Inventory Control for Eyeglass Supply Using the P Model Based on Sales Products Sales Forecasting (Case Study: Merry Optic Bandung)

Inventory is a resource owned by the company to be used in the production process to meet consumer demand. Companies must be able to control inventory appropriately in order to avoid excess or shortage of inventory by using inventory control. Inventory control is a necessary part of a company that requires an appropriate inventory policy to meet uncertain needs. Based on this background, this study discusses the single item inventory model in the form of photochromic glasses at Merry Optik to find the optimal total inventory cost. In meeting the uncertain needs of the company, the Additive Decomposition forecasting method is used in order to find out the forecast sales data pattern in the future. Uncertain demand causes the inventory system to be probabilistic, so it is necessary to carry out probabilistic inventory control. The P model of the case of back orders was chosen because the range of ordering periods is fixed and the company can buy inventory when it runs out before the time the inventory order is made so that buyers can wait until the inventory arrives. By using Model P for the case of back orders, the company can obtain the period between orders, the total cost of inventory, and the optimal level of service. Based on the results of this study, a pattern of sales forecast data is obtained which repeats every 12 months. Companies must order glasses within a period of 32 days between orders so that it is optimal and able to provide a reduction in the total inventory cost of IDR 21,828,771 with a service level of 95%. Companies can save on inventory costs if they use shorter periods between orders. The total cost of inventory can be more optimal if the company reduces the cost of storing inventory in the warehouse.


Introduction
Retail marketing or retail business is the activity of selling goods or services to individuals for their own needs.Retail marketing is effective marketing because it involves selling goods directly to end consumers so that consumers can get products quickly.The eyewear retail industry is developing rapidly in line with the development of technology in this digital age.This has resulted in greater competition in the eyewear business, resulting in more and more eyewear innovations The existence of inventory, especially in a company, needs to be regulated in such a way as to produce the expected product at the minimum possible cost with optimal results both in terms of quantity and quality.In inventory control there must be a system for recording and counting inventory, because this affects financial reporting.Inventory system is a system used to manage inventory in the warehouse.Inventory information system is a system used to collect and maintain data that describes commodity inventories, transforms data into information and reports to users.The problem with companies that often occurs is that the demand for an item often changes every time.
Merry Optik is a company located at Jalan Nanjung KM 4, Margaasih District, Bandung City.Merry Optik is a company engaged in the optical industry, namely, a company engaged in the health sector that provides health services in the field of eyewear.Sales of glasses at Merry Optik change over time, sometimes increasing or decreasing and are expected to have seasonal influences.The inventory policy that needs to be carried out by Merry Optics is to use the P model with back order cases based on forecasts of eyeglass sales using the Additive Decomposition method.
Previous studies related to the method used by Fatma and Pulungan to analyze the condition of a company's inventory using the probabilistic inventory method, including simple probabilistic control, the P model, and the Q model.The result is that the P model provides the cost and amount of safety stock.
This problem can be solved by using forecasting methods to determine the amount of demand in the future, then it will be determined the appropriate product inventory policy based on the forecasting results.The state of the art in this research can be seen in Table 1.  1 and the problems above, the main discussion in this research is to combine the additive decomposition forecasting method with the P Model probabilistic inventory method with back order condition to solve inventory problems in Merry Optik.

Inventory Control
Inventory control is a series of control policies to determine inventory levels that must be maintained, when orders to increase inventory must be made, and how large orders must be held (Render et al., 2011).

Probabilistic Inventory Control Method
According to Render et al., (2011), a probabilistic inventory control method is an inventory model where conditions are not known with certainty, but the expected value, variance and distribution pattern can be predicted.The probabilistic inventory control policy is known by the existence of two methods, which are P Model and Q Model.The difference between the two models lies in the time of order.

P Model with Back Order Condition
P Model is a probabilistic inventory model related to the determination of operating stock and safety stock.In P Model, order time is the main parameter and the period between ordered orders is constant (Bakker, 2012).In a back order condition, when inventory is not available, the buyer wants to wait for the requested product until it is available in the warehouse and the company will make an emergency purchase.Cost formulations considered in inventory control include: The total inventory cost equation ( ) is the sum of all inventory costs can be seen in equation 5.
To get the inventory solution with the P Model with back order condition, the value needs to be minimized by determining the optimal value of and .To obtain this value, the Hadley-Within algorithm can be calculated in the following way (Bakker, 2012): a) Calculate the initial value of with the Wilson Formula √ (6) b) Next the value of the possible shortage of inventory will be calculated and the value will be calculated after ( 7) Then calculated total cost of inventory with the following equation: d) Recalculate the value of using the following equation and then return to step (2) (10) e) If the value of ( ) less than ( ) , then return to step (4).If the value of ( ) more than ( ) , then return to step (4) with the reduction iteration

Forecasting
Forecasting is used to estimate how much demand will be in the future which includes needs in terms of quantity, quality, and time required in order to meet demand for goods (Makridakis, 2008).One of the forecasting methods is the time series method in which the analysis is carried out based on the forecast results which are compiled on the relationship pattern between the variables being sought and the time variable that influences them.The purpose of the time series is to find patterns in historical data series and extrapolate these patterns to the future (Li et al., 2023).The types of data patterns in time series are divided into four, which are horizontal, seasonal, cyclical, and trend.

Additive Decomposition
Additive Decomposition forecasting is a method used for data that contains trend and seasonal elements, where the seasonal elements indicate a relatively constant seasonal fluctuation.According to makridakis (2008).The equation used for forecasting with the Holt-Winter Exponential Additive method is as follows: a) Calculating the moving average of the period whose length is is equal to the seasonal length ( ) and b) Determine the seasonal value ( ) In the calculation of the seasonal value we will remove the error with medial average and adjustment value, Medial average is averaging the values in each period minus the minimum and maximum values in that period.Adjustment value is medial average sum divided by sum of medial average.c) Determine the trend value ( ) with e) Determine the forecast value ( ) (16)

Validation of Forecasting Method Accuracy
In this research, the calculation of forecasting accuracy is used with the Mean Absolute Percentage Error (MAPE).MAPE is a measurement of accuracy by calculating the total percentage between forecasting data that deviates from the actual data (Baykal et al., 2022).The MAPE formula is as follows: The MAPE criteria according to Baykal et al. (2022) can be seen in

Materials
The object of this research was conducted at Merry Optik which is a company engaged in the optical industry, a company engaged in the health sector that provides health services in the field of eyewear.The main product that is Merry Optik's mainstay is photochromic glasses.The company is located at Jalan Nanjung KM 4, Margaasih District, Bandung City.The data in this study are primary data, namely eyeglass sales data in the period January 2017 to December 2021.Microsoft Excel and SPSS are the software used.

Methods
The research method used in this research is descriptive quantitative method.The reason for using the quantitative method is because the research data used is in the form of numbers and being analyzed using a model then the results will be given a discussion.It is said to be descriptive because the results obtained will be described and explained regarding the object under the research through the data that has been collected.As for the research process, data collection methods are obtained as follows:

Results and Discussion
The data shown are the graph of sales data patterns for glasses products in Figure 1.13).The result of calculating seasonal value without error are presented in Tables 4 and 5.  Calculation is calculated by using equation ( 14).The result of calculating trend value is presented in Tables 6.
Table 6: The value of trend value the period 1 to 60 Period ( )  Based on calculations through equation ( 17), the results show that the MAPE value is less than 20%.where the MAPE value is 6.373%.
After knowing the results of product forecasting, then a normality test will be carried out on product sales data.The normality test uses the Kolmogorov-Smirnov test with the test hypothesis:   4, the significance value is greater than 0.05.This indicates that the hypothesis is accepted and the data is normally distributed.Because the data is normally distributed, the data can be used in inventory control calculations using the Model P probabilistic inventory method with back order conditions.
The data needed for the probabilistic inventory method calculation process Q Model with lost sales conditions can be seen in Table 16.Calculations are performed using equations ( 6), ( 7), ( 8), (9), and (10).The inventory control calculation results for each product are presented in Table 9 and 10.

Conclussion
The results showed that the Additive Decomposition forecasting method is a good method used to forecast the demand for glasses at Merry Optik because the forecasting calculation produces a MAPE value of less than 20%.By using the P model based on sales forecast data, companies can save on total inventory costs by 9.77% and cut the period between orders to 32 days with a service level of 94.35%.The additive decomposition method can be used to determine forecasting sales data.
with the following test criteria:a.If the significant value then accepted b.If the significant value then rejected Calculations are calculated with SPSS software to carry out the Kolmogorov-Smirnov Test process.

Table 1 :
State of the art research

Table 2 Table 2 :
The

Table 4 :
The value of seasonal value with error the period 7 to 54

Table 5 :
The value of seasonal value the period 1 to 12 Period ( ) Season 1 Season 2 Season 3 Season 4 Medial average Seasonal ( )

Table 7 :
The value of cycle the period 7 to 54

Table 9 :
P Model probabilistic inventory method calculation data with back order condition

Table 10 :
Hadley-Within calculation results for product inventory Iteration( )