Pengaruh Pengurutan Baris dan Kolom Matriks Transportation Problem pada Vogel's Approximation Method dan Supply Selection Method

Maghfirah, Faizah Nurdianti (2025) Pengaruh Pengurutan Baris dan Kolom Matriks Transportation Problem pada Vogel's Approximation Method dan Supply Selection Method. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Transportation Problem (TP) merupakan salah satu permasalahan dalam linear programming problem yang berperan penting dalam pengambilan keputusan di bidang logistik. TP berfokus pada penentuan jumlah alokasi supply terhadap demand supaya menghasilkan total cost yang paling minimum. Proses penyelesaian TP terdiri dari dua tahap, yaitu pencarian Initial Basic Feasible Solution (IBFS) dan pencarian solusi optimal. Berbagai metode telah dikembangkan untuk menentukan IBFS, seperti VAM (Vogel's Approximation Method) dan SSM (Supply Selection Method). Namun, belum terdapat studi yang menganalisis pengaruh susunan baris dan kolom pada matriks TP terhadap hasil total cost. Tugas akhir ini bertujuan untuk mendapatkan aturan susunan baris dan kolom matriks yang dapat meminimalkan total cost pada metode penyelesaian TP, VAM dan SSM. Penelitian dilakukan pada 37 set data, dengan ukuran matriks maksimal 5×5, serta implementasi program menggunakan bahasa C. Hasil penelitian menunjukkan bahwa, aturan penyusunan baris dan kolom matriks yang terbaik pada VAM adalah dengan mengurutkan baris berdasarkan jumlah cost secara ascending dan mengurutkan kolom berdasarkan nilai demand secara ascending. Susunan ini mampu menghasilkan total cost yang lebih rendah sebanyak 7 soal dengan rata-rata Improvement Percentage (Ip) sebesar 0,81%, dan rata-rata Deviation Percentage (Dv) sebesar 2,72%. Sementara itu, pada SSM, aturan susunan terbaiknya adalah dengan mengurutkan baris berdasarkan jumlah cost secara ascending, terlepas dari bagaimana kolom disusun. Aturan ini mampu menghasilkan total cost lebih rendah sebanyak sebanyak 3 soal dengan rata-rata Ip sebesar 0,26%, dan rata-rata Dv sebesar 0,54%.
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The Transportation Problem (TP) is a type of linear programming problem that plays a crucial role in decision-making processes in the field of logistics. TP focuses on determining the optimal allocation of supply to meet demand with the objective of minimizing total cost. The solution process of TP typically involves two main stages: the determination of an Initial Basic Feasible Solution (IBFS) and the identification of an optimal solution. Various heuristic methods have been developed to obtain the IBFS, such as Vogel’s Approximation Method (VAM) and Supply Selection Method (SSM). However, existing literature lacks studies investigating the influence of matrix row and column arrangements on the total cost in TP solutions. This final project aims to identify matrix row and column arrangements that can minimize total cost when solving TP using the VAM and SSM methods. The research was conducted using 37 datasets, with matrix sizes up to 5×5, and the implementation was carried out using the C programming language. Experimental results indicate that, the best row and column arrangement rule for VAM is to sort the rows in ascending order based on the total cost and to sort the columns in ascending order based on demand values. This arrangement was able to produce lower total costs in 7 cases, with an average Improvement Percentage (Ip) of 0.81% and an average Deviation Percentage (Dv) of 2.72%. Meanwhile, for SSM, the best arrangement rule is to sort the rows in ascending order based on the total cost, regardless of how the columns are arranged. This rule produced lower total costs in 3 cases, with an average Ip of 0.26% and an average Dv of 0.54%.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	initial basic feasible solution, matrix preprocessing, transportation problem
Subjects:	Q Science > QA Mathematics > QA402.6 Transportation problems (Programming) 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) > T58.62 Decision support systems
Divisions:	Faculty of Intelligent Electrical and Informatics Technology (ELECTICS) > Informatics Engineering > 55201-(S1) Undergraduate Thesis
Depositing User:	Faizah Nurdianti Maghfirah
Date Deposited:	30 Jul 2025 03:10
Last Modified:	30 Jul 2025 03:10
URI:	http://repository.its.ac.id/id/eprint/122713

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