Application of Fuzzy Time Series (FTS) Algorithm in Production Planning of Indonesia’s Oil Refining Company

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INTRODUCTION
Z Company is one of the Republic of Indonesia State-Owned Enterprises (BUMN) companies that focuses on oil and energy processing. In order to meet the demand, Z Company has 6 refinery units spread across Indonesia. One of the processes carried out is refining crude oil and naptha into fuel oil (BBM) and one of its products is Premium. Premium is very popular in Indonesia and in high demand in 2019. It is relatively cheap price since it receives subsidies from the state budget. Even tough there is an issue that Premium production will be stopped due to bad impact for environment, but this research will still be useful by proposing an approach for accurate production planning applicable for other products.
Seeing the large amount of Premium demand so that good planning is needed starting from accurate sales forecasting to effective aggregate planning strategies to allocate the capacity of the resources that are owned to meet the predicted demand so as to minimize production costs. With accurate sales forecasting, material requirements planning (MRP) and production scheduling will be effective which ultimately can satisfy the customer's desires [1].
At present, forecasting by Z Company uses qualitative methods which only rely on intuition from the expert so that the accuracy cannot be known and the subjectivity is very high. It will be very risky for the failure of planning. In this study, forecasting for the next 3 months namely March, April and May 2019 will be done using Fuzzy Time Series (FTS)-based Algorithm which is compared with other methods. Then, the most accurate forecasting method will be used as input in aggregate planning using the heuristics or graphical method so that low production costs can be obtained to meet Premium sales forecasting.
A similar study was conducted by Gansterer (2015) [2] who used time series-based forecasting which is then continued with aggregate planning using the simulation model. Mantilla et al. (2017) [3] conducted aggregate planning by evaluating 2 strategies, namely Zero inventory and Vary Inventory with input demand obtained from MPS. Fajar and Lestari (2017) [4] conducted aggregate planning using Model 2 and Model 4 introduced by Heizer (2008) [5]. Whereas Gulsun et al. (2009) [6] conducted forecasting using the multiplicative decomposition model with trends and seasonal patterns which is then continued with aggregate planning using Linear Physical Programming method. Compared to previous research, it has not been studied about forecasting using the FTSbased Algorithm which is then continued with heuristic-based aggregate planning especially applied in Oil Refining Company. Table 1 shows the historical data obtained from the company report. The amount of data in forecasting greatly determines the accuracy of the forecasting. Therefore, it is necessary to test the adequacy of data using Equation (1) [7]. Furthermore, production cost data can be seen in Table 2 that will be used in aggregate planning stage.

Data Collecting
By using 95% confidence level (k) and a degree of accuracy (s) of 10%, calculate with formula 1, it is obtained N' = 10.8 which is less than 26 (N). Because N'<N, then it can be said that 26 historical data are sufficient enough to be used as the basis for time-series analysis. It is worth noting that forecasting result will be poor if time horizon is too long. Therefore, in this research, the time horizon is determined only for the next 3 months namely March, April, and May 2019. Z Company also has several company policies including safety stock = 50,000 Bbl / month, Z Company does not recruit new workers and lay off workers for production needs in the refinery, but will be outsourced. The company also does not subcontract if it is unable to fulfill a number of requests, but will try to increase production capacity as requested. If the production capacity is still not fulfilled, the company will allow stockout. At present, Z Company has 120 workers/day, which in one day is divided into 3 shifts, each shift working for 8 hours. To determine the ability of workers in Premium production, obtained from the production rate in February 2019 amounted to 1349992 Bbl/28 days = 48214 Bbl/day = 48214 Bbl/24 hours = 2008.9 Bbl/hour. The number of workers per day in February 2019 is 154 workers, so each worker can produce = 2008.9 Bbl/hour /154 = 13 Bbl/hour. So, it takes 0.077 hour for workers to produce 1 Bbl Premium.
In order to test the reliability of algorithm, comparison analysis is needed. Since historical data have a horizontal pattern, the other methods are also used that are suitable for forecasting with horizontal data pattern like moving average (MA), weighted moving average (WMA) and single exponential smoothing (SES). The main difference between the FTS-based algorithm of a time series and classical time series or even machine learning and deep learning is that the values are represented by fuzzy sets rather than real crisp values. The error measurement used are Mean Absolute Deviation (MAD) and Mean Absolute Percentage Error (MAPE) with formula shown in Equation (2) dan Equation (3) [5]. At informs actual data in t period, Ft informs forecasting data in t period, and n informs number of historical data used.

Forecasting Using FTS Algorithm
The FTS Algorithm is a forecasting technique that follows fuzzy theory to predict uncertainty in the future. There are some FTS algorithms proposed by researchers since it gives promising results, some of them are developed by Cheng et al. [8], Qiu et al. [9], Cagcag et al. [10], Liu et al. [11], Hwang et al. [12] and Lee & Chou [13]. The difference may happen in determining interval length to form fuzzy logical relationships and or fuzzy logical relationship groups, level of order, But, in this research, FTS algorithm developed by Jasim et al. [14] is used. The reason because it belongs to the first order and time-variant methods that sometimes give better result. Then the calculation is done by following these steps [15] [16].  Table 3. Table 4. FLR is described as Aj → Ai, where the left side is called the current state and the right side is called the next state. 6. Determining Fuzzy Logical Relationship Group (FLRG) showed in Table 5. FLRG is formed to see the tendency of changes in data from certain state to the next state which will later determine the results of forecasting. 7. Calculating forecasting results. In this step, certain provisions are used as described in previous research [10].

Aggregate Planning
In this research, aggregate planning is carried out using graphical method, where cost calculations will be carried out using strategies as follows [17].
1. Level strategy: the amount of production is fixed and the inventory that arises can be used to meet the excess demand for the product for a certain period. 2. Chase strategy: this strategy provides that the amount of production is equal to the number of demands. 3. Hybrid strategy: this strategy is a combination of level strategy and chase strategy. Where in this case, the amount of production is obtained from a minimum of the existing forecasting value. In certain circumstances, it can change according to company policy. Figure 1 shows the steps carried out in this research.

Forecasting Results
The four methods used for forecasting are FTS, MA with M = 3, WMA with M = 4 (W1 = 0.4, W2 = 0.3, W3 = 0.2, and W4 = 0.1), and SES (alpha = 0.8). The result of forecasting will be displayed as graphic that can be seen in Figure 2. Testing the level of accuracy is done by comparing the measurement criteria for Mean Absolute Deviation (MAD) and Mean Absolute Percentage Error (MAPE) in Table 6. Table 6 shows that FTS have significantly smaller MAD and MAPE values than other methods. Then, FTS result will be used to predict the period of March 2019 until May 2019 which is then used as input in aggregate planning shown in Table 7.

Aggregate PlanningRresults -Level Strategy
In this strategy, the amount produced in everyday is the same as the average sales forecast. Average Requirement = (1200500 + 1349000 + 1349000)/92 = 40760,869 Bbl/day and initial inventory in March = 148000 Bbl. The table of calculation of level strategy can be seen in Table 8 and the graphic produced if the company implements level strategy showed in Figure 3. Table 8. Level strategy calculation. So that the total production cost obtained amounted to Rp 4,969,500,000.

-Chase Strategy
The table of calculation of chase strategy can be seen in Table 9 and the graphic produced if the company implements a chase strategy showed in Figure 4. With the same calculation as at the level strategy. The total production cost obtained in the chase strategy is Rp 4,976,500,000. Table 9. Chase strategy calculation.

-Hybrid strategy
In a hybrid strategy, the company produces production with the same amount of production as the minimum number of forecasting, which is 1,200,500 Bbl per month. The table of calculation of hybrid strategy can be seen in Table 10 and the graphic produced if the company implements a hybrid strategy showed in Figure 5. Because the company has a safety stock policy of 50,000 Bbl/month, the strategy needs to be revised. Then the solution is to increase the level of production to meet the policy. Therefore, in April 2019 a total of production is 1,200,500+50,500=1,251,000. Revision of this strategy can be seen in Figure 6. With the same calculation as at the level strategy. The total production cost obtained in the hybrid strategy is Rp 3,272,000,000.  Figure 6. Revised hybird strategy graphic.

Discussion
From the result of forecasting using FTS, it can be seen that this method is more accurate than the other methods. The company can use this method in forecasting Premium sales with very high accuracy, where the amount of MAPE is only 0.87%. From the results of aggregate planning, it was found that the lowest production costs could be achieved by using a hybrid strategy where the company produces Premium at the lowest forecasting value, then if there is a stockout and shortages of stocks beyond the safety stock limit (such as in April 2019) then the solution is to increase production capacity, this is because Z Company does not do subcontract, so increasing production capacity is the right choice. The implementation of the hybrid strategy only costs as much as Rp 3,272,000,000 for the next 3 months. The comparison between the 3 strategies in aggregate planning at Z can be seen in Table 11.

CONCLUSIONS
From the results of the previous discussion, it can be taken from this research that the FTS method has a significantly more accurate than the moving average (MA), weighted moving average (WMA) and single exponential smoothing (SES). With MAPE = 0.87% and MAD = 10824 in forecasting Premium sales, The number of Premium sales for the March, April and May 2019 that must be fulfilled based on the FTS is 1200500 Bbl, 1349000 Bbl and 1200500 Bbl in sequence. Based on the results of aggregate planning using heuristics or graphical method, it is found that the lowest production costs can be achieved by the company using a hybrid strategy, which produces Premium at the lowest forecasting amount of 1200500 Bbl every March and May. However, in April there was a stockout and exceeded safety stock limit so that the level production in April was 1251000 Bbl. The implementation of hybrid strategy can produce production costs of Rp 3,272,000,000 which is 34.3% lower than the chase strategy and lower by 34.2% compared to level strategy. The proposed approach in this research also can be used for other products to enhance production planning, not only Premium.