Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Undergraduate Project for University Students
Typology: Thesis
1 / 38
This page cannot be seen from the preview
Don't miss anything!
Geert Roseboom BMI-paper April 2005
Vrije Universiteit Amsterdam Faculty of Exact Sciences Business Mathematics and Informatics De Boelelaan 1081a 1081 HV Amsterdam
Preface
In the last year of the doctoral program Business Mathematics and Informatics (BMI) at the Vrije Universiteit in Amsterdam every student has to write a paper on a self-chosen subject related to its curriculum. This is the so- called BMI-paper. Because the aim of the BMI program is to combine the fields of Business Management, Mathematics and Computer Science, a BMI- paper should cover at least two of those three areas.
Since my bachelor internship at TNO-Physics and Electronics Laboratory (TNO-FEL) in The Hague (NL), where I worked on an implementation of the TABU-search heuristic for an optimization problem, I developed an interest for modern learning techniques, also known as computational or artificial intelligence. Even though these modern techniques sometimes lack solid mathematical background, they have been applied successfully to a wide range of practical problems. The result of this interest was that I chose my academic courses mainly in the field of artificial intelligence, programming and statistics. During the last year I also became interested in stochastic modeling and simulation.
After I followed his course on Data Mining I asked Wojtek Kowalczyk for an interesting subject for my BMI-paper, which would contain/combine elements like: simulation, modern learning techniques, forecasting and/or optimization. This resulted in the idea to apply these three approaches to a specific field of forecasting problems and investigate, which differences exist between modern learning techniques and conventional mathematical methods. Due to time limitations we restricted our research to a short literature study and some experiments.
At last I want to express a few words of gratitude. I would like to thank Sandjai Bhulai for his help finding the right mathematical articles and his patient, enthusiastic attitude whenever I came to him for questions. I thank Menno Dobber for putting one of his datasets at disposal. And finally I want to thank my supervisor Wojtek Kowalczyk for his support in my last academic year in general. He was always there and the interesting discussions with him made me feel aware of the rightness of my choice for this academic program.
I hope the reader will enjoy this paper.
Geert Roseboom
Wageningen, April 2005
Management summary
This paper aims to provide an insight in the role intelligent forecasting methods can play in the world of Inventory Management. An important assumption throughout this investigation is that data originating from real life processes can behave in a capricious and non-stationary manner. In such case adaptive methods, capable of making accurate forecasts while they need to respond to changes in demand over time, can bring relief and are a must to maintain control over the supply chain.
In the first part the fields are explored where sophisticated forecasting strategies can play a significant role. We pay attention to the difficulties and limitations that have to be overcome. To emphasize the surplus value these strategies can have for business we illustrate our story with some examples of recent implementations from major players in business intelligence such as SAS, SAP and IBM. Clearly they see interesting opportunities too, as they have set in a trend with the development of a wide range of applications that are all presented as sophisticated demand forecasting algorithms.
Unfortunately these implementations are more an exception than a rule. Therefore one of the goals of this paper is to contribute to the publicity of these intelligent forecasting techniques and make the reader aware of the opportunities for businesses.
The second part of this paper can be viewed as an introduction to the methods that lay on the foundation of these applications. The conventional techniques to solve forecasting problems have their roots in applied mathematics. However, in the last decade modern learning techniques, such as artificial neural networks, have caught up fast and their successful implementations are encouraging to build new applications. Since companies rarely give away competitive information, we turned to literature and looked for mathematical as well as modern learning methods. Subsequently we selected the most common approaches, which are:
In the currently available literature it remains unclear which of these approaches deserves recommendation. We found just one article that made an actual comparison between mathematical and artificial intelligence techniques. An explanation for this lack of comparisons is that, traditionally these two schools approached problems from different perspectives. During this investigation we learned that the typical contrasting aspects between the schools are diminishing, so it is likely to expect that comparisons will be made in the near future.
The lack of comparisons made us feel challenged to setup our own very basic experiments with interesting real life datasets. The primary focus was to develop a feeling for the performance of our selection of methods. In these
experiments the neural networks were the clear winner. Although the results are of modest importance from a scientific point of view; it provides a basis and hopefully encourages people to do further work in comparing mathematical approaches with modern learning techniques.
1. Introduction
In this paper we shall explore the world of forecasting and the value forecasting methods have in optimizing business objectives. Although this is tremendously interesting, with the huge amount of available information sources in our information era it is also quite ambitious. To narrow the scope of this project and give it a concrete bias, we have chosen to put our focus on a specific area of application: Inventory Management (IM).
In the first paragraph of this chapter we give a short description of the field of IM. The second paragraph contains the problem description/research objective. In paragraph three we describe the research methodology. The last paragraph gives an overview of the contents of each chapter in this report.
In the last decades manufacturers and companies have moved from a production push environment, which is merely focused on achieving production efficiency in single chains of the total logistic process, to a consumer pull environment, that is mainly focused on meeting the expected consumer demand.
Therefore controlling and fully understanding the consumer demand is crucial to have an effective grip on product costs and customer satisfaction. This control phenomenon, also known as Demand Management (DM), is considered as the most important factor in Supply Chain Management (SCM).
The objective of SCM is to bring the penetration point as close to the supply as possible (Figure 1.1 gives an overview of the activities within SCM). Since in most cases product demand is not known in advance, it is necessary to make forecasts/predictions of the demand. Seen from this perspective, looking after a proper DM becomes a key driver to the success of any SCM enterprise.
Figure 1.1 Activities within SCM applications [22] In practice, frameworks that support or make possible SCM are developed by leading software companies like IBM, Microsoft, Oracle, SAS, and SAP. At the moment these companies are taking a step further as they are starting to concentrate on achieving higher levels in SCM. For example by implementing tools that can accurately and autonomously predict sudden increases in workload demand.
The application environment for forecasting methods in IM can be seen from a broad perspective; for example also in private use we can expect that the future will bring us several personal forecasting applications; e.g. imagine a refrigerator that keeps track of a person’s groceries and automatically reorders the products whenever its stock is below some threshold.
Of course such ordering systems can be applied to many other processes, and each ordering system for each process will be implemented differently. The theoretical field that deals with the development of methods/strategies that lay on the ground of these ordering systems is known as Inventory Management. With these methods, which can be mathematical approaches and/or modern learning techniques, it is the goal to forecast demand, gain control and optimize as many aspects of the process at hand.
For centuries mankind has endeavored to forecast all kinds of phenomena out of a variety of interests. The idea and desire to forecast processes can be applied to almost any process we put our mind at. In the past this concerned mostly natural phenomena such as predicting the orbit of a planet. Nowadays forecasting methods are used as a way to control and optimize business objectives. This can be a considerably more demanding process, especially if the underlying processes are not behaving according to some stationary pattern.
Whenever working with real-life data such non-stationary behavior will be a recurring and standard situation. In most practical cases the data will be difficult to observe, and conclusions one can draw will be based on partial information. Fortunately with time forecasting methods have evolved, which should enable us to make predictions even when data changes over time. The field that tries to make such sophisticated predictions is christened Adaptive Forecasting.
With this introduction we arrive at the main objective of this paper, which is to provide an insight/ overview in the role Adaptive Forecasting methodologies can play in the field of Inventory Management. To gain this insight we divide the main objective in the following phases:
The general introduction is meant to make the reader familiar with the most important aspects and methods in Inventory Management. We briefly discuss how the field has developed and what the requirements on forecasting methods are today. Rather than to get lost in details, we just discuss general issues and some of the advantages and disadvantages of available techniques. Next to discussing the features that should be captured by intelligent forecasting procedures we look at some recent business implementations.
In the second part of this investigation we have made a selection from techniques that form the heart of these business implementations. In our selection we have looked to what extend our methods are capable of taking into account properties like: adaptability to deal with the changing customer
The report is built up as following; Chapter 2 gives a brief survey of developments in the area of our interest over the last two decades. This is done to elucidate the role intelligent demand forecast procedures can play for business objectives. Chapter 3 contains the description of our example shop model. Armed with this model we proceed to discuss our selection of mathematical and artificial intelligence techniques. The simple experiments performed to develop a feeling for some commonly used forecasting techniques can be found in Chapter 4 together with its results. In Chapter 5 the conclusions are presented and discussed.
2. Intelligence in Business Applications
Before discussing which forecasting techniques are available in Inventory Management, let us become acquainted with developments in supply chain and demand management over the last decades and emphasize the role intelligent demand forecast procedures can play for business objectives. In the second paragraph we will go into details with some actual implementations/frameworks from the major companies that operate in the field of our interest.
In the early years of the twentieth century, industrialization made it possible to efficiently and effectively produce on a large scale against relatively low costs. Since companies are always under influence of a competing market, there exists a constant pressure to improve their processes in such a manner that they can meet demand and stay ahead of competition.
The next major contribution to this efficiency strike has been the development of computers. Due to computers we have become able to automate and organize processes more efficiently. Simultaneously analytical methods have been developed to optimize production in a single link of the supply chain. In the latter decades one became aware that efficiency in a single link not necessarily leads to efficiency in the total chain. With this understanding we have caught the heart of what Supply Chain Management is all about; striving for efficiency in the total supply chain.
Pursuing an effective SCM goes hand in hand with the development of the appropriate analytical methods. From figure 1.1 we have learnt that all processes in SCM heavily depend on effective Demand Management. Given this significance, prudence is in order with the use of forecasting methods, since inaccurate product demand forecasts can easily ruin all the effort that is put in a carefully designed supply chain system.
A well-known effect that might have catastrophic consequences when using imperfect forecasting techniques in SCM is known as the bullwhip effect, which implies that demand variability increases as one moves up the supply chain i.e. as one moves away from customer demand (more details on this effect can be found in [5]). Consequences of such phenomena are expressed in excessive inventory levels, which can cause a company to end up with too much of its assets tied up in inventory, restricting its ability to respond to changes in its market environment etc. To prevent the occurrence of such effects man is constantly looking for the most accurate forecasting technique.
Now we have become familiar with the importance of adequate demand forecasting, we take a look at their basic requirements. Of course such
applied mathematics and will therefore be familiar for most technically skilled users. The resulting out-of-sample forecasts were claimed to allow extrapolation beyond historical operation regions, but this only holds true when the functions have not been tuned on a specific region.
A basic problem with function fitting is that the user is required to know which type of function will best describe the demand. Even for skilled professionals it remains difficult to decide if the equations will satisfactorily fit the complex trends of consumer demand. In most cases models will be based on a group of functions, where each function is used to describe a different region of the demand function. And a great potential danger of the out-of-sample forecasting lies in the fact that new developments might behave in a completely different way.
Other problems arise when mathematical relationships are difficult to expose, also for experts it can be quite hard to discern the key variables that affect demand. Whether the reason behind it is lack of knowledge or just a very complex process, it often requires that simplifying assumptions have to be made to make the problem tractable. Even when these simplifying assumptions can be made, statistical modeling requires a significant amount of expert effort to develop adequate models. It can be extremely disappointing whenever it turns out that the models not function as well as hoped due to unavoidable whimsicalities of real life processes. Therefore one is constantly looking for methods that generalize well and yet remain accurate.
As we have stated before, today’s markets are in constant movement as they need to respond to a variety of changing influences like:
Products with short life cycles, for example mobile telecommunication devices, need fast and accurate predictions of the amount of product that is needed. In an ideal situation models are forehand even before going to market, so that reservations made by enthusiasts prior to an introduction can help forecast actual demand over the product life cycle.
Next to that the models should be able to easily process the extra information that comes available during their lifecycle, as to continuously update predictions. With the introduction of new technologies like Radio Frequency Identification (RFID) Tags (more technical details can be found in [1]) more accurate demand and sales data become available, which offers excellent tracking opportunities to respond to customer behavior.
The shortcomings of conventional methods open the field of forecasting for new technologies that can support marketing and sales in decision making and actually take into consideration all variables which can influence demand for a given product. From the mathematical corner advances are made in the field of Bayesian methods, stochastic approximation algorithms and models based on Markov Decision problems. Eyes are also fixed upon modern approaches like artificial neural networks and reinforcement learning, which are successfully applied to a widening scale of problems. The idea is that these generic, black box models built on historical sales data are the answer to the need for robust and accurate demand forecasting models.
In the following sections we attempt to take away some of the mystic/ profoundness of business intelligence methods by providing some illustrative examples of recent implementations in this field. Three examples cover summaries of success stories taken from the well-known business intelligence companies’ websites like SAS, Cap Gemini and IBM. The last example is that of Evant, a company that develops demand planning software for the retail industry, whose encouraging story shows that advancements in this field are not solely made by the big companies.
From the internet article “IBM unveils 'self-healing' tools” by Ann Bednarz of 03/10/2003 on the IBM website, we can conclude that also IBM has acknowledged the surplus value of intelligent forecasting methods. With the introduction of a new dynamic provisioning tool IBM claims to have moved closer to achieving its vision of self-healing, self-configuring systems. The tool is designed to predict and respond to sudden increases in data center workloads.
The actual software consists of three modules: The Adaptive Forecasting module, which uses mathematical models to anticipate to the progression of an unexpected surge in demand. The Online Capacity Planning module, that estimates the resources required to maintain service-level targets during peaks and allows a hot swap of resources from one workload to another. And the Rapid Reconfiguration piece, which uses new capabilities in WebSphere Application Server 5.0 to add and remove nodes as resource demands fluctuate.
In the past IBM already had forecasting tools that can prepare systems for predictable spikes, such as seasonal traffic bursts. But dealing with unexpected surges requires something more sophisticated. When workload starts to deviate significantly from what is expected, IBM's new tool will start to track how things are changing. By using probabilistic methods that can deal with short-term forecasts the system tries to get ahead of the surge, and makes the necessary requests for the appropriate amount of server power to
The new Spirits and Wine SCM System relies its success on two major strengths. One is that the procurement operation, including order planning and future stock simulation, previously carried out by individual staff, is systemized and automated. The other is the seven-model system specially developed for the spirits and wine business to forecast demand and prepare the shipping plan. The models are specially designed by arranging dozens of analytical methods, including methods based on past data, methods reflecting the latest performance, and methods for seasonality. Simulations are run using models with different variables and patterns chosen for product characteristics, subsequently users can choose the most relevant forecast among the seven.
Other issues, such as inabilities to incorporate forecast data, have also been taken care of in the new system. With this function, it has become possible to continuously monitor actual data on sales performance and other relevant figures. Furthermore, an alarm function is adapted to notify the user of deviations from the forecast in the actual figures, which enables them to take appropriate measures against the change.
The article concludes that the new system has brought many immediately noticeable positive results. One of the most significant results is that, instead of being attained with doing forecasts to determine the appropriate order volume themselves, staff employees can focus on verification of forecasted values and further sophistications of the newly used system.
The story of Evant should appeal to any enterprising academic person, given that it is founded to put theory into practice. Evant is co-founded by Professor H. Lee, an authority on supply chain and inventory management as he is: Professor of Operations, Information, and Technology at Stanford Graduate School of Business, founder and director of the influential Stanford Global Supply Chain Management Forum and current editor-in-chief of Management Science. In [15] Lee puts forward two forces that have great potential for intelligent, demand-based SCM. First, companies with strong partnerships and sound information systems to track data flows across the supply chain can now turn those into intelligence. Second, companies that have streamlined their supply chains and improved their operating performance can realize bigger value by combining their marketing efforts and demand management with their supply-chain management initiatives.
These ideas are encapsulated in Evants technology, which has been successfully implemented for the pharmaceutical company Longs Drug Stores. Longs Drug Stores forms a chain with 470 retail outlets, good for an annual turnover of $4.5 billion. From their start in the late 30s the company has emphasized excellent customer service. This was translated into a
corporate strategy of never-empty shelves, which often comes hand in hand with lots of excess inventory.
Even though pharmacists and buyers were aware of the seasonal demand patterns for their major drugs, such as flu and allergy seasons, they were unable to master the complex inventory challenge. With Evant`s software, Longs established a next-generation inventory-planning tool. Since 1997 Longs' inventory has decreased 65% at its distribution centers, while the corresponding store inventory has dropped 38%. The company's annual savings from using scientific methods to run its data-rich demand chain was $36 million.
The system's methodologies should allow more accurate forecasts as it claims to optimize demand-chain activities as: forecasting, inventory control, transportation, material handling, and warehousing. Important is that the system is data-driven, which should minimize guesswork for most of the products. The core features of Evant`s technology are:
each discrete step in time. Suppose time is also discrete and we find ourselves at time unit. At this moment we have a stock of items and we are interested in the profit we will have from now on.
At the beginning of each point in time we can order an amount of items. We will call this decision. The magazine of our shop has a maximum capacity of items, which means that we can maximally order items.
We assume that our order is delivered instantaneously against certain order costs that are given by the function. The order results in a new stock level of items, which are held in store for the entire period against costs.
In that same period we experience a total demand for items, which is given by probability. We assume that our unknown demand, which is generated by all our customers, can be modeled as a Geometric distribution with a certain unknown parameter. This means that for each step in time we have probability function that gives the demand probability for items, with.
At the end of each period we have sold a certain amount of items against price. This amount is the minimum of our available stock and the total demand of our customers in that period, which can be written as. Note that this means that keeping inventory levels too low will result in lost sales and perhaps even more important for our estimate that we are unable to observe the true demand.
At time we will start with stock , where the notation is used to indicate that only non-negative values are allowed. Therefore in the next period our costs will be , where is used as a discount factor to represent the value depreciation between the current and the next state.
Because this problem returns for each point in time, we can write all our previous modeling work in one dynamic programming recursion step:
with:
In our explanation we have assumed that we experience a demand for exactly items, but this is unknown. Therefore in the recursion step we weight over all possible k with. Because we are speaking in terms of profit we take the maximum of all possible `s we can choose, which is denoted as.
Now we have specified a model that helps us to maintain an optimal level of our costs, we have to find techniques that provide us with accurate estimates for our unknown parameter of the demand distribution.
From the previous chapter we have learnt that conventional mathematical techniques are not suited to deliver adequate estimates when the demand function is unknown and changes over time. Note that for clearness this last
property causes us to change in to express the time dependence, which will be the notation from this moment on. In the next paragraphs we look into methods that should be capable of providing better estimates as more information becomes available.
In 1985 Kumar [13] produced a survey of results in stochastic adaptive control. He divides the field of Adaptive Control into two parts, Bayesian Adaptive Control Problems (BACP) and Non-Bayesian Adaptive Control Problems (NACP). Examples of NACP (in this article) are methods like self- tuning regulators and Markov chains. Since the paper aims to provide more insight in the techniques that were available in the total field of adaptive control, it does not refer to specific achievements concerning IM. The overall conclusions, at that time, were that still a lot of work was needed to provide efficient schemes for implementation of the algorithms and studies for the rates of convergence.
Following the by Kumar proposed division it comes quite naturally that in the next sections we shall discuss the concept, advantages and disadvantages of a Bayesian and a Non-Bayesian implementation, in this case Stochastic Approximation. The last section of this paragraph is devoted to a discussion of one of the few and recent articles on Adaptive Inventory Control.
One of the earliest works on non-stationary (or varying) stochastic demand problems is ascribed to Karlin [12] and stems from 1960. Karlin analyzes a dynamic inventory model in which the demand distributions can change from one period to another and discusses concepts of partial information.
In the same period (1959-1960) H.E. Scarf was one of the first to work on Bayesian methods in adaptive control, which can be used as a method to solve stationary partial information problems. Until that time most dynamic inventory models with stochastic demand assumed that the underlying demand distribution was known with certainty. When using a Bayesian approach to estimate the unknown distribution function, the idea is that with each step in time more information will have been gathered about the actual distribution function of the demand process. Since with each update information is added, the shape of the distribution function has a sharper and more accurate variance.
In the beginning of the 80`s, Scarf and Karlin’s work on inventory control and unknown demand was extended by Azoury [2, 3]. The Bayesian dynamic inventory problem can be modeled as a dynamic program with a multidimensional state variable. The state space is expanded to include one or more variables that describe past information about the demand distribution. This multidimensionality was considered as a serious disadvantage and has been an obstacle to apply Bayesian methods on
