Methods for optimisation of logistics systems

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Methods for Optimisation of Logistics Systems

by

Tamas Janoshalmi, Dipl. Eng.

A Thesis submitted in partial fulfilment of the PhD requirements

Supervisor: Dr Katalin Tanczos Department of Transport Economics

Budapest University of Technology and Economics

2002

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List of Figures

Page

Figure 1.1 Forces driving globalisation 14

Figure 1.2 Risk-return trade-offs for global operations 15 Figure 1.3 Relationship between logistical service level and cost 18

Figure 1.4 Logistical integration 18

Figure 1.5 Logistics information requirements 19

Figure 1.6 Logistical performance cycles 21

Figure 2.1 Workflow on a typical machine in a job shop 38 Figure 2.2 Inventory balances for a re-order level policy in which 47

demand during the lead-time is always average

Figure 2.3 Variation of operational cost with replenishment 49 order quantity

Figure 2.4 Graphical interpretation of minimum order quantities 50 Figure 3.1 Tank network of ULG95 at Stanlow 59 Figure 3.2 Four Blender Tank Level Time Series 60 Figure 3.3 Two Pipeline and Two Delivery Tank Level Time Series 61 Figure 3.4 Hourly Outflow from the Four Blender Tanks 63

Figure 3.5 Hourly Inflow to Pipeline Tanks 63

Figure 3.6 Hourly Inflow to Delivery Tanks 64

Figure 3.7 Total Hourly Outflow from the Tank Distribution Network 64 Figure 3.8 Total Hourly Inflow to the Tank Distribution Network 65 Figure 3.9 Illustration of a Time to Stockout Calculation 66 Figure 3.10 (a) Stock Level and Daily Demand Time Series 67

(b) Times to Stockout Time Series (c ) Times to Stockout Histogram

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Figure 3.11 Daily, over all Days Averaged Periodic Variation in 68 Demand for ULG95

Figure 3.12 Daily Periodic Variation in Outflow from 69 Delivery & Pipeline Tanks

Figure 3.13 Daily Averaged Periodic Variation in Total Inflow 70 to the ULG95 Network

Figure 3.14 Autocorrelation Function and Partial Autocorrelation 71 Function for Total Inflow to The Network

Figure 3.15 Residuals versus Fitted Values of Total Inflow 72 Figure 3.16 Autocorrelation and Partial Autocorrelation Function 73

of Total Outflow

Figure 3.17 Residuals versus Fitted Values of Total Outflow 73

Figure 3.18 Total ULG95 Demand Time Series 75

Figure 3.19 Road Delivery Demand Time Series of ULG95 76 Figure 3.20 Pipeline Demand Time Series of ULG95 77

Figure 3.21 Weekly Road Demand of ULG95 78

Figure 3.22 Time Series of Response and Independent Variable Data 80

Figure 3.23 Time Series of Residuals 82

Figure 3.24 Frequency Histogram of Residuals 82 Figure 3.25 Residual versus Fitted Values 83 Figure 3.26 Normal Probability Plot for Residuals 84

Figure 4.1 Main movement flows of SKS Ltd 90

Figure 4.2 Main movement flows of Freudenberg SH Ltd 92

Figure 4.3 Assessment Flow Chart 99

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List of Tables

Page Table 2.1 Key Purchasing Performance Benchmarks 23 Table 2.2 Cross - Industry Comparison of Standard Benchmarks 28

(Source: Centre for Advanced Purchasing Studies, USA, 2001)

Table 2.3 Standardised test scores 29

Table 2.4 Correlation matrix of purchasing performance benchmarks 30 Table 2.5 Eigenvalues of the correlation matrix 30 Table 2.6 Matrix of ten normalised eigenvectors of the 31

correlation matrix

Table 2.7 Unstandardised and standardised purchasing performance 31 benchmark component scores for eighteen different

industrial sectors

Table 2.8 Matrix of principal component loadings 33 Table 2.9 Variation represented by the principal components in 34

each original purchasing performance benchmark

Table 4.1 Calculated Logistic Sensitivity Indices 94

Table 4.2 Scoring Guidelines 97

Table 4.3 Individual Question Scores 97

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Preface

The purpose of my thesis is to provide performance monitoring and optimisation techniques in the discipline of logistics with a focus on using operational research methods. I have dealt with the subject from the viewpoint of a logistics professional, who is concerned with the solution of real problems and with the implementation of those solutions. The emphasis is on developing models that will yield workable solutions.

The examples that are quoted are based on my actual experience and that of colleagues with whom I have worked. However, where appropriate, the identities of firms have been disguised and some of the figures have been scaled up or down. Some of the ideas and techniques have been around for years, but they are still useful and valid today.

Other ideas are new, at least when applied to logistics.

I have attempted to present a comprehensive discussion of the field, emphasising an analytical framework wherever possible. Some description of the technology and processes is necessary, but the primary emphasis is on concepts. The important task is to develop a framework that will serve well as the field evolves.

In preparing my thesis I have also drawn on the ideas of others and have sought to do a thorough research on previous works and publications, in particular on the following authors: D.J.Bowersox, J.Prezenszki, H-Ch.Pfohl, L.Gaspar-J.Temesi, C.den Heijer- R.Dekker and K.J.Meldrum. Some topics had to be omitted for lack of space, however, because logistics concentrates in application, it is a bridge between concepts. The logistics concept itself is a framework, drawing on a wide variety of disciplines. The richness of the field comes not from these individual areas alone but from the combined effect that they present as an integral system.

The use of operational research methods proposed in the thesis is practice driven.

A synergetic effect has been present by applying these methods and their final form is a result of pragmatic adjustment during their application.

I have been fortunate to work with many creative thinkers and practitioners in logistics over the last few years and they have profoundly influenced my approach on how I see logistics as a core business process.

Acknowledgements

There are a number of people who have contributed to the completion of this thesis and I would like to express my thanks to them all.

In particular, I would like to sincerely thank my supervisor Professor Katalin Tanczos, Head of the Department of Transport Economics, Budapest University of Technology and Economics, for her constant guidance, encouragement and support, throughout the project.

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There are scores of people to whom I am indebted, for advice, criticism and inspiration, spread over many years. These people include Dr Phil Jonathan, Shell Global Solutions, Shell Research Ltd., Dr Michael Cox, Professor in Operations Research at the University of Newcastle upon Tyne, my parents and my brother Gabor.

General overview

Today, more than ever, there is an immediate need for competitive advantage in a global marketplace. This positioning requires a solid business strategy integrated into a supply chain system. The new realities forcing strategic development into supply chain implementation are these:

• Technology, politics, economics, and life-styles are changing at a pace of lightening acceleration every few years.

• There are no more protected markets with the rise of global trade. The world is now filled with high quality competitors from industrialised countries and low cost competitors from developing countries.

• Increased competition has created more sophisticated and demanding customers.

Good quality, on-time delivery, and good price products can no longer compete.

Value is the competitive strategy for today. This means exceeding all expectations and total fulfilment of the customer’s requirements.

Measuring, monitoring and optimising the effectiveness of an organisation’s supply chain system directly relates to the aforementioned customer-driven strategies and matches them against best practices, benchmarking performance data, and optimal software applications. These measurements allow supply chain professionals to identify critical changes in the customer’s environment. In particular those customer requirements that are emerging, forecast their future direction, derive their implications for effective planning, and make plans for advantages they may offer or improve their consequences if they negatively impact the supply chain.

Outline of the thesis

The thesis is structured with a systematic approach. The first chapter looks at logistics systems both at macro and micro levels and examines subsystems, system elements and the interrelationships among them. Having outlined the system itself, the second part of the thesis investigates the development of methods for logistical system performance analysis. The emphasis is on corporate logistical functions.

The first section looks at, from a material-flow point of view, the first element of the supply chain, and focuses on identifying key purchasing performance measurements by using principal components analysis.

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This application of principle component analysis is new in identifying key purchasing performance indices and provides a straightforward technique to reduce analytical complexity with broad applicability. The second section goes further in the supply chain, and presuming that the goods receipt has been done, applies integer linear programming with branch and bound to such job shop scheduling scenario - each job has exactly m operations, one on each machine - where the optimisation emphasis is on minimising the mean flow time.

The third section develops, by introducing the Langrange multiplier to the problem, new optimum replenishment quantity calculations that could reflect the interdependent nature of production scheduling and inventory management. Harmonised inventory management provides room for further job shop scheduling improvements and it is true vice-versa. It exhibits optimum calculations of inventory re-order levels and replenishment order quantities when the demand per unit time is variable but the lead time is fixed and when demand and lead time duration are both variable. Multi-product inventory situations are further developed with attention to optimisation of economic order sizes when a limitation is set on capital invested in stocks and when a limitation is set on total storage space.

Since demand as a system variable plays a key role in the above-mentioned optimum calculations, the third chapter scrutinises operational demand analysis. The basis of my work was the successful statistical performance analysis I conducted at Shell Research Ltd. The focus is on demand modelling with the application of autocorrelation and residual analysis. No previous dissection has been conducted that examines demand time series of this kind as thoroughly as in this section. Further, linear modelling is used to determine the appropriate model. Many different sophisticated statistical tools have been applied and have proved to be adequate for the analysis. It definitely indicates my keenness on exercising statistical techniques to system analysis scenarios.

Having paid particular attention to elements of the logistical system in the previous sections chapter four goes back to the investigation level that was present in the first chapter and identifies logistics strategy factors and logistics systems’ requirements.

The first part focuses on the analysis of the efficiency of logistical operations and its indices, whereas the second part details the development of a complete corporate logistics performance audit system. Here, the methods used are based on my actual corporate logistics system audit experience and these techniques provide an ultimate tool for professionals to evaluate logistical system performances.

Finally, chapter five discusses the results and achievements of the thesis and details the applicability of the methods developed. It also makes suggestions for further and future work.

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Chapter 1 Overview of Logistics Operations and Processes of the Industrial Supply Chain

1.1 Logistics – competitive advantage

Modern logistics is a paradox. Logistics has been performed since the beginning of civilisation: it is hardly new. However, implementing best practice of logistics has become one of the most exciting and challenging operational areas. Logistics involves the integration of information, transportation, inventory, warehousing, material handling, and packaging. All of these areas of work provide a variety of stimulating jobs.

The operating responsibility of logistics is the geographical positioning of required raw materials, work-in-progress, and finished inventories where and when required at the lowest cost possible. It is through the logistical process that materials flow into the vast manufacturing capacity of an industrial nation and products are distributed through marketing channels to consumers. Despite impressive cost comparisons, the true excitement of logistics is not cost containment or reduction. The excitement comes from understanding how organisations position their logistical competence to gain competitive advantage. Organisations that enjoy world class logistical competence can gain competitive advantage by providing customers with superior service.

1.2 Logistics on a global scale

Micro-logistics focuses on performing value-added services in a relatively controlled environment. Macro-logistics operations must accommodate all domestic requirements and also deal with the increased uncertainties associated with distance, demand, diversity, and documentation.

Global operations increase logistics cost and complexity. In terms of complexity, global operations increase uncertainty and decrease capability to control. Uncertainty results from greater distances, longer lead times, and decreased market knowledge.

Control problems result from the extensive use of intermediaries coupled with government intervention in such areas as customs requirements and trade restrictions.

These unique challenges complicate the development of an efficient and effective global logistics system. There are many forces driving organisations to enter the international area. These forces serve both as motivators and facilitators. Enterprises are motivated to expand global operations to grow and survive. Global operations are also facilitated through developing technologies and capabilities (Tanczos, 1998). The five forces driving global operations are economic growth, supply chain perspective, regionalisation, technology, and deregulation. These forces and their interaction are depicted in Figure 1.1.

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Figure 1.1 Forces driving globalisation

1.2.1 Global operating levels

While logistics principles are the same at both the macro and micro-logistics levels, operating environments are more complex and costly globally. Cost and complexity are represented by the four D’s – distance, documents, diversity in culture, and demands of the customers (Bowersox, 1996). Distances are longer, documentation is more extensive. Customers demand variation in products and services to satisfy cultural differences, within both countries and regions. Developing strategies and tactics to respond to the “four D” environment is the global challenge logistics faces. Global logistics development requires the creation of an international operating philosophy and vision. The vision must result in operating strategies, performance expectations, measurement, and decision alternatives.

This section traces the levels of enterprise evolution from domestic logistics operations to becoming a global competitor. The duration of each level is a reflection of strategic philosophy rather than elapsed time. Figure 1.2 illustrates the risk and return associated with each operating stage.

• Arm’s-length relationship

Level 1 is characterised by an arm’s-length relationship between an enterprise and an international distributor that serves a country or region. The enterprise, which probably has limited international experience, either sells or consigns its goods to the international specialist, which accepts responsibility for ordering, providing international transportation, completing documentation, as well as co-ordinating marketing, inventory management, invoicing, and product support.

Economic growth

Regionalisation Supply chain perspective

Technology Deregulation

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• Internal export

Level 2 enterprises develop the expertise to co-ordinate and manage international transportation and documentation. However, the local distributor is kept to provide marketing, inventory management, invoicing, and product support.

• Internal operations

Level 3 is characterised by the development of operations in the local or foreign country.

Internal operations include combinations of marketing, sales, production, and distribution. Establishment of local facilities and operations increases market awareness and sensitivity. This is typically referred to as local market presence.

• Insider business practises

The fourth level further internalises international operations and institutes local business practices. This level of sophistication typically involves hiring host country management, marketing, and sales organisations and may include the use of local business systems.

• Denationalised operations

The denationalised operations level maintains foreign country operations and develops a regionalised headquarters to oversee the co-ordination of operations in the area.

Figure 1.2 Risk-return trade-offs for global operations

Arm’s length (Level 1)

Internal export (Level 2)

Internal operations

(Level 3)

Insider business practices (Level 4)

Denationalised operations

(Level 5) Risk to return

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1.3 Logistical competence through efficient processes

This part of the chapter introduces logistical competence starting with a description of how logistical competence fits into an organisation’s overall strategic positioning. It is fundamentally important to view logistics in the context of how it can be exploited as a core competence. Next, the logistical mission of a typical enterprise is reviewed in terms of service, cost, and operating objectives. This generic mission statement explores the operational dynamics of logistics.

A useful way to view logistical competence is to develop an integrated framework that defines and relates key concepts. Such an integrative framework serves to relate the most finite aspects of logistics to overall enterprise strategy. The geographical scope of logistical operations means that the vast majority of the essential work is performed outside the vision of direct supervision. Within the broad assortment of different logistics jobs, countless specialised tasks are required. Each of these specific tasks is a potential target for work standardisation, simplification, or potential elimination during logistics reengineering. The essence of integration is to position functional excellence so that it can make maximum contribution to the overall logistical process competence.

Logistical competence is a relative assessment of an organisation’s capability to provide competitively superior customer service at the lowest possible total cost. When a company decides to differentiate itself on the basis of logistical competence, it seeks to outperform competitors in all facets of operations. Expectations concerning logistical competence directly depend on an organisation’s strategic positioning. All enterprises must perform logistics to achieve their basic business goals. How important logistics is in a strategic sense depends on the emphasis placed on proactively using such competence to gain competitive advantage. When logistics becomes a cornerstone of basic business strategy, it must be managed as a core competence. On the basis of this discussion of how logistics fits into overall business strategy, it is possible to examine the typical mission in greater detail.

1.3.1 The logistical mission

It has been established that the logistics of an enterprise is an integrated effort aimed at helping create customer value at the lowest total cost. Almost any level of logistical service can be achieved if an organisation is willing to commit the necessary resources. In today’s operating environment, the limiting factor is economics, not technology (Kata, 1992). Basic logistical service is measured in terms of (1) availability, (2) operational performance, and (3) service reliability. Availability means having inventory to consistently meet customer material or product requirements. According to the traditional paradigm, higher inventory availability required greater inventory investment. Technology is providing new ways to achieve high inventory availability without associated high capital investments. Developments in inventory availability are critical because of its fundamental importance.

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Operational performance deals with the elapsed time from order receipt to delivery. Operational performance involves delivery speed and consistency. Other aspects of operational performance are also important. An organisation’s operational performance can be viewed in terms of how flexible it is in accommodating unusual and unexpected events in the supply chain. Another aspect of operational performance is malfunction and recovery. Few firms can promise and perform perfectly in every situation all the time. It is important to gauge the likelihood of something going wrong.

Malfunction refers to the probability of logistical performance involving failures, such as damaged products, incorrect assortments, or inaccurate documentation. When such malfunctions occur, an organisation’s performance can be measured in terms of required time to recover. Operational performance is concerned with how an organisation handles all aspects of the supply chain system requirements, including service failure on a day in day out basis.

Service reliability involves the quality attributes of logistics. The key to quality is accurate measurement of availability and operational performance. Only through comprehensive performance measurement is it possible to determine if overall logistical operations are achieving the desired service goals. To achieve service reliability, it is essential to identify measures to assess inventory availability and operational performance.

In the context of overall business performance, logistics exists to allow inventory to achieve desired time, place and possession benefits at the lowest total cost. Besides total cost minimisation, the other logistical objective is to maximise the service level. On the one hand a raise in service level increases logistical costs, on the other hand it decreases the additional cost of logistical service failures. This usually leads to decision- making problems. The total cost curve is obtained from the interpolation of the logistical basic cost curve and cost of logistical discrepancies curve, depicted in Figure 1.3. The optimal logistical service is achieved where the total cost curve reaches its minimum.

Inventory has little value until it is positioned, at the right time and location to support ownership transfer or value-added creation. If an organisation does not consistently satisfy time and place requirements, it has nothing to sell. To achieve the maximum strategic benefits of logistics at micro-logistics level, the full range of functional work must be performed on an integrated basis. Excellence in each aspect of functional work is relevant only when viewed in terms of improving the overall efficiency and effectiveness of integrated logistics. This requires that the functional work of logistics be integrated to achieve business goals.

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Figure 1.3 Relationship between logistical service level and cost

1.3.2 Integrated logistics

The conceptualisation of integrated logistics is illustrated in the shaded area of Figure 1.4. Logistics is viewed as the competence that links an enterprise with its customers and suppliers. Information from and about customers flows through the enterprise in the form of sales activity, forecasts, and orders. The information is refined into specific manufacturing and purchasing plans. As products and materials are produced, a value-added inventory flow is initiated that ultimately results in ownership transfer of finished products to customers. Thus, the process is viewed in terms of two interrelated efforts, inventory flow and information flow.

Figure 1.4 Logistical integration

1.3.3 Inventory flow

The operational management of logistics is concerned with the movement and storage of materials and finished products. Logistical operations start with the initial shipment of a material or component part from a supplier and are finalised when a manufactured or processed product is delivered to a customer. From the initial purchase of a material or component, the logistical process adds value by moving inventory when and where needed. Providing all goes well, a material gains value at each step of its transformation into finished inventory.

0 1 2 3 4 5 6 7 8 9 10

0 1 2

Service level

Cost

Logistical basic cost Extra cost due to logistical service failures Total cost

Customers Physical

distribution

Manufacturing support

Purchasing

Suppliers

Information flow Inventory flow

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Physical distribution. The area of physical distribution concerns the movement of finished product to customers. In physical distribution, the customer is the final destination of a marketing channel. The availability of the product is a vital part of each channel participant’s marketing effort.

Manufacturing support. The area of manufacturing support concentrates on managing the work-in-progress inventory as it flows between stages of manufacturing. The primary logistical responsibility in manufacturing is to participate in formulating a master production schedule and to arrange for timely availability of materials, component parts, and work-in-progress inventory. Thus, the overall concern of manufacturing support is not how production occurs but rather what, when, and where products will be manufactured.

Purchasing. Purchasing is concerned with purchasing and arranging the inbound movement of materials, parts, and/or finished inventory from suppliers to manufacturing or assembly plants, warehouses, or retail stores.

1.3.4 Information flow

Information flow identifies specific locations within a logistical system that have requirements. Information also integrates the three operating areas. The primary objective of developing and specifying requirements is to plan and execute integrated logistical operations. Within individual logistics areas, different movement requirements exist with respect to size of order, availability of inventory, and urgency of movement. The primary objective of information sharing is to reconcile these differentials. The overall relationship between the two logistical information flows is illustrated in Figure 1.5.

Figure 1.5 Logistics information requirements

Strategic objectives

Capacity constrains

Logistics requirements

Manufacturing requirements

Purchasing requirements

Forecasting

Inventory deployment

Inventory management

Order management

Order processing

Distribution operations

Transportation

and shipping Purchasing PLANNING AND CO-ORDINATION FLOWS

OPERATIONS

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Planning and co-ordination flows. Co-ordination is the backbone of the overall information system architecture among value chain participants. Co-ordination results in plans specifying strategic objectives, capacity constraints, logistical requirements, inventory deployment, manufacturing requirements, purchasing requirements, and forecasting. The primary drivers of the overall value chain are strategic objectives that result from marketing and financial goals. Capacity constraints co-ordinate internal and external manufacturing requirements. For non-manufacturing participants in the value chain, this form of capacity planning is not required (Prezenszki, 1995). Logistics requirements specify the work that distribution facilities, equipment, and labour must perform to implement the capacity plan. Using inputs from forecasting, scheduling, customer orders, and inventory status, logistics requirements specify the value chain performance. Inventory deployments are the interfaces between planning / co-ordination and operations that detail the timing and composition of where inventory will be positioned. From an information perspective, deployment specifies the what, where, and when of the overall logistics processes. In production situations, manufacturing plans are derived from logistical requirements and typically result in inventory deployment. The primary deliverable is a statement of time-phased inventory requirements that drives master production scheduling (MPS) and manufacturing requirements planning (MRP).

Purchasing requirements schedule material and components for inbound shipment to support manufacturing requirements. Forecasting utilises historical data, current activity levels, and planning assumptions to predict future activity levels. Logistical forecasting is generally concerned with relatively short-term predictions.

Operational requirements. The second aspect of information requirements is concerned with directing operations to receive, process, and ship inventory as required to support customer and purchase orders. Operational information requirements deal with order management, order processing, distribution operations, inventory management, transportation and shipping, and purchasing. Order management refers to the transmission of requirements information between value-chain members involved in finished product distribution. Order processing allocates inventory and assigns responsibility to satisfy customer requirements. Distribution operations involve information flows required to facilitate and co-ordinate performance within logistics facilities. The primary purpose of a logistical facility is to provide material or product assortments to satisfy order requirements. Inventory management is concerned with using information to implement the logistics plan as specified, whereas transportation and shipping information directs the movement of inventory. Finally, purchasing is concerned with the information necessary to complete purchase order preparation, modification, and release while ensuring overall supplier compliance.

1.4 Logistical performance cycles

The primary unit of analysis for integrated logistics is the performance cycle.

Viewing logistical integration in terms of performance cycles provides a basic perspective of the dynamics, interfaces and decisions that must be linked to create an operating system.

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At a basic level, suppliers, the organisation being examined, and its customers are linked together by communications and transportation (Pfohl, 1990). The facility locations that performance cycles link together are referred to as nodes as shown in Figure 1.6. In addition to nodes and links, a logistical performance cycle requires inventory. Inventory is measured in terms of asset level deployed to support operations.

Inventory committed to a system consists of base stock and safety stock positioned to protect against variance. It is at the facility nodes that work related to logistics occurs.

Within nodes, inventory is stocked or flows though the node, necessitating a variety of different types of material handling and at least limited storage. While a degree of handling and in-transit storage takes place within transportation, such activity is minor in comparison to that typically performed within a logistical facility, such as a warehouse.

Performance cycles become dynamic as they accommodate input / output requirements.

The input to a performance cycle is an order that specifies requirements for a product or material. A high-volume system will typically require a variety of different performance- cycle arrangements to satisfy overall order requirements. When requirements are highly predictable or relatively low, the performance cycles required to provide logistical support can be simplified. System output is the level of performance expected from the logistical operation. To the extent that operational requirements are satisfied, the performance-cycle structure is effective in accomplishing its mission. Efficiency is related to resource expenditure necessary to achieve logistical effectiveness. The effectiveness and efficiency of performance cycles are a key concern in logistics management.

Regardless of the number of different types of performance cycles an organisation uses to satisfy its logistical requirements, each one must be individually designed and operationally managed. The fundamental importance of performance-cycle design and operation cannot be overemphasised. In essence, the performance-cycle structure is the framework for the implementation of integrated logistics.

Figure 1.6 Logistical performance cycles

Material source

1^st phase manufacturing plant

2^nd phase manufacturing plant

Distribution warehouse

Customer

Purchasing Cycle

Manufacturing Support Cycle

Physical Distribution

Cycle

Node

Transportation links Communication

links Legend:

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Chapter 2 Development of Methods for Logistical System Performance Analysis

2.1 Identifying Purchasing Performance Measurements by Using Principal Components Analysis

2.1.1 Introduction

It is difficult to document the influence purchasing departments have on corporate profits or other measures of overall corporate performance. If the cost savings come at the expense of quality or responsiveness, the overall result could be disastrous. Thus, it is demanding to analyse the affect purchasing departments have on corporate profits.

This section develops a method that uses principal components analysis to purchasing performance analysis. The investigation first briefly looks at purchasing management strategies and then identifies measuring strategies.

2.1.1.1 Purchasing management strategies

Firms have a wide range of choices when deciding how to conduct their purchasing activities. Choices include the nature and extent of long-term purchasing commitments, when to share design information and with whom, how to implement supplier quality improvement programs, and how to organise purchasing departments.

All firms operate with some uncertainty, and fluctuating customer demand, material availability, quality levels, governmental regulations, and the level of competition that can increase uncertainty. It is evident that in uncertain environments, firms must struggle to minimise inventory and obsolescence costs while avoiding out-of- stock situations.

Firms that compete through product differentiation are likely to face more uncertain environments than firms competing with commodity type products. Demand for unique products is unstable, and historical performance is probably non-existent (David, et al, 1999). If the firm produces customised products for its customers, extensive interaction among the firm, customers, and even suppliers is likely. If the firm modifies its products frequently, production processes must be flexible, and long-range purchasing contracts are rare. Firms operating in more functional markets, on the other hand, must constantly strive to lower their costs. Because they do not face the pressures of high uncertainty, they can process purchases efficiently and place more emphasis on price.

These firms succeed if they structure their purchasing departments to minimise transaction costs and purchase prices.

2.1.1.2 Purchasing performance

Purchasing department performance can be measured with a number of efficiency and effectiveness measures. Efficiency measures are ratios of outputs to inputs.

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Examples of efficiency measures include purchasing value per purchasing employee, purchase value to sales value, purchase value relative to purchase operating expenses, and purchase order cycle time. Effectiveness measures relate to the desired outcomes of purchasing activities. Examples of effectiveness measures include inventory levels, incoming defects, rework / scrap, delivery schedules, lead time reductions, and participation in supplier quality improvement programs.

2.1.1.3 Measuring strategies

To measure purchasing strategies, key characteristics were identified from prior literature (Centre for Advanced Purchasing Studies, USA, 2001). Table 2.1 shows the key purchasing performance benchmarks. Ten of these benchmarks have been selected for the analysis. Each benchmark can be analysed separately using principal components analysis to determine if the related variables represent the same underlying factor, or if they measure different dimensions of the purchasing performance.

Table 2.1 Key purchasing performance benchmarks

Purchasing Performance Benchmarks Selected for Analysis

Purchasing $ as % of Sales $ Yes

Purchasing Operational Expense $ as % of Sales $ Yes Purchasing Operational Expense $ as % of Purchasing $ Yes Purchasing Employees as % of Corporate Employees Yes

Sales $ per Purchasing Employee No

Purchasing $ per Purchasing Employee Yes

% Purchasing $ Managed / Controlled by Purchasing Yes Average Training Hours per Purchasing Employee Yes Average Annual $ Spend on Training for the Purchasing

Function per Purchasing Employee

No

% Cost Reduction Saving as % of Purchasing $ Generated by Purchasing

No

% of Active Suppliers that Account for 80% of Purchasing $

Yes

% Purchasing $ Spent with Minority Owned No

% Purchasing $ Spent with Women Owned No

% Purchasing $ Spent with Small Businesses No

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% Purchasing $ Spent through EDI Yes

% Purchasing $ Spent via Strategic Alliances Yes

% Purchasing $ Spent through Electronic Auctions No

% Purchasing $ Spent through Consortia No

The challenge of performing this analysis was identifying ways to analyse purchasing performance. While a wide range of individual variables was available, combining the variables into meaningful constructs required additional statistical analysis. Principal components analysis was performed because the technique enables researchers to analyse a group of variables to determine whether they represent one or multiple underlying dimensions of the construct. The following describes the technique.

2.1.2 The technique explained

2.1.2.1 Introduction

The aim of principal components analysis is to linearly transform the correlated variables Y1, Y2, …, Yp to a new set of uncorrelated variables, called principle components (Meldrum, 1993). These components may be unstandardised (denoted X1, X2, …, Xp), or standardised (denoted Z1, Z2, …, Zp). Standardisation is a process, whereby raw data are transformed into new measurement variables with a mean of 0 and standard deviation of 1 by subtracting the mean from each measurement value and by dividing the difference by the standard deviation. The technique of principal components analysis can be applied to either correlation or covariance matrices (Shao, et al, 1999).

When dealing with correlation matrices the variables Y₁, Y₂, …, Y_p will be standardised.

2.1.2.2 Derivation of the unstandardised components

The first unstandardised principal component, X1, is a linear combination of the variables; that is, X1 = a1Y1 + a2Y2 + … + ap Yp. Subject to the restriction a12 + a22 + … ap2 = 1, the coefficients a1, a2, …, ap are chosen so that X1 has maximum variance. The second unstandardised component is X2 = b1Y1 + b2Y2 + … + bp Yp;the coefficients are chosen such that, of all linear combinations of Y₁, Y₂, …, Y_pwhich are uncorrelated with X₁, the variable X₂ has maximum variance and b₁² + b₂² + … b_p² = 1.

In the same way the third component, X3, is a linear combination of Y1, Y2, …, Yp, such that it is uncorrelated with both X1 and X2, and has maximum variance (again, subject to the condition that the sum of squares of the coefficients is unity). This process may be continued until all unstandardised principal components X1, X2, …, Xp have been extracted. The components are obtained as follows:

Table 2.1 Key purchasing performance benchmarks (continued)

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Suppose the sample correlation matrix R = (r_ij) of the variables Y₁, Y₂, …, Y_p has eigenvalues e₁, e₂, …, e_p. Then it may be shown, mathematically, that the first unstandardised principal component is

X1 = h11Y1 + h21Y2 + ….+ hp1Yp = u1Ty,

Where u1T = (h11, h21, …, hp1) is the normalised eigenvector corresponding to e1, the largest eigenvalue of R, and that var (X₁) = e₁. The other components are obtained in like manner; that is

Xi = h1iY1 + h2iY2 + ….+ hpiYp = uiTy,

Where uiT = (h1i, h2i, …, hpi) is the normalised eigenvector corresponding to ei, the i-th largest eigenvalue of R, and var (Xi) = ei, i= 1,2,…,p.

The orthogonal matrix H of order p, is then introduced here, namely

H = [ u1, u2,…up] =

















pp p

p

p p

h h

h

h h

h

h h

h

...

.

...

2 1

2 22

21

1 12

11

Then the equations

X1 = u1Ty = h11Y1 + h21Y2 + ….+ hp1Yp

X2 = u2Ty = h12Y1 + h22Y2 + ….+ hp2Yp

. . .

Xp = upTy = h1pY1 + h2pY2 + ….+ hppYp

Can be written in matrix notation, namely x = H^T y,

where x^T = (X₁, X₂, …, X_p) and y^T = (Y₁, Y₂, …, Y_p).

Since H is orthogonal it follows that y = H x, giving

Y1 = h11X1 + h12X2 + ….+ h1pXp

Y₂ = h₂₁X₁ + h₂₂X₂ + ….+ h_2pX_p

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. . .

Yp = hp1X1 + hp2X2 + ….+ hppXp.

Hence each variable Yi (i=1, 2, …, p) can be expressed as a linear combination of the components Xj (j=1, 2, …,p).

2.1.2.3 Derivation of the standardised components

If we standardise X1, X2, …Xp we obtain the standardised principal components Z1, Z2,

…, Zp; that is

j j

j X

Z 1e

= j=1,2,…,p.

2.1.2.4 The loading matrix Let L = diag {e₁, e₂, …, e_p} ; then

L^1/2 = diag { e₁ e₂,..., e_p }.

A very important matrix in principal components analysis is the matrix of component loadings (correlations), W = (wij), i,j = 1,2,…, p, which is defined by

W = H L^1/2 . The following results apply:

(1) W is the matrix of the correlations (called component loadings) between Yi and Zj

(or Xj); that is,

wij = corr (Yi, Zj) = corr (Yi, Xj), (i,j = 1,2,…,p).

(2) H^T R H = L.

(3) W^T = L^1/2H^T.

(4) R = H L H^T = W W^T. 2.1.2.5 Importance of a component

For the sample correlation matrix R = (rij) each diagonal element of the correlation matrix has a value of one.

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Consequently, if we are working in p dimensions, the trace of R is p, and if the p eigenvalues of R are e₁, e₂, …, e_p, then it follows that e₁ + e₂ +… + e_p = p.

Since the variance of the first unstandardised component is e1, then the importance of this first component is measured by the ratio e1 / p; similarly, the importance of the other components is ei / p, i=2, …, p (MacGregor, Kourti, 1995).

Excluding one particular type of correlation matrix (one whose rank is r < p), all p components need to be extracted in order to explain the total variation in the variables Y₁, Y₂, …, Y_p. However, it is common practice, especially if p is large, to make use of only the first few components. If the first r components (r < p) explain a large amount of the total sample variance, then it may be that the remaining (p – r) components are of no practical importance. For instance, if p = 6, it may be that most of the variation could be explained by one component, or by only two or three components and in such cases the original variables may be replaced by a smaller number of components. In general, principal components analysis looks for a few components, which can be used to summarise the data, so that as little information as possible is lost in the process. This attempt to reduce dimensionality is called parisimoniuos summarisation of the data.

2.1.3 The technique applied

Ten purchasing performance benchmarks were selected from Table 2.1, and cross-industrial purchasing performance data were put in Table 2.2. Table 2.3 shows the corresponding matrix of standardised test scores.

Table 2.2 Cross - industry comparison of standard benchmarks (Source: Centre for Advanced Purchasing Studies, USA, 2001)

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28 Variables Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Original Data Purchasing $ as % of Sales $

Purchasing Operational Expense $ as % of Sales $ Purchasing Operational Expense $ as % of Purchasing $ Purchasing Employees as % of Corporate Employees Purchasing $ per Purchasing Employee

% Purchasing $ Managed / Controlled by Purchasing Average Training Hours per Purchasing Employee

% of Active Suppliers that Account for 80% of Purchasing $

% Purchasing $ Spent through EDI

% Purchasing $ Spent via Strategic Alliances Aerospace/ Defense 40.77 1.07 2.72 3.72 4.92 98.01 28.91 10.43 10.67 9.27 Beverage 51.70 0.15 0.23 0.78 70.50 77.40 58.00 3.20 11.01 4.93 Cable Telecommunications 59.60 0.07 0.13 0.51 46.35 48.90 31.00 4.70 17.34 5.81 Carbon Steel 56.71 0.16 0.29 0.76 44.64 70.79 27.00 0.63 1.17 19.15 Chemical 49.47 0.17 0.39 1.15 34.14 93.60 26.78 20.60 0.59 32.50 Computer/ Telecom Equip/ IT Service 52.50 0.35 0.75 1.10 20.37 92.00 28.00 5.90 22.80 39.00 Engineering/ Construction 51.03 0.51 1.03 2.96 6.43 94.64 13.00 8.78 0.13 4.75 Food Manufacturing 33.80 0.18 0.58 0.61 24.30 82.00 28.00 4.80 17.10 29.10 Machinery55.30 0.66 1.47 2.08 11.96 92.00 26.00 2.80 5.81 24.00 Mining 47.26 0.27 0.59 1.00 40.48 0.76 37.70 12.02 6.33 22.48 Paper 36.20 0.20 0.47 0.67 11.11 88.40 26.30 4.90 4.63 24.00 Petroleum26.20 0.09 0.95 1.47 54.30 61.34 28.00 6.56 17.88 15.58 Pharmaceutical 34.76 0.14 0.42 0.60 26.33 76.16 32.00 15.80 1.70 9.89 Semiconductor 48.34 0.26 0.59 1.30 19.15 91.67 34.00 11.71 3.14 39.92 Shipbuilding 38.00 0.50 1.40 1.10 5.82 78.00 20.00 4.30 1.30 23.00 Telecommunication Services 40.00 1.64 2.75 0.39 43.10 85.00 34.00 21.00 16.70 27.00 Textiles/ Apparel 49.40 0.15 0.52 0.45 19.13 67.00 48.00 19.00 9.12 25.00 Transportation 31.80 0.30 0.75 0.32 24.91 54.90 26.90 9.10 8.75 19.90 Mean 44.60 0.38 0.89 1.17 28.22 75.14 30.76 9.24 8.68 20.85 Standard Deviation 9.62 0.40 0.76 0.91 18.48 23.42 9.87 6.30 7.12 10.86

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29The corresponding matrix of standardised test scores is shown in Table 2.3. Table 2.3 Standardised test scores Variables Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Aerospace/ Defense-0.40 1.72 2.402.80 -1.26 0.98 -0.19 0.19 0.28 -1.07 Beverage0.74 -0.58 -0.87 -0.42 2.29 0.102.76 -0.96 0.33 -1.47 Cable Telecommunications1.56 -0.78 -1.00 -0.72 0.98 -1.12 0.02 -0.72 1.22 -1.39 Carbon Steel 1.26 -0.55 -0.79 -0.44 0.89 -0.19 -0.38 -1.37 -1.05 -0.16 Chemical 0.51 -0.53 -0.66 -0.02 0.32 0.79-0.40 1.80 -1.14 1.07 Computer/ Telecom Equip/ IT Service 0.82 -0.08 -0.18 -0.07 -0.42 0.72 -0.28 -0.53 1.981.67 Engineering/ Construction 0.67 0.32 0.18 1.97 -1.18 0.83-1.80 -0.07 -1.20 -1.48 Food Manufacturing-1.12-0.50 -0.41 -0.61 -0.21 0.29 -0.28 -0.70 1.180.76 Machinery1.11 0.70 0.761.00 -0.88 0.72 -0.48 -1.02 -0.40 0.29 Mining 0.28 -0.28 -0.39 -0.18 0.66 -3.18 0.70 0.44 -0.33 0.15 Paper -0.87-0.45 -0.55 -0.54 -0.93 0.57-0.45 -0.69 -0.57 0.29 Petroleum-1.91-0.73 0.080.33 1.41 -0.59 -0.28 -0.42 1.29 -0.49 Pharmaceutical -1.02-0.60 -0.62 -0.62 -0.10 0.040.13 1.04 -0.98 -1.01 Semiconductor 0.39 -0.30 -0.39 0.15 -0.49 0.710.33 0.39 -0.78 1.76 Shipbuilding -0.69 0.30 0.67 -0.07 -1.21 0.12 -1.09 -0.78 -1.04 0.20 Telecommunication Services -0.483.15 2.44-0.85 0.81 0.420.33 1.87 1.130.57 Textiles/ Apparel 0.50 -0.58 -0.49 -0.78 -0.49 -0.35 1.75 1.55 0.06 0.38 Transportation -1.33-0.20 -0.18 -0.93 -0.18 -0.86 -0.39 -0.02 0.01-0.09 Mean 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.000.00 St Dev 1 1 1 1 1 1 1 1 1 1

Methods for optimisation of logistics systems