2007
*Christian Spegt
Table of contents
Preface ... 4 Acknowledgements ... 4 1 Introduction ... 5 Background ... 6 Problem statement ... 8 2 Research methodology ... 93 Complexity according to Waidringer ... 15
3.1 Introduction ... 15
3.2 A conceptual model of complexity ... 15
3.3 An integrated approach ... 21
3.4 Measuring complexity of transportation and logistics systems ... 23
3.5 An example of the application of Waidringer’s method ... 25
4 Waidringer’s complexity in the Beer Distribution Game ... 32
4.1 Introduction ... 32
4.2 Starting points for the application ... 32
4.3 Components of complexity in the basic design ... 33
4.4 Components of complexity in the alternative design ... 37
4.5 Evaluation ... 43
5 Other complexity drivers and measures ... 47
5.1 Introduction ... 47
5.2 An information-based measure of system complexity ... 47
5.3 A specialized measure for logistics system complexity ... 48
5.4 Evaluation ... 49
6 A cybernetics perspective on control decisions ... 51
6.1 Introduction ... 51
6.2 A cybernetics perspective on control in the Beer Distribution Game ... 52
6.3 Evaluation ... 54
7 A proposal of alternative complexity measures ... 57
7.1 Introduction ... 57
7.2 Starting points for new complexity measures ... 57
7.3 Alternative complexity measures ... 58
August 25, 2007
Page 3
8 Measuring complexity ... 62
8.1 Introduction ... 62
8.2 A description of the total system ... 63
8.3 The system for slurry ... 66
8.4 The system for chemicals ... 69
8.5 Evaluation ... 72
9 Conclusions and recommendations ... 73
Recommendations for future research ... 75
References ... 76
Appendix A: A description of the Beer Distribution Game ... 79
Appendix B: Self-report scale to assess mental effort ... 81
Preface
The process of writing a thesis has proven to be an overwhelming experience. On the upside were the many moments of apparent clarity, at which I got the feeling that I was really on to something. Although such moments were usually soon followed by a new set of practical obstacles, I feel that at this stage, a smaller part of the feeling of clarity still remains. Hopefully, this thesis will succeed in sharing some of this clarity with the reader.
Acknowledgements
I would like to thank the many people who have supported me in various ways during the process. I thank my supervisor Bas Brinkman for his creative input, optimism and
patience. I thank the many friends and family who have provided both technical and emotional support (especially PJ and Ismaêl, supplying some helpful ideas).
Groningen, August 25, 2007
August 25, 2007
Page 5
1
Introduction
The idea of writing a thesis on the subject of complexity in logistics systems appeared after an assignment on an article written by Jonas Waidringer (2001). Any references to Waidringer made in this thesis concern this same article. Within it, he explores the notion of complexity, mostly within the context of transportation and logistics.
As a word, complexity means something to everyone, and for many people this meaning will be something like ‘hard to understand’, which is actually not so different from a particular definition of complexity:
“Any system we cannot intuitively understand is complex.” (Ashby, 1956)
With this meaning, people tend to use ‘complex’ as a label for a specific problem they’re dealing with, or for the subject matter of a conversation. Among these people are the majority of scientists that deal with complexity; they label a specific scientific problem complex to express that it is ‘a hard nut to crack’.
Waidringer’s article represents one of the scientific publications on the subject of complexity itself, rather than on any subject for which complexity serves as just a label. Within the context of transportation and logistics, he tries to identify what the label of ‘complex’ means, that is applied to the problems encountered there. I find this approach to the subject of complexity intriguing, for it can be seen to represent the search for specifics of the label ‘hard to find’.
Waidringer provides some foundations for the way scientists or managers can analyze, or deal with, the complex problems in the field of logistics. His article has inspired me to search for answers to questions on the subject of complexity within the area of logistics.
Background
A number of trends make the task of managing the logistics system increasingly complex (Waidringer, 2001), (Perona and Miragliotta, 2004), (Blecker et al., 2005):
The globalization of business has created international flows of resources as well as of products. These flows cover larger geographical distances and are often harder to
coordinate because they consist of several partial transports (for example a part by plane and a part by truck). Moreover, an international transport is often confronted with a greater variety of laws and regulations.
Another trend is the replacement of production to stock by production to order. Increased diversity in customer demand and the shortening of product life-cycles have forced companies to cut back on the inventory for their products, to avoid losses due to
obsoleteness. Frequent, small-sized shipments are used to compensate for this reduction of inventory.
Many companies feel the need to become more flexible and responsive to customer demand, to avoid the loss of business. This trend towards customization includes providing what the customer wants as well as providing it when the customer wants it. Providing what the customer wants adds to the variety of products offered, as well as to the variety of resources needed for production. Both complicate the logistics process, because they demand a greater variety of flows of both goods and resources. Providing the product when the customer wants it is also reflected in the trend towards a 24-hour economy. For the logistics system, expanding service hours this way means even more shipments have to be managed. Another part of providing at the right time is that the transport has to take as little time as possible. Time buffers within the transport chain have to be minimized to reduce response- and transit times. Increasingly, this results in integration of logistics processes with supply chain partners.
August 25, 2007
Page 7
has the system to be controlled become larger, the interdependence of its parts is felt more clearly now that slack resources are being removed. A control decision may have effects all through the system, all of which should (ideally) be considered when making the decision. The manager facing the task of controlling the logistics system may find it hard to grasp its totality.
If complex control problems place a greater burden on managers, some of the costs of complexity may be related to job pressure. Moreover, if additional complexity represents a greater burden, highly complex problems may well overburden managers. In such cases, poor management decisions can be expected.
Past research has related a specific category of logistics costs to poor management
decisions: costs associated with the bullwhip effect. This effect represents the tendency of orders to become more volatile as one traces them upstream (towards the producer) in the distribution channel (Dornier et al., 1998). Such volatility is harmful to the efficiency of the system, because excess resources (overcapacity, safety stocks) are now needed to provide the same level of customer service. The effect occurs through the decisions of managers in the system, even though it is undesirable to each of these managers.
Although complexity may well be costly to the business community, the scientific proof for such a relation is still lacking. Any investigation of the cost effects of complexity should collect cost data for different levels of complexity. However, measuring
complexity still represents a major problem for science. Some complexity measures have been proposed by other authors, but no single measure has gained widespread acceptance among scientists. Apparently, each of the existing measures has its own set of limitations.
Problem statement
Here, the research problem for this thesis arises:
How can existing complexity measures be used to investigate the relation between system complexity and bullwhip costs?
The measures proposed by Waidringer suffer from the limitation that they make statements about components of complexity, but fail to combine these into a total measure. This thesis tries to assess this total value by collecting data on the burden the system imposes on managers. In an experiment, this burden can be assessed under
different scenarios for component complexity. In this way, the research may specify how Waidringer’s component complexities are related to total complexity. The thesis tries to design such scenarios in the context of the Beer Distribution Game. This game simulates a specific logistics system, in which the bullwhip effect typically occurs. As a result, the experiment that is aimed for will provide the means to specify and test different
complexity values, while simultaneously assessing the bullwhip costs associated with the level of complexity.
The following research questions will be answered throughout this thesis:
• What concepts and measures of complexity exist that can be applied to the context of a logistics system?
• What limitations do these concepts and measures have?
August 25, 2007
Page 9
2
Research
methodology
The main objective for this thesis is to specify how the relation between system complexity and bullwhip costs can be investigated in a controlled experiment. A first benefit of using an experiment is that the researcher can control the variables that may cause the bullwhip effect. Another benefit is that the researcher is forced to specify different levels of system complexity in a concrete way. This thesis will evaluate to what extent several existing complexity concepts are fit for that purpose.
The Beer Distribution Game
The Beer Distribution Game (BDG) is proposed as the experimental context for the research. The game simulates a production distribution system for the beer industry, and is considered a credible model for a logistics system. A detailed description of the game is provided in appendix A.
The bullwhip effect
The BDG can be used to illustrate the ‘bullwhip effect’ that was described in the previous chapter. The effect was first identified by Forrester (1958), and has since been observed in several industry studies (Lee et al., 1997), (Sterman, 2000).
Wu and Katok (2006) categorize existing explanations of the effect. One category focuses on operational causes that shape rational behavior. The other focuses on
behavioral causes that lead to sub-optimal decision making (Croson et al., 2005). In the first category, Lee et al. (1997) have listed four causes and provided some strategies to reduce their effect. These causes are all related to the structure that shapes human decision making:
• In case of supply shortages, supplier policies may ration shipments based on the amounts ordered by the various customers. Customers may thus be tempted to order more than they actually need. At a later stage, orders will be cut back to eliminate excess inventory.
• Upstream players may make flawed forecasts of final demand based on the signals they receive from their downstream partners. Fluctuations in final demand not only affect expected demand, but also the target amount of safety stock for the retailer. Orders placed by a retailer contain represent a signal that contains two parts, whereas the supplying wholesaler may perceive only one: fluctuations in expected demand. When each stage in the chain uses downstream orders to predict demand, inaccurate forecasts of final demand may accumulate.
The first three of these operational causes are absent in the basic design of the BDG; there are no transaction costs to ordering, prices are fixed, and players have at most one direct upstream partner and one direct downstream partner. The impact of the last
behavioral cause (demand signal processing) can be eliminated by using a stable demand distribution and informing players about this distribution. Croson and Donohue (2002) review research using the BDG and find that the bullwhip effect remains even when all four operational causes listed above are controlled for. This supports the idea that the bullwhip effect may also be caused by sub-optimal decisions of the players.
The following behavioral explanations are suggested (Wu and Katok, 2006):
• The human mind has trouble dealing with dynamic systems containing delayed effects, indirect, or nonlinear relations between variables. Players in the BDG tend to only consider part of their supply line (Sterman, 2000).
August 25, 2007
Page
Some other publications support the notion of behavioral causes to the bullwhip effect. The review by Croson and Donohue (2002) lists sharing point-of-sale (POS) information (Croson and Donohue, 1999a), sharing inventory information (Croson and Donohue, 1999b), and reducing lead times (Kaminsky and Simchi-Levi, 1998) as treatments that enable players to make better decisions.
Additionally, player strategies (Nienhaus et al., 2002) and personality characteristics (Ruël et al., 2006) are suggested as explanations for the bullwhip effect. Table 1 provides an overview of the various causes suggested for the bullwhip effect.
Authors Operational cause Behavioral cause
Lee et al. (1997) Order batching
Price fluctuations
Inventory rationing
Demand signal
processing
Sterman (2000) Inability to model dynamic effects
mentally
Croson et al. (2005) Coordination risk
Croson and Donohue (1999a)
Lack of POS data
Croson and Donohue (1999b)
Lack of inventory information
Kaminsky and Simchi-Levi (1998)
Lead time
Nienhaus et al. (2002) Player strategies
Ruël et al. (2006) Personality characteristics
Table 1: Suggested causes for the bullwhip effect
understand the game system sufficiently to make optimal decisions. From this
perspective, the behavioral causes listed above may be among the things that contribute to a system’s complexity.
Measuring complexity
If complexity contributes to the bullwhip effect by overloading players’ mental abilities, these players may also find their task to be more difficult. The concept of cognitive load is suggested here as a way to assess system complexity. It is proposed here as a way to validate analytic measures of complexity.
August 25, 2007
Page
occurred. This thesis assumes that successful learning reduces the strength of the bullwhip effect in the game.
The conceptual model below illustrates the most important concepts and relations that are used in this thesis. The dotted arrows and boxes apply to secondary case study data reported in chapter 8. They will be explained at the start of that chapter. Although the concepts used are slightly different, the same logic applies there.
Figure 1: Conceptual model of the research in this thesis
The remaining chapters to some extent reflect the research process, in which objectives have changed a number of times. Waidringer’s complexity concept and measures are described in chapter 3, and then applied to the Beer Distribution Game in chapter 4. The level of detail applied in these chapters is somewhat out of line with the rest of the thesis. This is because the chapters represent the initial intent of the thesis: to apply
measures. Chapter 6 works toward new measures by integrating insights from various publications. Adapted versions of Waidringer’s measures are then proposed (chapter 7) and applied to secondary case study data (chapter 8). The final chapter provides
August 25, 2007
Page
3
Complexity according to Waidringer
3.1 Introduction
As a first step to investigating the proposed relation between complexity and bullwhip costs, a specification is needed of the complexity concept used, as well as the means to measure it. This chapter describes the concept and measures for complexity that are proposed by Waidringer ( 2001). His article has provided the basis for most of this thesis, and is therefore described in detail. The structure of the chapter largely follows
Waidringer’s article. Section 3.5 provides an added example of the application of his method.
3.2 A conceptual model of complexity
Waidringer works towards his concept of complexity by first discussing complexity as a general concept. He then proceeds by specifying what complexity means in the context of transportation and logistics. This leads to the identification of three ‘core’ properties of complexity of transportation and logistics systems, as well as a larger number of ‘extended’ properties. The properties are the basis for his model of complexity. The model is accompanied by an operational definition of complexity.
The concept of complexity
Although complex problems have been researched for centuries, the research of
complexity itself is quite young. This explains the existence of diverging definitions of the complexity and related concepts. Waidringer discusses some of the historical observations he finds most relevant for his thesis.
• Ashby gives a general definition of complexity, that is widely understood, but has little value for practical application:
“Any system we cannot intuitively understand is complex.” (Ashby, 1956)
• Edmonds argues that we should distinguish between ignorance and complexity, or any discussion of complexity becomes meaningless. He suggests complexity should refer to our model of the system. In this way, we can be certain that the complexity we perceive does not actually reflect our ignorance. Unfortunately, his definition does not allow any comparisons of systems based on complexity:
“Complexity is that property of a model which makes it difficult to formulate its overall behavior in a given language, even when given reasonably complete information about its atomic parts and their interrelations.” (Edmonds, 1999b)
Waidringer aims for a context-dependent definition that fits the pragmatic nature of his thesis better. He chooses not to distinguish between ignorance and complexity, but to focus on the predictive power of the model. He argues that to the manager facing a complex system, the origin of complexity isn’t the most important aspect. With time, more can be learned about the system, allowing improvement of the model and reduction of the complexity due to ignorance. Waidringer will treat complexity as a comparative measure, as is the scientific norm. Since any problem can be considered more or less complex, depending on the level of detail used in describing the problem, an absolute measure appears unfeasible.
Properties of complexity
August 25, 2007
Page
The network property represents structural characteristics or design of a transportation or logistics system. This includes the type of network (rail, road, water, air) and its overall structure and connectedness in terms of nodes and links. Nodes are physical locations with a specific function in the logistics system, such as a warehouse. Links are the infrastructure (such as roads) that connects the links. Basically, the complexity derived from the network assumes optimal use of the network, which means any inefficient links or trajectories of links will be excluded.
Formally, the network property is the topology of the network used, together with the quality of the nodes and links that belong to that network.
The process property represents the operations of an actual setup of a transportation or logistics system. It depends on the type of flow (goods, information, etc.), the activities the process consists of, their interfaces and the function of the process. The essence of the process property is the dynamic behavior of the process, which is strongly affected by the way activities within the process interact. Activities may be performed in parallel, in sequence, or they may be disconnected through a buffer of inventory or information. The complexity derived from the process assumes the optimal combination of activities. Formally, the process property is the description of the dynamic process that is taking place in order to perform the task.
The stakeholder property represents the management and control of the process and network. A stakeholder is any decision maker or decision making body with a specific interest in the system studied. It should be described on a specific hierarchical level . Within this level, it depends on the impact and outreach of the decisions made by
stakeholders. It also depends on any interactions between stakeholders and their demands and goals.
Figure 2: The properties of transportation and logistics systems’ complexity
The figure above is taken from Waidringer’s article. It shows the complexity of transportation and logistics systems, represented by the figure as a whole. Each of the properties of the system represents part of this complexity. The darker corners of the figure contain the core properties, each accompanied by the extended property most closely associated with it. The center of the figure contains the remaining extended properties. All properties influence one another as well as the total complexity of the system, meaning the representation in the figure is somewhat arbitrary. This
interconnectedness off properties can be labeled the ‘system property’ of the complexity and it represents a source of complexity itself.
Waidringer’s description of the extended properties is superficial, because they are not as important to his model as the core properties. Some of these properties (variety,
uncertainty, entropy, connectivity, dynamics and cognition) will reappear in chapters 5 and 6 of this thesis.
August 25, 2007
Page
Variety is a prerequisite for system complexity. Any system’s behavior can be described as a sequence of states in time. Variety appears as differences between these states. If there is no variety in a system’s behavior, managing the system will never be complex. Entropy is closely related to variety. It is a measure of how much information is required to describe a system. The greater the variety in the system, the more information is required to describe it, and the greater its entropy value.
Uncertainty adds to the complexity of managing a system because any management decisions under conditions of uncertainty must be based on assumptions or estimates. This means the effects of decisions are not known in advance, so the system cannot be fully controlled.
Adaptivity is a system’s tendency to adapt to its environment through time. The system’s behavior becomes harder to predict, as it changes in time. Flexibility is a measure of the capacity to adapt, adding to a system’s complexity much like adaptivity.
Abstraction refers to the ability to understand and use abstract models and tools in the management of the system. Like cognition, it refers not to the system, but to the person interacting with the system. More abstraction means less complexity is perceived in managing the system.
Goals and demands for stakeholders in the system may differ. This may add to the complexity of making the system behave in the desired way.
The size of the system contributes to the complexity of managing it. A system containing more elements will usually (but not necessarily) be more complex. When combined with interconnections between elements, size will increase a system’s complexity.
The last three extended properties are more closely related to the complexity measures that are introduced later:
places, and so on, that are used for the specific logistics system. Connectivity is the extended property most closely related to Waidringer’s network property.
Dynamics represent the dynamic behavior of the system. Within Waidringer’s model of transportation and logistics systems, dynamics exist in the process and its activities. Dynamics add to system complexity because it means system behavior may change as time passes, thus making system behavior harder to predict. The dynamic behavior of a system can be described using algorithms, which is the basis for the concept of
‘algorithmic complexity’. Dynamics is the extended property most closely related to Waidringer’s process property.
Cognition represents the ability of users of a model to understand abstract and complex systems. In the context of logistics this means that the transportation and logistics
systems’ complexity is high when the stakeholders involved find it difficult to understand the totality of the system. Cognition is related to ‘cognitive complexity’, which is based on the (difference between the) users’ mental models of the system. Cognition is the extended property most closely related to the stakeholder property.
Waidringer proposes the following operational definition of the complexity of transportation and logistics systems:
3.3 This logist that i system logist comp mode Figur system The m triang small The n (facil netwo section desc tics system. s meant to b ms. The mod tics research plexity of a t el is included re 3: Perspe ms model shows gle, the persp ler, dark tria
network pers lities, such a ork is given, An in cribes a struc Figure 3, be be used for th del is made u h. These pers transportatio d in section 3 ctives and m s the triangle pectives can angles contai spective focu as factories) a , the process Aug ntegrated a ctured metho elow, is taken he analysis o up of three p spectives sho n or logistic 3.5. measures for e that is the s n be found, e
ining the com
uses on struc and links (in s and stakeho gust 25, 2007 Page approach od for the an n from Waid of complexit perspectives ould be appl cs system. An complexity system’s com ach opposite mplexity me cture, and de nfrastructure olders involv 7 nalysis of the dringer’s the ty in transpor well-known ied in an int n example o of transport mplexity. At e its focus. In asures Waid escribes the s : roads, railw ved in that p e complexity esis. It shows rtation and l n in transpor egrated way f the applica
ation and log
The complexity of the structure can be handled by the decomposition of the system into subsystems.
Topological complexity concerns the complexity of the infrastructure used in the specific logistics system design. It is a measure based on the number of nodes and links in the network (which together give the size of the network), or in the graph that can be drawn to represent the network. Apart from system size, topological complexity is influenced by the structure and size of sub graphs.
The process perspective models the system as a process of activities coupled by transfers of resources (goods or information). Traditionally, this kind of representation is used for production processes, where goods flow between various stages of handling. Within a logistics process, this approach considers storage or (un)loading of goods an activity, to be set apart from the transfer of resources. The process perspective translates the function of the process into required activities and flows. The network and stakeholders serve as boundary conditions.
From a process perspective, the interactions between system components are important. The different system goals and their time horizons contribute to the dynamic
characteristics of the process. These characteristics define which transmissions and transformations of information are required in the process. The process design should be robust and stable to deal with the complexity of the process, that may show itself in disturbances.
Waidringer suggests algorithmic complexity as the best measure for the complexity of the process. It assesses the amount of activity occurring in the system. A somewhat
simplified measure for algorithmic complexity could be based on the minimum amount of steps required in the process to solve the logistical problem.
The stakeholder perspective focuses on perceptions, and describes the system in terms of the stakeholders actually involved in the execution of the transport. The main issue from this perspective is the impact of the decisions of stakeholders (individuals or
August 25, 2007
Page
given, the problem of a transport is how to choose the process and network to fulfill the demands and goals of these stakeholders.
From the stakeholder perspective the decision-making and its origins are important. The stakeholder should be provided with an interface that filters all of the available
information and is adapted to the mental model used by this stakeholder.
Cognitive complexity basically represents stakeholders’ mental models of a system. The logistics system’s complexity is high when stakeholders involved find it difficult to comprehend the totality of the system. Cognitive complexity also reflects differences in the mental images stakeholders have of the system; the more complex, the more
divergent the mental models. Cognitive complexity will be much harder to measure objectively than the other two complexity measures.
3.4 Measuring complexity of transportation and logistics systems Waidringer proceeds by using case study data in an attempt to measure complexity. Here, he replaces the measures for complexity that were mentioned in the last section by
measures that are more easily used in practice. As can be seen below, these measures are all based on connectivity, as opposed to the many different complexity drivers identified in his analysis of the components of complexity.
Waidringer starts out with the following mathematical definition of the Complexity of Transportation and Logistics Systems, stating that it depends on the Network property (N), Process property (P) and Stakeholder property (S):
It is not possible to define this function exactly without knowledge of the way the properties are related. Instead, Waidringer defines the different properties separately by studying them one at a time, keeping the value of the other properties at zero. This way, the network complexity, process complexity, and stakeholder complexity are:
NC = f(N;0;0) PC = f(0;P;0) SC = f(0;0;S)
For each of these components he introduces a density measure:
NC = l/n; number of links in the network / number of nodes in the network
PC = i/a; number of interactions in the process / number of activities in the process SC = r/s; number of relations between stakeholders / number of stakeholders
An upper and a lower bound are introduced for each of the measures, the lower bound being zero. For the network complexity, the upper bound is the maximum connectivity: the number of links in the completely connected graph divided by the number of nodes. In a completely connected graph, each node is linked to each other node.
Maximum connectivity = (n(n-1)/2)/n = (n-1)/2
For the other components, the upper bound is calculated in the same way.
The complexity value for each component can now be compared to its theoretical maximum, resulting in a relative measure for each component. The relative network complexity is shown here. It indicates the system’s network complexity as a percentage of the maximum network complexity the system could theoretically have, based on the number of nodes it contains:
August 25, 2007
Page
Waidringer concludes by drawing 3-dimensional graphs illustrating the relative complexity positions of systems. In these graphs, each axis represents one of the components of complexity. The maximum values on each axis are 100, because they represent a percentage of a maximum complexity value. Each such graph is therefore a cube, in which the complexity position of the system is represented (as a box or cube). Figures 7 and 10 in the next section are examples of such graphs.
3.5 An example of the application of Waidringer’s method
This section has been included to illustrate Waidringer’s method. Two systems are compared from a complexity perspective. An evaluation is provided at the end of this section.
A company producing furniture supplies four retail stores in each of two countries. It is currently using a central warehouse, but considers switching to the use of decentralized warehouses, one in each country. How do the two designs compare when viewed from a complexity viewpoint?
Design 1: Central warehousing
From a network perspective, the system is made up of ten nodes: eight retail stores, a central warehouse and a factory (the last two representing the company). Links exist between the warehouse and the factory, as well as between the warehouse and each of the retail stores. We assume no goods flow directly from the factory to the retailers, nor do any goods flow between retail stores.
Figure 4: the network for the central warehousing design
The network complexity for this design is: NC = l/n = 9/10. When this complexity is related to the complexity the network could have maximally had, given its current number of nodes, the relative network complexity results.
The relative NC = (l/n)/((n-1)/2) = 1/5, or 20%.
From a process perspective, the system represents the process performed on the network: moving furniture from the factory to any one of the retail stores. This means only one retail store is included in the process description. Differences between retail stores might have lead to differences in the process if, for instance, one group of retailers was located overseas. In such a case, different process descriptions would be warranted for the different groups of retail stores. In our case, however, the retail stores can largely be regarded as a homogenous group.
August 25, 2007
Page
Figure 5: activities and interactions in the process for the central warehousing design In the figure, dotted arrows represent flows of information, while solid arrows represent flows of goods. The interactions in the figure are:
1 The retail store (R) places an order with the company (C) 2 The company forwards the order to the warehouse (W), … 3 … as well as to the factory (F).
4 The factory ships the goods to the warehouse.
5 The warehouse ships the goods ordered to the retail store.
The process complexity for this design is: PC = i/a = 5/4. The relative PC = (i/a)/((a-1)/2) = 5/6, or 83%.
From a stakeholder perspective, the system consists of four stakeholders; decision making bodies with a specific interest in the system. The retail store is related to the company through the order placed and delivered. The company is related to both the factory and the warehouse, through decisions like the inventory policy, the number of trucks operated or working conditions in general. There is no direct relation between warehouse and factory; they are only indirectly related through their common relation to the company. In figure 6, each stakeholder is represented by an oval. The vertical
position of an oval represents the stakeholder’s level in the stakeholder hierarchy, while the width of the oval indicates the influence on the performance of the process.
Overlapping ovals represent stakeholder relations.
Figure 6: stakeholder diagram for the central warehousing design The stakeholder complexity for this design is: SC = r/s = 3/4.
Company
F R
The relative SC = (r/s)/((s-1)/2) = 3/6, or 50%.
The relative complexity position for this design is shown in figure 9 as the box demarked by the dashed lines. The larger cube represents the maximum complexity the design could have, based on the numbers of nodes, activities and stakeholders it contains.
Figure 7: A graphical representation of the relative complexity position for design 1
Design 2: Decentralized warehousing
The network for this design contains 11 nodes (factory, two warehouses and eight retail stores). Since each of the warehouses only supplies one country, each is linked to only four retail stores, as well as to the factory. In total, there are 10 links in the network. For this design, the network complexity is: NC = 10/11.
The relative NC = (10/11)((11-1)/2) = 2/11, or 18%.
August 25, 2007
Page
When the decentralized warehousing design is viewed from a process perspective, two representations can be made. The first is a copy of the process for the central warehouse design. The second makes a distinction between the two groups of retail stores as well as between the two warehouses supplying them. Making this distinction basically means adding detail to the analysis. The second representation is used here, because the comparison of warehousing options calls for detail concerning warehouses.
Figure 9: the process for the decentralized warehousing design
1a A retail store in country 1 places an order with the company. 1b A retail store in country 2 places an order with the company. 2 The company forwards the order to the factory, …
3a and to either warehouse 1, …
3b or to warehouse 2, whichever is appropriate for this particular retailer. 4a The factory ships the goods ordered to either warehouse 1, …
4b or to warehouse 2, whichever is appropriate for this particular retailer. 5a Warehouse 1 ships the goods ordered to the retailer, …
5b or warehouse 2 ships the goods to the retailer.
Represented this way, the process contains six activities and nine interactions. The process complexity is: PC = i/a = 9/6.
From a stakeholder perspective, the design with decentralized warehouses resembles the other design. Both warehouses are only directly related to the company. Any decisions the company makes with an impact on warehousing will likely affect both warehouses in the same way. Therefore, figure 6 above also represents a stakeholder diagram for this design. Thus, the network complexity and relative network complexity are 3/4 and 3/6, respectively. Figure 10 shows the relative complexity position for this design.
Figure 10: relative complexity position for the decentralized warehousing design
Comparison of the two designs
Waidringer proposes three components of a logistics system’s complexity that together should adequately reflect this complexity. Furthermore, he proposes a way to measure each of them. Still, the degree to which his theory equips the user to compare systems based on complexity has its limits:
August 25, 2007
Page
complexity value, we can safely assume it is the most complex network. This point applies to the process and the stakeholders as well.
• The exact relation of either of the components to the total system’s complexity is unknown. Intuitively, the total complexity will be some product of its
components:
C total = αC network * βC process * γC stakeholder
The values for the parameters α, β, and γ are unknown, however. Assuming each value is some positive number, any increase in one of the components of complexity will yield a higher total complexity. Still, a higher value for one component could be offset by a lower value for another. This means we can only say one system is more complex than another when the first has a higher complexity value for at least one component, while the values for the remaining components at least equal those of the other system. To be able to say anything more about changes in total system
complexity, more information about the parameters is required.
In our example, the network for the decentralized warehousing design is slightly larger than the other network: 10 links and 11 nodes compared to 9 links and 10 nodes. Its network complexity value is also slightly higher: 10/11 compared to 9/10. Since the decentralized warehousing design has both the larger network and the higher network complexity, we may conclude the network for this design is more complex.
The process complexities are 1,25 for central warehousing and 1,5 for decentralized warehousing. Because the process for the second design is larger as well (2 more
activities and 4 more interactions), we can conclude that the process is more complex in the design of decentralized warehousing.
From the stakeholder perspective, both designs are similar.
4 Waidringer’s
complexity
in
the Beer Distribution Game
4.1 Introduction
This chapter attempts to specify system complexity for the Beer Distribution Game using Waidringer’s complexity measures. Additionally, an attempt is made to develop an adapted design of the BDG with a different system complexity value. The adapted design will be developed to represent a higher network complexity value, with process and stakeholder complexities equal to the basic version. If such a design can be proposed, it can be used to investigate the impact of network complexity on bullwhip costs. The chapter pays much attention to what changes to the game design would mean in the real-life equivalent of the game system. This reflects the idea that without such caution, Waidringer’s measures may produce somewhat arbitrary results. The chapter considers the limited information players have in the game a characteristic that should not be affected by any redesign. This reflects the objectives for this thesis at an earlier stage.
4.2 Starting points for the application
Waidringer’s concept of complexity and his method for analysis are meant for real-life logistics systems. The application assumes the BDG can be considered a model of a real logistics system in which there is little cooperation between supply chain partners. The factory in the BDG is considered to represent the logistics function performed at the factory in the corresponding real system. Finally, the three-period delay between the time the factory orders goods and the time they become available for shipment, represents time required for flows within the factory, because no suppliers are identified in the BDG.
The application will study the system on the supply chain level of aggregation, mainly because this fits best with the information provided for the BDG. At this level of
August 25, 2007
Page
these are represented as a single element. System characteristics that are related to what happens inside of each stage are excluded, such as the internal flows for the factory. The factory will thus be represented as an activity that encompasses these flows. Stakeholders on a hierarchical level transcending the supply chain, such as the government, are also excluded from the analysis.
Below, the application of the components of complexity to the BDG will be described. The basic version of the game will be analyzed in section 4.3, followed by the alternative design in section 4.4. Waidringer’s relative measures of complexity will not be included here, because we see no value in them for our analysis.
4.3 Components of complexity in the basic design
Network complexity
Figure 11: Network for the basic design
The network complexity for the basic design is: NC = l/n = 3/4.
This value for network complexity is the lowest value possible for a network containing 4 nodes.
Process complexity
The process that is modeled by the BDG is the physical transport of the product (beer) to the final consumer. Each of the parties in the logistics network represents an activity in the process. Here, the final customer is also considered part of the process, ordering goods and picking them up at the retailer. The basic version of the BDG thus contains five activities, which are linked by interactions based on flows of information and goods. The beer industry produces to stock, rather than to order. This means production at the factory is carried out in anticipation of demand. The same goes for the logistics process, which ‘pushes’ the beer towards the customer prior to the actual customer order. In Waidringer’s terminology, the activities are ‘decoupled’ through buffers of inventory. As long as sufficient inventory is available, the retailer can supply the customer upon
August 25, 2007
Page
Figure 12: Process for the basic design
1 The customer places an order (actually, a number of customers all place orders which are accumulated over a period to become consumer demand for that period) (I).
2 The retailer places an order with the wholesaler (I) 3 The wholesaler places an order with the distributor (I) 4 The distributor places an order with the factory (I)
5 The factory ships the goods ordered to the distributor (G) 6 The distributor ships the goods ordered to the wholesaler (G) 7 The wholesaler ships the goods ordered to the retailer (G) 8 The retailer supplies the customer (G)
The numbers in the figure can be seen to represent the sequence in which the flows would occur if no inventory were present in the supply chain at the time the customer order was placed. Since inventories are in fact usually present throughout the chain, one may argue that the delivery by the retailer should represent the second flow in the process, rather than the eighth. In this interpretation, the remaining flows could represent the
replenishment of inventories throughout the chain, based on updated expectations of what inventory levels are required to meet future demand. The representation used here was chosen because it resembles the process descriptions in Waidringer’s case studies, which all lead from customer order to final delivery. For the process complexity value the choice of sequence doesn’t make a difference, as long as all the flows and activities are included.
Stakeholder complexity
Each of the players in the BDG represents a stakeholder in the logistics system. The final customer should also be considered a stakeholder; the customer decides whether or not to buy beer from the retailer. This decision affects the entire logistical system, because it activates the system. The real system will of course include more than one final customer, but the customers can be treated as a homogeneous group, which can be represented by a single stakeholder in the analysis.
The stakeholders roughly perform equal shares of the logistics process, and they all operate on the same hierarchical level. Each of the stakeholders is directly related to its supplier and customer, because these represent the parties that directly affect how the stakeholder will operate within the logistics system (what will the stakeholder supply and/or order?).
Figure 13: Stakeholders and their relations for the basic design
There are 4 direct relations between the 5 stakeholders present in the basic version of the game. The stakeholder complexity value for this design is:
August 25, 2007
Page
4.4 Components of complexity in the alternative design
Network complexity
The alternative design should be characterized by a high value for network complexity. To obtain a higher value for Waidringer’s network complexity component, the number of links per node will have to be increased. Eliminating a node would theoretically increase complexity if the number of links would remain unchanged. In practice, it is impossible to do this: as soon as a node is removed, some links also disappear. Additional links will therefore have to be introduced to increase the network complexity value.
Introducing additional links between the parties in the basic design proves somewhat problematic. The BDG focuses on what can happen in a supply chain because of insufficient (sharing of) information. To illustrate the effects, the flow of information between players has to be restricted: players only receive information from their direct customer. Introducing additional links between the players in the system means adding flows of information between them. A goods flow from distributor to retailer, for instance, would have to be based on an order by the retailer, which would represent an information flow that should be avoided. It would be possible, however, to introduce another player on an existing stage in the supply chain. Information would link this player to a customer and a supplier as well, but this wouldn’t conflict with the purpose of the game.
goods to one another from their own inventory. This may be a way to temporarily deal with situations in which one of the retailers is running low on inventory, while the other still has plenty. Such a solution may be a faster way to deal with an impending shortage then the regular ordering from the supplier.
Adding more retailers in this way would increase the network complexity value further, but the design change will be limited to one additional retailer. The network for this design is illustrated in figure 14.
Figure 14: Network for the alternative design
The network complexity for this design is: NC = 5/5.
August 25, 2007
Page
Figure 15: Adjusted network for the basic design
For the remaining components of complexity, the same level of detail will be used. Adjusted descriptions of the process and stakeholders in the basic design are included, as well as the corresponding adjusted complexity values.
Process complexity
The process complexity value for this design should be the same as for the basic design, to single out the impact of network complexity on total complexity. To make differences in complexity values credible, both game designs should clearly represent different real situations. The additional retailer is insufficient for this purpose, but the link between the retailers in the alternative design sets the real situations modeled apart. The link
represents a cooperative arrangement between parties in the supply chain. This conflicts with the assumption of little cooperation within the supply chain, which was identified as a characteristic of the real system modeled by the basic design for the BDG.
Since a consistent level of detail is applied, the arrangement represented by the link should also be visible in the other components of complexity, or the link shouldn’t have been included in the network. The implications for the process are described below.
available for shipment, such as a company car. Information could be shared through a telephone. The receiving retailer could either pay for the goods received, or send an equal amount of goods in return as soon as a shipment from the wholesaler arrives. In the latter case, the supplying retailer in the arrangement wouldn’t profit much directly. Still, the tables may be turned in the future, making cooperation worthwhile. If it takes more time to get the goods from the wholesaler, this cooperation may be a realistic option.
Additional costs can be justified by comparing them with the cost of sales that would be lost otherwise.
The process for the alternative design is illustrated in figure 16. Below it is the specification of the flows in the process.
Figure 16: Process for the alternative design
1a The customer places an order with either retailer 1, … (I) 1b … or retailer 2 (I).
August 25, 2007
Page
4b Retailer 2 places an order with the wholesaler (I). 5 The wholesaler places an order with the distributor (I). 6 The distributor places an order with the factory (I). 7 The factory ships the goods ordered to the distributor (G). 8 The distributor ships the goods ordered to the wholesaler (G). 9a The wholesaler ships the goods ordered to retailer 1 (G). 9b The wholesaler ships the goods ordered to the retailer 2 (G). 10a Retailer 1 supplies the customer, … (G)
10b … or retailer 2 supplies the customer (G).
In this design, there are 6 activities and 16 interactions. This process description includes any activities and flows connected to a customer order for either retailer 1 or retailer 2. The complexity value for the process is: PC = 16/6.
For the basic design, a different process description results when the second retailer is included in the process description. Figure 17 contains the adjusted description of the process in the basic design. Below it are the corresponding specification of flows, as well as the corresponding process complexity value.
Figure 17: Adjusted process for the basic design.
2a Retailer 1 places an order with the wholesaler (I). 2b Retailer 2 places an order with the wholesaler (I). 3 The wholesaler places an order with the distributor (I). 4 The distributor places an order with the factory (I). 5 The factory ships the goods ordered to the distributor (G). 6 The distributor ships the goods ordered to the wholesaler (G). 7a The wholesaler ships the goods ordered to retailer 1 (G). 7b The wholesaler ships the goods ordered to the retailer 2 (G). 8a Retailer 1 supplies the customer, … (G)
8b … or retailer 2 supplies the customer (G).
The complexity value for the adjusted process is: PC = 12/6.
Stakeholder complexity
In the alternative design, an additional retailer has been introduced, which has been represented in the descriptions of both network and process. From a stakeholder perspective, the second retailer is a decision maker directly affecting the operations of other parties in the supply chain. There are relations between the second retailer and the customer, wholesaler, and first retailer. The 6 stakeholders and the 7 relations between them in the alternative design are shown in figure 18.
Figure 18: Stakeholders for the alternative design SC = 7/6.
August 25, 2007
Page
retailer is indirect in this design, and therefore excluded from the analysis. Figure 19 shows the adjusted stakeholders and relations for the basic design.
Figure 19: Adjusted stakeholders for the basic design SC = 6/6.
4.5 Evaluation
As described at the start of this chapter, the aim of the application was to first describe the basic design of the BDG using Waidringer’s concepts. Then, an alternative design was to be developed, which would have the same process and stakeholder complexity values as the basic design, but a higher value for network complexity.
The basic version of the BDG represents a logistics system with low complexity values for each of the components identified by Waidringer.
In the second part of the application, some problems were encountered. First, the restrictions on information flows within the BDG turned out to limit the ways in which the network complexity value could be increased. Thus, additional links could only be introduced within a stage in the supply chain. A second retailer was introduced for this purpose, to be linked to the customer, wholesaler and other retailer. The level of
aggregation used in the analysis had to be adapted in order to make this adjustment to the basic design visible in a comparison. Consequently, the analysis of the basic design had to be adjusted as well, to maintain consistency in the level of aggregation used. When compared to this adjusted representation of the basic design, the alternative design represents higher values for each of the components of complexity, rather than just for the network component. This means this part of the application was unsuccessful, because the complexity values for the process and stakeholders could not be controlled.
Some questions arise as a result of the application:
Is the lack of control related to the restrictions for the Beer Distribution Game? Without the restrictions for the BDG, it would have been possible to introduce a link between (for instance) the factory and the wholesaler. Such a link would only be relevant for the logistics system if it would be used in the process. This would mean some flow would also have to be introduced in the system, for in the basic design, there are no flows between the factory and the wholesaler. Likewise, the introduction of a flow between parties that were not yet connected in the basic design would require additional
August 25, 2007
Page
Are there any ways to control the components identified by Waidringer in an experiment? At the outset of the application, it seemed possible to control the individual components. Based on Waidringer’s case studies, some representations were made for the alternative design that maintained constant values for the process and stakeholder complexity. However, in the course of the application, it became apparent that these representations were based on inconsistent levels of aggregation. These inconsistencies didn’t matter for the purpose of Waidringer’s article, since his article is meant to show that the
components can be applied to a logistics system in a meaningful way.
Since the aim for this thesis is to measure the total complexity, the analysis of the components should be performed using a consistent level of aggregation.
Some options can be identified that seem to only affect the complexity value for one component. It may be possible to either introduce a second link between nodes that are already connected, or to introduce another flow between activities that already interact. Within the BDG, such an additional link could be introduced, for instance, between the distributor and the wholesaler. Since the process and stakeholder complexities are to remain unaffected, the same stakeholders should be responsible for the use of this link, and it should be used for a flow that is already present in the basic design. Then, the distributor would be using two options simultaneously for shipment of beer to the wholesaler. This could make sense if one link is preferred, but has a limited capacity. However, it would also take the application beyond Waidringer’s use of links. Although he briefly mentions the characteristics that may apply to any link, Waidringer doesn’t mention the possibility of more than a single link between two nodes.
An additional flow, performed by stakeholders present in the basic design, using
For any experiment aimed at specifying the relation between the components of
complexity and the total complexity, these options are still insufficient, for they still offer no way of independently manipulating the stakeholder complexity. The introduction of an additional relation for a pair of stakeholders, that is already related in the basic design, seems impossible.
At this point, it has become clear that the interdependence of Waidringer’s concepts of complexity limits their potential for measuring the total complexity of a logistics system. This does not mean that Waidringer’s analysis of complexity is wrong, however.
August 25, 2007
Page
5 Other
complexity
drivers and measures
5.1 Introduction
The previous chapter has shown that Waidringer’s complexity measures offer insufficient means to relate bullwhip costs to different levels of system complexity. This chapter describes two other existing complexity measures, and evaluates their potential for the proposed application to the Beer Distribution Game.
5.2 An informationbased measure of system complexity
The information theoretic approach to measuring complexity uses entropy measures that indicate the amount of information required for the description of a system. An example of this stream of publications is an article on supply chain complexity in the
manufacturing industry (Frizelle et al., ????).
Their way of measuring system complexity first identifies all the possible states of the system (all combinations of values the variables of the system can have). Any of the states that appear in the production schedule represent planned system behavior. The production schedule is also used to assign each planned state a probability of occurring. Then, the static complexity can be calculated:
This measure represents the expected amount of information required for describing any deviations from scheduled system behavior, which appear due to uncertainty. Here, P is the probability of the system being ‘under control’ (behaving according to plan), and ns is the number of unscheduled states a resource may be in when the system is ‘out of
control’.
This superficial description already illustrates two fundamental problems for an application to the Beer Distribution Game:
• No production schedule is available to specify planned performance in the BDG. As a result, there appears to be no basis for assigning probabilities to each of the states that may occur in the game.
• Output data are used for the calculation of dynamic complexity. Therefore, complexity can never explain bullwhip costs, because both are simultaneously defined by system performance.
5.3 A specialized measure for logistics system complexity An article by Perona and Miragliotta explores management of complexity and supply chain performance in the Italian household appliances industry (Perona and Miragliotta, 2004). Although their research concerns manufacturing companies, it also covers
logistics aspects.
The authors propose various complexity measures for each of five different functional areas. For the logistics function, three complexity indices are proposed: the duration of relationships with suppliers, the use of Just-In-Time and demand pull principles for ordering, and the use of a rolling order mechanism versus that of spot contracting. A rolling order mechanism is an arrangement in which the customer provides information about its projected demand for the supplier’s product (Klotz, 2005). It can serve to make demand for the suppliers’ product more stable and predictable.
August 25, 2007
Page
stable relations with suppliers and customers. More stable relations suggest less variety in the set of logistics partners. In turn, this may make the logistics process more predictable. The authors further distinguish between actual complexity and perceived variety. Actual complexity reflects variety in the system, while perceived complexity reflects what variety is perceived by managers in the system. Actual complexity can be reduced by selecting reliable supply chain partners, while perceived complexity can be managed by improved exchange of information.
Two problems appear when the measures are applied to the Beer Distribution Game: • Stability of relations hardly make supply chain partners more predictable in the
BDG. In the game, stable relations are not associated with improved sharing of information.
• The exact calculation of each of the two measures is not provided by the authors.
Although the unpredictability of the decisions made by supply chain partners appears to be important in the BDG, these measures assess it in an inaccurate way. However, the lack of a concrete description of the measures is the most fundamental problem.
5.4 Evaluation
Source: Drawbacks for application to BDG: Frizelle et al. (????) Based on game outputs
No production schedule is available in the BDG Perona and Miragliotta (2004) Stability of relations is a flawed concept for the BDG
No concrete specification of measures Waidringer (2001) So far only captures component complexities
Manipulation of components is problematic Effects of system size on complexity are ignored
Table 2: Complexity measures and their drawbacks when applied to the BDG.
The remainder of the thesis aims to develop complexity measures that meet the
requirements for the proposed experiment. The next chapter will provide a better basis for the new complexity measures. So far, the approach has been to start with a complexity concept and then to see how it may be related to poor decisions. The following chapter starts with decision making instead, focusing on the reasons why the best decisions are not being made. These reasons are then compared to complexity drivers in the
August 25, 2007
Page
6
A cybernetics perspective on control decisions
6.1 Introduction
Ashby (1956) provides an introduction to cybernetics that serves as a starting point for this chapter. Cybernetics considers a (logistics) system a machine, transforming inputs into outputs in a way defined by the structure of the machine. This perspective is applied to the Beer Distribution Game to see how the structure of the game system produces the bullwhip effect. Game characteristics that make it hard to control system behavior are interpreted as drivers for complexity. Figure 20 shows graphically how complexity is expected to increase the bullwhip costs incurred in the game.
Figure 20: Expected relation between complexity and bullwhip costs
The analysis will show which elements of existing complexity measures are relevant in the BDG. These elements will be included in the adapted measures proposed later. Additionally, the analysis will suggest ways in which complexity can be reduced in the BDG to yield lower bullwhip costs.
6.2 A cybernetics perspective on control in the Beer Distribution Game
From a cybernetics perspective, controlling a system means restricting the variety of system outputs that may occur. To control the costs incurred in the BDG, a team of players tries to control the values of inventories and backorders during the game. If no such control would be exercised, large backorder costs can be expected for the position of the retailer. By exercising control, a team of players tries to have the system produce lower-cost outputs instead.
Ashby’s Law of Requisite Variety states that any variety in the system can only be controlled by variety in the control system. Figure 21 provides a cybernetics
representation of the BDG. The analysis below it will show how excess system variety makes full control of system outputs impossible. As a result, the system will produce unintended outputs, possibly including bullwhip costs.
Figure 21: A cybernetics representation of the BDG
The control objective in the BDG is to minimize accumulated costs. These costs can be seen as an output of the system. They arise as a result of the values of other system variables: inventory levels and backorder levels throughout the game (arrow 1). If no inputs are provided to the system, only a single output state is possible, which is then determined by the starting values for the system.
Final demand introduces variety to the system (arrow 2); different inventory and
August 25, 2007
Page
the effects of any control decision are delayed by the lead times in the system (arrow 3). What happens during this delay is dictated by any variety in final demand. If there is any variety in final demand, it makes full control of system outputs impossible.
To avoid costs associated with time delays, decision makers act on predictions besides the data about the current system state. When predictions are fully accurate, the control system can respond optimally to disturbances, even when control effects are delayed. Failure to control the system in such a case reflects that the predictive model has turned out to be inaccurate; the system shows variety relative to what was predicted.
If system complexity is what causes flawed control decisions, then it appears through the decision makers’ inability to accurately predict the system’s behavior. To understand the difficulty in predicting system behavior in the BDG, consider figure 22, below. It shows three vectors, the elements of which describe the system at any moment. Here, system inventory also includes any goods flowing towards a downstream destination. Orders in-transit represent goods orders that have yet to be received by the relevant supplier.
Figure 22: Vectors defining any system state in the BDG
