Optimization of Drinking Water Distribution Costs Using Vogel's Approximation Method (VAM) and Three Modified Methods of VAM (Case Study: Sikumbang Kampar Spring)

Sri Basriati; Elfira Safitri; Dewi Sartika

doi:10.25217/numerical.v5i2.1419

Authors

Sri Basriati Mathematics Study Program, Sultan Syarif Kasim State Islamic University Riau
Elfira Safitri Mathematics Study Program, Sultan Syarif Kasim State Islamic University Riau
Dewi Sartika Mathematics Study Program, Sultan Syarif Kasim State Islamic University Riau

DOI:

https://doi.org/10.25217/numerical.v5i2.1419

Keywords:

Improved Vogel's Approximation Method, Max-Min Vogel's Approximation Method, Modified Vogel's Approximation Method, Vogel's Approximation Method

Abstract

Distribution system Springs Sikumbang Kampar is from the primary seller, and the distributor distributes it to the public. The Sikumbang Kampar Springs distributor is experiencing the problem of increasing the cost of distribution because it does not have a distribution pattern. Therefore, it takes a transportation model to complain distribution problems experienced by the distributor of Springs Sikumbang Kampar. The research was conducted to obtain the minimum cost in distributing the drinking water to help distributors solve these problems. For this reason, a method is needed in compiling a mathematical model appropriate to the distribution problem. The methods used in the study are Vogel's Approximation Method (VAM), Improved Vogel's Approximation Method (IVAM), Max-Min Vogel's Approximation Method (MM-VAM), and Modified Vogel's Approximation Method (MVAM). Based on the results of the study, Vogel's Approximation Method generates total cost different initial solutions. Vogel's Approximation Method is more efficient, as it has few iterations to obtain the optimal solution using the stepping stone method. Distributors can consider the use of Vogel's Approximation Method in optimizing the distribution costs of drinking water from Sikumbang Kampar Springs. Total distribution transportation costs Sikumbang Kampar Springs per week uses transportation model is Rp 4,580,485.00. This result is more optimal for transportation costs distributor, that is Rp 5.050.000.000,00, so there is a reduction in transportation for Rp 469,515.00.

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