Pengaruh Pengurutan Baris dan Kolom Matriks Transportation Problem pada Northwest Cost Method

Maghfirah, Faizah Nurdianti (2025) Pengaruh Pengurutan Baris dan Kolom Matriks Transportation Problem pada Northwest Cost Method. Project Report. [s.n.], [s.l.]. (Unpublished)

Text 5025211134-Project_Report.pdf - Accepted Version Restricted to Repository staff only Download (3MB) | Request a copy

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 Northwest Cost Method (NWCM) dan Vogel's Approximation Method (VAM). Namun, belum terdapat studi yang menganalisis pengaruh susunan baris dan kolom pada matriks TP terhadap hasil total cost. Kerja praktik ini bertujuan untuk mendapatkan aturan matrix preprocessing yang dapat meminimalkan total cost pada metode penyelesaian TP, yaitu NWCM . Penelitian dilakukan pada 37 set data, dengan ukuran matriks maksimal 5×5, serta implementasi program menggunakan bahasa python. Hasil penelitian menunjukkan bahwa penerapan matrix preprocessing pada suatu matriks TP sebelum melalui NWCM dengan aturan kolom diurutkan berdasarkan cost baris pertama secara descending dan baris diurutkan berdasarkan cost kolom pertama secara ascending dapat menghasilkan total cost yang lebih unggul dibandingkan dengan total cost pada matriks TP yang tidak melaui matrix preprcessing. Aturan matrix preprocessing yang didapatkan ini menghasilkan total cost lebih unggul pada 28 dari 37 soal TP dengan rata-rata Improvement Percentage (Ip) sebesar 0,15%, dan rata-rata Deviation Percentage (Dv) sebesar 0,16%.
===================================================================================================================================
Transportation Problem (TP) is a type of linear programming problem that plays a crucial role in decision-making within the field of logistics. TP focuses on determining the allocation of supply to demand in a way that minimizes the total cost. Solving TP involves two main stages: finding the Initial Basic Feasible Solution (IBFS) and obtaining the optimal solution. Various methods have been developed to determine IBFS, such as the Northwest Corner Method (NWCM) and Vogel’s Approximation Method (VAM). However, there has been little research on how the arrangement of rows and columns in the TP matrix affects the resulting total cost. This internship project aims to identify a matrix preprocessing rule that minimizes the total cost in solving TP using the NWCM method. The study was conducted on 37 data sets, with matrix sizes up to 5×5, and the program was implemented using Python. The results show that applying matrix preprocessing to a TP matrix before using NWCM—specifically by sorting the columns in descending order based on the first row's cost and sorting the rows in ascending order based on the first column's cost—can yield a lower total cost compared to TP matrices without preprocessing. This preprocessing rule produced a lower total cost in 28 out of 37 TP cases, with an average Improvement Percentage (Ip) of 0.15% and an average Deviation Percentage (Dv) of 0.16%.

Item Type:	Monograph (Project Report)
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:	14 Jul 2025 03:37
Last Modified:	14 Jul 2025 03:37
URI:	http://repository.its.ac.id/id/eprint/119616

Actions (login required)

View Item