Metode Average-Min (AMM) Untuk Mencari Initial Basic Feasible Solution Pada Transportation Problem

Nathania, Nadia Evi (2026) Metode Average-Min (AMM) Untuk Mencari Initial Basic Feasible Solution Pada Transportation Problem. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Transportation Problem (TP) merupakan cabang ilmu matematika penting yang digunakan oleh berbagai sektor industri untuk meminimalkan biaya. Sebagai sebuah teknik optimasi, TP dapat dimodelkan secara tepat menggunakan pemrograman linear. Untuk mendapatkan solusi optimal dalam TP, langkah pertama yang harus dilakukan adalah menghitung Initial Basic Feasible Solution (IBFS), yang kemudian akan dioptimalkan pada tahap berikutnya. Penelitian ini mengusulkan sebuah metode IBFS bernama Average-Min Method (AMM) yang dikembangkan melalui modifikasi struktural terhadap Maximum Range Method (MRM). Transformasi dilakukan dengan mengubah penalti nilai ekstrem pada MRM menjadi selisih antara rata-rata biaya sel aktif dan biaya minimum. Modifikasi ini bertujuan untuk meredam dampak data outlier dan merepresentasikan karakteristik distribusi biaya matriks secara lebih akurat. Evaluasi dan analisis performa dilakukan dengan membandingkan hasil algoritma yang diusulkan dengan beberapa algoritma lain yang sudah ada sebelumnya. Hasil pengamatan menunjukkan bahwa metode AMM mampu menghasilkan IBFS yang optimal baik untuk TP seimbang maupun tidak seimbang, dengan jumlah contoh soal solusi optimal dicapai adalah 42 dari 50 contoh soal, menunjukkan peningkatan dari MRM yang hanya mencapai 36 contoh soal. Selain itu, metode ini juga mampu menghasilkan solusi IBFS yang asimtotik atau sangat mendekati solusi optimal, karena cenderung memiliki persentase deviasi dari nilai optimal yang rendah dibandingkan dengan algoritma lainnya, yaitu sebesar 0.49%.
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The Transportation Problem (TP) is a vital branch of mathematics utilized by various industrial sectors to minimize distribution costs. As an optimization technique, TP can be accurately modelled using linear programming. To obtain an optimal solution in TP, the initial step involves calculating the Initial Basic Feasible Solution (IBFS), which is subsequently refined in the next phase. This study proposes a new IBFS method called the Average-Min Method (AMM), developed through a structural modification of the Maximum Range Method (MRM). The transformation is achieved by altering the extreme value penalty used in MRM into a dinamic gap between the average cost of active cells and the minimum cost. This modification aims to mitigate the impact of outlier data and represent the matrix cost distribution characteristics more accurately. Performance evaluation and analysis were conducted by comparing the results of the proposed algorithm against several existing benchmark algorithms. The experimental results demonstrate that the AMM algorithm successfully generates an optimal IBFS for both balanced and unbalanced TPs, achieving the direct optimal solution in 42 out of 50 test cases, which indicates an improvement over MRM that only achieved 36 cases. Furthermore, this method is capable of producing asymptotic solutions that closely approximate the optimal solution, as it yields a remarkably low average deviation percentage of 0.49% from the optimal value compared to other algorithms.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Transportation Problem, IBFS, biaya minimal, solusi optimal, algoritma, Transportation Problem, IBFS, minimal cost, optimal solution, algorithm
Subjects:	Q Science > Q Science (General) > Q180.55.M38 Mathematical models Q Science > QA Mathematics > QA401 Mathematical models. Q Science > QA Mathematics > QA9.58 Algorithms T Technology > T Technology (General) > T57.6 Operations research--Mathematics. Goal programming T Technology > T Technology (General) > T57.74 Linear programming
Divisions:	Faculty of Intelligent Electrical and Informatics Technology (ELECTICS) > Informatics Engineering > 55201-(S1) Undergraduate Thesis
Depositing User:	Nadia Evi Nathania
Date Deposited:	25 Jul 2026 12:04
Last Modified:	25 Jul 2026 12:04
URI:	http://repository.its.ac.id/id/eprint/138027

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