consumption, and bank loan payments. In this study, to make it more realistic, the present value of money is also incorporated into the model. The objective function of the model is the Average Total Cost (ATC) which is calculated using the sum of all related expenditures, including maintenance and operating costs of the machine. To determine the time to replace the machine, the ATC is calculated for each year, when the machine is in operation. This yearly calculation terminates when the ATC, which is a unimodal function, reaches its critical point. The critical point is proven to be the most economical point to replace the machine. This study has a great impact on the printing and manufacturing industries in addition to its theoretical achievements. It determines the optimum replacement time for the Heidelberg SM74-4 by considering factors such as maintenance, energy, and loan payments. The findings show that the economic life of the machine ends after 17 years, even though it was in operation for 20 years. This extended time period shows the machine’s durability but also highlights increased costs and declining efficiency over time. While the model offers a practical framework for making decisions on replacements, it does not currently account for factors like inflation and market fluctuations. Future improvements could enhance its relevance and adaptability. In conclusion, this data-driven approach supports timely and cost-effective decision-making, improving operational efficiency and financial outcomes in machinery-dependent industries.
Ant colony optimization algorithm to solve deterministic multi-objective assignment problem
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Pathirana, C.P.S.; Daundasekera, W.B.
This study proposes a metaheuristic algorithm known as the Ant Colony Optimization Algorithm (ACOA) to solve the deterministic Multi-Objective Assignment Problem (MOAP). MOAP consists of several objectives to be optimized simultaneously. ACOA is one of the most prominent biologically inspired algorithms to solve optimization problems. Multi-Objective Ant Colony Optimization Algorithm (MOACOA), which is based on the ACOA, is a probabilistic approach for finding the optimal path of the MOAP. The proposed algorithm is parameterized by the number of ant colonies and the number of pheromone trails. In this study, MOACOA is applied to solve a MOAP, where the assignment costs are randomly generated following the Uniform distribution. Initially, for the first row of each of the Assignment Cost Matrix (ACM) corresponding to the objective function, the transition probabilities with equal weights are determined by applying the MOACOA. Then, under the pheromone update rule, the optimal assignment for the first row of each ACM is determined by comparing the cumulative probability solution set and the generated random set. The optimal solution for the first row of each of the ACMs is recorded, and afterward, the row and the column of each of the ACMs corresponding to the selected path are excluded. This process is repeated for the rest of the rows of each of the ACMs and the optimal solution with respect to each row is recorded. This process terminates when the proposed iterative technique converges to the optimal solution of the MOAP. The proposed algorithm is coded in Python programming language and the efficiency of the algorithm is compared with an existing method known as Technique for an Order of Preference by Similarity to Ideal Solution (TOPSIS). The proposed MOACOA is proven to be capable of solving large-scale MOAP in less computational time compared to the TOPSIS method.
Computing h- function of the complement of a slit via parallel-slit mapping and validation via different conformal mapping
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Arunmaran, M.; Piriyalucksan, P.
In potential theory, h-function is a concept intimately connected to Brownian motion and serves as a method for depicting the geometry of a domain. Consider a particle released from a fixed location z₀ in a region Ω and permitted to move randomly throughout Ω, exhibiting Brownian motion, until it first encounters the boundary. The distance from the starting point z₀ at the time of impact is recorded. Also, the process with millions of Brownian particles that were discharged from the same point z₀ is repeated. This information is formally expressed as a function known as the h-function of the given region Ω with respect to the specified basepoint z₀. The h-function is an increasing function and takes only the values in the interval [0,1]. This study forms the h-function of a simply connected region Ω formed by deleting a slit from the complex plane when the basepoint z₀ is fixed along the line of the slit, by two different methods. The first method starts with parallel-slit mapping, which is in terms of the prime function. This map transforms the interior of the unit disc D(ζ) to the region Ω. A Cayley-type map is used to transform the region D(ζ) to the lower half-plane and the boundary of the disc to the real line. A function W(ζ) is formulated whose imaginary part is harmonic, and the Im[W(ζ)] evaluated at ζ₀ produces the h-function of the region Ω, where ζ₀ is the preimage of the basepoint z₀. The second method is used to cross-check the formed h-function. In this method, a sequence of conformal maps whose composition transforms the given region Ω to the half-plane is used instead of the prime function. Subsequently, the intersection between the boundary of the region Ω and the closed ball of radius r centered at z₀ and its image in the half- plane is traced. Both methods produce the same h-function.
Some results related to a new type of connectedness in topological spaces
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Piriyalucksan, P.
General topology facilitates the study of important qualitative properties of spaces and maps, such as continuity, connectedness, and compactness. New forms of continuity and compactness have recently been introduced in topology; they are referred to as F-continuous and F-compact, respectively. An open subset A of the topological space (X, τ) is called F-open if A̅\A is finite. A map k: (X, τ) → (Y, σ) is F-continuous, if k⁻¹(U) is F-open in X for every open set U in Y. Similarly, a topological space (X, τ) is F-compact if and only if any open cover of X has a finite subcover of F-open sets. This study focuses on some recent findings concerning the new concept called F-connectedness. A topological space (X, τ) is called F-connected, if it cannot be written as the union of two disjoint F-open sets. Initially, this study proves that a surjective F-continuous image of an F-connected space is connected. In general, the continuous image of a connected space is connected, however in F-setting, surjectivity should be needed. Subsequently, the following is proved: If (X, τ) is a F-connected space, and (Y, σ) is a F- homeomorphism of(X, τ), then the latter space is F-connected. Next, the study proves that if A, B are two subsets of a topological space such that A ⊆ B ⊆ A̅and A is F-connected, then B is also F-connected. Finally, it is proved that the finite union of a family of F-connected sets is also F-connected, provided that the intersection of the family is non-empty. In the future, it is intended to extend this study to investigate F-separation axioms. Also, this study expects to extend the results obtained to bitopological or tritopological environments.
A Non-linear optimization model for cost-effective and space- efficient architectural layout design: a case study of a single-story residential building
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Herath, H.M.H.M.G.T.M.; Daundasekera, W.B.
Reducing construction costs while optimizing usable space according to client’s preferences is essential for achieving economical and functional building designs. Architectural layout design optimization (ALDO) addresses this challenge by refining building layouts to achieve an optimal balance between cost efficiency, functionality, and spatial usability while satisfying predefined constraints. This research focuses on optimizing a building layout by developing a Non-linear Optimization model. The objectives are to minimize total construction cost and maximize the usable area while adhering to dimensional constraints, such as width, length, and total area. The case study focuses on a residential building located in the Central Province, Sri Lanka. Construction costs are calculated using the Building Schedule of Rates (BSR) Central Province–2024, while dimensional constraints for rooms are based on the Planning and Development Regulations issued by the Minister of Urban Development and Housing (MUDH). Data and background information for the study were gathered through BSR, MUDH, literature review, and consultation with a building architect. The case study is conducted on a rectangular land with dimensions 18 × 9 m²(60 × 30 feet²). The formulated model is solved using Excel Solver and compared with the manual design; the optimized results demonstrate high flexibility, allowing adjustments to better meet client preferences while effectively addressing the objectives. Results were exhibited using 3D graphs in OriginPro, highlighting the impact of design weights on cost and usable area, and offering insights to support informed decisions by clients and stakeholders. The study assumes fixed material and labor rates based on BSR–2024, a uniform wall height of 3 meters, and a single-story residential layout with rectangular-shaped rooms. The limitations of the study are, excluding structural elements, aesthetic considerations, and multi-story design aspects. This study highlights the effectiveness of ALDO and suggests future work on multi-story layouts, structural and aesthetic integration, and the inclusion of additional design preferences.
A Novel mixed integer linear programming model to solve multiple trip vehicle routing problem
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) T. Samarakkody
The complexity of the development of mathematical models for vehicle routing problems increases with the addition of more variables and constraints. In this study, a mathematical model was developed for a multiple-trip vehicle routing problem by relaxing the constraints of the single-trip model. The novelty has brought to the study through a simple three-index formulation developed for the multiple-trip vehicle routing problem, with a fewer number of constraints. The model was developed using the mixed integer linear programming (MILP) technique considering a heterogeneous fleet of vehicles, time window, pickups, capacity constraints and single deport. Three-index formulation without a trip index and a new integer variable for the number of trips assigned to a vehicle in a given time unit are introduced into the model. Since most of the past studies considered the number of vehicles available for the routing plane with a separate index, this study reduces complexity and facilitates an easy- solving approach. Hence, it reduces the difficulty of determining vehicle utilization rates and provides managerial implications through identifying under-utilized resources. The model was tested and solved using a real-world data set from a small-scale enterprise in Sri Lanka by applying the Branch and Cut algorithm. Time and distance matrices and vehicle capacities were fed to the model. The output of the experimental analysis showed a clear reduction in the distance traveled and the number of vehicles used compared with the method adopted by the enterprise. It shows that the proposed method can be applied to real-world cases to reduce transportation costs and the complexity of vehicle scheduling. This study contributes to the existing knowledge gap through the proposed mathematical model.
Optimizing investment portfolios using quadratic modelling for risk and return management
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Fernando, M.L.N.V.; Rodrigo, W.N.P.
The economic crises of recent years have underscored the critical role of diversification in investment portfolios to ensure stability and optimal returns in unpredictable and volatile markets. Traditional portfolio management techniques often fall short in effectively balancing risk and return, particularly during periods of financial uncertainty. As financial markets become increasingly complex, there is a growing need for advanced mathematical optimization techniques that can efficiently allocate assets while minimizing exposure to risk. This study explores the applicability of quadratic programming (QP) as a competitive portfolio optimization method, emphasizing its capability to reduce risk while maintaining adequate returns across a diversified range of asset classes. The study formulated and implemented a QP model for a case study to analyze and compare the proposed method with an existing optimization method. A comparative analysis evaluates the computational efficiency, feasibility, and performance of using QP in dynamic financial environments. The results demonstrate that QP enhances portfolio allocation strategies, ensuring better sector diversification and risk-adjusted returns. Furthermore, the research highlights the scalability and adaptability of QP in managing investment portfolios of varying complexity and size, making it a valuable technique for financial decision-making. The findings establish QP as a tool in modern portfolio management, offering a structured, data-driven approach for risk minimization, enhanced diversification, and long-term financial stability. Also, this study reinforces the potential of QP as a computationally efficient, flexible, and robust optimization technique, addressing the limitations of traditional portfolio selection methods and paving the way for more sophisticated financial strategies in fluctuating market conditions.
An Upper bound for star chromatic index of simple connected sub-cubic graphs
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Fernando, C.L.R.; Athapattu, A.M.C.U.M.
This study explores the star chromatic index χ′st(G) of any simple connected sub-cubic graph G, which is a significant parameter in graph theory that measures the minimum number of colours needed to colour the edges of a graph such that no path or cycle of length 4 is bi- coloured. The idea of star edge colouring was introduced by Liu and Deng in 2008, motivated by its vertex version, and since then, it has been studied extensively by many authors. Computing the star chromatic index for a graph can be a challenging problem, and finding an algorithm for it is an active area of research in graph theory. Numerous studies have been conducted introducing upper bounds for the star chromatic index, and the best known upper bound is 7. The primary objective of this study is to establish a better upper bound for the star chromatic index of simple connected sub-cubic graphs, partially answering to the conjecture posed by Dvorak et al. in 2013. The method of colouring introduced in this study is based on categorizing any simple connected sub-cubic graph with respect to its connectivity. Subsequently, it is decomposed into a matching (possibly with paths of length 2) and a collection of disjoint paths and cycles such that every vertex is contained in some path or cycle in the collection. Showing χ′st(G) = 6 for the 3-regular graph of 10 vertices, where all the non-adjacent edges in the matching and in the collection are at a distance 2 from each other was a major result, and it was extended to prove that χ′st(G) ≤ 6 for any simple connected sub-cubic graph.
Z-Sets in large scale geometry
(Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Laka, 2025-07-04) Chandralal, P.D.D.A.; Amarasinghe, A.K.
This study introduces an analogous version of the Z-set in large-scale geometry, inspired by its foundational role in infinite-dimensional topology. A closed subset A ⊆ X is called Z-set of X, if there exist arbitrary small maps from X into X\A; that is, for every open cover U of X, there exists a map from X into X\A which is U-close to the identity. Although the Z-set does not seem very appealing, it is the most central concept in infinite-dimensional topology. Extending this idea to large-scale geometry, we define Coarse Z-sets by analyzing their behavior under arbitrarily small maps of X into X\A and examining their structural properties in a global context. A subset A ⊆ X is called Coarse Z-set if there exists a function from X into X\A that is “close” to identity map in the sense of large-scale geometry. Characterized by maps that are “close” to the identity, the Coarse Z-set can be thought of as a small set in a larger space; removing it does not change the overall structure of the original space. This study demonstrates that if a subset is a Coarse Z-set, the associated function is a quasi-isometry, guaranteeing coarse equivalence between the space and its complement. This equivalence preserves asymptotic dimensions, as expressed by asdim(X) = asdim(X \ A). Furthermore, Coarse Z- sets are invariant under coarse equivalence, showcasing their robustness in large-scale geometry.

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