There are many definitions of Supply Chain Management (SCM). SCM is:
the integration of key business processes that products, services, and information were provided from original suppliers to ultimate consumer (Lambert and Cooper 2000).
a set of approaches utilised to efficiently integrate the functions of operations management in order to minimise costs while maintaining a certain service level (Simchi-Levi et al. 2000).
''the systematic, strategic coordination of the traditional business functions and the tactics across these business functions within a particular company and across businesses within the supply chain, for the purpose of improving the long term performance of the individual companies and the supply chain as a whole.'' (Mentzer et al. 2001)
As customers are increasingly demanded and sophisticated, all manufacturers are facing the intensive global competition driven by this change. Then, the concept of SCM was introduced. The evolution in the relationship between suppliers and buyers has been stressed in this modern theory. Some researchers, such as Davis (1993), Hoesktra and Romme (1992) also advocate, in the concepts of the SCM, customer demand would exert a ''pull'' to the finished stock rather than to the manufacturing point. This is also in accordance with ''Lean Thinking'' (Womack and Jones 1996).
In the next section, a fundamental problem encountered in most of supply chains will be presented.
Inventory
No matter what the definition of SCM is, as a supply chain player, one fundamental problem encountered everyday is probably to decide how much to order to enable the supply chain to satisfy its customers' demand - a production / inventory problem.
Business holds inventory for various good reasons. The primary purpose is being a buffer to provide customers products with a better Customer Service Level (CSL). Inventory levels must be high enough to cover demand during the production and distribution lead-time, simply because customers usually will shop elsewhere if the product is not available on the shelf. The secondary purpose is to buffer the production system against the customer by absorbing the short term day-to-day demand variance, thus allowing the production system to work to a more level schedule. This is important that costs associated with constant changing production levels are often significant. Other benefits of holding an inventory include: decoupling or separating different parts of production process will make customisation much easier, taking advantage of quantity discounts, hedging against inflation and upward price change.
Conversely, there are also a number of good reasons not to hold inventory associated with considerable costs. Bonney (1994), in his excellent review of inventory philosophy, of trends and aspects of inventory management, addresses the opportunity cost associated with binding money up in inventory that could be used in a more productive manner, the costs of stock space, and the costs needed to manage the inventory. There are also less obvious costs associated with inventory, such as obsolescence costs, deterioration costs.
In fact, there is a complicated balancing when managing inventory - the goal is to maintain a minimum reasonable inventory (MRI) that is to reduce holding costs to a just enough level whilst maintaining CSL and buffering production at the same time (Grunwald and Fortuin 1992).
Bullwhip Effect
The Bullwhip Effect refers to the scenario where the demand fluctuation is amplified upstream from customers to suppliers. It is a common phenomenon in supply chain system and were first coined by Lee et al. (1997a, b).
What is causing the Bullwhip Effect? Lee et al. (1997a, b) categorise five major operational causes of bullwhip: demand signal processing, lead-time, order batching, price fluctuations, and rationing and shortage gaming. Demand signal processing describes the behaviour that decision makers adjusting the parameters of the inventory replenishment rule. Because supply chain networks are often very complicated, operating in a highly uncertain environment with limited access to data. Their updates on target stock levels, safety stocks, and demand forecasts seem rational, but actually sub-optimal, and always result in the disharmony in the supply chain. Now it is generally believed that centralised inventory control like Distribution Requirements Planning (DRP) and Vendor Managed Inventory (VMI) is superior to decentralised control.
Lead-time includes: the physical delays and the information delays. The lead-time is a key factor determining safety stock, reorder points, and OUT levels. The increase in lead-time will result in magnified demand variability. These time delays can be eliminated or reduced through time compression techniques and the proper design of feedback loops to improve the information flow across organisational boundaries (Towill 1994). Some well-known techniques already applied in industries include: supplier hubs, logistics integrators, direct channels (the Dell model), web-enabled communication, EDI, e-procurement and so on.
Order batching refers to the practice of ordering, production, and transportation in batches in order to gain economies of scale. Burbidge (1996) discusses the problem order batching causes and develops a range of practical approaches as far back as the 1960s (Towill 1994). Using simulation, Holland and Sodhi (2004) reveal that the order variance is proportional to the square of the batch size and demand variation. Price fluctuations refer to the practice of retailers offering price discounts, quantity discounts, coupons or in-store promotions. This results in forward buying, and the potential demand-depressing side effects thereafter, which also has serious impacts on supply chain dynamics. Rationing and shortage gaming refer to the practice of players in a supply chain placing inflated orders during shortage periods. These tend to magnify the Bullwhip Effect.
Furthermore, some scholars indicate that behavioural causes result in bullwhip as well. Croson and Donohue (2002) and Sterman (1989) found that decision makers do not have a clear idea of what is available in the supply chain, which leads to decision bias. Strategies to alleviate this problem include: sharing Point-Of-Sales data, sharing inventory and demand information, centralising ordering decisions, and using formal forecasting techniques correctly.
We refer to Geary et al.'s (2006) comprehensive review for more supply chain researches on Bullwhip Effect. It is worth to mention that conventional thinking suggests bullwhip should always be minimised within the supply chain. Recently, however, by examining the relationship between the bullwhip and production strategy, Potter, Towill, Bohme and Disney (2009) propose a cutting-edge strategy called minimum reasonable bullwhip (MRB) for the companies have shared resources and capacity constraints.
In the following sections, a range of approaches and methodologies applied in the subject will be reviewed.
Methods applied to study Bullwhip Effect
Scholars have used various methods, such as statistical or operational research (OR) methods, management games, system dynamics and simulation, and control theory, to study the bullwhip.
Statistical / OR methods are often used to quantify performance in the real world. This approach uses difference equations to provide insights into the effects of operating conditions such as demand, forecasting, lead-times, and ordering processes on inventory costs and the Bullwhip Effect. Lee et al. (2000) investigate the impact of autocorrelation in the demand, and find that the benefits of information sharing on the manufacturer's inventory costs increase as the autocorrelation factor increased. Chen et al. (2000) quantify the impact of different forecasting mechanisms and lead-times on the Bullwhip Effect in a simple supply chain where a centralised demand information strategy is applied. Daganzo (2004) focuses on the relative value of past demand on the bullwhip. However, this approach fails to provide in-depth insights into the cause and effect of system structure on performance, as well as how to reduce or eliminate the Bullwhip Effect.
Management games have been developed to understand the Bullwhip Effect and inventory problem in supply chains. One of the well-know games is the Beer Game (Sterman 1989). This game illustrates a typical four-echelon beer distribution supply chain, where the players (factory, distributor, wholesaler, and retailer) managing each echelon enact and re-enact the process of ordering beer through the supply chain. It has been to study how people react during the game, to gain insights into their behaviour, and to convince people that this is an important issue. The Beer Game represent many supply chains in the real world and it is therefore, not surprisingly, being used in many bullwhip related studies (Croson and Donohue 2003, 2006; Disney et al. 2004).
The Beer Game is limited in the sense that nothing can be proved from the game itself, although it does provide a valuable source of anecdotal evidence. Since that time, researchers have attempted to improve the depth of understanding gained from the game. They developed a number of simulation models allowing players to test out strategies and inventory control models (Hong-Ming et al. 2000; Mason-Jones et al. 1997; Mason-Jones and Towill 1997; Van Ackere et al. 1993).
Simulation is closely related to systems dynamics. Forrester (1961) advocated simulation as a method of investigating the dynamics in large and complex systems. He has demonstrated the power of using simulation for understanding and communicating the dynamic responses in large non-linear systems. Despite the fact that the work of Forrester was published 60 years ago, it continuously contributes to supply chain issues. A good summary of Forrester's work has been written by Edghill and Towill (1989). Generally, three approaches of simulation, system dynamics, and control theory are often used together, in our research as well. Simulation alone, however, has the drawback of being cumbersome, time consuming and only limited insights provided (Popplewell and Bonney 1987).
Control theory is particularly useful for studying the structure and dynamics of a supply chain as well as forecasts and ordering policies. The object is considered as an input-output system, then converted into transfer functions, and analysed the impact on the Bullwhip Effect. Different demand patterns, forecasting techniques, and ordering policies also have been investigated using this method by a number of scholars. Axsater (1985) summarise the pros and cons of the approach by reviewing early works. He concludes that the control theory is extraordinary to illustrate dynamical effects and feedback, but appears to fail to solve some production planning issues like lot size problem and sequencing. Disney (2001) also makes a good summary of the reasons for using transfer function techniques.
There are two options to apply the control theory: discrete time analysis or continuous time analysis. Laplace transform, as well as a whole range of tools like loosely termed control theory are used for studying continuous time systems. These transform functions are applicable if the system is linear, time invariant, and the system has no initial conditions, especially in Single Input and Single Output (SISO) scenarios. Buck and Hill (1971) as well as Grubbstrom (1967) have found the transform that describe cash flows are directly related to the Net Present Value (NPV) of the cash flows. Disney and Lambrecht (2007) summarise the transforms and their properties related to bullwhip studies. Another limitation of the Laplace transform is that it cannot independently handle a pure time delay such as a lag. However, the problem can be solved by using differential equations and Laplace transform together.
The discrete time analogue of Laplace transform is the z-transform, developed in the 1940s and 1950s, by Tustin and Tsyplin independently (Bissell 1996). Jury (1964) first compiled all of the developments of the z-transform into a book, but Vassian (1955) perhaps is the first person to apply the z-transform to a production / inventory system. The discrete time series analysis is probably more applicable to studying inventory problem and the Bullwhip Effect, because the inventory level usually is not continuously monitored. No matter what method the inventory level is reviewed, we often ignore what happened between the intervals, and therefore, it always can be seen as discrete time series. In terms of advantages, z-transform and Laplace transform are quite similar, but the z-transform also has to be applied into a linear, time invariant system with no initial conditions. Nevertheless, the problems of pure time delay exist in the Laplace transform are completely avoided in the z-transform.
Control theory and dynamics system dynamics simulation have much influence on the research of LSDG (Logisitcs System Dynamics Group) in Cardiff University. Towill (1982) studied an Inventory and Order Based Production Control System (IOBPCS) using simulation, block diagrams, Laplace transform and coefficient plane models. Later, he (1988) presented a simulation technique which adapted control theory and supply chain behavioural knowledge called the EXSMO (EXponential SMOthing) equations. These works formulated the start point that LSDG develops a generic ''family'' of simulation models analysed different supply chain scenarios. Examples include: Olsmats, Edghill and Towill (1988), Edghill and Towill (1989), Evans, Naim and Towill (1994), Berry, Naim and Towill (1995), John, Naim and Towill (1995), Towill, Evans and Cheema (1997), Disney and Towill (2002), Towill (2005), Zhou and Disney (2006), Zhou, Disney and Towill (2010).
Since system dynamics simulation and discrete time control theory are main methodologies adapted in our research to study the Bullwhip Effect and other indicators, let us briefly review some of the recent important works we based on.
Disney and Towill (2002) develop a discrete transfer function model of a VMI supply chain. They use causal loop diagrams, block diagrams, difference equations and z-transforms to determine the dynamic stability of the system. Dejonckheere, Disney, Lambrecht and Towill (2003) use z-transform to investigate the Bullwhip Effect induced by common forecasting methods such as moving averages, exponential smoothing with a classical OUT policy.
Disney and Towill (2003) deduct the equations for quantifying the inventory variance and the bullwhip in discrete time when the customer demand is drawn from an i.i.d. random distribution:
where is the time domain solution to the difference equations for the impulse response, and is the solution to the difference equations for the order rate.
Both continuous and discrete time approaches are applied by Disney, Towill and Warburton (2006), to study the production / inventory control system with an OUT policy. Although the exact results may differ, the management insights gained from both approaches are very similar. The equivalence of discrete and continuous Bullwhip Effect expressions is also found in Warburton and Disney's (2007) study. Besides, they deduct the expression of OUT policy in continuous time series.
Forecasting
Forecasts, the prediction of future events, are vital important to business activities, especially to production / inventory control. Hendry and Kingsman (1989) advocate that balancing supply and demand begins with making accurate forecasts. Gardner Jr. (1990) states that forecasting is a prerequisite to inventory decisions in practice. Traditionally, forecasting methods are based on mathematical models that use available historical data or simulated data, or on qualitative methods that draw on managerial experience and judgments, or they may be based on a combination of both. Among them, mathematical models still occupy the dominant position.
The most popular approaches to time series forecasting are exponential smoothing and ARIMA models identified by Box-Jenkins (2008). Two large-scale empirical studies have found little difference in forecast accuracy between exponential smoothing and ARIMA models (Makridakis et al. 1982; Makridakis and Hibon 1979). Makridakis et al. (1982) also has shown simple exponential smoothing to be a good choice for one-period ahead forecasting. And empirical evidences have confirmed the popularity of exponential smoothing, perhaps this is because the surprisingly accuracy that can be obtained with minimal effort in model identification. However, there was and always is so little agreement on the most accurate time series methodology in academia (Fildes 1979; Gardner Jr. 2006). Gardner Jr. (1985) has a remarkable critical review of the research in exponential smoothing since the original work by Brown and Holt.
Unavoidably, in the literature, researchers had some misunderstanding in terms of forecasting techniques. For example, Armstrong (1986) argued that there is little to be gained in time series forecasting because the few differences in accuracy among different time series models, therefore the choice of forecasting appears to have no important difference in determining inventory investment and customer service. However, he failed to consider the interest of managers as the measurement. Gardner (1990) has used some measures which could be meaningful to managers such as total variable costs in his research, and demonstrates that the choice of forecasting mechanism is an important factor in inventory decision-making.
Then, what kind of forecasting technique should be adapted in our research?
In terms of long-term forecasts, the majority of researchers agree that trend should be damped as the horizon increases, and linear models have the theoretical advantage of being critically damped. Brown's linear trend model is a typical approach which can be used for any forecasting horizon. Although it is widely held that the Brown's method is as accurate as Holt-Winters, empirical research shows this is a reasonable assumption only at short time (Gardner Jr. 1985).
Three alternative approaches to trend extrapolation have been proposed by Gardner Jr. and McKenzie (1985), probably the most recommended in large forecasting system, such as in inventory control, is to modify Holt's linear exponential smoothing model with an AD-parameter. Compared to models which assume a linear trend, the model proposed improves long-term forecast accuracy without apparent cost in short-term performance, no matter when the trend is erratic or persistent. The details of this forecasting mechanism will be discussed in the Methodology chapter.
Research gaps
In the last two decades, the majority of studies on production / inventory problems concern the impact of forecasting and inventory policy on supply chain performance such as Bullwhip Effect. The time line they investigate is usually less than 3 years. There is no research on the bullwhip in an entire product life cycle. And academia lacks of studies which apply damped trend forecasting into a production / inventory system on every time series, although many attempts have been made to improve on this practice by selecting individual methods on each series.
