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qbus3330 Precise ​sales
Creation date：2024-05-30 17:35:00
Belonging category：市场营销Marketing
Precise ​sales

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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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30 June 2023 14:16:28
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)
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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