Hardijansyah, Ramadhan Arif (2024) Metode Transpose Minimum Selection (TMSM) Untuk Menemukan Initial Basic Feasible Solution Pada Transportation Problem. Other thesis, Institut Teknologi Sepuluh Nopember.
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05111940000162-Undergraduate_Thesis.pdf - Accepted Version Restricted to Repository staff only until 1 April 2026. Download (3MB) | Request a copy |
Abstract
Transportation Problem (TP) adalah sebuah permasalahan yang bertujuan untuk mengurangi hasil total biaya minimum, atau perkalian dari biaya atas jarak dan barang, untuk mendistribusikan sejumlah barang dari beberapa persediaan ke beberapa permintaan. Menemukan Initial Basic Feasible Solution (IBFS) merupakan langkah penting untuk menemukan biaya minimum dalam menyelesaikan TP. Namun, pendekatan-pendekatan IBFS yang sudah ada tidak selalu menghasilkan solusi awal yang terbaik, baik metode tradisional seperti North-West Corner Rule (NWCR), Least-Cost Method (LCM), dan Vogel's Approximation Method (VAM), maupun metode-metode yang lebih baru yang dikembangkan dari jurnal-jurnal penelitian seperti Juman Hoque Method (JHM) dan Total Opportunity Cost Matrix - Minimal Total (TOCM-MT). Tugas Akhir ini menggunakan sebuah teknik yang baru dan lebih efektif yang dikenal sebagai Transpose Minimum Selection Method (TMSM) untuk mendapatkan solusi awal yang lebih baik untuk masalah balanced Transportation Problem. TMSM merupakan pendekatan yang dikembangkan dengan Supply Selection Method (SSM) sebagai basisnya. Modifikasi yang dilakukan adalah cara penanganan bentuk matriks alokasi barang dan perubahan pemilihan alokasi dari maksimum ke minimum dalam kasus di mana terdapat difference yang sama antara First Least Cost (FLC) dan Second Least Cost (SLC). Proses penanganan bentuk matriks alokasi barang dilakukan dengan memeriksa apakah jumlah demand / jumlah supply ≥ C, dan jika kondisi tersebut tidak terpenuhi, maka dilakukan operasi transpose pada matriks TP. Modifikasi kedua adalah mengubah pemilihan alokasi dari maksimum ke minimum pada kasus dimana terdapat difference yang sama antara FLC dan SLC, yang membuat TMSM mengoptimalkan alokasi sumber daya, yang pada akhirnya menghasilkan solusi yang lebih efisien. Teknik ini dibandingkan dengan berbagai teknik IBFS seperti Vogel's Approximation Method (VAM), Juman Hoque Method (JHM), Total Opportunity Cost Matrix - Minimal Total (TOCM-MT), Bilqis Chastine Erma method (BCE), dan Supply Selection Method (SSM) untuk menilai efisiensinya. Sebanyak 40 data uji terdiri dari 31 data yang diambil dari berbagai publikasi jurnal, 4 kasus data sintesis, dan 5 data real digunakan untuk mengevaluasi teknik baru ini. Hasil penelitian menunjukkan bahwa TMSM menawarkan solusi dasar awal yang lebih baik dibandingkan metode lainnya, dengan solusi optimal yang dicapai pada 34 dari 40 data uji, dimana VAM, JHM, TOCM-MT, BCE, dan SSM mencapai solusi optimal masing-masing sebesar 22, 27, 23, 32, dan 27. Sebagai perbandingan, TMSM memiliki 16 hasil yang lebih unggul dari VAM dengan IP sebesar 40%, 10 hasil yang lebih unggul dari JHM dengan IP sebesar 25%, 14 hasil yang lebih unggul dari TOCM-MT dengan IP sebesar 35%, 4 hasil yang lebih unggul dari BCE dengan IP sebesar 10%, dan 9 hasil yang lebih unggul dari SSM dengan IP sebesar 22.5%. TMSM memiliki persentase deviasi rata-rata sebesar 0.58%, sedangkan VAM, JHM, TOCM-MT, BCE, dan SSM memiliki persentase deviasi rata-rata sebesar 2.83%, 2.17%, 1.51%, 1.12%, 1.80%, dan 0.58%. Hasil analisis menunjukkan bahwa TMSM memberikan nilai optimal tertinggi dengan total biaya minimum yang paling rendah secara keseluruhan dibandingkan dengan metode lainnya dengan nilai akurasi sebesar 85% dan nilai error sebesar 15%, dimana metode lainnya, yaitu VAM, JHM, TOCM-MT, BCE, dan SSM mencapai nilai akurasi masing-masing sebesar 55%, 67.5%, 57.5%, 80%, dan 67.5% dan nilai error masing-masing sebesar 45%, 32.5%, 42.5%, 20%, dan 32.5%.
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A Transportation Problem (TP) is a problem that aims to reduce the result of the minimum total cost, or the multiplication of cost of distances and items, for distributing some items from several supplies to several demands. Finding the Initial Basic Feasible Solution (IBFS) is a critical step for finding the minimum cost in solving the TP. However, existing IBFS approaches do not always produce the best initial solution, whether traditional methods such as North-West Corner Rule (NWCR), Least-Cost Method (LCM), and Vogel's Approximation Method (VAM), or newer methods developed from research journals such as Juman Hoque Method (JHM) and Total Opportunity Cost Matrix - Minimal Total (TOCM-MT). This Final Project utilizes a new and more effective technique known as Transpose Minimum Selection Method (TMSM) to obtain a better initial solution for a balanced Transportation Problem. TMSM is an approach developed with the Supply Selection Method (SSM) as its basis. The modifications are the way of handling the matrix form of goods allocation and changes in allocation selection from maximum to minimum in cases when there is an equal difference between First Least Cost (FLC) and Second Least Cost (SLC). The process of handling the matrix form of goods allocation is done by checking whether the sum of demand / the sum of supply ≥ C, and if the condition is not met, a transposition operation is performed on the TP matrix. The second modification is to change the allocation selection from maximum to minimum in cases where there is an equal difference between FLC and SLC, which makes TMSM optimize the resource allocation, which ultimately results in a more efficient solution. This technique was compared against various IBFS techniques as Vogel's Approximation Method (VAM), Juman Hoque Method (JHM), Total Opportunity Cost Matrix - Minimal Total (TOCM-MT), Bilqis Chastine Erma method (BCE) and Supply Selection Method (SSM) to assess its efficiency. A total of 40 test data consisting of 31 data taken from various journal publications, 4 cases of synthesized data, and 5 real data were used to assess this new technique. The results show that TMSM offers a better initial basic solution compared to other methods, with optimal solutions achieved in 34 out of 40 test data, where VAM, JHM, TOCM-MT, BCE, and SSM achieved optimal solutions of 22, 27, 23, 32, and 27, respectively. In comparison, TMSM has 16 results superior to VAM with an IP of 40%, 10 results superior to JHM with an IP of 25%, 14 results superior to TOCM-MT with an IP of 35%, 4 results superior to BCE with an IP of 10%, and 9 results superior to SSM with an IP of 22.5%. TMSM has a average percentage deviation of 0.58%, while VAM, JHM, TOCM-MT, BCE, and SSM have average percentage deviations of 2.83%, 2.17%, 1.51%, 1.12%, 1.80%, and 0.58%, respectively. The analysis results reveal that TMSM provides highest optimal value with the lowest overall minimum total cost compared to the other methods with an accuracy value of 85% and an error value of 15%, where the other methods, namely VAM, JHM, TOCM-MT, BCE, and SSM achieve accuracy values of 55%, 67.5%, 57.5%, 80%, and 67.5% respectively and error value of 45%, 32.5%, 42.5%, 20%, and 32.5% repectively.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | IBFS, Total Biaya Minimal, Transportation Problem, Minimum Total Cost |
| Subjects: | T Technology > T Technology (General) > T57.6 Operations research--Mathematics. Goal programming T Technology > T Technology (General) > T57.74 Linear programming T Technology > T Technology (General) > T57.84 Heuristic algorithms. |
| Divisions: | Faculty of Intelligent Electrical and Informatics Technology (ELECTICS) > Informatics Engineering > 55201-(S1) Undergraduate Thesis |
| Depositing User: | Ramadhan Arif Hardijansyah |
| Date Deposited: | 12 Feb 2024 03:44 |
| Last Modified: | 12 Feb 2024 03:44 |
| URI: | http://repository.its.ac.id/id/eprint/106841 |
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