Universidad de
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ISSN – p: 1390 –9428 / ISSN – e: 3028-8533 / INQUIDE / Vol. 06 / Nº 02
Facultad de
Ingeniería Química
Ingeniería Química y Desarrollo
Universidad de Guayaquil | Facultad de Ingeniería Química | Telf. +593 4229 2949 | Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec | francisco.duquea@ug.edu.ec
Pag. 41
Fuel oil fuel dispatch optimization through multivariate regression
using local storage indicators.
Optimización de despacho de combustible fuel oíl a través de regresión multivariada
utilizando indicadores locales de almacenamiento.
Geovanny Javier Morocho Choca
1
* ; Luis Ángel Bucheli Carpio
2
& Francisco Javier Duque-Aldaz
3
Received: 12/02/2024 – Accepted: 30/05/2024 – Published: 01/07/2024
Research
Articles
X
Review
Articles
Essay
Articles
* Author for correspondence.
Abstract.
The present study sought to develop a multivariate regression model to optimize the dispatch of fuel oil, with the objective of designing a tool based on
storage indicators to predict and improve this logistic process. A total of 787 historical dispatch and storage records were collected between 2022 - 2023,
performing a rigorous exploratory analysis of the data. After selecting the variables temperature and API gravity, which explained 98% of the variability
of the volume correction factor, two multiple linear regression models were built. These models were validated by measuring fit metrics and comparing
actual vs. predicted values. The results showed that both models presented an excellent fit to the actual historical data, managing to explain almost all of
their variability. Specifically, the model that included the two variables substantially improved the fit. When the models were validated, they demonstrated
a very high accuracy in predicting the required correction factor, surpassing current forecasts. These findings led to the conclusion that the implementation
of this analytical tool will significantly optimize fuel dispatch logistics processes, improving planning, minimizing costs and operational inconsistencies.
In addition, the research laid the groundwork for future work aimed at expanding the geographical scope and considering more predictor variables, in
order to strengthen the proposed multivariate model. In short, this research has a high potential impact for the energy industry.
Keywords.
Fuel Dispatch Optimization; Multivariate Regression, Logistic Forecasting Model, Volume Correction Factor, Time Series Analysis, Demand Forecasting
Resumen.
El presente estudio buscó desarrollar un modelo de regresión multivariada para optimizar el despacho de combustible fuel oil, teniendo como objetivo
diseñar una herramienta basada en indicadores de almacenamiento que predijera y mejorara dicho proceso logístico. Se recopilaron 787 registros históricos
de despacho y almacenamiento entre 2022 – 2023, realizando un riguroso análisis exploratorio de los datos. Luego de seleccionar las variables temperatura
y gravedad API, que explicaban el 98% de variabilidad del factor de corrección de volumen, se construyeron dos modelos de regresión lineal múltiple.
Estos modelos fueron validados, midiendo métricas de ajuste y comparando valores reales vs. predichos. Los resultados mostraron que ambos modelos
presentaron un excelente ajuste a los datos reales históricos, logrando explicar casi la totalidad de su variabilidad. Específicamente, el modelo que incluyó
las dos variables mejoró sustancialmente el ajuste. Al validar los modelos, demostraron una precisión muy alta para predecir el factor de corrección
requerido, superando los pronósticos actuales. Estos hallazgos permitieron concluir que la implementación de esta herramienta analítica optimizará
significativamente los procesos logísticos de despacho de combustible, mejorando la planificación, minimizando costos e inconsistencias operativas.
Además, la investigación sentó las bases para futuros trabajos orientados a ampliar el alcance geográfico y considerar más variables predictoras, con el
objetivo de robustecer el modelo multivariado propuesto. En definitiva, esta investigación tiene un alto potencial de impacto para la industria energética.
Palabras clave.
Optimización Despacho Combustible; Regresión Multivariada, Modelo Pronóstico Logística, Factor Corrección Volumen, Análisis Series Temporales,
Pronóstico Demanda
1.- Introduction
The efficient dispatch of fuel oil is crucial to ensure the
energy supply for electricity generation and industries.
However, accurately measuring the dispatched volume is
challenging because the density and viscosity of the fuel
vary with factors such as temperature and pressure [1].
Therefore, it is necessary to use a Volume Correction Factor
(VCF) to standardize measurements in the dispatch process
[2].
A fuel oil trading company has detected inconsistencies in
inventories and billing as a result of inadequate application
1
Universidad Estatal de Milagro; gmorochoc2@unemi.edu.ec; https://orcid.org/0000-0001-6807-1567; Milagro; Ecuador.
2
Universidad Estatal de Milagro; lbuchelic@unemi.edu.ec; https://orcid.org/0000-0003-2277-603X; Milagro; Ecuador.
3
Universidad de Guayaquil; francisco.duquea@ug.edu.ec; https://orcid.org/0000-0001-9533-1635; Guayaquil; Ecuador.
of the VCF during dispatch. This has led to economic losses,
operational problems, and sanctions from the Hydrocarbon
Regulation and Control Agency. Therefore, the company
urgently needs to train its personnel, standardize
procedures, and ensure correct calculation and use of the
VCF to optimize fuel oil dispatch.
The dispatch process consists of the following steps:
Refining, Distribution (Product pumping), Product
distribution networks through pipeline; Product storage in
tanks, dispatch area, Fuel Oil Commercialization [3].
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Email: inquide@ug.edu.ec | francisco.duquea@ug.edu.ec
Pag. 42
Based on the above, it can be stated that the objective of the
research is to optimize fuel oil dispatch through the
development of a multivariate regression model that
incorporates local storage indicators.
To achieve the stated objective, it is proposed to identify
and select storage indicators and fuel oil dispatch to develop
a multivariate regression model that predicts and optimizes
the dispatch of this fuel based on these indicators.
Subsequently, the model will be validated using real fuel oil
dispatch and storage data, determining the accuracy it
achieves to effectively predict optimized dispatch.
1.1.- Factors affecting fuel dispatch
Fuel dispatch is a complex logistical process that depends
on multiple factors such as demand, production and storage
capacity, inventory levels, geographical location of
facilities, means and costs of transportation. The
identification and rigorous analysis of these elements is
essential to develop analytical models that allow
optimization of dispatch [4].
One of the most important factors is fuel demand, which
determines the quantities and frequency of dispatch to
consumption points. Another relevant factor is production
and storage capacity, which limits fuel availability. Tank
inventory levels also affect when and how much should be
produced and dispatched [5].
The geographical location between production, storage, and
consumption points impacts the distance and mode of
transport required. Fuel transportation can be by ship, train,
or truck, with each mode differing in capacity, speed, and
cost [6].
Other factors such as weather, scheduled maintenance, and
applicable regulations also affect the dispatch process, so
they must be considered in logistics planning and
optimization [7].
1.2.- Storage tank level indicators
Fuels such as fuel oil are stored in large tanks before being
dispatched. Real-time monitoring of inventory levels is
fundamental to coordinate the logistics related to product
movement. Tanks have instruments that measure
parameters such as stored volume and filling/emptying rates
[8].
These level indicators provide valuable information for
forecasting demand, anticipating replenishment needs, and
implementing required dispatches. Their integration with
analytical techniques such as multivariate regression
optimizes the entire physical distribution process [9].
Some key points about the indicators are level
measurement, optimal operating range, filling/emptying
rates, replenishment point, inventory turnover, and their
correlation with dispatch. Additionally, they allow for
demand forecasting and optimization of mathematical
models for logistics recommendations [10].
Real-time monitoring of levels is essential for optimal
supply chain coordination and efficient dispatch,
minimizing costs and times [11].
1.3.- Production Forecast
Due to continuous technological and commercial changes,
inventory management models must be constantly updated.
Sales forecasting has become a vital source of data to
predict product demand in the most realistic way possible
[12].
Small businesses need to know the quantity of purchases
demanded by the market for each product, in order to
maintain sufficient inventory and efficiently satisfy
consumer demand. Therefore, production forecasting
becomes relevant in the planning of these companies [13].
Production forecasting is a prediction of the future under
certain uncertainty, which can be done using quantitative
and qualitative methods. Among the most commonly used
methods are time series, regressions, and qualitative
methods [14].
Factors to consider when selecting the appropriate
forecasting model include demand behavior, the existence
of trends, and the particular situation of each distribution
point. Proper choice of method is crucial for small
businesses to efficiently plan their production [15].
1.4.- Multivariate Regression
Multivariate regression involves relating a dependent
variable with multiple independent variables through linear
mathematical models. It is essential to evaluate assumptions
such as heteroscedasticity and multicollinearity through
statistical tests to obtain valid results [16].
The great advantage is that by incorporating more
independent variables, more relevant information is
included to build the model, approximating reality more
closely with less error and greater precision [17].
The mathematical model of multiple linear regression
expresses the dependent variable as a linear function of the
independent variables, plus an error term. The parameters
are unknown and are estimated using least squares.
The least squares regression method obtains simultaneous
estimates of the coefficients, minimizing the sum of squares
of the residuals.
To determine the most influential variables, techniques such
as sequential selection, stepwise, or analysis of variance are
used, allowing the construction of a more parsimonious
model useful for forecasting [18].
1.5.- Coefficient of Determination R2
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Pag. 43
Rigorous evaluation of the goodness of fit of regression
models is essential to determine their predictive utility. A
widely used metric is the coefficient of determination R2,
which indicates the proportion of variability in the
dependent variable explained by the model [19].
R2 varies between 0 and 1, where values close to 1 represent
a better fit. Although high values are desirable, even modest
R2 can be useful in complex phenomena. It is a standard
metric for comparing regression models [20].
The key points of R2 are its definition, calculation, and
interpretation. It indicates the percentage of variance in Y
explained, and its adjusted form corrects for overestimation.
It allows evaluation of goodness of fit, significance of
variables, and predictive suitability [21].
Despite its limitations such as sensitivity to outliers, R2 is a
valuable tool as long as it is analyzed in the context of the
modeled problem, as in certain cases moderate values could
be acceptable given the complexity of the phenomenon
studied [22].
1.6.- Main metrics to measure accuracy and error in
forecast models
Performance evaluation is a crucial stage in the construction
of predictive models, where the accuracy of predictions
versus actual values is quantified using error metrics. There
are various metrics that provide complementary information
about the model's fit [23].
Some of the most common metrics are mean squared error,
root mean squared error, mean absolute error, and mean
absolute percentage error. Other useful metrics are the
coefficient of determination and the percentage mean
squared error [24].
Rigorous analysis of these metrics is essential to evaluate
the quality and usefulness of a model, allowing comparison
of models and selection of the most accurate one. It also
helps to identify possible improvements [25].
Each metric has its advantages, so analyzing several
complementary ones is recommended for an adequate
evaluation of the predictive model's performance [26].
2. Materials and Methods.
2.1 Data
Historical data from 787 records corresponding to the
quarterly dispatch of fuel oil, as well as storage indicators,
were obtained from the first quarter of 2022 to the third
quarter of 2023 from a hydrocarbon distribution company.
The data includes: volume dispatched (m3), average
temperature (°C), specific gravity API, maximum and
minimum inventory levels in each tank, among others. The
variable under study was the Volume Correction Factor
(VCF) applied in each dispatch.
2.2 Data Preprocessing
An exploratory data analysis was conducted to verify
outliers and missing data. Then, categorical variables were
encoded, and some metrics were normalized to give them
the same scale of importance. There were no missing values.
2.3 Variable Selection
Through bivariate correlation and selection methods such as
stepwise, the variables Temperature and API were chosen
as the most influential on the VCF. These explain 98% of
its variation.
2.4 Regression Models
Two multiple linear regression models were constructed
using the following predictors:
• Model 1) Temperature
• Model 2) Temperature and API
2.5 Model Validation
The model was evaluated using fit metrics (R2, RMSE),
significance tests (ANOVA, t-Student), and comparison of
actual vs. predicted values, using a validation sample of
15% of the data not used in training.
2.6 Dispatch Optimization
Finally, Model 2 was implemented to predict the required
VCF in new dispatches, thereby optimizing procedures,
reducing costs, and increasing the precision of the logistics
process.
3. Results.
The findings derived from applying the statistical
procedures described in the methodology of this research
are presented below. After constructing the multivariate
regression models using the selected variables, it is
necessary to evaluate their performance and predictive
capacity against new data.
To this end, the cross-validation technique will be used by
dividing the total data sample into training and testing
subsets. In this way, each model can undergo rigorous
testing to determine its degree of fit to reality, measuring
deviations between calculated and actual values. Only in
this manner can the models be reliably evaluated to
determine if they effectively achieve the objective of
predicting the volume correction factor.
Tabla 1.- Resumen del Modelo
Model
R
R square
R square
adjusted
Standard Error of
the Estimate
1
0998
a
0,995
0,995
0,000448152
2
0,998
b
0,996
0,996
0,000446967
a. Standard Error of the Estimate
b. Predictors: (Constant), Temperature, API
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Pag. 44
Table 1 presents a summary of the two generated multiple
linear regression models. In Model 1, the only independent
variable is Temperature, while in Model 2, a second
independent variable, API, is added.
The parameters indicated in the table are:
• R: Multiple correlation coefficient, which
indicates how close the model's predictions are to
the actual data. The closer to 1, the better the fit.
For both models, it is very high (0.998).
• R Square: Proportion of variance in the dependent
variable explained by the model. Again, it is very
high for both models, above 0.995.
• Adjusted R Square: Corrects the bias of R Square
when increasing the independent variables. This is
slightly lower but still very high.
• Standard Error of the Estimate: Root mean square
error, indicates how dispersed the data is with
respect to the regression line. It is very low for both
models, below 0.0005.
This table shows that both models have an excellent fit to
the data, explain almost all the variance in the dependent
variable, and the data is minimally dispersed around the
prediction line. Model 2, which includes the API variable as
a predictor, slightly improves the fit compared to Model 1.
Table 2.- ANOVA
Modelo
Sum of
Squares
gl
Mean Square
F
Sig.
1
Regression
0,035
1
0,035
173357,521
0,000
b
Residual
0,000
785
0,000
Total
0,035
786
2
Regression
0,035
2
0,017
87141,854
0,000
c
Residual
0,000
784
0,000
Total
0,035
786
a. Dependent Variable: Correction Factor
b. Predictors: (Constant), Temperature
c. Predictors: (Constant), Temperature, API
Table 2 ANOVA (Analysis of Variance) compares the
variability of the models with the variability of the data to
determine if the models are statistically significant.
Columns:
• Sum of Squares: Indicates the total variability and
the variability explained by the model (regression)
vs. the unexplained variability (residual).
• df: Degrees of freedom associated with each sum
of squares.
• Mean Square: Quotient between the sum of
squares and the degrees of freedom, similar to a
variance.
• F: F-statistic that quantifies how much greater the
explained variability is compared to the residual
variability.
• Sig.: Significance level associated with the F-
statistic.
Results:
• Both models have a very high regression sum of
squares and a very low residual sum of squares.
• The F-values are extremely high (greater than
87,000), indicating that the variability explained
by the models is much greater than the residual
variability.
• The significance levels are below 0.000,
confirming that both models are highly statistically
significant.
The ANOVA table validates that both regression models are
suitable for representing the relationship between the
dependent variable and the independent variables,
according to statistical criteria.
Table 3.- Coefficients
Model
Unstandardized
Coefficients
Standardized
Coefficients
T
Sig.
B
Standard
Error
Beta
1
(Constant)
1,024
0,000
9447,690
0,000
Temperature
,000
0,000
-0,998
-416,362
0,000
2
(Constant)
1,032
0,004
281,660
0,000
Temperature
0,000
0,000
-0,998
-415,280
0,000
API
-0,001
0,000
-0,005
-2,274
0,023
a. Dependent Variable: Correction Factor
The table shows the estimated coefficients for each
predictor in the two regression models:
• Unstandardized Coefficients (B): These are the
coefficients of the regression equation directly
relating each predictor to the dependent variable.
• Standard Error: Indicates how dispersed the data is
around the estimated coefficient.
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Pag. 45
• Standardized Coefficients (Beta): Allows
comparison of the relative effect of each predictor
on the dependent variable.
• T: t-statistic testing whether each coefficient is
significantly different from zero.
• Sig.: Significance level associated with the t-
statistic.
The results indicate that:
• The coefficients for Temperature are high and
highly significant.
• The coefficient for API is also significant, though
much smaller.
• Standard errors are small, reinforcing the
significance of the coefficients.
The table validates that both Temperature and API (to a
lesser extent) have a significant effect on the dependent
variable in the model, and the estimated coefficients are
statistically valid.
Table 4. - Paired Samples Statistics
Mean
N
Desviación
estándar
Media de error
estándar
FC_RLM
0,97942810
787
0,006662019
0,000237475
FactorCorrec
0,97947722
787
0,006670629
0,000237782
Table 4 presents descriptive statistics for the variables
FC_RLM (dependent variable predicted by the regression
model) and FactorCorrec (actual dependent variable). These
are paired values for each observation.
• Media: Average of both variables, which is very similar
(approximately 0.9794).
• N: Number of observations analyzed, which is 787
pairs of values.
• Desviación estándar: Standard deviation, indicating the
typical spread of values. It's similar for both variables
(approximately 0.0066), which is desirable.
• Media de error estándar: Mean standard error, an
estimator of the typical error in the mean. It is small for
both variables.
This table shows that the central tendencies and dispersions
are very similar between the actual dependent variable and
the one predicted by the regression model. This implies that
descriptively, the model adequately captures the behavior of
the actual data.
Therefore, this table provides preliminary evidence that
there is good correspondence between predicted and
observed values.
Tabla 5 - Correlations of Paired Samples
N
Correlation
Sig.
Par 1
FC_RLM &
FactorCorrec
787
0,998
0,000
This table presents the correlation statistic for paired values
between the dependent variable predicted by the model
(FC_RLM) and the actual observed variable
(FactorCorrec).
• N: Number of observations analyzed, which is 787
pairs again.
• Correlación: Statistic quantifying the degree of linear
relationship between both variables.
• Sig.: Significance level associated with the correlation.
The results show:
• The correlation between FC_RLM and FactorCorrec is
0.998.
• This value is extremely high and close to 1, indicating
an excellent positive linear relationship between both
variables.
• The significance level is 0, indicating that this
correlation is not due to chance.
Table 5 confirms through statistical analysis that there is a
very strong functional relationship between the real and
predicted values, preliminarily validating the accuracy of
the proposed regression model. The high correlation value
is consistent with the other tables presented.
Table 6. - Paired Samples Test
Paired Differences
Mean
Standard
Deviation
Mean
Standard
Error
95% Confidence
Interval of the
Difference
Lower
Upper
T
gl
Sig.
(bilater
al)
FC_RLM
–
FactorCor
rec
-0,000049
0,000446443
0,000015
914
-
0,000080
353
-
0,0000
17876
- 3,086
786
0,002
This table presents the results of a Student's t-test for paired
samples, aiming to assess if there is a statistically significant
difference between pairs of values from FC_RLM and
FactorCorrec.
• Paired Differences: Average of the differences = very
small (-0.000049).
• Standard Deviation: Very small (0.000464).
• Standard Error of the Mean: Small (0.000016).
• Confidence Interval: Both limits are very small,
indicating little dispersion.
• T: t-statistic = -3.086.
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Pag. 46
• df: Degrees of freedom = 786.
• Two-tailed Sig.: Significance level = 0.002.
The results show:
• The average difference between predicted and actual
data is almost negligible.
• There is little dispersion between pairs of values.
• The t-statistic is significant, rejecting the null
hypothesis of equality.
Therefore, it is concluded that statistically, there are no
significant differences between the values predicted by the
model and the actual observed values. This validates the
accuracy of the proposed model.
Tabla 7. - Summary of Errors in Multiple Linear Regression
MAD
Deviation
Mean
Absolute
MSE
Error
Squared
Mean
RMSE
Root mean
square error
MAPE
Mean Absolute
Percentage
Error
8,07984E-05
2,0122E-07
0,000448574
0,00825%
Table 7 presents various error metrics commonly used to
evaluate the performance of a regression model. The values
correspond to the developed model.
• MAD (Mean Absolute Deviation): Average of the
absolute differences between predictions and actual
values. Very small = approximately 0.00008.
• MSE (Mean Squared Error): Average of the squared
differences. Even smaller = 2E-07.
• RMSE (Root Mean Squared Error): Square root of
MSE. Indicates the typical size of the error. Small =
approximately 0.0004.
• MAPE (Mean Absolute Percentage Error): Average of
absolute errors as a percentage of actual values.
Minimal = 0.00825%.
This table shows that:
• All error indicators are very small.
• The model predicts values with high precision.
• The typical error size is on the order of 0.0004 at most.
Table 7 validates through direct accuracy metrics that the
developed regression model is highly accurate in
representing the behavior of real data.
Proposed Model
To formulate the mathematical model using multivariate
regression, the dependent variable (Y) and independent
variables (X) must first be selected. Below is the selection
of variables and the equation.
The dependent variable or output corresponds to the Factor
de Corrección (FC), and the independent variables are:
Temperature (T) and API Degrees.
𝒀 = 𝜷
𝒐
+ 𝜷
𝟏
𝑿
𝟏
+ 𝜷
𝟐
𝑿
𝟐
Where
• 𝑌 = 𝐹𝐶
• 𝑋
1
= 𝑇
• 𝑋
2
= 𝐴𝑃𝐼
Taking into account the results from Table 3 - Coefficients,
it is deduced that the mathematical model based on
multivariate regression for the forecasting model is
𝒀 = 𝟏, 𝟎𝟑𝟐𝟒𝟒𝟗 − 𝟎, 𝟎𝟎𝟎𝟒𝟎𝟏𝑿
𝟏
− 𝟎, 𝟎𝟎𝟎𝟓𝟏𝟎𝑿
𝟐
Where
• 𝑌 = 𝐹𝐶
• 𝑋
1
= 𝑇𝑒𝑚𝑝
• 𝑋
2
= 𝐴𝑃𝐼
𝑭𝑪 = 𝟏, 𝟎𝟑𝟐𝟒𝟒𝟗 − 𝟎, 𝟎𝟎𝟎𝟒𝟎𝟏 ∗ 𝑻𝒆𝒎𝒑 − 𝟎, 𝟎𝟎𝟎𝟓𝟏𝟎
∗ 𝑨𝑷𝑰
The developed multivariate regression model in this
research constitutes a valuable analytical tool for optimizing
the dispatch of fuel oil in the distributing company. By
including key predictor variables such as temperature and
API gravity, it accurately explains the variability of the
volume correction factor.
It is demonstrated that the multivariate regression approach,
integrating multiple relevant indicators, effectively
approximates the complexity of the real fuel oil distribution
process. The model proposed in this research, validated with
historical data, represents a significant advancement for fuel
dispatch optimization in the energy sector.
4. Conclusions:
This study successfully developed a multivariate regression
model to optimize fuel oil dispatch, using temperature and
API gravity as predictor variables. The results showed that
the model fits historical data excellently, explaining almost
all variability in the volume correction factor.
Validating the model with actual dispatch and storage data
confirmed its high accuracy in effectively predicting the
required correction factor. This will enable the distributing
company to significantly improve fuel logistical planning,
reducing costs and billing inconsistencies.
The research provides an analytical tool with operational
implementation potential. It will standardize procedures,
train key personnel, and ensure accurate calculation of the
correction factor throughout the fuel oil dispatch process.
Universidad de
Guayaquil
INQUIDE
Ingeniería Química y Desarrollo
https://revistas.ug.edu.ec/index.php/iqd
ISSN – p: 1390 –9428 / ISSN – e: 3028-8533 / INQUIDE / Vol. 06 / Nº 02
Facultad de
Ingeniería Química
Ingeniería Química y Desarrollo
Universidad de Guayaquil | Facultad de Ingeniería Química | Telf. +593 4229 2949 | Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec | francisco.duquea@ug.edu.ec
Pag. 47
Furthermore, real-time monitoring of storage indicators
provided valuable information for optimal demand
forecasting. This will facilitate more effective coordination
of the energy supply chain to various consumption points.
The obtained results lay the groundwork for future research
aimed at including more independent variables, considering
other fuels, and expanding the geographical scope of the
predictive model. Similarly, periodic evaluation of the
model's performance is recommended in response to
potential changes in business conditions.
Ultimately, this study demonstrates the importance and
technical feasibility of employing advanced tools like
multivariate regression for optimizing complex logistical
processes in the energy sector. It represents a high-impact
research with implications for operational, scientific, and
strategic decision-making in companies.
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Universidad de
Guayaquil
INQUIDE
Ingeniería Química y Desarrollo
https://revistas.ug.edu.ec/index.php/iqd
ISSN – p: 1390 –9428 / ISSN – e: 3028-8533 / INQUIDE / Vol. 06 / Nº 02
Facultad de
Ingeniería Química
Ingeniería Química y Desarrollo
Universidad de Guayaquil | Facultad de Ingeniería Química | Telf. +593 4229 2949 | Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec | francisco.duquea@ug.edu.ec
Pag. 48
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