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Ahmed, Hasanain Hamed
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Nonlinear Programming Models for Robust Queuing Systems under Fuzzy Sets Ahmed, Hasanain Hamed
Jurnal Pendidikan Matematika Vol. 2 No. 4 (2025): August
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v2i4.1991

Abstract

This paper proposes a procedure for constructing the membership functions of performance measures in finite-capacity queuing systems where both arrival and service rates are represented as fuzzy numbers. By applying the (\alpha)-cut method, a fuzzy queue with finite capacity is transformed into a family of conventional crisp queues, allowing for more precise modeling of system characteristics. The study focuses on a queuing model with an unreliable server, where key parameters such as service and breakdown rates are fuzzy values. The developed parametric nonlinear programming approach facilitates the derivation of new constraints, providing a robust framework for analyzing queuing behaviors under uncertainty. The findings demonstrate that the proposed fuzzy mathematical model yields more realistic outcomes than traditional crisp models, thereby enhancing the applicability of queuing theory in practical scenarios.
Efficient Management of Resources in Complicated Transport Systems: The Use and Extension of Goal Programming to Overcome Multi -Objective Multi-Item Transportation Problems Ahmed, Hasanain Hamed
Jurnal Pendidikan Matematika Vol. 3 No. 2 (2026): February
Publisher : Indonesian Journal Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47134/ppm.v3i2.2468

Abstract

The study focuses on the important problem of resource allocation in large, complicated networks of transportation by utilizing goal programming (GP) technique. On the other hand, multi-objective multi-item transport problem is considered under competing objectives such as minimization of transportation costs and reduction in delivery time, environmental impact abatement plus maximization of vehicle utilization. In this paper, such a DSP model is constructed as viewed in its entirety and tightly embedded with a fuzzy goal reaching technique under realistic modifications of transportation circumstances. The model is calibrated using synthetic data from a hypothetical Iraqi road network, and the optimization problem is solved in WinQSP software. Comparison of the final solution indicates that the goal programming outperforms single-objective approaches, showing 18-24% cost reduction with less service level violation and carbon emission. The study is useful for urban logistics planning in the aim of sustainable development, and it also enriches the transport optimization analysis methods for decision maker. This is especially important in emerging countries characterized by limited resources, where “trade-offs” and not just the maximization of some social welfare function play a crucial role for managing transportation systems.
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