Supply chain engineering useful methods and techniques (2010) alexandre dolgui, jean marie proth

4 1 Introduction to Pricing itemoneofpriceinchange % solditemsofquantityin change %demand of The demand curve also called the selling curve is the curve that represents the relationship

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Alexandre Dolgui · Jean-Marie Proth

Supply Chain Engineering

Useful Methods and Techniques

123

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Centre for Industrial Engineering

and Computer Science

57045 Metz CX 1 France

Jean-Marie.Proth@inria.fr

ISBN 978-1-84996-016-8 e-ISBN 978-1-84996-017-5

DOI 10.1007/978-1-84996-017-5

Springer London Dordrecht Heidelberg New York

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Preface

Supply chain engineering is an emerging field based on analysis and sion of the essential principles of production and distribution systems This scien-tific domain concerns the methodical evaluation and optimization of production systems, logistics networks, and their management policies to increase the effectiveness of multifaceted demand and supply chains

comprehen-Worldwide competition has grown ever stronger since the beginning of the 1980s The pressure of the competitive global market has intensely affected the production systems, calling for:

• integration of the activities that cover the whole production spectrum from tomers’ requirements to payment;

cus-• flexibility in the face of customer-demand changes;

• drastic reduction of production costs

To reach these objectives, radical changes have been introduced in production systems, thanks to new manufacturing technologies that increase efficiency and IT technologies that improve system organization and management

Furthermore, dynamical pricing and revenue management, which proposes proaches that define the price of the products based on market situations, attracts more and more researchers and practitioners Pricing stresses the return on the in-vestment

ap-Supply chains are emblematic examples of the renewal of production systems

in recent decades It is through this new paradigm that cost reduction and service enhancement can be achieved To make this easier to implement, new types of manufacturing systems have been introduced, for example: reconfigurable manu-facturing systems (RMS), assembly lines with worker’s flexibility, bucket bri-gades or U-shaped assembly lines Over the same period, new technologies arose

to monitor the state of systems in real time We can mention radio-frequency tification (RFID), Internet applications or “intelligent” storage facilities, to name just a few These technologies favor one of the most important objectives of pro-duction systems management: the ability to make a decision almost immediately Radical changes in the criteria that express the new objectives of production systems in the face of competition are another important aspect The introduction

iden-of some new criteria reflects the just-in-time (JIT) requirements For instance, conventional scheduling optimization is now restricted, in the best case, to decid-

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ing the order products are launched in production In other words, the tional scheduling activity migrated from the tactical to the strategic level In actual production systems, this is replaced by a real-time scheduling, also called real-time assignment Other criteria are used to reflect quality, flexibility and work-in-progress (WIP): adequate quality is now unavoidable to meet customers’ satisfac-tion; flexibility is a necessary condition to remain competitive in an ever-changing market; and reduction of WIP is a factor to minimize the production cost and the probability of obsolescence

conven-The authors of this book collaborate closely with companies conven-They have been charged with numerous contracts covering a wide range of industrial activities, in-cluding steelmaking, aerospace research, car manufacturing, microelectronics, and

in the machining industry In these areas, the authors worked on design and agement problems They reached the following conclusions:

man-• The difficulty for companies lies much more in determining the exact nature of

a problem and defining the criteria to be taken into account, than in solving the problem itself

• The models available in the literature are often difficult to apply in real life, due

to the assumptions that were made in order to have a treatable model

• To be acceptable to companies, models must be simple, easy to apply and justable to the systems under study

ad-These conclusions are also taken into account in this book

This reference work presents a general view of new methods, techniques, sources and organizations that have erupted in the production domain during the past two decades The objective of the authors was to furnish the best applied ap-proaches Of course, if a theoretical approach is more convenient to provide the essentials of the system under study, then it was included Furthermore, when a simple and efficient model exists to represent an industrial situation, we discard more complicated models that do not provide significantly better results, even if they are widely cited in the literature

re-The book is organized into 11 chapters with 5 appendices re-The following topics are covered

Chapter 1 should be considered as an introduction to pricing After outlining

the importance of pricing to increase revenue, and providing the most common definitions in use in the field, pricing strategies are presented The mechanisms that link costs, price and margin are analyzed The selling curve is introduced and several methods to find the characteristics of importance to customers are devel-oped This chapter ends with price strategy in the oligopoly market

Chapter 2 has as a main goal to introduce stochastic dynamic pricing models

with salvage values The constraints to apply to make this model manageable are given Pricing models for time-dated items, with no supply option, in a monopolis-tic environment, and with myopic customers are presented in detail

Chapter 3 concerns outsourcing, which is little studied academically in spite of

its importance in the actual global market place After defining the main notions, the most common benefits that may be expected from outsourcing are presented

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Preface vii

The steps that lead to outsourcing are detailed In particular, a vendor selection and evaluation model is developed and several approaches to solve this multicrite-ria problem are proposed The strategic outsourcing in the case of a duopoly mar-ket is then developed exhaustively The arguments of the pro and cons are ex-plored One of the original aspects of this chapter lies in the analysis of offshoring

in China Some arguments in this discussion are quite different from those usually used in the literature The reason may be that the effects of offshoring on workers

in developed countries are taken into account

Chapter 4 considers inventory management in supply chains The advantages

of sharing information among the different levels of a supply chain are discussed Particular attention is given to the bullwhip effect and the actions to be taken in order to reduce this undesirable phenomenon Some usual and robust models are highlighted, such as the newsboy (or newsvendor) model, finite-horizon model with stochastic demands and the well-known (R, Q) and (s, S) models For the last two models, we show how simulation can be used to find the “optimal” values for their parameters Echelon stock policies, which are tools that meet supply chain requirements, are analyzed along with their complimentary tools, such as material requirements planning (MRP) and manufacturing resources planning (MRP2) Due to the importance of the subject (mainly at the design level), we also review the most common lot-sizing models

Chapter 5 gives a brief description of the RFID (radio-frequency identification)

technology An analysis of the parameters of importance when selecting tags is conducted and a succinct guideline for RFID deployment is suggested Some ap-plications are reviewed and the importance of this technology for the efficiency of supply chains is outlined The main domains where RFID is applied routinely are listed The evaluation of this technology, and in particular the financial implica-tion, is performed A special section deals with privacy concerns that are an im-portant problem of RFID in today’s situation The last section raises the problem

of authentication, which is especially significant for the case of counterfeit tags

Chapter 6 presents an overview of manufacturing system organizations This

chapter is influenced by the heavy demands for flexibility and adaptability of manufacturing systems in the modern environments The history of the idea of flexibility is presented and the majority of production system concepts are ana-lyzed: dedicated manufacturing lines (DML), flexible manufacturing systems (FMS), agile manufacturing systems (AMS), reconfigurable manufacturing sys-tems (RMS) and lean manufacturing systems (LMS) Each is defined, its advan-tages and drawbacks are studied and some illustrative examples are reported Comparisons are made among them and their appropriateness to supply chains is highlighted

Chapter 7 develops a complex and essential issue (particularly for lean

manu-facturing) of line balancing, which consists in minimizing the total idle time The models examined in this chapter have deterministic times The COMSOAL ap-proach is analyzed comprehensively along with possible improvements Other al-gorithms the most frequently mentioned in the literature, such as RPW, KW-like heuristic, B&B-based and mathematical programming approaches, are also pre-

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sented and illustrated The use of metaheuristics is shown in the third part of this chapter Simulated annealing, tabu search and genetic algorithms are discussed Then, the properties and evaluation of line-balancing solutions are underlined We also go over the evaluation criteria for line balancing from the literature

Chapter 8 generalizes assembly-line-balancing models presented in the

previ-ous chapter to stochastic operation times The problems tackled in this chapter are examined from a practical point of view In particular, probabilities are defined as

is usually done in companies, i.e., by three parameters: minimum, most frequent and maximum values of the variable under consideration This leads to the notion

of triangular density Problems are solved numerically A powerful tool is posed for computing the integration of functions: Tchebycheff's polynomial ap-proach Numerical examples are presented to illustrate these realistic solutions Mixed assembly-line models with several types of products are also considered Other interesting generalizations, such as line balancing with equipment selection, are introduced Finally, the new concepts of dynamical work sharing are explained using the examples of the bucket brigades and U-shaped assembly lines

pro-Chapter 9 is devoted to the control reactivity, which is becoming a pivotal

fac-tor for competitiveness We show that the static scheduling is slowly vanishing from the industrial environment It is being replaced by dynamic scheduling and real-time assignment approaches that are able to provide an optimal or near-optimal solution in real time The most popular priority (or dispatching) rules are presented first, followed by a second type of dynamic scheduling called the “re-pair-based approach” that consists of computing a static schedule at the beginning

of the working period and adjusting it in the case of unexpected events

Chapter 10 concerns facility layout design Until the 1980s, the objective was

to optimize the layouts assuming that the environment remained basically steady This situation is referred to as static facility layout (SFL) Linear layouts, func-tional department layouts and cellular layouts are studied in the first part of this chapter, as well as tools and algorithms used to perform optimal layout designs In the middle of the 1990s, the problem evolved toward dynamic facilities layouts (DFL) and robust layouts (RL) to meet the needs of enterprises manufacturing multiple products in a rapidly changing market Most results in these areas con-cern only the location of manufacturing entities on the available factory surface at the design stage Rapid advances in mechanical engineering and manufacturing organization may lead to the possibility of real-time rearrangement in the near fu-ture

Chapter 11 presents warehousing Certainly, warehouses are critical

compo-nents of production systems In this chapter, their usefulness is highlighted and various functions and equipment are analyzed Recent advances such as the value-added services and their corresponding areas are covered Special attention is paid

to the warehouse management, in particular, to the main difficulties faced by their managers The design stage is also extensively considered via developing storage algorithms for unit-load warehouse as well as examining warehouse sizing static and dynamic models The last section of this chapter concerns the location of warehouses Single- and multiflow location problems are put forth Remember

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Preface ix

that layout techniques, which also concern warehouses, were presented in ter 10

Chap-Five types of optimization techniques are reported and illustrated at the end of

the book in the appendices Each of the approaches covered in these appendices

has been used in at least one chapter to solve real-life problems:

• The first appendix explains the stimulated annealing method

• The second is devoted to dynamic programming based on the optimality ciple

prin-• The well-known branch-and-bound (B&B) approach is explained in the third

• The fourth presents tabu search techniques

• Genetic algorithms are presented in the last appendix

We had several audiences in mind when this book was written

In companies, the people in charge of management, production, logistics, ply chains, and those looking for suggestions to improve the efficiency of their systems, will be certainly interested in many of the advances covered in this book They also will appreciate the way explanations are given by using basic examples, providing detailed algorithms, while discarding complex and unnecessary theo-retical developments This book is written for managers and engineers with ana-lytical backgrounds, who are interested in capturing the potentials and limits of the recent advances in production and operations management

sup-The academic audience consists of the many researchers working in topics lated to operations research, supply chain management, production system design, facility layout, scheduling, organization, etc This book will also be useful to pro-fessors who teach industrial and systems engineering, management science, opera-tions management as well as business management specifically because of the carefully chosen examples that are provided and the application oriented approach

re-in which the notions are re-introduced

To summarize, this book is within the comprehension of industrial managers having an analytical background and eager to improve the efficiency of their com-pany, as well as researchers and students working in various related areas

The authors acknowledge Mrs Marie-Line Barneoud for help in the formatting

of this book and Mr Chris Yukna for his help in proofreading the English

Alexandre Dolgui Jean-Marie Proth

France, February 2009

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1 Introduction to Pricing 1

1.1 Introduction 1

1.2 Definitions and Notations 3

1.3 High- and Low-price Strategies 4

1.4 Adjustable Strategies 5

1.4.1 Market Segmentation (or Price Discrimination) Strategy 6

1.4.2 Discount Strategy 7

1.4.3 Price Skimming 8

1.4.4 Penetration Pricing 9

1.4.5 Yield Management (Revenue Management) 9

1.5 Margin, Price, and Selling Level 9

1.5.1 Notations 10

1.5.2 Basic Relation 10

1.5.3 Equilibrium Point 12

1.5.4 Items Sold with Regard to Price (Margin Being Constant) 13

1.6 Price Versus Sales Volume: the Selling Curve 15

1.6.1 Introduction 15

1.6.2 Cost-plus Method 16

1.6.3 Price Testing 16

1.6.4 Estimation Made by Experts 17

1.6.5 Market Analysis 17

1.6.6 Customer Surveying 20

1.7 Conjoint Measurement 20

1.7.1 Introduction and Definitions 20

1.7.2 Profile Method 21

1.7.3 Two-factor Method 26

1.7.4 Clustering for Market Segmentation 29

1.8 Price Strategy in Oligopoly Markets 32

1.8.1 Reactions of Competitors 33

1.8.2 Decreasing Prices 33

1.8.3 Increasing Prices 35

1.9 Conclusion 37

References 38

Further Reading 446

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xviii Contents

A Simulated Annealing 449

B Dynamic Programming 459

C Branch-and-Bound Method 483

D Tabu Search Method 503

E Genetic Algorithms 519

Authors’ Biographies 531

Index 533

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AGV Automated Guided Vehicle

BOM Bill-of-material

Lines

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xx Abbreviations

JIT Just-in-time

ROI Return-on-investments

VMI Vendor–Management–Inventory

WIP Work-in-progress

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Introduction to Pricing

Abstract Price is a major parameter that affects company revenue significantly

This is why this book starts by presenting basic pricing concepts The strategies, such as for instance, market segmentation, discount strategy, revenue manage-ment, price skimming, are developed and illustrated Particular attention is paid to the relationships among margin, price and selling level Then, the impact of prices

on selling volume is analyzed, and the notion of a selling curve is introduced lated pricing methods are presented such as price testing, cost-plus method, in-volvement of experts, market analysis and customer surveying Included in the last category is the conjoint measurement concerned with finding what parameters of the items are important to customers The profile method and a simplified version, the two-factor method, are also detailed and illustrated They provide a set of part-worths (i.e., numerical values) for each tester In other words, the opinion of each tester can be represented by a point in a space whose dimension is the number of

Re-part-worths By applying a clustering method, specifically K-mean analysis, we

obtain a limited number of clusters, each of them representing a market segment The chapter ends with the introduction of price strategies in oligopoly markets

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2 1 Introduction to Pricing

Increasing a market share depends on the competitiveness of the company In turn, competitiveness depends not only on price, but also on the ability of the company to meet customer’s requirements.1 Indeed, while price plays a role to meet this objective, it is not decisive, in particular when the product is new on the market A recent example is the strategy of Apple to dominate in the MP3 player market: Apple based its marketing strategy on i-Pod quality and aesthetics and won the leadership in the domain despite the fact that the i-Pod was the most ex-pensive among similar products

The introduction of a sophisticated pricing process is more recent Pricing strategy was a concern for companies prior to academic research

Numerous objectives motivate the use of pricing such as, for instance:

• Increase market share in order to decrease the long-term production cost, ing a given return of investment

reach-• Maximize the revenue in order to maximize long-term profit by increasing ket share and lowering costs (scale effect)

mar-• Maintain price leadership

• Maximize unit profit margin (useful when the number of items sold is casted to be low)

fore-• Reach high quality level to position the product as the leader

The first two chapters are dedicated to the influence of prices on companies’ revenues

It should be noted that changing a price is obviously easier and faster than veloping a process to reduce production costs or to increase the market share Fur-thermore, the price parameter influences directly and strongly the profit margin as well as market share It has been shown that modifying the price by 1% results in

de-a chde-ange of de-at lede-ast 10% in the everydde-ay consumption

Thus, price as an adjustment parameter for profit is the easiest and fastest way

to increase competitiveness

Indeed, fixing a price is the first step of any selling process and we will discuss this point, but pricing strategy does more It tries to take advantage of:

• time by playing, for instance, with seasonality of demand;

• customers’ preferences and purchasing behavior;

• spectrum of available products

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mate-These aspects are the most important where pricing is concerned and they are not exclusive As mentioned in (Talluri and Van Ryzin, 2004), pricing strategy is beneficial when:

• Customers are heterogeneous, which means that their purchasing behavior over time varies, their willingness to pay varies from customer to customer, and they are attracted by different benefits offered by the same type of products

• Demand variability and uncertainty are high, which guarantees a flourishing revenue to those who master pricing

• Production is rigid, which allows playing with prices when demand varies

A successful application of pricing strategy requires a strong commitment from management and a detailed monitoring of the system under consideration that, in turn, implies an efficient information processing and communication system Initially, pricing was used by the airline industry, followed by retailers and, more recently, by companies in the energy sector Note that these sectors are char-acterized by production (or offer) rigidity, variability of demand and heterogeneity

of customers

1.2 Definitions and Notations

Production cost is the sum of fixed and variable costs Fixed costs include

mainte-nance, wages and upkeep Note that fixed costs may increase when production ceeds some production threshold or when the company invests in a next-

ex-generation technology Variable costs depend on the number of items produced

They include components, raw material, working, transportation and inventory costs

The revenue is the total amount of money that flows into the company, coming

from product sales, venture capital, government support, personal funds

The average cost of an item is the ratio of the total cost to the number of items

sold

The marginal revenue is the increase of the revenue resulting from an

addi-tional unit of output

The marginal cost of an additional unit of output is the cost of the additional

inputs needed to produce that output More formally, the marginal cost is the rivative of total production costs with respect to the level of output

de-Price elasticity of demand measures the responsiveness of the number of items

sold to the price of an item More precisely, elasticity of demand is the percentage

of change in quantity of items sold with regard to the percentage of change in price per item:

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itemoneofpriceinchange

%

solditemsofquantityin

change

%demand

of

The demand curve (also called the selling curve) is the curve that represents the

relationship between the price of an item and the number of items customers are a willing to purchase during a given period It is assumed that the environmental conditions are steady during this period

A monopoly market is a market in which we have only one provider for the

type of items under consideration

A duopoly market is a market dominated by two firms (providers) that are large

enough to influence the equilibrium price (i.e., the market price) The market price

is where quantities supplied and quantities produced are equal

An oligopoly market is a market dominated by a small number of providers

Each provider (firm) is aware of the actions of the other providers (competitors) and the actions of one provider influence the others Providers operate under im-perfect competition

Imperfect competition is a market situation in which the characteristics of

per-fect competition are not satisfied

Perfect competition is characterized by:

• all providers have equal access to technologies and resources

Nash equilibrium is a market situation involving at least two providers and

where no provider can benefit by changing his/her strategy while the other ers of the system keep their strategy unchanged

provid-Some of the previous definitions will be developed later

1.3 High- and Low-price Strategies

In the previous section, we presented an example of high price that did not prevent the i-Pod to be the leader in the MP3 player market This high-price strategy was successful because the product was new on the market, the promotion was based

on quality and aesthetics, and the potential customers were attracted by logical performance and high-quality acoustics In general, the amount of money customers are prepared to pay depends on their level of interest in the item For in-

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techno-stance, if customers are swayed by technological novelties, then they are prepared

to pay a lot to purchase a personal computer with new capacities

Another example is the Mercedes-Benz class A The price of this product has been set at a higher level than the cost analysis result by the car company Never-theless, the production capacity was fully utilized during the first production year The explanation is the power of the corporate image of Mercedes-Benz

Numerous other examples can be found in the cosmetic industry and, more generally, in the luxury goods industry

To summarize, high price is accepted if it agrees with the value of the product perceived by the customers, otherwise such a strategy leads to commercial failure

A low-price strategy may also lead to a commercial success, as we can often observe in the food retailing sector For instance, low-price retailers such as Lidl, Aldi or Leader Price are currently achieving success in Europe Another example

is Dell Computer that distributes low-price PCs and allows customers to ize their PC Amazon.com gained an important share of the book market by reduc-ing the prices by 40 to 50% and providing greater choice These last two compa-nies base their strategy on the use of the Internet to directly distribute their items

personal-to cuspersonal-tomers, which results in a huge reduction of costs that, in turn, allows a nificant reduction of prices and thus improves their competitiveness

sig-The success of a low-price strategy depends on the number of clients attracted

by the product since the low margin should be compensated by a huge number of items sold We will see in this chapter that trying to compensate a reduction of price by attracting more customers is risky

Some disadvantages should be outlined in companies applying a high- or price strategy For instance, the image of the items sold by the company is frozen and a long-term price expectation is established, which reduces the flexibility of the decision-making system

low-High- and low-price strategies could be described as frozen strategies since they try to attract clients by making the most of the corporate image The draw-back is the inability of these strategies to adapt themselves to fundamental distur-bances For instance, a global impoverishment of a country may sharply penalize companies devoted to luxury and expensive items

Other strategies are much more adjustable We provide a short description of these strategies in the next section

1.4 Adjustable Strategies

An adjustable strategy can either evolve with the constraints of the environment or

is applied during a limited period Some examples are introduced in this section

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1.4.1 Market Segmentation (or Price Discrimination) Strategy

The development of a strategy based upon the fact that different groups of tomers attach different levels of importance to diverse benefits offered by a type

cus-of product or service is called market segmentation For instance, the same car model may be proposed in different versions (two-door or four-door, different en-gine powers, different finishing levels, etc.), and each version may attract a par-ticular type of customer Numerous other examples can be found in the hotel busi-ness (different classes of hotels proposed by the same company or, in the same hotel, different categories of rooms) The tourism industry, and even the food in-dustry, where packaging plays a major role in attracting some segments of cus-tomers, is another example Services are another way to introduce value differen-tiation

This strategy is applicable to a type of item in the case of a monopoly market It consists of segmenting the market and charging segments with different prices, depending on the willingness of the customers of each segment to pay more or less

to purchase the item Indeed, some “rate fences” should be introduced in order to make sure that the customers of a segment will pay the price assigned to the seg-ment These “rate fences” can be the promotion of some benefits that attract the customers of a specific segment, or by offering some particular services to the cus-tomers of a specific segment Again, the customers belonging to a given segment should be similar or, in other words, characterized by the same parameters, and dissimilar from the customers of other segments Similarity and dissimilarity are related to buying habits

The approach to market segmentation is a four-stage process that can be marized as follows:

sum-• Identify the parameters that customers are interested in For instance, in the personal computer market, training, software level, memory size, disc and CPU sizes and quality of after-sales service are parameters of interest This identifi-cation is usually done by carrying out a survey among customers

• Identify the part-worths (i.e., the characteristics of the parameters, also called benefits, as defined in Section 1.7) that are of interest for customers This can

be done using conjoint measurement

• Define part-worth (or benefit) subsets that correspond to clusters of customers

(using K-mean analysis, as explained in Section 1.7)

• Identify the parameters that characterize the customers of a cluster, for stance, adherence to a socioeconomic class, geographic location, consumption habits, gender, religion, age, etc

in-Market segmentation is the relationship between subsets of customers and sets of benefits Each subset of benefits is a market segment To be acceptable, segments should be homogeneous within the segments and heterogeneous from one segment to another

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sub-Remark: It is also possible to use correspondence analysis, a method belonging

to data analysis, to establish a relationship between subsets of customers and

sub-sets of benefits Correspondence analysis is a technique that will provide

informa-tion about the “proximity” of benefits to characteristics of customers

1.4.2 Discount Strategy

A discount sale consists in selling a given set of items at a reduced price for a

lim-ited period Such a price reduction should generate enough supplementary sales to

compensate the reduction of incomes; however, this is rarely the case Few

com-panies realize what the true cost of discounting is When a discount is offered for a

given period, it applies to all sales, which often leads to disastrous consequences

Let us consider a set of items sold at the price c each During a period T, the

re-tailer usually sold m items and the benefit is b for each item sold The rere-tailer

de-cides to apply a x% discount, assuming that x c/100≤b, which means that the

rebate is less than the benefit The question is: how many supplementary items

should be sold to compensate the reduction of incomes? We denote by z the

num-ber of supplementary items that should be sold

The benefit made during period T when items are sold at the regular price is

c x m

−

100 : it is the minimum additional sale that

compensates the reduction of benefit due to the discount

Example

Assume that 2000 items would be sold at the full price of 100 € and that the

bene-fit would be of 20 € per unit during period T Assume also that the retailer applies

a 10% discount How many supplementary items should be sold to reach the same

benefit as when no discount applies?

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In this example, m=2000, x=10, c=100 and b=20 Applying Relation 1.1 it turns out that z≥2000 For a discount of only 10%, it appears that the re-tailer has to double the sales to compensate the reduction of benefits!

Let us consider z* as the function of x Since z* should remain positive, this

function makes sense only for x∈[0,100b/c)=I Furthermore, z* = 0 for x = 0 and z* tends to infinity when x tends to 100b / c

Let us relax the integrity constraint on the number of items

The derivative of z* with regard to x is:

b c

Thus, for x∈I , z* increases with regard to x

The second derivative is:

b c m

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Price skimming usually applies when customers are relatively less price tive (clients of the cosmetic industry, for instance) or when they are attracted by some novelty (in particular electronic items such as computers)

sensi-Price skimming is useful to reimburse huge investments made for research and development Indeed, a high price cannot be maintained for a long time, but only

as long as the company is in a monopolistic situation with regard to the item’s novelty

1.4.4 Penetration Pricing

Penetration pricing consists of setting an initial price lower than that of the market The expectation is that this price is low enough to break down the purchasing hab-its of the customers The objective of this strategy is to attain a huge market share This strategy can be defined as the low-price strategy enriched by the time factor Penetration pricing leads to cost-reduction pressure and discourages the entry

of competitors

1.4.5 Yield Management (Revenue Management)

The goal of yield management is to anticipate customers’ and competitors’ ior in order to maximize revenue Companies that use yield-management review periodically past situations to analyze the effects of events on customers’ and competitors’ behavior They also take into account future events to adjust their pricing decisions

behav-Yield management is suitable in the case of time-dated items (airplane tickets)

or perishable items (fruits, processed food) A mathematical model will be posed in the next chapter

pro-1.5 Margin, Price, and Selling Level

In this section, we explain the mechanism that links costs, price and margin Note that a strong assumption is made: we consider that any number of available items can be sold

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1.5.1 Notations

Price affects margin, but may also affect cost The higher the price, the greater the

margin per item, but increasing the price may result in a fall-off in sales On the

contrary, when the price decreases, the number of items sold may increase, and

thus the production costs may decrease due to the scale effect

Let us introduce the following variables and assumptions:

• c (s) is the variable cost per item when the total number of items sold during a

given period (a month for instance) is s The function c (s) is a non-increasing

function of s

• f (s) is the fixed cost, that is to say the cost that applies whatever the number

of items sold during the same period as the one chosen for the variable cost

Nevertheless, f (s) may increase with regard to s if some additional facilities

are necessary to pass a given production threshold The function f (s) is a

non-decreasing function of s

In fact, c (s) (respectively, f (s)) is either constant, or piecewise-constant

• R is the margin for the period considered

• p is the price of one item

1.5.2 Basic Relation

We assume that all the items produced are sold, which implies that the market

ex-ists and the price remains attractive to customers Under this hypothesis, which is

strong, Relation 1.2 is straightforward:

)()

As we will see below, it is often necessary to compute the number of items to

be sold in order to reach a given margin, knowing the price, the variable cost per

item and the fixed cost Let us consider two cases

1.5.2.1 Both the Variable Cost per Item and the Fixed Cost are Constant

In this case, Equation 1.2 becomes:

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Remember that ⎡ ⎤a is the smallest integer greater than or equal to a

Indeed, the price is always greater than the variable cost per item

The margin being fixed, it is easy to see that the number of items to be sold is a

decreasing function of the price and an increasing function of the variable cost per

item

1.5.2.2 At Least One of the Two Costs is Piecewise-constant

In this case, the series of positive integer numbers is divided into consecutive

tervals for each cost, and the value of this cost is constant on each one of these

in-tervals To find the number of items to be sold, we consider all the pairs of

inter-vals, a pair being made with an interval associated with the variable cost per item

and an interval associated with the fixed cost We use the costs corresponding to

these intervals to apply Relation 1.3 If the resulting number of items to be sold

belongs to both intervals, this number is a solution to the problem; otherwise

an-other pair of intervals is tested This approach is illustrated by the following

ex-ample

Example

We assume that the price of one item is 120 € and that the required value of the

margin is 100 000 € The fixed cost is 8000 € if the number of items sold is less

than 2000 and 11 000 € if this number is greater than or equal to 2000 Similarly,

the variable cost per item is 50 € if the number of items sold is less than 1000 and

40 € otherwise

1 We first assume that the fixed cost is 8000 € and the variable cost per item is

50 € Applying Relation 1.3 leads to:

154350

To be allowed to select 50 € as variable cost per item, the number of items sold

must be less than 1000, which is not the case Thus, this solution is rejected

2 We now assume that the fixed cost is 8000 € and the variable cost per item is

40 € In this case, we obtain:

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135040

3 If we consider that the fixed cost is 11 000 € and the variable cost per item is

50 €, then we obtain s = 1586 items This fits neither with the variable cost per

item nor with the fixed cost Therefore, this solution is rejected

4 Finally, if the fixed cost is 11 000 € and the variable cost per item is 40 €, then

s = 1388 items: this does not fit with the fixed cost This solution is rejected To

conclude, we have to sell 1350 items to reach the margin of 100 000 €

1.5.3 Equilibrium Point

The equilibrium point is the minimum number of items to sell in order not to lose

money We simply have to assign the value 0 to R and apply Relation 1.3 We still

assume that all the items that are produced are sold We will examine how the equilibrium point evolves with regard to the price in the following example

Example

We consider the case when c(s)= c=120€, f (s)= f =100000€ and we sume that the price evolves from 200 € to 320 € The data obtained by applying Relation 1.3 are collected in Table 1.1

as-Table 1.1 Equilibrium point with regard to price

Price 200 210 220 230 240 250 260 270 280 290 300 310 320 Equil

point 1250 1112 1000 910 834 770 715 667 625 589 556 527 500

It is not surprising (see Equation 1.3) that the equilibrium point is a decreasing function of the price, and that the slope of the curve decreases as the price in-creases

The equilibrium point as a function of price is represented in Figure 1.2

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Figure 1.2 Equilibrium point function of price

1.5.4 Items Sold with Regard to Price (Margin Being Constant)

We still assume that both the variable cost per item and the fixed cost are constant

In this case, Relation 1.3 holds If we relax the integrity constraint, this relation

Assume that the price increases by ε , which results in a variation of η in the

number of items sold Relation 1.4 becomes:

(

)

(

c p c p

f

R

−+

−

=

ε

εη

Taking into account Relation 1.4, this equality can be rewritten as:

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In terms of ratio, we obtain:

c p

Assume that R, f and c are given Let p0 be a price and s0 the corresponding

number of items to be sold in order to reach the margin R

According to Relation 1.6:

c p

p

−+

−

=

εε

where ε is the percentage the price increases with regard to p% 0 and η the %

percentage of items sold decreases with regard to s0, to reach a given margin R

Consider the function:

c p

p

f

−+

This function is increasing and tends to 0 when ε tends to infinity

Further-more, f (ε) is equal to –1 for ε=c, less than –1 when ε<c, and greater than

–1 when ε>c As a consequence, the decrease in the percentage of items sold is

faster than the augmentation in the percentage of price increase as long as the

in-crease in price remains less than the variable cost per item When the inin-crease of

price becomes greater than the variable cost per item, the percentage of price

in-crease is greater than the percentage of inin-crease of items sold Note that these

re-marks hold for a given margin and a given initial price Remember also that we

assume that the market exists or, in other words, that the market can absorb all

items produced Function f (ε) is represented in Figure 1.3

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Example

In this example, the variable cost per item is equal to 80 €, the initial price p0 is

equal to 200 € and the fixed cost is equal to 100 000 € Both the variable cost per item and the fixed cost are constant Table 1.2 provides the decrease in the per-centage of the number of items sold according to the percentage increase in price

Table 1.2 Effect of the price on the number of items sold

1.6 Price Versus Sales Volume: the Selling Curve

1.6.1 Introduction

Customers intuitively compare the price of an item to the value they associate with

it According to a well-known axiom, customers do not buy items, they buy fits or, in other words, they buy the promise of what the item will deliver If the evaluation made by the customer is higher than the price of the item, then the cus-tomer will buy it; otherwise, he/she will not

bene-If several types of items are as attractive to the customer, he/she will buy the item with the biggest difference between his/her own evaluation and the price Several approaches are available to fix the price of an item:

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1.6.2 Cost-plus Method

Several types of cost-plus methods are available, but the common thread of these methods is to:

1 Calculate the cost per item

2 Introduce an additional amount that will be the profit

The profit can be a percentage of the cost or a fixed amount

The cost per item can be calculated either by using a standard accounting method based on arbitrary expense categories for allocating overheads, or by de-riving it from the resource used (i.e., linking cost to project), or considering in-cremental cost

Retailers assume that the purchase price paid to their suppliers is the cost The pivotal advantages of the cost-plus method are the following:

• The price is easy to calculate, which is of utmost importance when a huge number of prices must be established every day, for instance in volume retail-ing

• The price is easy to manage

• The method tends to stabilize the market

The most important disadvantages are:

1 Customers and competitors are ignored

2 Opportunity costs are ignored

The cost-plus methods should be avoided since they ignore customers’

behav-ior as well as the parameters they use to build their own evaluation Defining a price requires analyzing the market and the behavior of customers with regard to the price The objective is to establish a relationship between the number of items

sold and the price The curve that reflects this relationship is called the selling

curve

1.6.3 Price Testing

This approach consists of modifying the price of the item under consideration and recording the number of items sold or the market share This can be done by play-ing with a scale shop or a shop simulated on a computer This testing should be done with different classes of customers, these classes being characterized by the age of the customers, their gender, the level of incomes and/or the buying habits, etc This helps not only to define a price, but also to select the most profitable market niche

The price-testing method is even easier to apply if the item is sold via the net since changing the price is straightforward Unfortunately, in this case, cus-

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Inter-tomers cannot be completely identified, and thus the marketing strategy cannot take advantage of customers’ characteristics

1.6.4 Estimation Made by Experts

This is the only available method when a new type of item is launched, or when a fundamental evolution of the technology modifies an existing item, or when a drastic change appears in the competition

The first step of the method consists in recording the opinion of several experts (at least ten) that are not in contact with each other One usually obtains selling curves that are quite different from each other

The objective of the next step is to organize working sessions with these perts in order to make their estimations/recommendations move closer to each other

ex-Indeed, the drawback when applying this method is the fact that customers do not intervene in the building process of the selling curve, which increases the probability of error

1.6.5 Market Analysis

This method is based on the history of the item under consideration This implies

that the item (or a similar item) has a history (i.e., is not new in the market) and

that the current market environment is the same as (or similar to) the environment when the data were collected

Assume that the previous conditions hold and that the history provides ties sold at different prices Let p i,i=1,2,L,n be the prices and s i,i=1,2,L,n

quanti-the corresponding quantities sold

The objective is to define a function s=a p+b that fits “at the best” with the

data In other words, we compute a and b that minimize:

2 1

)(

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1

i n

i

i i n

i

s b

p

a

p s

=+

i

i n

i i n

i

i n

i

s b

p

a

p s p

b

p

a

1 1

2

1 1 1

2

1

2 1 1

2

1 1 1

)(

n i i n

i

n i i n

i i i n

i

n i i n

i i n

i

i i

p p

n

p p s p

s

b

p p

n

p s p

s

n

a

(1.7)

In Figure 1.4, we show how a set of 6 points denoted by A, B, C, D, E and F

has been interpolated by a straight line that represent equation s=a p+b, the

co-efficients a and b being derived from the coordinates of the points using

Figure 1.4 Linear interpolation of a set of points

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Relations 1.7 minimize the sum:

2 2

where A (respectively, ' B,'C,'D,'E' and F') is the point of the straight line

having the same abscissa as A (respectively, B, C, D, E and F)

Note that any set of points belonging to R2 can be interpolated by a straight

line, even if they are far from being organized around a straight line We thus have

to justify the use of a linear interpolation for a given set of points This is done

us-ing the correlation coefficient r:

n i i i

n

i

n i i i

n i i n

i i i n i

i

s s

n p p

n

p s p s n

r

2 2

1 1 1

)()

(

(1.8)

If the correlation coefficient is equal to +1, then the points (p i,s i) are on a

straight line, and the slope of this line is positive If r=−1, the points are on a

straight line, but the slope of this line is negative

In practice, we assume that the interpolation of a set of points by a straight line

is possible if the correlation coefficient is either close to –1 or to +1

Example

We propose an example with 10 points defined in Table 1.3

Table 1.3 Number of items sold as a function of price

Price p i 4 5 6 8 9 10 11 13 14 15

Number of items sold s i 22 27 33 44 48 53 60 66 72 80

We compute the correlation coefficient in order to verify if this set of points

can be considered as being distributed along a straight line We apply Relation 1.8

and obtain: r = 0.99777, which is very close to +1 As a consequence, we consider

that a linear interpolation is applicable to this set of points

We apply Relations 1.7 that lead to:

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1.6.6 Customer Surveying

Questioning customers about the price of an item was widely used in the 1960s

At that time, direct questions were asked such as, for instance:

• What is the maximal amount of money you are prepared to pay for this item?

• What is, in your opinion, the right price for this item?

• Would you buy this product at the price of x monetary units?

This approach is rarely in use nowadays since it gives too much importance to the price that is only one of the parameters customers are interested in Prices can

no longer be considered in isolation

This is why methods that try to evaluate characteristics of interest to the

cus-tomers have been developed One of them is the well-known conjoint

measure-ment

1.7 Conjoint Measurement

1.7.1 Introduction and Definitions

The conjoint measurement is becoming increasingly popular as a tool to find the characteristics of importance for customers in items (products or services) As a consequence, it provides information to increase the value added of items and market segments

Conjoint measurement starts by listing the parameters that are supposed to be

of some importance for customers in the item under consideration The istics of importance will be extracted from this list For instance, if the item is a personal computer, we may have (if we use figures from recent years):

character-• A parameter related to the hard disk size It takes the value 1 if the size belongs

to [50 GO, 80 GO], the value 2 if the size belongs to (80 GO, 120 GO] and the value 3 if the size is greater than 120 GO

• A parameter related to the memory size It takes the value 1 if the size belongs

to [256 KO, 512 KO] and 2 otherwise

• A parameter related to the training It takes the value 2 if the training is free and

1 otherwise

• A parameter related to after-sales service It takes the values 1, 2 or 3 ing on the type of services

depend-For this example, we have 3×2×2×3=36 sequences of five parameter values

Such a sequence is called a stimulus Thus, this example gives birth to 36 stimuli

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Note that the value of a parameter does not reflect an assessment, but a choice This point is important

Splitting the broad evaluation of an item among the values of its parameters implies that the overall evaluation of an item is the sum of the evaluations as-signed to the values of the parameters In other words, the utility function is as-sumed to be additive This assumption is strong since it implies that parameters

are disjoined (i.e., independent of each other from the point of view of customers’

perception of the item value) The evaluation of a parameter value is called the

part-worth We obtain a set of part-worths from each tester It helps to answer the

following questions:

• How to differentiate customers from each other? Customers that present close part-worths can be considered as similar (i.e., as belonging to the same group in terms of purchasing behavior)

• How to fix the price of an item? It is possible to introduce the price as one of the parameters and ask customers to select a price range among a set of prices

(i.e., a set of parameter values)

• How will the market share evolve if the price changes?

• Which parameter value should be improved first in order to increase the ceived value of the item?

per-Conjoint measurement is used not only to evaluate the importance of the values

of the parameters of products (i.e., the part-worths) It also applies to service

qual-ity, reliabilqual-ity, trademark reputation, etc

Each tester is asked to rank the stimuli in the order of his preference Another possibility is to give a grade to each stimulus The objective of the method is to derive from this ranking (or grading) the part-worths or, in other words, the evaluation of each one of the parameter values

The method that requires ranking (or grading) the whole set of stimuli is called

the profile method The drawback of this method is the number of stimuli to rank

(or grade) since this number increases exponentially with the number of istics and their “values” Assume, for instance, that an item has 5 parameters and 3 values for each, which is a medium-size problem Then, 35 = 243 stimuli must be ranked (or graded), which is quite impossible in practice

character-The two-factor method tries to overcome the previous difficulty character-The idea is to

consider just two characteristics at a time and then to combine the information to derive the part-worths

We first consider the profile method

1.7.2 Profile Method

Assume that m parameters have been selected for defining a given item and that

parameter r∈{1,2,L,m} has N r values denoted by {1,2,L,N }

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Supply chain engineering useful methods and techniques (2010) alexandre dolgui, jean marie proth

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