Review Article
The Maximum Attainable Flow and Minimal Cost Problem in a Network
Amanuel Belachew Beyi,
Temesgen Alemu Godana*
Issue:
Volume 9, Issue 2, June 2024
Pages:
22-37
Received:
31 March 2024
Accepted:
6 May 2024
Published:
17 May 2024
DOI:
10.11648/j.ajmcm.20240902.11
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Abstract: This paper, presents an efficient algorithm that solves such a large class of optimization problems. Ford-Fulkerson determines the maximum flow in a network by iteratively augmenting flow paths until no further improvement is possible. On the other hand, Dijkstra's algorithm excels in finding the shortest path in a weighted graph, making it suitable for minimizing costs in network traversal. However, this paper simultaneously optimizes both objectives (flow and cost) dependently in unique iterations by considering all constraints and objectives holistically. The aim of this work is to develop efficient algorithms that can handle complex optimization problems in transportation, network design, and other fields, ultimately improving resource utilization and minimizing costs as its crucial for enhancing decision-making processes, improving efficiency in resource utilization, and achieving cost savings in diverse applications ranging from transportation networks to production planning. This paper deals about formulating the linear programming for the optimizations problems and finding the maximum amount of flow that can be sent from a source node to a sink node while minimizing the total cost of sending that flow by using simplex method (Two phase method). Through computational experiments and case studies, everybody demonstrate the effectiveness and efficiency of the proposed approach in solving real-world network flow problems. Our method yields efficient algorithms with in smallest numbers of iterations and time that enable the optimal allocation of resources within networks, achieving both maximum flow and minimum cost simultaneously.
Abstract: This paper, presents an efficient algorithm that solves such a large class of optimization problems. Ford-Fulkerson determines the maximum flow in a network by iteratively augmenting flow paths until no further improvement is possible. On the other hand, Dijkstra's algorithm excels in finding the shortest path in a weighted graph, making it suitabl...
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Research Article
Matlab-Simulink Model of CHMT for Internal Climate in Greenhouses
Dickson Kande,
Fredrick Nyamwala*,
Titus Rotich*
Issue:
Volume 9, Issue 2, June 2024
Pages:
38-53
Received:
31 March 2024
Accepted:
16 April 2024
Published:
27 August 2024
Abstract: Over the past twenty years, Kenya's food security has been threatened by the sub-division of land into tiny areas and the clearance of forests to make way for settlement. These actions have an impact on soil moisture, rainfall patterns, and regional temperature changes. Clear response plans and adaption techniques have been required to address the threats that have arisen. Greenhouse farming, where warmer temperatures are attained and the impact of unfavourable weather conditions on plants is mitigated by the enclosure, is one strategy being used to combat the production of food and climate change. Nevertheless, crop production and quality are negatively impacted by traditional techniques of regulating temperature and humidity through arbitrary opening and closing of the greenhouse walls. In light of this, the goal of this research was to enhance greenhouse farming as it exists today by implementing a dynamic, adjustable system that would create ideal climate conditions for plant growth. This mostly entailed controlling the greenhouse's humidity, temperature, and vapour pressure deficit to the ideal ranges needed by various plants. The humidity and air temperature within the greenhouse were the controlled microclimate conditions. These were accomplished by simulating the convectional heat transfer and mass transfer that occur inside the greenhouse to control the temperature and humidity, and by developing mathematical model utilizing differential equations. Proportional Integral Derivative (PID) was utilized to automatically modify SIMULINK, a block-based modelling and simulation tool. Regardless of the different external conditions, the numerical values for internal temperature and humidity were calculated and graphically depicted. The model made it possible to modify the outcomes according to the needs of the plant. To increase crop productivity in greenhouse farming, it was suggested that a physical prototype model be constructed and integrated into the greenhouse construction.
Abstract: Over the past twenty years, Kenya's food security has been threatened by the sub-division of land into tiny areas and the clearance of forests to make way for settlement. These actions have an impact on soil moisture, rainfall patterns, and regional temperature changes. Clear response plans and adaption techniques have been required to address the ...
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