Impact of forecasting methods on variance ratio in ... - Springer Link

Int J Adv Manuf Technol (2012) 59:413–420 DOI 10.1007/s00170-011-3485-1

ORIGINAL ARTICLE

Impact of forecasting methods on variance ratio in order-up-to level policy Matloub Hussain & Anamitra Shome & Dong Myung Lee

Received: 9 February 2010 / Accepted: 20 June 2011 / Published online: 1 July 2011 # Springer-Verlag London Limited 2011

Abstract This paper considers the impact of forecasting methods on the bullwhip effect for a simple replenishment system in which a first-order autoregressive process describes the customer demand and an order-up-to inventory policy characterizes the replenishment decision. The impact of exponential smoothing and minimum mean squared error forecasting is measured for both the bullwhip effect and inventory variances. Previous similar studies have focused on investigating the impact of forecasting methods on bullwhip effect. However, little research has been carried out to explore the impact of forecasting methods for both bullwhip effect and inventory variances. Through simulation experiments, it has been found that depending on the structure of the demand process, the appropriate selection of forecasting technique can reduce, or even eliminate (i.e., “dewhip”) the bullwhip effect. However, in terms of inventory variances it has been shown that the inventory variances for the exponential smoothing are greater than the minimum mean squared error forecasting method and that gap increases as lead time increases. These findings will help companies to choose the appropriate forecasting technique depending on the nature of demand. These guidelines can help companies to reduce the bullwhip effect and inventory variances across supply chain. M. Hussain College of Business Administration (COBA), Abu Dhabi University, P.O. Box 59911, Abu Dhabi, UAE A. Shome Brock University, 500 Glenridge Avenue, St. Catharines, ON L2S 3A1, Canada D. M. Lee (*) Department of Venture Technology & Management, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143-701, Korea e-mail: [email protected]

Keywords Bullwhip effect . Demand forecasting . Minimum mean squared error forecasting . Supply chain management

1 Introduction Increasing competition in the market generally leads to a high fluctuation in the demand of products. Such fluctuations pose a very severe problem. A large number of companies still lack a demand planning process. The most common reason given is that “we know forecasts will be wrong” or “ours is an industry in which it is impossible to forecast”. Forecasting product demand is crucial to any supplier, manufacturer, or retailer. Forecasts of future demand will determine the quantities that should be purchased, produced, and shipped. In general practice, accurate demand forecasts lead to efficient operations and high levels of customer service, while inaccurate forecasts will inevitably lead to inefficient, high cost operations and/or poor levels of customer service. Most companies are forecast driven rather than demand driven [1]. Normally they make forecasts based on historical data and use those forecasts to maintain their inventory requirements. Different forecasting model produce different demand estimation and companies places order on the basis of their forecast. One of the impacts of inaccurate forecast is demand amplifications also known as bullwhip effect. To explain the effect further, the variance of the orders may be larger than that of sales and distortion tends to increase as one move upstream in the chain. Forecasting models also play an important role in inventory control. The essence of the inventory control system theory is to forecast future demand and use such forecasts together with estimates of replenishment lead time to adjust the controlling of inventory policies. To prevent lost sales due to inaccurate forecasts, extra inventory is often carried

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which increases inventory holding cost. The problems compound further when the lead times of replenishment are long and uncertain. Because of the longer lead time, the uncertainty in the forecasting of the future demand increases, and consequently the variability of the order quantity and inventory level increases. It has been recognized that the demand process, lead times, and the forecasting models employed have significant bearing on the bullwhip effect [2–4]. Most of the previous research focused on determining the impact of forecasting methods and lead times on bullwhip effect. Damping variability in orders may have negative impact on customer service by increasing inventory variances. The bullwhip effect contributes to upstream costs, while the variance of the net stock increases the cost of the retailer. Little research has been carried out to analyze the impact of forecasting methods and lead times on inventory variances. Inventory variances represent the net stock variations. The higher the net stock variance the more safety stock required to meet the desired service. Therefore, in this paper, the impact of forecasting methods, exponential smoothing (ES) and minimum mean squared error (MMSE) forecasting techniques, and leads times are measured for both order and inventory variances. Further, previous research have applied statistical approaches while exploring the impact of different forecasting methods, but Hosoda and Disney [5] point out that “the statistical approaches become unmanageable when net inventory variances are considered as the expressions for the covariance between the states of the system are very complex”. Simulation is applied in this paper so that these intractable expressions between order rate and inventory variances are avoided, and the impact of ES and MMSE forecasting techniques on both order and inventory variations can be investigated. The graphical results gained from simulation studies provide a clearer picture of the situation than the corresponding statistical and mathematical results. The structure of this paper is as follows. Section 2 reviews the related literature. Section 3 discusses the order-up-to level model and AR (1) demand process. Section 4 compares the bullwhip effect under ES and MMSE forecasting techniques. Section 5 compares the inventory variances under ES and MMSE forecasting techniques. Section 6 offers some concluding remarks.

2 Literature review The order-up-to level (OUT) policy is a basic periodic review system for issuing orders on the basis of incoming demand and inventory position. OUT policy is optimal when there is no fixed ordering cost and both holding and shortage costs are proportional to the volume of the on-hand inventory or shortage [3]. Impacts of forecasting

Int J Adv Manuf Technol (2012) 59:413–420

methods on the bullwhip effect with the OUT policy have been studied by several researchers. Chen et al. [6] evaluated the moving average (MA) and ES forecasting techniques with respect to bullwhip inducement in an OUT policy. They found that exponential smoothing forecasts are more likely to amplify demand variations than moving average forecasts. Alwan et al. [7] studied the bullwhip effect in an OUT policy with mean squared error (MMSE) forecasting for the AR (1) demand process (autoregressive is a stochastic demand process which can be described by weighted sum of previous demand plus white noise error. AR (1) demand process means only previous immediate demand value has an impact on the current demand process.) They found that using such a forecasting policy, the bullwhip effect can be eliminated or mitigated depending on the demand autocorrelation. Zhang [8] also investigated the impact of forecasting methods in an OUT policy with autoregressive AR (1) demand process. Zhang found that, in comparison with MA and ES forecasting techniques, the use of MMSE forecasting technique improves the inventory performance for the downstream echelons. Sun and Ren [9] made the comparison of the effects of MA, ES, and MMSE forecasting on the bullwhip effect in an OUT model. Sun’s findings indicate that for negatively correlated demand process, MMSE forecasting method performs better while for positively correlated demand ES and MA should be preferred. Hosoda and Disney [5] use the transfer function technique and have developed an exact expression for the bullwhip effect and inventory variance using MMSE forecasting in a three-stage supply chain. Luong [10] develops the bullwhip measure for the AR (1) demand process in a simple order-up-to level supply chain that uses the MMSE forecasting. He found that the bullwhip effect depends on the value of demand autocorrelation and an upper bound for the demand amplification exists when the lead time increases. Lead time uncertainty is known as a type of supply uncertainty that affects ordering policies, inventory levels, and product availability level [11]. The impact of lead time on the bullwhip effect has also been investigated by Chen et al. [6], Zhang [8], Chatfield et al. [12], Kim et al. [13], and Duc et al. [14]. Chatfield et al. [12] and Duc et al. [14] analyzed the bullwhip effect with stochastic lead time and found that lead time variability exacerbates variance amplification in supply chains. Kim et al. [13] measured the impact of stochastic lead time on bullwhip effects for a k-stage supply chain and found that the bullwhip effect was higher under the lead time variability. Bayraktar et al. [15] analyzed the impact of exponential smoothing forecasts on the bullwhip effect for electronic supply chain management applications. A simulation model was developed to experiment the different scenarios of selecting right parameters for the exponential smoothing forecasting technique. It was found

Int J Adv Manuf Technol (2012) 59:413–420

that longer lead times and poor selection of forecasting model parameters lead to strong bullwhip effect in E-supply chains. Most studies on lead time have shown that longer lead times or larger lead time variations have a negative effect on supply chain performance, implying that lead time or lead time variability should be minimized. Uncertainties inherent in customer demands result in loosing sales opportunities or keeping excessive inventories. Syntetos et al. [16] has presented an excellent 50-year review of impact of forecasting on inventory planning. Lio and Chang [17] proposes the use of meta heuristic, to combine with exponential smoothing methods, in forecasting future demands and in determining the optimal inventory policy. The results indicate that the inventory cost increases with increasing lead time and the best demand forecasting method for minimizing inventory cost varies with the inventory policy used and lead time. Heydari et al. [18] studied the impact of lead time variability in a serially connected supply chain with four levels and found that the increase in the lead time variance will lead to inventory fluctuations. Sharma [19] has proposed and analyzed a method in which the demand of a strategically selected item is exchanged with another suitable item in the group. Previous research into OUT policy focused on determining the impact of forecasting methods on the bullwhip effect by using statistical approaches [2, 6, 20, 21], but Hosoda and Disney [5] point out that “the statistical approaches become unmanageable when net inventory variances are considered as the expressions for the covariance between the states of the system are very complex”. Simulation is applied to this analysis in this paper, so that these intractable expressions between order rate and inventory variances are avoided and the impact of the ES and the MMSE forecasting techniques on both order and inventory variations can be investigated. Sterman [22] states: “Simulation is essential for effective systems thinking, even when the purpose is insight, even when we are faced with a “mess” rather than a well structured problem”. The graphical results gained from Fig. 1 Block diagram of order-up-to level (OUT) model

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simulation studies provide a clearer picture of the situation than the corresponding statistical and mathematical results.

3 Model description This section studies the basic periodic review inventory and production control system. The basic structure of the model is the same as the one studied by Lee et al. [2]. The block diagram of the model studied is presented in Fig. 1. The details of the model are explained below. 3.1 Demand process The standard periodic review based stock OUT replenishment policy is used. External demand for a single item occurs at the retailer, where the underlying demand process faced by the retailer is an AR (1) process. The retailer’s demand from the customer is a mean centered demand pattern: i.e., Dt ¼ d þ rðDt1  dÞ þ "t

ð1Þ

where Dt represents the demand in period t, d is the average demand, ρ is the first-order autocorrelation coefficient, −1 < ρ < 1, and εt is an independent and identically distributed normal process (I.I.D.) with mean 0 and variance s 2" . It is assumed that s " is significantly smaller than d, so that the probability of negative demand is negligible [20]. The demand variance equals s 2D ¼ s 2" =1  r2 . By varying the value of ρ, a wide range of process behaviors can be observed. When ρ=0, we have an I.I.D. process with mean μ and variance s 2" . For −1