=Paper=
{{Paper
|id=Vol-2714/icaiw_wdea_1
|storemode=property
|title=Demand Forecasting for Inventory Management using Limited Data Sets: A Case Study from the Oil Industry
|pdfUrl=https://ceur-ws.org/Vol-2714/icaiw_wdea_1.pdf
|volume=Vol-2714
|authors=Jorge Ivan Romero-Gelvez,Esteban Felipe Villamizar,Olmer Garcia-Bedoya,Jorge Aurelio Herrera-Cuartas
|dblpUrl=https://dblp.org/rec/conf/icai2/Romero-GelvezVG20
}}
==Demand Forecasting for Inventory Management using Limited Data Sets: A Case Study from the Oil Industry==
https://ceur-ws.org/Vol-2714/icaiw_wdea_1.pdf
Demand Forecasting for Inventory Management
using Limited Data Sets: A Case Study from the Oil
Industry
Jorge Ivan Romero-Gelvez, Esteban Felipe Villamizar, Olmer Garcia-Bedoya and
Jorge Aurelio Herrera-Cuartas
Universidad de Bogotá Jorge Tadeo Lozano, Bogotá, Colombia
Abstract
This document’s main focus is to present a way to solve forecasting issues using open source tools
for time series analysis. First, we present an introduction to the hydrocarbon sector and time series
analysis, later we focus on the solution methods based on supervised learning trained (support vector
regression) with bio-inspired algorithms (Particle swarm optimization). We expose some benefits of
use support vector machines and open source tools that focuses on variables like trend and seasonality.
In this work, we chose the fb-prophet package and support vector regressor with scikit-learn as the
primary tools because they have representative results dealing with limited data sets and Particle swarm
optimization as training algorithm because of their speed and adaptability. Finally, we show the results
and compare them with their RMSE obtained.
Keywords
Hydrocarbon, Forecasting, small time-series, support vector regressor, particle swarm optimization
1. Introduction
The hydrocarbon sector is the protagonist of the world economy’s growth, seeking to expand
as a critical piece of economic development through energy consumption, exploration, and
production of oil where its primary producers are the USA, Russia, Saudi Arabia Iraq, Canada,
and Iran. In 2019, 83 million barrels per day were produced, and Colombia reached participation
of 863 thousand barrels, being the country number 22 within the scale of producers worldwide.
In Colombia, the hydrocarbon sector has contributed significant growth, standing out as the
engine of the country’s development. The ACP estimates that the investment in production
in 2020 will be around USD 4,050 million, that is, 25% higher than that of 2019 (USD 3,250
million). By region, 90% of the investment will be carried out in the Llanos Orientales, Valle
Magdalena, and Caguán - Putumayo basins. By department, the following stand out: Goal
USD 1,924 million, Santander USD 560 million, Casanare USD 496 million, Putumayo USD 239
ICAIW 2020: Workshops at the Third International Conference on Applied Informatics 2020, October 29–31, 2020, Ota,
Nigeria
" jorgei.romerog@utadeo.edu.co (J.I. Romero-Gelvez); estebanf.villamizar@utadeo.edu.co (E.F. Villamizar);
olmerg@gmail.com (O. Garcia-Bedoya); jorgea.herrerac@utadeo.edu.co (J.A. Herrera-Cuartas)
0000-0002-5335-0819 (J.I. Romero-Gelvez); 0000-0002-6964-3034 (O. Garcia-Bedoya); 0000-0003-0273-4043 (J.A.
Herrera-Cuartas)
© 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
million, and Arauca USD 101 million.
Also, the ACP projects that in 2020 there will be an investment in exploration and production
of oil and gas of USD 4,970 million, 23% higher than in 2019. Indeed, the largest company in
the country and the leading oil company in Colombia belong to the group of the 39 largest oil
companies in the world and is one of the top five in Latin America. They have hydrocarbon
extraction fields in the center, south, east and north of Colombia, two refineries, ports for
the export and import of fuel and crude oil on both coasts, and a transportation network of
8,500 kilometers of pipelines and pipelines to throughout the entire national geography, which
interconnect production systems with large consumption centers and maritime terminals.
Given this panorama, the industries must plan strategies to manage and control their inven-
tories since their importance lies in obtaining profits. Inventory management plays a vital role
within the business chain, which is the buffer between two processes, supply, and demand. This
can be known or unknown, variable, or constant. The sourcing process contributes goods to
inventory while demand consumes the same inventory. This is necessary due to differences in
rates and times between supply and demand, and this difference must be attributed to internal
or external factors. Endogenous factors are policy issues, but exogenous factors are uncon-
trollable. Internal factors include economies of scale, smoothing of operation, and customer
service, the most important exogenous factor being uncertainty.
Given that inventory control is a critical aspect for effective management and administration,
in order to guarantee the availability of equipment, spare parts, and materials to meet the
needs of expenses and projects with the expected quality, cost, and opportunity. Likewise,
the materials management process is to ensure that the materials that register stock in the
warehouse correspond to optimal levels of inventories, such quantity must fully meet the needs
of the company with the minimum investment.
2. Literature review
There are applications in forecasts using SVR and it is more common to find them in recent
years, since there is a special interest in machine learning applications to make predictions on
time series. An example of this can be seen in [1] with financial forecasts, [2, 3] over rainfall
predictions, electric load forecasting [4, 5, 6], forecasting carbon price [7] among many oth-
ers. Next, we present a brief introduction to the time series and later we will deal with the
comparison of the applied models.
2.1. Time series analysis
The analysis of time series and demand forecasts becomes the primary input for the MRP model.
For this reason, it is proposed to contrast different methods that allow considering seasonal
periods, and that may also include new demand observations to adjust the model in real-time.
According to [8] Time-series methods refers to a set of observations of real phenomena (like
mathematical, biological, social sciences, physical, economic among others) given as part of
a discrete set in time. The main thought is that past data can be utilized to generate future
estimations. In time series analysis is common to try to get patters of data as trend, seasonality,
cycles, and randomness as inputs to modeling the phenomena.
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• Trend: The data set exhibits a stable pattern of growth or decrease.
• Seasonality: A seasonality pattern are those that are repeated at fixed intervals.
• Cycles: The variation of cycles is similar to seasonality, except that the duration and the
magnitude of the cycle varies.
• Randomness: A random series is where you do not have a recognized pattern of data.
One can generate random series of data that have a specific structure. The data that
seems to have apparently a randomness , actually have a specific structure. Actually the
really random data fluctuate around a fixed average.
2.2. Support Vector machine and support vector regressor
According with [9] In machine learning, support vector machine proposed by Vapnik is one
of the most popular approaches for supervised learning [10, 11]. This model resembles logistic
regression in that a linear function 𝒘 ⊤ 𝒙 + 𝑏 drives both. Its main difference is that the logistic
regression produces probabilities, the support vector machine produces a class identity. The
SVM predicts that the positive class is present when 𝒘 ⊤ 𝒙 + 𝑏 is positive. Likewise, it predicts
that the negative class is present when 𝒘 ⊤ 𝒙 + 𝑏 negative. A notable feature of support vector
machines is the kernel, considering that many algorithms can be written in the form of a dot
product. As an example, the rewritten SVM linear function is shown as:
𝑚
𝒘 ⊤ 𝒙 + 𝑏 = 𝑏 + ∑ 𝛼𝑖 𝒙 ⊤ 𝒙 (𝑖) (1)
𝑖=1
where 𝑥(𝑖) is a training example and 𝛼 is a vector of coefficients. Rewriting the learning
algorithm this way allows us to replace 𝑥 by the output of a given feature function 𝜙(𝒙) and
the dot product with a function 𝑘 (𝒙, 𝒙 (𝑖) ) = 𝜙(𝒙) ⋅ 𝜙 (𝒙 (𝑖) ) called a kernel. The (·) operator
represents an inner product analogous to 𝜙(𝒙)⊤ 𝜙 (𝒙 (𝑖) ). For some feature spaces, we may not
use literally the vector inner product. In some infinite dimensional spaces, we need to use
other kinds of inner products, for example, inner products based on integration rather than
summation. After replacing dot products with kernel evaluations, we can make predictions
using the function
𝑓 (𝒙) = 𝑏 + ∑ 𝛼𝑖 𝑘 (𝒙, 𝒙 (𝑖) ) (2)
𝑖
This function is nonlinear with respect to 𝑥, but the relationship between 𝜙(𝒙) and 𝑓 (𝑥)
is linear. Also, the relationship between 𝛼 and 𝑓 (𝑥) is linear. The kernel-based function is
exactly equivalent to preprocessing the data by applying 𝜙(𝒙) to all inputs, then learning a
linear model in the new transformed space. The kernel trick is powerful for two reasons. First,
it allows us to learn models that are nonlinear as a function of 𝑥 using convex optimization
techniques that are guaranteed to converge efficiently. This is possible because we consider 𝜙
fixed and optimize only 𝜶 , i.e., the optimization algorithm can view the decision function as
being linear in a different space. Second, the kernel function 𝑘 often admits an implementa-
tion that is significantly more computational efficient than naively constructing two vectors
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and explicitly taking 𝜙(𝑥) their dot product. In some cases, 𝜙(𝑥) can even be infinite dimen-
sional, which would result in an infinite computational cost for the naive, explicit approach.
In many cases, 𝑘 (𝒙, 𝒙 ′ ) is a nonlinear, tractable function of x even when 𝜙(𝑥) is intractable.
As an example of an infinite-dimensional feature space with a tractable kernel, we construct
a feature mapping 𝜙(𝑥) over the non-negative integers 𝑥. Suppose that this mapping returns
a vector containing 𝑥 ones followed by infinitely many zeros. We can write a kernel function
𝑘 (𝑥, 𝑥 (𝑖) ) = min (𝑥, 𝑥 (𝑖) ) that is exactly equivalent to the corresponding infinite-dimensional
dot product.
2.3. Support vector regressor
According to [12] the basic idea of SVR is to map the data 𝑥 into a high dimensional feature
space by nolinear mapping 𝜙 and to do linear regression in this space. Also, according to
[13] we can consider a set of training data 𝑓 (𝑥) = (𝑤 ⋅ 𝜙(𝑥)) + 𝑏, where each 𝑥𝑖 ⊂ 𝑅 n denotes
the input space of the sample and has a corresponding target value 𝑦𝑖 ⊂ 𝑅 for 𝑖 = 1, … , 𝑙, where
corresponds to the size of the training data. The idea of the regression problem is to determine
a function that can approximate future values accurately. The generic form of SVR can be seen
as follows
𝑓 (𝑥) = (𝑤 ⋅ 𝜙(𝑥)) + 𝑏 (3)
where, 𝑤 ⊂ 𝑅 n , 𝑏 ⊂ 𝑅 and 𝜙 denotes a nonlinear transfor to high-dimensional space. Our goal
is to find the value of and such that values of can be determined by minimizing the regression
risk
𝓁
𝑅reg (𝑓 ) = ∑ 𝐶 (𝑓 (𝑥𝑖 ) − 𝑦𝑖 ) + 𝜆‖𝑤‖2 (4)
𝑖=1
where 𝐶(⋅) is a cost function, 𝜆 is a constant, and vector 𝑤 can be written in terms of data
points as
𝓁
𝑤 = ∑ (𝛼𝑖 − 𝛼𝑖∗ ) 𝜙 (𝑥𝑖 ) (5)
𝑖=1
By substituting eq.5 into eq.3, the generic equation can be rewritten as
𝓁 𝓁
𝑓 (𝑥) = ∑ (𝛼𝑖 − 𝛼𝑖∗ ) (𝜙 (𝑥𝑖 ) ⋅ 𝜙(𝑥)) + 𝑏 = ∑ (𝛼𝑖 − 𝛼𝑖∗ ) 𝑘 (𝑥𝑖 , 𝑥) + 𝑏 (6)
𝑖=1 𝑖=1
In eq.6, the dot product is replaced with a kernel function 𝑘 (𝑥𝑖 , 𝑥) = (𝜙 (𝐱𝑖 ) ⋅ 𝜙 (𝐱𝑗 )). Kernel
functions enable the dot product to be performed in high-dimensional feature space using low-
dimensional space data input without knowing the transformation 𝜙. All kernel functions must
satisfy Mercer’s condition that corresponds to the inner product of some feature space. The
radial basis function RBF is commonly used as the kernel for regression
{ }
𝑘 (𝑥𝑖 , 𝑥) = exp −𝛾 |𝑥 − 𝑥𝑖 |2 (7)
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2.4. Particle swarm optimization
Particle swarm optimization is a computational technique that optimizes a problem by iter-
atively attempting to promote a candidate solution concerning a given degree of quality. It
solves a problem by producing a population of candidate solutions called particles and moving
them around the search-space with particular position and velocity. Each particle’s movement
is influenced by its local best-known place but is also guided toward the best-known positions
in the search-space, which are renewed as another particle found better solutions. This is ex-
pected to move the swarm toward the best solutions. According to [14] the main inputs for the
formulation of this algorithm can be seen as follows:
• 𝐷 is the dimension of the search space.
• 𝐸 is the search space, a hyperparallelepid defined as the euclidean product of 𝐷 real
intervals.
𝐷
𝐸 = ⨂ [min, max] (8)
𝑑 𝑑
𝑑=1
The standard form of the algorithm composes by a set of particles (called swarm), made of
a position in the search space, the fitness value at each position, a velocity for displacement,
a memory that contains the best position and last the fitness value of the previous best. The
search is performed in two phases, initialization of the swarm and a cycle of iterations. The
main steps can be seen as follows:
• Initialisation of the swarm: pick a random position in search space and pick a random
velocity.
• Iteration: compute the new velocity, move and compute the new fitness.
• Stop .
2.5. The prophet forecasting model
Prophet is an open source tool for forecasting time series observations based on an additive
model in which nonlinear trends adjust to seasonality. Their results improve with data that
includes compromises with strong seasonal effects and a considerable amount of historical
data. We use Prophet open-source software in Python [15] based in a decomposable time series
model [16] components: trend, seasonality, and vacations. They are combined as follows:
𝑦(𝑡) = 𝑔(𝑡) + 𝑠(𝑡) + ℎ(𝑡) + 𝜖𝑡 (9)
Were 𝑔(𝑡) is the trend function which models non periodic changes in the value of the time
series, 𝑠(𝑡) represents periodic changes, and ℎ(𝑡) represents the effects of vacations which occur
on potentially irregular schedules over one or more days. The error term 𝜖𝑡 represents any
idiosyncratic changes which are not accommodated by the model; We will make a parametric
assumption with normally distributed 𝑡.
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2.5.1. Prediction model
The development of an algorithm is necessary to obtain a data history in which the breakdown
of the monthly inventory value is represented by the BSE material and transit corresponding
to two years. In this analysis of generated data, factors such as inventory value and material
dependence are taken into account. These have a significant influence on the model’s behavior
since they provide realism and specific variations of the trend line, which are of interest to
optimize its management. All these data have been obtained from the materials management
system. Subsequently, these data will be processed and analyzed in order to see the interaction
between them, carrying out a parameterization that allows characterizing the logic of genera-
tion of the historical.
3. Data description
The warehouse corresponds to the code assigned in the information system that represents an
organizational unit or warehouse, corresponds to the physical place where the materials are
stored, which allows differentiation of material stocks. In this case, the logistics center 2000
is taken, as a Detail describes the types of warehouse: Imported: corresponds only to mate-
rial in transit of expenses or projects. Expenses: the types of warehouses are associated with
new material in good condition and repaired material in good condition. These materials are
characteristic of the operation and maintenance, such as spare parts, consumables, and sup-
plies for the operation, equipment, lubricants, consumption tools, parts from manufacturers,
spare parts. Projects: this material is part of the business investment with a physical location
in patios and covered warehouse, this material is acquired according to the project’s require-
ment, given that the material is no longer required by the project, it is assigned as not required
material or in the process of sale which is offered to other projects of the business group.
4. Solution method and results
In order to solve the problem, we contrast two methods, the fb-prophet and PSO-SVM.
• Forecasting Model selection: In order to use the method that generates less error
𝜖𝑡 . First, we apply support vector machine with particle swarm optimizations as global
optimization algorithm. In addition, Fb-prophet (black box method) is also used. Next,
we select the method with the least error of them
• IDE: IPython/Jupyter notebooks and Google-Colab.
4.1. Results
5. Conclusions
The main forecast topic with a variety of backgrounds should make more forecasts than they
can do manually—the first component of our forecast. The system is the new model that we
116
Figure 1: Fb-prophet black box model implementation
Figure 2: Initialization of the PSO-SVM model
Table 1
RMSE error
RMSE
fb-prophet 3471658053
pso-svm 0.022833
have developed in many prediction iterations of a variety of data in FbProphet. We use a
simple modular regression model that often works well with predetermined parameters, and
that allows you to select the components that are relevant to your forecast problem and quickly
make adjustments as needed. The success of model lies in its ability to adjust the positions of
all particles in an area of search space with satisfactory solutions.
According to a determined objective function to minimize, in this case, the root mean square
error. It measures the dispersion of error in forecast, this value is the difference between real
demand and the forecast squaring, disabling those periods where the difference was higher
compared to others. From this calculation, decisions against forecast models and their results
117
Figure 3: Results of PSO-SVR
are guided to the best choice. Likewise, it is established that this type of problems are solved by
evolutionary algorithms, the importance of using these algorithms as the swarm of particles
lies in the high efficiency in generating predictions with better performance, the formulation
is reduced to characterize the movement of the particles based on a speed operator that must
associate exploration and convergence by decomposing the speed into three components in
order to decipher the study behavior.
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