ISSN: 2231-2196 (Print)

ISSN: 0975-5241 (Online)

ISSN: 0975-5241 (Online)

**IJCRR - Vol 4 Issue 12, June**

**Pages:** 177-190

**Date of Publication:** 22-Jun-2012

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**Author:** T.V.S. Raghavendra, A. Rama Krishna Rao, P.V.Chalapathi

**Category:** Technology

**Abstract:**Supply chain is a bridge between demand and supply. It conveys the demand to the supply point and

delivers the quantity to the demand point. It is a network, that facilities the functions of procurement of

materials, transformation of these materials into intermediate and finished products and the distribution of

these finished products to customers. The Bullwhip Effect represents the information distortion in a

Supply chain. It represents the phenomenon where orders to supplier tend to have larger variance than

sales to the buyer. The customer demand is distorted. This demand distortion also propagates to upstream stages in an amplified form in the supply chain. The demand forecasting is one of the key-factors to influence the bull-whip effect. Winter's Triple Exponential smoothening model is applied to forecast the future demand. The purpose of this study is to analyze the impact of exponential smoothing parameters on the bullwhip effect for Supply Chain Management (SCM). A simulation model is developed to determine the Forecasted demand and bullwhip ratio value. Further, accuracy of Forecasting alculated by the Winter's model is examined by applying Tracking Signal Technique. A sensitivity analysis is done to experiment with the different values of parameters in the forecasting technique. It is found that longer

lead times and poor selection of forecasting model parameters lead to strong bullwhip effect in SCM. The

optimized values of parameters help to reduce the bullwhip ratio. The most significant managerial mplication of this study lies in applying best forecasting technique with accuracy testing of forecasting model, to mitigate the bullwhip effect. The managers are suggested to utilize the best exponential smoothing by selecting lower values for alpha and beta and a mid-value for gamma to keep the bullwhip

ratio low, besides the forecasting accuracy.

**Keywords:** Bullwhip ratio; Forecasting; Exponential smoothing constants; MAD; SCM; Tracking Signal

**Full Text:**

**INTRODUCTION **

The sources of uncertainty in a supply chain, lie in the process of matching demand that includes delivery lead times, manufacturing yields, transportation times, machining times and operator performances [10], all lead to uncertainty in the supply chain performance. SCM includes a set of approaches and practices to reduce the uncertainty along the chain through enabling a better integration among `suppliers, manufacturers, distributors and customers [6]. It is the efficient management of the end-to-end process, which starts with the design of the product or service and ends with the time when it has been sold, consumed, and finally, discarded by the consumer‘‘ [12]. Demand forecasting is an essential tool for production and inventory planning, capacity management and the design of the customer service levels. The need to forecast the demand at each level of the supply chain amplifies the forecast errors, known as bullwhip effect in the supply chain. It represents the phenomenon where orders to supplier tend to have larger variance than sales to the buyer, and the customer demand is distorted [7]. This demand distortion also propagates to upstream stages in an amplified form. In return, high inventory levels and poor customer service rates along the supply chain constitute. They are the typical symptoms of bullwhip effect. In addition, production and inventory holding costs as well as lead times increase, while profit margins and product availability decrease [3][8]. In the earlier research, the similar problem is analytically examined by [1][2] for autoregressive demand structures and with linear trend in the demand, ignoring the demand seasonality.].This paper hence presents the sensitivity analysis part and validates forecasting accuracy using Tracking Signal concept. Setting of experimental design is identified, followed by simulation results. Conclusions are in the final section. A simulation model is developed to reduce the bullwhip effect with forecasting parameter optimization [9]. Tracking signal is computed by dividing the total residuals by their mean absolute deviation (MAD). If the tracking signal is within 3 standard deviations, then applied forecasting model is considered to be good enough. Literature survey Uncertainty can be defined as unpredictable events in a supply chain that affects pre-planned performance [5]. The bullwhip effect was first noticed and studied by [4] in a series of simulation analysis. He named this problem as ??demand amplification‘‘. It is suggested [11] that operations managers be provided necessary training on the bullwhip effect. However, [7] indicates that bullwhip effect is present, even though all members of the supply chain behave in an optimal manner unless the supply chain is redesigned with different strategic interactions. Of all causes, the major emphasis has been placed on demand forecasting. Researchers had developed different methodologies to explore the impact of demand forecast on bullwhip effect. Few AR models are developed to quantify the bullwhip effect [1] with the moving the average forecasting model in a two-level supply chain. Their findings support the significance of reducing lead times to mitigate the bullwhip effect. Under similar assumptions, [2] also investigated the double exponential smoothing forecasting technique for demand process with a linear trend. [13] The impact of forecasting parameters, demand patterns and capacity tightness of the supplier on the performance of the supply chain in terms of total cost and service level is investigated by [13]. In fact, demand forecasting has been recognized as one of the four main causes of the bullwhip effect [7]. As described by [9], Winter?s triple exponential smoothening model is used to determine forecasted demand and the optimized values of forecasting parameters are calculated. The changes occurring by altering the values of parameters in the given range is computed. The time horizon (Year) is divided into three seasons based on either actual demand for the product (or) seasonality index An attempt is made to analyze, the effect of changes in given range of optimal values of smoothening constants in the given season. Finally Tracking Signal values are computed to validate **forecasting accuracy. **

**Model Development **

The supply chain consists of four members as, a manufacturer, a distributor, a retailer and a consumer as shown in Fig 1.

An attempt is made to apply Winters? Triple Exponential Model to calculate the forecasted demand values for the given Factory, Distributors and Retailers data. Corresponding values of ordering quantity for Factory, Distributors and Retailers are calculated.

The Winter?s Triple Exponential Smoothing Model is used to calculate the forecast demand for Manufacturer, Distributors and Retailers. The formula as follows

At the beginning of each period, the retailer receives the delivery of the distributor. Mean while the actual customer demand emerges at the marketplace. The retailer fulfils the customer demand (plus back-orders if any) by on-hand inventory, and any unfulfilled customers demand are backordered. After the actual customer demand is satisfied, the retailer analyzes the historical demand data and makes a demand forecast. The retailer decides the quantity of items to order for the distributor using its inventory control policy. In this case, the manufacturer, Distributor and Retailer follows a simple “order up to policy” to manage the inventory. The ordering quantity is determined by the following relation.

Qt = Ft + z σ_{t}

Where Ft is forecasted demand, σt is the standard deviation of forecasting error and z is constant chosen to meet a desired service level. It should be noted that z is also known as the safety factor. Let the retailer selects a 95 % fill rate and selects a threshold z value of 1.65.Since the model explicitly analyzes the impact and focuses on the role of forecasting models on the bull-whip effect and this has a significant diversion from the model. A similar assumption has also been made in several studies [2].

According to [7], the bullwhip ratio is given by the relation

Comparative Analysis A comparative analysis is carried out for before and after application of Winters‘ triple exponential smoothening model to determine the forecasted demand, ordering quantity and bullwhip ratio. They are presented in Table 1 to Table 4. They are further illustrated graphically in Fig. 3 to Fig. 7. Sensitivity Analysis: The Part – I of sensitivity analysis deals with changes occurring in the values of bullwhip ratio, when for one parameter takes value in the specified range for 3 seasons and other two parameters are kept constant. They are presented in Table. 5. They are illustrated graphically in Fig. 8 to Fig. 13. The Part – II of sensitivity analysis deals with calculation and analysis of Tracking Signal for Factory, Distributor and Retailer‘s statistics on month-wise for 3 years. They are presented in Table. 6 and Table. 7. They are illustrated graphically in Fig. 14 and Fig. 15.

**Development of ****Soft-ware**** Programme **

A Computer programme is developed in ?C – Language?. It takes input values as Three years‘ actual demand statistics and values of α, β and γ

**SENSITIVITY ANALYSIS**

**Part – I **

**Analyzing the effect Range of Values of α, β, γ on Bullwhip Effect **

The values of Alpha varies in the range ( 0.7 to 0.9) while values of Beta and Gamma are kept at a constant values as 0.01 each. The values of Beta varies in the range ( 0.005 to 0.05) while values of Alpha and Gamma are kept at a constant values as 0.76 and 0.01 respectively. The values of Gamma varies in the range ( 0.005 to 0.05) while values of Alpha and Beta are kept at a constant values as 0.76 and 0.01 respectively. The values are presented in the Table 4.1.

**Part – II : **

**Analyzing Tracking signal for both Retailer?s and Distributor's statistics**

The values of Tracking signal for both retailers‘ and distributors‘ data is calculated and tabulated. The tabulated values are as shown below and analyzed to test the accuracy of forecasted model applied to the given data.

**CONCLUSIONS**

The Distributor and Retailer are advised to follow a specific Forecasting method to estimate the future forecasting demand and ordering quantity for next periods. Winters‘ Triple Exponential Smoothening model is suggested.

From the study of comparative analysis, the Bullwhip Ratio is minimum for Lower value of Alpha, lower values of Beta and small higher values of Gamma.

The Year is divided into Three Seasons namely Higher, Medium and Lower. An analysis of the relation between Bullwhip Effect with a range of values of Alpha, Beta and Gamma with variations of Seasonality is determined and the following inferences are drawn.

1) During High Seasonality, to minimize the Bullwhip Effect, the values of Alpha should be at the lowest.

2) During High Seasonality, to minimize the Bullwhip Effect, the values of Beta should be at the lowest.

3) During High Seasonality, to minimize the Bullwhip Effect, the values of Gamma should be at the lowest.

4) During Medium Seasonality, to minimize the Bullwhip Effect, the values of Alpha should be at the lower value near to optimal value.

5) During Medium Seasonality, to minimize the Bullwhip Effect, the values of Beta should be at the higher value.

6) During Medium Seasonality, to minimize the Bullwhip Effect, the values of Gamma should be at the lowest value.

7) During Low Seasonality, to minimize the Bullwhip Effect, the values of Alpha should be at the optimal value

8) During Low Seasonality, to minimize the Bullwhip Effect, the values of Beta should be at the optimal value.

9) During Low Seasonality, to minimize the Bullwhip Effect, the values of Gamma should be at the higher value.

After analyzing the phenomena (pattern) of Tracking signal for Retailer‘s Statistics, and Distributors‘ statistics, the following inferences are drawn

*Tracking signal curve for Retailers‘ Statistical data is having a range of +3.0 to - 3.0 for many months during the 3 years of time horizon considered, except with 2 peaks of over estimation at July 2007 and January 2009 months, as shown in Table 6 and followed by graph Fig 14.

*Tracking signal curve for Distributors‘ Statistical data is having a range of +4.0 to - 4.0 for many months during the 3 years of time horizon considered, except with 1 peak of over estimation at March 2010 month, as shown in Table 7 and followed by the graph Fig 15.

*Hence the applied winters‘ model is found to be more accurate.

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