供應(yīng)鏈庫(kù)存是簡(jiǎn)易的
 
小的變化在整個(gè)鏈條中傳遞，在最終產(chǎn)品的需求產(chǎn)生了放大效果，導(dǎo)致了整個(gè)鏈條振蕩。這種效應(yīng)被稱為牛鞭效應(yīng)，這個(gè)導(dǎo)致了一系列問(wèn)題，其中包括低效率的生產(chǎn)或庫(kù)存過(guò)多，除了增加安全庫(kù)存，增加財(cái)務(wù)費(fèi)用之外，也會(huì)使公司的無(wú)形資產(chǎn)受到損失。模擬的使用，已經(jīng)嘗試來(lái)比較已公布的解決方案是相同的。通過(guò)仿真分析進(jìn)行對(duì)因，以及獨(dú)立的參數(shù)，導(dǎo)致了以下幾點(diǎn)意見(jiàn)：第一，孤立的需求預(yù)測(cè)，即預(yù)測(cè)進(jìn)入只會(huì)導(dǎo)致牛鞭效應(yīng)的需求的基礎(chǔ)上，并且信息共享的做法可導(dǎo)致降低牛鞭效應(yīng)和后續(xù)的問(wèn)題造成的影響。進(jìn)一步的研究可以包括使用先進(jìn)的預(yù)測(cè)方法，其他排序技術(shù)的建模。
 
鳴謝
 
我非常感謝Seshadri教授為允許我開(kāi)展這個(gè)項(xiàng)目的工作。并且非常感謝他能夠指導(dǎo)和有益的建議，幫助我及時(shí)完成了研究項(xiàng)目。

Supply Chain Inventories Are Liable Economics Essay
 
Small variations in the end item demand creates oscillations that amplify throughout the chain. This effect, called Bullwhip Effect, leads to a host of problems, which include inefficient production or excessive inventory in addition to increase in safety stock, increase in financial costs, losses in the intangible assets of the company. Using simulation, an attempt has been made to compare the published solutions to the same. Analysis via simulation was carried out on the dependent as well as the independent parameters and resulted in the following observations: firstly, isolated demand forecasting, that is forecasting on the basis of incoming demand only leads to bullwhip effect, and that the information sharing practices can lead to lowering of the bullwhip effect and subsequent issues. Further studies can include usage of advanced forecasting methods, modelling of other ordering techniques.
 
Acknowledgement
 
I take immense pleasure in thanking Prof. Seshadri for having permitted me to carry out this project work. I am very much thankful for his able guidance and useful suggestions, which helped me in completing the research project in time. He helped in solving all the problems faced in carrying out the research. The research was not possible without his precious guidance.
 
I would also like to thank C.A. R.C Agarwal for providing every help and support I needed for completing this research. His immense knowledge was a great motivation for me to do my best while conducting the research.
 
Words are inadequate in offering my thanks to the friends/classmates, for their encouragement and cooperation in carrying out the project work.
 
Finally, yet importantly, I would like to express my heartfelt thanks to my beloved parents for their blessings, and wishes for the successful completion of this research.sing

Prashant Pathak
 
December 2012
 
Table of Contents
 
Introduction
 
Supply chain inventories are liable to experience instability more often than not. End item demand changes creates inventory and order oscillations that amplify as one moves up in the supply chain ( (Forrester, 1961); (Sterman, 2000)). This phenomenon of amplifications of oscillations through the supply chain is known as bullwhip effect ( (Lee, et al., 1997), (Chen, et al., 1998) (Xu, et al., 2001)).
 
Lee et al identified four main causes of bullwhip effect: (1) demand signal processing, (2) order batching, (3) promotions, which artificially stimulate demand, and (4) supply shortages, which also lead to artificial demands (Lee, et al., 1997). On the other hand, Chen et al argue that the bullwhip effect is due to, in part, the need to forecast the demand (Chen, et al., 1998). Sterman and Forrester showed that delays inherent within the supply chain together with demand forecasting and distortion can create the amplification of the demand oscillation (Sterman, 1989) (Forrester, 1961).
 
The effect has been documented as a significant problem in both experimental, managerial context (Sterman, 1989), and a variety of companies (Buzzell, et al., 1990), (Kelly, 1995), and (Metters, 1997). Many proposed strategies for mitigating the Bullwhip Effect have a history of successful application (Clark, 1994) (Gill & Abend, 1997) (Hammond, 1993) (Towill, 1997).
 
Fine discusses the Bullwhip Effect as one of the two laws that govern supply chain dynamics, focusing on the strategic issues that arise (Fine, 2000). Anderson and Morrice analyzed the Bullwhip Effect in service industries, which cannot hold inventory, and in which backlogs cannot only be managed by adjusting capacity (Anderson Jr. & Morrice, 2000). Anderson et al suggest the amplification of demand volatility is particularly large in distribution and component parts supply chains, e.g. machine tools (Anderson Jr., et al., 2000).
 
Literature and practice has primarily focused on coordination amongst the participants in a supply chain, information sharing in order to reduce the bullwhip effect. Chan et al argue that centralization of the demand information could significantly reduce the bullwhip effect (Chen, et al., 1998). Xu et al and Lee arrived at a conclusion that sharing of demand forecast and inventory information is effective in reducing order fluctuations and safety stocks (Xu, et al., 2001), (Lee & Whang, 1998). Gavirnevi further compares the no-information-sharing case against two different types of information-sharing policies used by the retailer (partial and complete sharing) in a simple one-retailer-one-supplier chain (Gavirneni, et al., 1999). In 2001, Gallego and Ozzer searched for the optimal policies for with and without demand information-sharing cases in a two-stage supply chain, where the retailer batches orders and faces Poisson demands (Gallego & Ozer, 2001).

Chen and Wu show how information sharing can reduce inventory costs in a two-level chain with multiple retailers (Chen & Wu, 2005). Dejonchkheere et al show that information sharing is very beneficial, if not indispensable in order-up-to-S policies since the magnitude of the bullwhip can thus significant reduced at higher levels in the chain. However, they note that the information sharing alone cannot eliminate the bullwhip completely (Dejonckheere, et al., 2004). Jeong and Maday in 1996 discussed the stability of a multi-echelon supply chain from a feedback control theoretic perspective (Jeong & Maday, 1996). Silver et al suggests demand sharing and echelon inventory policy implements. Authors propose that each stage apply echelon (s,S) policy in which an agent monitors its total echelon inventory level (Silver, et al., 1998). Chen et al demonstrate the fact that smoother demand forecasts reduce the bullwhip effect, and longer lead times increase it. They also show that for both moving average and exponential smoothing forecasts, the very inclusion and need for estimation of a linear trend parameter into the forecasting model results in increased bullwhip. They show that the bullwhip emanating from the trend detection algorithms (linear and quadratic or exponential smoothing) are reduced by lowering the exponential smoothing constant used in these algorithms. More recently, Datta et al analyzes the relationships between demand and order forecasting and bullwhip effect, and proposes an advanced forecasting model (GARCH) for supply chain management (Datta, et al., 2007).
 
There are primarily two definitions of bullwhip effect measurement used in literature. Lee et al having described the effect as a form of “information distortion” measured it by comparing the order variance with the demand variance (where order can also be interpreted as production release in a manufacturing setting). This definition captures the distortion of information flow that goes upstream (the downstream stage’s order is the demand input to the demand input to the upstream stage). A second definition, used in most empirical studies, compares the variance of order receipts (or shipments) with the variance of sales ( (Blinder, 1981) (Miron & Zeldes, 1988) (Allen, 1997) (Cachon, et al., 2007)).
 
Different techniques have been applied to reduce the bullwhip effect based to reduce the bullwhip effect and among them Genetic Algorithms (O'Donell, et al., 2006), fuzzy inventory controller (Xiong & Helo, 2006), distributed intelligence (De La Fuente & Lozano, 2007).
 
Techniques to reduce the bullwhip effect based on considering the supply chain as a dynamic system and the application of control techniques are summarized by (Sarimveis, et al., 2008). These control methodologies span from the application of a proportional control (Disney & Towill, 2003) to highly sophisticated techniques, such as model predictive control (Tzafestas, et al., 1997). Finally, Strozzi et al. propose a new chaos theory technique that consists of measuring the divergence of the system in state space and reducing the bullwhip and the costs connected to it by reducing that divergence (Strozzi, et al., 2008).
 
Discrete Event Simulation
 
In the Discrete Event Simulation, the simulation model is in a state S (could be vector-valued) at any given point of time. A system state is the set of data that captures the variables of the system and thus enable us to describe the system evolution over time. In a simulation program, the state is tored in one or more variables that represent various structures for example, the number of customers in a queue. Thus the current state can be defined in multiple ways, depending on the needs of the researcher, with the required level of detailed entered into the model.
 
For example, consider a bank. The teller at the bank is providing service to customers who are standing in a line. An upper view of the system is the number of the customers waiting in queue for their turn, but this does not allow for the computation of waiting times, because the customers are not clearly distinguished. On the other hand, if we were to increase the detail in the system, then the presence of distinguishable customers and associated data, such as their arrival time, allows us to compute waiting time. Thus in practice, the state definition of a system should be determined on the basis of the modeling requirements, pertaining to the statistics to be computed.

S(t) is a step function whose discontinuities are triggered by discrete events, which produce changes in the system, called state transactions at a given point in time. An event is a data structure that always has a field containing the time of its occurrence, and all the other fields related to it. The occurrence of an event in the computer simulation is produced due to execution of a corresponding code at the scheduled event, after which the event is said to be processed or executed.
 
A DES model is governed by a clock and a time-based list, event list. That is, the events are listed in the list as per their scheduled order of occurrence. The foremost event is called the most imminent event. Scheduling an event means the event is a part of the event list. The occurrence of an event means that the event has been de-linked from the list and has been processed.
 
The primary feature of the DES paradigm is that “nothing” happens in the system, that is remains constant, unless an event is processed, at which point the model undergoes a state transition. In other words, every event processing can change the state, but every state change is brought about by an event. Between two events, the state of the system is considered to be constant, even if the system is undergoing some activity.
 
Generalizing, we have the following algorithm for a DES simulator:
 
Set the simulation clock to an initial time (mostly 0) and then generate one or more initial events and schedule them,
 
If the event list is empty, terminate the simulation. Else find the most imminent event and de-link it from the list.
 
Advance the simulation clock to the time of the most imminent event, and execute the event.
 
Loop back to Step 2.
 
The above algorithm has been highly simplified and there is complexity hidden in the routines that execute events and the structures used by them. The DES is powerful due to the fact that DES paradigm is scalable and one can built highly complex systems from subsystem components. In addition to this, events can be as detailed as possible. Thus both large as well as complex system can be represented in the DES paradigm.
 
Advantages
 
Simulation modeling of supply chains can provide utility as well as a sense of realism, because simulation allows the accounting of the natural variations that occur in the multiple process of the supply chain, which are not possible to be captured on via analytical methods. Analytical modeling methods for example, restricts researchers to systems that require assumptions and other restrictions because such model inadvertently become more mathematically intractable. Thus simulation enables the study of inherently complex systems and the subsequent interactions between the elements. There exists a risk of losing out on the interactions when certain aspects are made constant in order to make the model more mathematically, but the same can be mitigated by the use of an appropriate modeling tool.
 
Disadvantages
 
The biggest disadvantage of simulation is that it is based upon the knowledge of the researcher, it banks on the modeler to completely address all the assumptions correctly. Even if one of these assumptions go wary, the entire results are incorrect. The second disadvantage is the general lack of acceptability of the management of the simulation results in a business environment due to its purely scientific approach.
 
Arena – Modeling Software
 
Arena is a simulation environment consisting of module templates, built around SIMAN language constructs and other facilities, and augmented by a visual front end.
 
SIMAN consists of two classes of objects: blocks and elements. More specifically, blocks are basic logic constructs that represent operations; for example, a SEIZE block models the seizing of a service facility by a transaction (referred to in Arena as “entity”), while a RELEASE block releases the facility for use by other transactions. Elements are objects that represent facilities, such as RESOURCES and QUEUES, or other components, such as DSTATS and TALLIES, used for statistics collection. Arena’s fundamental modeling components, called modules, are selected from template panels, such as Basic Process, Advanced Process, and Advanced Transfer, and placed on a canvas in the course of model construction. A module is a high-level construct, composed of SIMAN blocks and/or elements. For example, a Process module models the processing of an entity, and internally consists of such blocks as ASSIGN, QUEUE, SEIZE, DELAY, and RELEASE. Arena also supports other modules, such as Statistic, Variable, and Output among many others.
 
Arena has a graphical user interface (GUI) built around the SIMAN language. In fact, simulation models can be built using SIMAN constructs from the Blocks and Elements template panels alone, since Arena modules are just subprograms written in SIMAN. Still, Arena is far more convenient than SIMAN, because it provides many handy features, such as high-level modules for model building, statistics definition and collection, animation of simulation runs (histories), and output report generation. Model building tends to be particularly intuitive, since many modules represent actual sub-systems in the conceptual model or the real-life system under study. Complex models usually require both Arena modules and SIMAN blocks.
 
All in all, Arena provides a module-oriented simulation environment to model practically any scenario involving the flow of transactions through a set of processes. Furthermore, while the modeler constructs a model interactively in both graphical and textual modes, Arena is busy in the background transcribing the whole model into SIMAN. Since Arena generates correct SIMAN code and checks the model for syntactic errors (graphical and textual), a large amount of initial debugging takes place automatically.
 
An important part of the model building process is assignment and storage of data supplied by the user (input parameters) or generated by the model during a simulation run (output observations). To this end, Arena provides three types of data storage objects: variables, expressions, and attributes. Variables and expressions can be introduced and initialized via the Variable and Expression spreadsheet modules, accessible from the Basic Process template and Advanced Process template.
 
Variables
 
Variables are user-defined global data storage objects used to store and modify state information at run initialization or in the course of a run. Such (global) variables are visible everywhere in the model; namely, they can be accessed, examined, and modified from every component of the model. In an Arena program, variables are typically examined in Decide modules and modified in Assign modules. Unlike user-defined variables, certain predefined Arena (system) variables are read-only (i.e., they may only be examined to decide on a course of action or to collect statistics), and cannot be assigned a new value by the user; the system is solely responsible for changing these values. For instance, the variable NQ(Machine_Q) stores the current value of the number of entities in the queue called Machine_Q. Similarly, the variable NR(Machine) stores the number of busy units of the resource called Machine. Other important Arena variables are TNOW, which stores the simulation run's current time (simulation clock), and TFIN, which stores the simulation completion time.
 
Expressions
 
Expressions can be viewed as specialized variables that store the value of an associated formula (expression). They are used as convenient shorthand to compute mathematical expressions that may recur in multiple parts of the model. Whenever an expression name is encountered in the model, it is promptly evaluated at that point in simulation time, and the computed value is substituted for the expression name. Variables of any kind (user defined or system defined) as well as attributes may be used in expressions.
 
Attributes
 
Attributes are data storage objects associated with entities. Unlike variables, which are global, attributes are local to entities in the sense that each instance of an entity has its own copy of attributes. For example, a customer's arrival time can be stored in a customer attribute to allow the computation of individual waiting times. When arrivals consist of multiple types of customer, the type of an arrival can also be stored in a customer entity’s attribute to allow separate statistics collection for each customer type.
 
Detailed statistics collection in Arena is typically specified in the Statistic module located in the Advanced Process template panel. Selecting the Statistic module opens a dialog box. The modeler can then define statistics as rows of information in the spreadsheet view that lists all user-defined statistics. For each statistic, the modeler specifies a name in the Name column, and selects the type of statistic from a drop-down list in the Type column. The options are as follows:
 
Time-Persistent statistics are simply time average statistics in Arena terminology. Typical Time-Persistent statistics are average queue lengths, server utilization, and various probabilities. Any user-defined probability or time average of an expression can be estimated using this option.
 
Tally statistics are customer averages, and have to be specified in a Record module in order to initiate statistics collection. However, it is advisable to include the definition in the Statistic module as well, so that the entire set of statistics can be viewed in the same spreadsheet for modeling convenience.
 
Counter statistics are used to keep track of counts, and like the Tally option, have to be specified in a Record module in order to initiate statistics collection.
 
Output statistics are obtained by evaluating an expression at the end of a simulation run. Expressions may involve Arena variables such as DAVG(S) (time average of the Time-Persistent statistic S), TAVG(S)(the average of Tally statistic S), TFIN (simulation completion time), NR(), NQ(), or any variable from the Arena Variables Guide.
 
Frequency statistics are used to produce frequency distributions of (random) expressions, such as Arena variables or resource states. This mechanism allows users to estimate steady-state probabilities of events, such as queue occupancy or resource states.
 
Model Structure
 
We consider a three-echelon supply chain, consisting of a retailer, a distributor and the manufacturer. Each agent can only order from its upper agent. There is a lead time of 7 days between each agent. The ordered goods are immediately shipped, if there is sufficient inventory on hand. Orders can be either be fulfilled fully, partially or be backlogged if there is no inventory. The upper-most agent that is the manufacturer places an order to an unlimited source so there is no backlogging of the orders of parts and raw materials.
 
In order to be in line with the existing literature, time is taken as discrete, and also to represent the standard ordering policies like (s,S) and Order-up-to-S. There also exists the anchor-and-adjust ordering policy which is time-continuous.
 
Quality of Information
 
The information sharing can all go to waste if the quality of information shared is low. Since this information is used directly in the forecasting of inventory and lead-time, it affects the order streams, can produce stockouts. Quality of information can be defined as the accuracy of the information being used, the level of information being used for example the final lead-time demand realizations in place of incoming demands and lead time.
 
H3: Better the quality of information, lower is the bullwhip effect.
 
Observation
 
Independent Parameter Analysis
 
A number of experiments were carried out with the following observations were made,
 
Effect of auto-correlation: BWE increases when order-up-to-S or anchor-and-adjust policy is used. With the remaining policy of (s,S), it does not have a substantial effect on the inventory oscillations, because the batching of the orders make it less sensitive to demand auto-correlation.
 
Lead Time: With an increase in the lead time, there is a noticeable increase in the amplifications. This could be because of the fact that the level S and the supply line are both dependent on lead time. In policies where the order quantity and the frequency are not affected, this is not seen, such as in (s,S) policy.
 
Information Delay: There can be other delays, other than lead times, such as the delay in placing orders. In all of the policies studied, the effect shows increased effect due to the inclusion of the same, to the extent of direct proportion. This is in order with the earlier observation, since the delay in the relaying of information slows the time that is the increase the delay that is lead time.
 
Uncoordinated demand forecasting: From the experiments it came to light that there is a indirect co-relation between the demand EAT and the bullwhip effect. When the EAT increases the BWE decreases, that is the model becomes less likely to change, becomes less responsive.
 
Table Summary of policy-independent parameter analysis
 
Figure Net inventories when (s,S) policy is applied
 
Policy Dependent Parameter Analysis
 
A certain number of experiments were also done wherein the policy dependent parameters were studied, and following observations were made,
 
When the lead-time constant K in the order-up-to-S policy is increased, the effect also increases, where K is the weight used to calculate the expected demand in the order decisions.
 
When q in the (s,S) policy is increased, the amplifications and the magnitude both increase, where q is the multiplier of the expected demand in the formula of this policy.
 
When m, the desired inventory coverage constant is increased, the BWE increases. m is weight of the demand expectations in the anchor and adjust policy.
 
The above experiments show that the more the isolated is the demand forecasting, the more is the amplification and in a few cases, the oscillations too, which is in tandem with the existing literature of the subject. The roles of two reasons of bullwhip effect can be summarized from the experiments as:
 
Demand forecasting: From the various experiments performed it has become clear that the isolation of demand forecasting brings about the bullwhip effect, which means using simply the records of orders pouring in from the next level in the supply chain. The weight utilized in the forecasting of demand also plays an important role in the occurrence of the BWE. So, if the weight is higher, higher are the amplifications of the demand.
 
Order-batching: Of all the policies tested, only (s,S) requires orders to be batched. It has already been noted that batching increases the effect, and produces higher amplifications. But tests with constant values of s and S, that none of them were updated using with any forecast, show that there is no BWE whatsoever in the system. This is true because of the presence of similar batching techniques in the system, same amount is batched between the agents. Thus it can be safely concluded that the batching of orders which although by itself cannot be the sole reason for the production of BWE, possesses the ability to greatly enhance the effect, if it is already present. Also it can be seen that if the size of the batches differ between the stages, there can be an inherent BWE in the system, even when there is no demand forecasting.
 
Table Summary of policy-dependent parameter analysis
 
Figure Net inventories under (s,S) policy, without using any forecastingC:\Users\Prashant\Desktop\Studies\Trim XIV\Research Project 2\Graph 4.jpg
 
Information sharing
 
Information sharing is one of the many strategies put forward in the literature, as discussed in the introduction. Numerous publications, as given in the introduction, push for the same, as if it is the ultimate solution for the problem. Thus in order to ascertain this validity, the model was changed to accommodate the point-of-sales data from the lowest stage to all the upper stages. So all the stages use this end-point data while making forecasts, instead of relying on the incoming demand from the (i+1)th stage.
 
The inventory behavior that resulted for all the policies is shown in the figure. It can be seen that this reduces the effect to a great extent. This finding is in accordance with the existing literature.
 
The real question arises as to how to implement information sharing in the real-world. Supply chains that integrate the usage of VMI and CRP, the implementation of management solutions that allow the sharing of the POS data can effectively to reduce the effect of BWE.
 
Figure Net inventories when (s,S) policy is applied and demand is shared
 
Table Summary results of information-sharing policies
 
Conclusion and Further Studies
 
A number of simulation experiments were carried out in order to analyze the parameters of the supply chain and their effect on bullwhip effect.
 
The most general conclusion drawn from the simulation is that the bullwhip effect is present in all the cases, as long as the forecast is done solely on the basis of the incoming demand. So, uncoordinated demand forecasting was ascertained to be a major contributor to the bullwhip effect. We can also take this to mean that the level of the response shown by the forecasts to the demand in the system has an effect on the magnitude of the amplification of demand experienced. Forecasts that vary highly due to the changes in the demand increase the amplification, whereas those less responsive decrease it. Again, the weight of the demand forecast in the ordering equation is higher, then the amplification of demand in the system is also high. If the forecasts are not used at all, then the effect is missing. Thus the use of demand pattern may lead to eradication of bullwhip effect completely from the supply chain.
 
There were two other factors analyzed, the lead time and the batching of orders. The study shows that although the lead time does not significantly bring about the bullwhip effect, but when the effect is already present due to other reasons such as the local demand forecast, the lead time does in fact amplify the demand variation. Increased batching of the orders, and the increased lead times, bring about amplification of demand across the supply chain. Lot-ordering does bring about the bullwhip effect but this effect is limited unless all the levels on the supply chain utilize the same lot size. For the effect to effectively propagate throughout the supply chain, the upstream players should use increasing degrees of order batching.
 
A test for the effect of information sharing was also undertaken. It was found that the information sharing does in fact bring about a reduction of order amplification in all the ordering strategies. But it is important here to note that the demand and forecast information sharing does not eradicate the problem, but rather contains it.
 
BWE will remain in some part of the supply chain until the demand forecasts are not handled completely in tune with all the agents, instead of isolation by each agent in the supply chain. Use of technology for the sharing of the point of sales data with all the agents in the supply chain can go in a long way in the removal of the bullwhip effect. VMI, RFID, Collaborative Planning can be also used in conjunction to combat bullwhip effect as a whole. Lead time factor can be mitigated by the usage of just-in-time in the supply chain, and batching can be done away with the use of CRP.
 
As per Chen there are two other causes of BWE: rationing and price variations. Complex modelling is required in order to study these, and as such are beyond the scope of this study. Another potential topic of study can be the information sharing on supply network structures. Again, extrapolative methods and more sophisticated policies can be tested in a more realistic and complex settings.