Labor allocation is an important factor in coffee harvesting because differences in labor productivity, labor costs, working hours, and harvesting capacity can affect the effectiveness of resource utilization. This study aims to formulate and solve a mathematical optimization model for determining the optimal allocation of daily and contract labor to maximize coffee harvesting productivity at Mr Abdur’s coffee plantation. A quantitative mathematical optimization approach with a case study design was employed. Field data were collected through interviews and discussions with the plantation owner and included labor costs, working hours, harvesting capacity, and labor productivity. The problem was formulated as a Linear Programming model and first solved using the Simplex method as a continuous relaxation. Because the resulting decision variable was fractional. The model was subsequently solved as an Integer Linear Programming problem using the Branch and Bound method. The Simplex relaxation produced a continuous solution of approximately and , with an objective value of approximately 450,72 kg. Since the number of workers must be an integer, Branch and Bound was applied and resulted in the optimal integer solution and , yielding a maximum modeled productivity of 450 kf. This allocation requires 120 labor-hours and IDR 900.000 in labor expenditure, while its harvesting capacity reaches 3.120 trees, satisfying the available limits of 240 labor-hours, IDR 1.000.000, and 3.125 trees. The results demonstrate that the Simplex-Branch and Bound approach provides a mathematically feasible and operationally applicable solution for discrete labor allocation in coffee harvesting. The proposed model can support more systematic labor planning and resource allocation in smallholder coffee plantations.
This study examines the joint evolution of conventional and Islamic banking assets in Indonesia using a non-autonomous Lotka–Volterra competition model. The model was calibrated to a compiled annual series for 2016–2024 with time-dependent intrinsic growth and capacity terms, constrained nonlinear least squares, and adaptive Runge–Kutta integration. The working series includes two interpolated observations (2017–2018). For these inputs, the time-dependent model achieved in-sample MAPE of 1.52% for Islamic banking and 2.22% for conventional banking, while the fitted interaction coefficients were near zero under the imposed bounds. Nevertheless, the constant-parameter model had the lowest reported AICc, and five rolling-origin tests produced mean errors of 7.69% and 5.50%, respectively. Bootstrap and enlarged-bound analyses indicated weak identification of several growth and capacity parameters. Frozen-time Jacobian calculations yielded locally stable equilibria for the autonomous systems evaluated at the observed years, without establishing stability of the full non-autonomous system. A continuation to 2028 produced a conditional Islamic-market-share median near 7.2% and a reported 90% bootstrap interval of 6.4–9.2%. These outputs describe the behavior of the retained dataset and model assumptions rather than a causal effect of the 2021 BSI merger or a validated financial forecast. The results underscore the importance of complexity penalties, identifiability analysis, and source-data provenance in aggregate financial-dynamics modeling.
This study develops a three-dimensional nonlinear ordinary differential-equation model linking normalized deposits, loans, and liquidity through liquidity-dependent deposit pressure. The analysis derives the equilibrium conditions while retaining the regularization parameter, examines conditional positivity and boundedness, and evaluates local stability using the Jacobian and Routh–Hurwitz criterion. The nonnegative orthant is not generally forward invariant; therefore, global positivity is not claimed. For a literature-informed illustrative baseline, the model admits two positive interior equilibria. The lower equilibrium (D=0.165214, L=0.141010, R=0.047210) is unstable, whereas the upper equilibrium (D=0.999790, L=0.853321, R=0.285690) is locally asymptotically stable. The origin is also locally stable in the mathematical domain. Recalculated fourth-order Runge–Kutta simulations and ±5% one-at-a-time sensitivities show how the 50-year normalized indices respond to baseline parameters; deposit carrying capacity has the largest positive local sensitivity for deposits under the selected conditions. The numerical parameters are assumed or literature-informed rather than fitted to historical banking observations. Accordingly, the model offers a conditional theoretical account of nonlinear banking feedback and requires formal parameter estimation and external validation before operational or regulatory application.
Mathematical critical thinking in digital learning requires purposeful interaction among pedagogical tasks, digital tools, and students' interpretation and justification of mathematical ideas. This systematic literature review examines the complementary functions of GeoGebra, Problem-Based Learning (PBL), Artificial Intelligence (AI), Meaningful Learning, and Design Thinking. The manuscript reports a qualitative thematic synthesis of 15 primary empirical studies published within the 2020–2026 search period and identified through Scopus, ERIC, Google Scholar, DOAJ, and Garuda. The available reporting record does not preserve complete database-specific retrieval and screening counts or item-level methodological appraisal results; the review therefore does not claim a fully reproducible PRISMA 2020 selection record. Across the cited evidence, GeoGebra provides dynamic mathematical representations; PBL structures problem-centred inquiry; AI offers feedback and alternative approaches that require mathematical verification; and Meaningful Learning emphasizes connections with prior knowledge. Design Thinking is proposed as a learner-centred organizing process through Empathize, Define, Ideate, Prototype, and Test. These differentiated functions support a conceptually coherent, potentially testable instructional pathway rather than a demonstrated effect of the combined intervention. Future research should verify the primary-study corpus, document review procedures in full, and test the proposed relationships in classroom settings.
Abstract algebra requires students to coordinate formal definitions, algebraic properties, and proof structures rather than rely on procedural recall alone. This study describes the cognitive processes demonstrated by fifth-semester mathematics education students when solving introductory group theory problems, using the first four categories of the revised Bloom’s taxonomy as an analytical lens. The study employed a qualitative descriptive approach at the Mathematics Education Study Programme, Alkhairaat University, from 15 September to 6 November 2025. Four students (LF, WS, AR, and N), selected purposively from students enrolled in the algebraic structures course, completed two written tasks and participated in interviews used to clarify their responses. The first task examined students’ definitions of a group, while the second required them to state and prove a theorem about group properties. All four students recalled central elements of the group definition, although the precision of their explanations varied. In the proof task, LF produced a coherent argument for the uniqueness of the identity element, whereas WS, AR, and N attempted to use familiar group properties but showed difficulties in theorem selection, property identification, or the logical ordering of operations. Across the four cases, remembering was consistently supported, whereas evidence of understanding was partial for several participants, and applying and analyzing were most clearly demonstrated in LF’s proof. These findings suggest that assessment of group theory learning should distinguish the recall of definitions and properties from the ability to coordinate them within a valid proof.
