Metode Inverse Harmonic Weighted (IHW) untuk Menentukan Initial Basic Feasible Solution pada Transportation Problem

Saputra, Dana (2026) Metode Inverse Harmonic Weighted (IHW) untuk Menentukan Initial Basic Feasible Solution pada Transportation Problem. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Transportation Problem merupakan permasalahan optimisasi distribusi untuk menentukan pola pengiriman dari sumber ke tujuan dengan biaya minimum sesuai batasan supply dan demand. Salah satu tahap penting dalam penyelesaiannya adalah penentuan Initial Basic Feasible Solution (IBFS). Penelitian ini mengembangkan metode Inverse Harmonic Weighted (IHW) sebagai alternatif pembentukan IBFS pada balanced transportation problem. Metode IHW mengombinasikan pembobotan baris dan kolom, pemilihan biaya minimum, penalti berbasis Inverse Contra-Harmonic Mean, serta aturan pemilihan alokasi pada kondisi nilai yang sama. Pengujian dilakukan pada 709 data uji yang terdiri atas 42 data uji literatur, 27 data uji sintetis awal, dan 640 data uji sintetis terseleksi. Metode IHW dibandingkan dengan VAM, JHM, TOCM-MT, SSM, RCWMCAM, EXP-ICHM, dan MRM menggunakan metrik AP, DP, PoCIR, IP, FNOCS, OI, dan runtime. IHW menghasilkan 609 solusi optimal dengan AP keseluruhan sebesar 85,90%. Pada DU-2 dan DU-3, IHW memperoleh DP rendah, yaitu 0,76% dan 0,88%, serta PoCIR tinggi, yaitu 99,24% dan 99,12%. IHW juga memiliki rerata OI terendah pada DU-2 dan DU-3, serta runtime gabungan terendah pada DU-3 sebesar 126,18 ms. Namun, performa IHW masih kurang optimal pada matriks dengan biaya minimum terkonsentrasi, koridor biaya rendah dominan, biaya berulang, dan matriks sangat lebar. Dengan demikian, IHW dapat menjadi alternatif metode IBFS yang kompetitif dengan performa yang dipengaruhi oleh karakteristik matriks.
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The Transportation Problem is a distribution optimization problem that aims to determine the shipment pattern from sources to destinations at minimum cost while satisfying supply and demand constraints. One important stage in solving this problem is determining the Initial Basic Feasible Solution (IBFS). This study develops the Inverse Harmonic Weighted (IHW) method as an alternative for constructing an IBFS in balanced transportation problems. The IHW method combines row and column weighting, minimum-cost selection, penalties based on the Inverse Contra-Harmonic Mean, and allocation selection rules for equal values. The evaluation was conducted using 709 test datasets consisting of 42 literature-based test datasets, 27 initial synthetic test datasets, and 640 selected synthetic test datasets. The IHW method was compared with VAM, JHM, TOCM-MT, SSM, RCWMCAM, EXP-ICHM, and MRM using the AP, DP, PoCIR, IP, FNOCS, OI, and runtime metrics. IHW produced 609 optimal solutions with an overall AP of 85.90%. In DU-2 and DU-3, IHW achieved low DP values of 0.76% and 0.88%, respectively, as well as high PoCIR values of 99.24% and 99.12%, respectively. IHW also had the lowest average OI in DU-2 and DU-3, as well as the lowest combined runtime in DU-3 at 126.18 ms. However, the performance of IHW was still less optimal for matrices with concentrated minimum costs, dominant low-cost corridors, repeated cost values, and very wide matrices. Therefore, IHW can serve as a competitive alternative IBFS method, although its performance is influenced by matrix characteristics.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Transportation Problem, Initial Basic Feasible Solution, IHW
Subjects:	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:	Dana Saputra
Date Deposited:	08 Jul 2026 05:41
Last Modified:	08 Jul 2026 05:41
URI:	http://repository.its.ac.id/id/eprint/134479

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