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INTRODUCTION
Every company that produces drugs or what is known as a pharmaceutical company has a distributor to market its
products. Products from the factory will be sent directly to distributors and will offer these products to drugstores,
retailers, and other outlets. The role of distribution and transportation networks is very vital because it allows products
to move from production sites to consumer locations that often limited by very long distances1.
In order services to consumers, the problem of timeliness and number of deliveries is a problem faced by
pharmaceutical distributor companies, where companies must meet customer needs by delivering products in the exact
quantity, right place, and the right time. In distributor companies, the excess product can cause a decrease in revenue.
Therefore, one of the problems with pharmaceutical distributor companies is the large number of each product that
must be kept in stock. So that in its operational activities, the distributor company must be able to manage the strategy
for the entry and exit of goods2.
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Precise sales forecasting is a crucial and low-cost technique for every organization to increase revenues, lower
costs, and increase flexibility in the face of change. Proper sales forecasting, in other words, is used to capture the
tradeoff between customer demand satisfaction and inventory costs3. Due to the limited shelf-life of many
pharmaceutical items and the importance of product quality intimately tied to human health4, successful sales
forecasting systems can be advantageous for the pharmaceutical sector.
As faced by PT. Lenko Surya Perkasa Branch Office Sidoarjo that distributes medicines and health products with
an expiration date based on sales and warehouse data for the period October 2019 - August 2020, said the number of
damaged products continued to increase, around 23% of the total product, the low sales quantity, and manual restock
quantity estimation which often misses resulted in higher warehouse storage levels. Proven by several products reload
during the period October 2019 – August 2020, but no sales occurred, resulting in an increase in the number of products
in the warehouse and product damage due to being in the warehouse for too long.
Formulate a strategy for the entry and exit of appropriate goods into a problem at PT. Lenko Surya Perkasa Branch
Office Sidoarjo, forecasting is an alternative solution that can predict the number of sales in the future so that the sales
strategy is formulated according to sales in the market and can generate profits for the company. Because sales forecast
did with high accuracy and a short time, it is impossible to do it manually or traditionally. For this reason, it is
necessary to apply an appropriate forecasting method to increase the accuracy of sales forecasts and speed up the
process. As a result, the purpose of this study relates to an accurate sales forecasting model application for sales of
health products that occurred at PT. Lenko Surya Perkasa Branch Office Sidoarjo.
In this case, the forecasting model used is the Least Square Method (LSM), Simple Polynomial Regression, and
the Simple Moving Average (SMA) as a comparison model, all the methods commonly used in forecasting sales.
LITERATURE REVIEW
Forecasting
Forecasting is a process for estimating some future needs which include terms of quantity, quality, time, and
location needed to meet the demand for goods or services5. It involves collecting past data that is processed
mathematically using a particular model according to the characteristics of the data.
There are two sorts of forecasting methods: qualitative and quantitative. Quantitative forecasting is a statistical
method for creating future projections based on the past, whereas qualitative analysis is subjective and expert opinions.
Demand from solicited opinions modeled using qualitative approaches. Future activity anticipated utilizing
quantitative models from previous cycle sales for products with demand history available6.
Quantitative forecasting can be divided into two categories: time series and causal. Time series analysis uses
previous data and prior knowledge to forecast future characteristics. In order to forecast demand, this technique uses
time as the independent variable. The causal relationship is relevant if there is a causes and effects link between an
input variable and its corresponding output7.
Least Square
Least Square method is a curve fitting method that is widely used for data. Least Square is one of the most popular
methods used to determine the position of the trend line of a given time series. The resulting trend line is technically
called the best model8.
The time series analysis using the Least Square method is divided into two cases, the odd data case and the even
data case9. The Least Square method is one of the approaches used for forecasting, regression or equation formation
from discrete data points (in modeling), and measurement error analysis (in model validation). In the form of the
equation, the linear trend value is presented as follows:
̂ = + (1)
Where:
̂ = Forecasting value
x = Specific time in code form
a = Trend variable Coefficient
b = Trend Direction Coefficient
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In determining the value of x, alternative steps are often used by giving a score or code. In this case, the data is
divided into two groups, namely:
1. Even data, then used the score of value x: …, -5, -3, -1,1,3,5, …
2. Odd data, then used the score of value x: …-3, -2, -1,0,1,2,3, …
The principle of the Least Square method is to minimize the number of squared deviations (∑( − ̂)2) from the
value of the independent variable (y) with the forecast value (̂)8. By using partial derivatives, ∑( − ̂)2 can be
minimized, so that two equations will be obtained, namely:
∑ = . + . ∑ (2)
∑ = . ∑ + . ∑ 2 (3)
By solving the two normal equations simultaneously, the values of a and b of equation ̂ = + can be
calculated. To make the calculation simpler, the coding for the value of x is attempted in such a way that ∑ = 0,
thus, the above normal equation can be simplified to:
=
∑
(4)
=
∑
∑2
(5)
Where:
n = Count of data
x = Specific time, in code form
y = Data variabel
Polynomial Regression Through Least Square
When presented with a data set it is often desirable to express the relationship between variables in the form of an
equation. The most common method of representation is a kth order polynomial which which can be seen in Equation
614:
=
+ ⋯+ 1 + 0 + (6)
The above equation is the general polynomial regression model with the error serving as a reminder that the
polynomial will typically provide an estimate rather than an implicit value of the dataset for any given value of x.
The maximum order of the polynomial is dictated by the number of data points used to generate it. For a set of N
data points, the maximal order of the polynomial is k = N-1. But the best practice is to use the lowest possible order
to represent your dataset accurately. The higher the degree of the polynomial as it passes through each data point, it
can exhibit erratic behavior between these points due to a phenomenon known as polynomial wobble.
The general polynomial regression model can be developed using the method of least square. The least-square
model aims to minimize the variance between the values estimated from the polynomial and the expected values from
the dataset.The coefficients of the polynomial regression model ( , −1, … , 1)