Donia El Kateb

François Fouquet

Yves Le Traon

Johann Bourcier
email: johann.bourcier@inria.fr

Sputnik: Elitist Artifical Mutation Hyper-heuristic for Runtime Usage of Multi-objective Evolutionary Algorithms

Keywords: MOEA, Hyper-heuristic, Artificial mutation, Optimization, Cloud

 research on artificial mutation of fruits with X-Ray). Putting aside the analogy with natural selection , the present paper proposes an hyper-heuristic for MOEA algorithms named Sputnik 1 that uses artificial selective mutation to improve the convergence speed of MOEA. Sputnik leverages the past history of mutation efficiency to select the most relevant mutations to perform. We evaluate Sputnik on a cloud-reasoning engine, which drives on-demand provisioning while considering conflicting performance and cost objectives. We have conducted experiments to highlight the significant performance improvement of Sputnik in terms of resolution time.

INTRODUCTION

Beyond well known harmful computer viruses, Computer Science has also often been inspired by biological processes for more constructive purposes. For example, John Holland was inspired by the Darwinian evolution [START_REF] Darwin | The Origin of Species by Means of Natural Selection[END_REF] to design genetic algorithms [START_REF] Holland | Adaptation in natural and artificial systems[END_REF][START_REF] Goldberg | Genetic algorithms in search, optimization, and machine learning, addison-wesley[END_REF]. These algorithms are particularly efficient to solve complex problems which have very large solution spaces. Since their introduction in 1974, they have been applied in numerous contexts (biology, computer science, mathematics) for simulation, optimal allocation, function optimisation. Multiple-objective evolutionary optimization (MOEA) [START_REF] Deb | Multi-objective optimization. Multi-objective optimization using evolutionary algorithms[END_REF][START_REF] Van Veldhuizen | Multiobjective evolutionary algorithms: Analyzing the state-of-the-art[END_REF][START_REF] Deb | Multi-objective optimization. Multi-objective optimization using evolutionary algorithms[END_REF] is thus a domain that tackles a category of problems in which a decision maker aims at finding a solution that optimizes several conflicting objectives. MOEA are used nowadays in several design case studies [START_REF]Search-based genetic optimization for deployment and reconfiguration of software in the cloud[END_REF] like cloud organization optimization, however their applicability at run-time presents several issues related to performance. MOEA algorithms leverage an evolution principle based on Darwinian [START_REF] Reeves | Genetic algorithms-principles and perspectives[END_REF] rules that derives, from an initial population of solutions, new solutions combining acceptable trade-offs between objectives. Therefore, MOEA algorithms mimic the natural selection by leveraging a set of fitness functions to evaluate a solution to a specific problem. Additionally, they combine a set of operators [START_REF] Van Veldhuizen | Multiobjective evolutionary algorithms: classifications, analyses, and new innovations[END_REF] to drive population evolution by introducing small changes on individuals (i.e, mutation), composing new ones (i.e, crossover) or selecting the candidates that will compose next generations (i.e, selection). However, natural selection is based on a random mutation in order to mimic the equity of species expressed in Darwinian rules. The result of this algorithm is the genotype that is the closest to the optimal solution for the problem. However, this randomness leads to sub-optimal performance for multiple-objective resolution mainly because of the creation of several unused generations wasting computational resources. Besides, modern genetic does not try to mimic the real evolution process in labs. Instead, based on the founding work of Muller et al [START_REF] Plaskett | Artificial transmutationof the gene[END_REF], artificial mutation is now widely used to save time and generation cycles for instance to produce genetically modified organisms. Instead of relying only on crossover and natural selection, Muller et al [START_REF] Plaskett | Artificial transmutationof the gene[END_REF] studied artificial mutation using X-Ray to modify a fruit with an anticipated intent. These principles have led the genetic field to build instruments for such selective artificial mutation. Going along the same line, we study how such principles from the genetics could be adapted to MOEA to accelerate the convergence to a solution by guiding the evolutionary algorithms through dynamically selected mutation operators.

Our intuition is that operators applied in a smart and artificial way would provide better results than operators applied randomly, and in particular would reduce the number of useless solutions construction. So, the new algorithm we propose is no longer inspired by Darwinian evolution, but by "artificial mutation", based on a smart and dynamic selection of the best mutation operator to apply at a given step. By applying such operators in priority, we aim at orienting the evolution process of a given population in the right direction for the problem to solve. This makes our new algorithm a new category of hyper-heuristic [START_REF]A classification of hyper-heuristic approaches[END_REF] in the sense it aims at improving performance for a specific problem [START_REF]Pareto rank learning in multi-objective evolutionary algorithms[END_REF] as the search evolves.

In this paper, we present this new hyper-heuristic algorithm, called "Sputnik", inspired by artificial mutation. Its name "Sputnik" from a virus family which evolves and mutates together with their host in order to perfectly fit their environment and to replicate more quickly. In the same manner, Sputnik algorithm leverages a continuous ranking of operators according to their impact on fitness functions to smartly select dynamically the mutation operators according to the problem to solve. We focus on performance as a key factor for runtime usage to reach faster acceptable tradeoffs while saving computation time and generation cycles. For instance, the acceleration Sputnik provides is useful for adaptive systems when a solution/reaction has to be found in a short time. We evaluate our approach on a cloud reasoning engine which handles several conflicting objectives (i.e, latency, cost) and is able to continuously provision customers software by different available cloud providers. The validation focuses on the performance of our hyper-heuristic for multi-objective resolution. We have integrated Sputnik in the Polymer framework 2 and evaluated it using a model@runtime platform 3 . We have conducted an experiment to compare natural selection versus Sputnik. Our experiments highlight that Sputnik results in a faster convergence by reducing the number of generations while conserving the ability to achieve acceptable trade-offs on the considered use case. This paper is organized as follows. Section 2 describes the key concepts related to this paper. Section 3 presents Sputnik hyper-heuristic. Section 4 presents validation elements of our approach. Finally, section 5 and 6 discuss the related work, our conclusion and future work.

MOEA FOR AT-RUNTIME USAGE

Multi-objective evolutionary algorithms (MOEA) are optimization algorithms driven by elitism rules that favor the survival of strongest species [START_REF] Van Veldhuizen | Multiobjective evolutionary algorithms: classifications, analyses, and new innovations[END_REF] in analogy to natural selection. Applied to software engineering, species are candidate solutions to optimization problems which constitute what is called a generation. MOEA are based on an iterative search in which a set of individuals is selected and mutated in each iteration to constitute a new generation.

Fitness functions are used to evaluate solutions to solve a specific optimization problem, in analogy to natural selection where species qualities are evaluated according to their surrounding context. Genetic operators: crossover and mutation [START_REF] Van Veldhuizen | Multiobjective evolutionary algorithms: classifications, analyses, and new innovations[END_REF] are used to emulate natural mutation in order to generate new generations composed of mutated solutions. Mutation operators introduce small changes with a small probability to preserve the population diversity [START_REF] Mahfoud | Niching methods for genetic algorithms[END_REF] whereas crossover operators create new individuals by genetic recombination. MOEA algorithms can be used to solve at runtime optimization problems, for instance a load balancing problem, therefore performance becomes a major issue to consider [START_REF] Jensen | Reducing the run-time complexity of multiobjective eas: The nsga-ii and other[END_REF]. Among the contributions that have addressed these issues, hyperheuristics [START_REF]A classification of hyper-heuristic approaches[END_REF] are self-tuning heuristics that are based on parameters adaptation during optimization processing. In general, hyperheuristics introduce modifications on the algorithm itself, in order to improve its efficiency to handle a specific purpose [START_REF]Pareto rank learning in multi-objective evolutionary algorithms[END_REF].

The contribution of this paper, detailed in section 3, falls into the category of hyper-heuristics that embed learning mechanisms to achieve performance improvement over a set of software engineering problems [START_REF]Hyper-heuristics for performance optimization of simultaneous multithreaded processors[END_REF][START_REF] Özcan | A comprehensive analysis of hyper-heuristics[END_REF]. It relies on an heuristic selection mechanism that evaluates search parameters during the search process and grants higher priority for the most effective ones.

SPUTNIK

The randomness introduced by natural selection of evolutionary approaches leads to suboptimal performance in terms of compu-2 http://http://kevoree.org/polymer 3 http://kevoree.org tational power and memory usage. Random selection of mutation operators produces useless candidate solutions that lead to computational resources waste and therefore does not meet run-time optimization constraints. In modern biological studies, after identifying a gene impact on individual phenotype trait, scientists like Muller et al [START_REF] Plaskett | Artificial transmutationof the gene[END_REF] leverage artificial mutation to directly produce an individual combining the foreseen modification.

Our hypothesis is that the artificial mutation concept can be introduced in evolutionary algorithms to mimic modern biological genetic, thus reducing the number of required generations to reach acceptable solutions. The a priori scientific knowledge of a gene modification impact, could be replaced by a continuous ranking and learning approach leveraging execution history. Therefore, in this paper we aim at optimizing MOEA, by dynamically reducing the usage of mutation operators that are less effective in improving fitness functions scores. At the same time, we maintain the equity of natural selection, to ensure that the modified evolution algorithm is able to reach any solution. Thus, we replace the random mutation operator selection by an hyper-heuristic that detects for each individual the most pertinent operator to apply in order to achieve a faster trade-off.

After each application, mutation operators are classified according to the delta variance they introduce on each fitness function. Internally, Sputnik maintains an elitist group of mutation operators that are relevant to improve a fitness function score. To enhance operators selection, Sputnik, considers the current fitness scores reached by a solution, and selects the most relevant mutator in elite groups to improve next generation 4 .

Sputnik workflow, depicted by the flowchart of Figure 1, takes as inputs an initial population and a generation number. As most of MOEA variants like (NSGA-II, ε-MOEA, SPEA 2 [START_REF] Van Veldhuizen | Multiobjective evolutionary algorithms: Analyzing the state-of-the-art[END_REF]) the major part of the algorithm is an individual ranking step according to fitness function evaluation and a non dominating population construction. Sputnik introduces a favoritism operator approach in the mutation process.

We consider a multi-objective evolutionary optimization of f with n objectives ( f 1 , f 2 ,..., f n ). The average fitness score for a generation g i is defined by ∑ n i=1 f i /n. We define △ impact f g i as the fitness score variation between the average of fitness function evaluation for a generation g i-1 and a generation g i :

△ impact f g i =(∑ n i=1 f i /n) g i - (∑ n i=1 f i /n) g i-1
. Sputnik records the selection occurrence for the different mutation operators that have been involved in each generation. Once all mutators have been selected at least once, △ impact f g i is evaluated for all the operators and Sputnik can be configured to select the operators that have △ impact f g i > 0 in the generation g i+1 with the two following settings:

• Elitist Strategy: The operator that has the highest delta impact positive is always chosen in the generation g i+1 . This configuration accords higher chance to the "winner operator" to be selected in the next generation. • Caste Strategy: A selection probability is partitioned between operators that have △ impact f g i > 0 and is defined as

P selection = △ impact f g i ∑ n i=1 △ impact f g i This configuration
gives more equity in terms of selection probability for all operators which have a positive impact on a fitness. SPUTNIK-based mutation operators selection is described in Algorithm 1. In both settings a probability of 10% is maintained for pure random selection of operators to not discriminate worst ranked operators. Sputnik keeps 10% of mutation to give chance to less selected operators to be reintroduced in the elite group of a fitness function. By this mechanism we keep a minimal equity of species while conserving 90% of the Pareto for most efficient mutation.

VALIDATION

We validate our approach through a reasoning engine for an hybrid cloud management system: A cloud customer aims at hosting some of his applications on a set of virtual machines that are dedicated for his internal usage in a private cloud provider. The customer aims at reducing costs inherent in a setting based on private cloud model by exporting some applications to a public cloud. The problem can be formulated as follows: "Given a dedicated set of VMs allocated by a private cloud provider, how to optimize software placement in VMs to reduce costs and to reduce latency that can be introduced by a distant hosting?".

We define a cloud configuration as an architecture model which leverages virtual machine and component (i.e, provisioned software in our context) concepts. Based on our architectural model, an Individual represents a solution vector x ∈ X that corresponds to a cloud infrastructure model. A gene corresponds to a component or a virtual machine in our model. A population corresponds to a set of cloud infrastructure models. A Genetic mutation operator corresponds to an elementary flip in the model like AddComponent(c,A). For the sake of space limitations, we will not give ample details about the operators defined in this paper. The reader may refer to our open source Polymer framework which gives ample details about our architectural model 5 .

A Cloud infrastructure multi-objective optimization problem is represented by the following Triplet (I,F,CO). I denotes a cloud infrastructure model which represents an abstraction of a set of (VM). Each (VM) hosts n software components (C). CO denotes a set of possible configurations in I that satisfy F. A configuration co ∈ CO is obtained through a mapping from components to (VMs), for example co = (V M 1 (c 1 , c 2 , c 3 )) denotes a configuration with a single virtual machine V M 1 hosting 3 components c 1 , c 2 , c 3 .

The vector F(X) is composed of the following 2 objective functions, F(X) = ( f 1 (x), f 2 (x)) that have to be minimized: 1) f 1 (x)= Cost(x): denotes the cost which is proportional to the number of active VMs. 2) f 2 (x)= Latency(x): The latency function is calculated on the basis of the average of latency of all components in the model, considering both redundancy and distant hosting impacts.

The multi-objective optimization problem aims at finding a configuration co ∈ CO such as min F(X) co . We have implemented Sputnik prototype in the Polymer framework which leverages a model based encoding to perform MOEA optimization. Indeed, using model@run.time paradigm [START_REF] Blair | Models@ run.time[END_REF], our cloud models can be seamlessly deployed in a real large-scale production environment [START_REF]Dissemination of reconfiguration policies on mesh networks[END_REF] like a cloud infrastructure. The evaluation of cloud Sputnik based reasoning engine is out of scope of this paper, only the gain achieved by the hyper-heuristic will be evaluated in this paper.

Research Questions

This validation section aims at exploring the effectiveness of Sputnik to reduce the generations number to reach a certain level of trade-off. Secondly, we provide evidence that the results are comparable in terms of level of trade-off achieved.

Finally, we explore the effectiveness of Sputnik once embedded in most popular MOEA algorithms such as MOEA-D and NSGA-II. To compare the solutions of the different algorithms under study, we choose the hypervolume metric as Pareto-front quality indicator [START_REF]The hypervolume indicator revisited[END_REF]. Our validation steps can be summarized in the following research questions: RQ 1 ) Considering that an acceptable trade-off is 90% of the best solutions, is the Darwin Sputnik operator selection strategy successful to reduce the number of generations to reach the acceptable trade-off compared to a classical random strategy? RQ 2 ) Does Sputnik produce comparable results in terms of trade-off achieved regarding classical random mutation selection? RQ 3 ) Is Sputnik relevant for common MOEA algorithms?

Experimental results

To answer RQ 1 , we run Sputnik in a cloud optimization engine which contains 100 virtual nodes and several components that have to be dispatched. Our cloud reasoning engine is configured with one of the most popular MOEA algorithm NSGAII [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: Nsga-ii[END_REF]. The experiment is run 3 times for 300 generations, Sputnik with caste strategy, Sputnik with elitist strategy and finally with random. The results are shown in the Figure 2. We consider that a solution achieves an acceptable trade-off if it reaches 90% of the best obtained solution. In our case study, the best obtained solution achieves an hyper-volume of 0.79 (acceptable hypervolume value is 0.71 in our case), it has been reached with a 2000 generations previous run. A run with Sputnik (with both strategies) reaches this value after 176 generations whereas a run with random operators selector reaches this value after 279 generations. Sputnik strategies are very similar in terms of hypervolume achievements. We notice that elitist converges slighly faster however, the caste strategy can reach better hyper-volume scores because it takes benefit from mutators diversity. In average, Sputnik (both with cast and elitist) outperforms random selector by reducing around 37% the number of necessary generations. This confirms our first hypothesis which states that a smart mutators selection strategy is successful to reduce the number of generations to reach an acceptable trade-off compared to a classical random selection strategy.

To reply to RQ 2 , we run a similar experiment with both random and Sputnik selector until we reach an unchanged value of hypervolume for 50 generations. Final values for Sputnik (elitist: 0.77 and caste: 0.81) and random (0.78) (±1% each difference) allow us to conclude that our hyper-heuristic does not decrease the quality For RQ 3 , we set up common MOEA algorithms with Sputnik. The results shown in

RELATED WORK

Several approaches have proposed hyper-heuristics that operate on top of MOEA to improve their run-time usage. In [START_REF]Pareto rank learning in multi-objective evolutionary algorithms[END_REF], the authors embed learning techniques in classical MOEA. They assume that objective functions are expensive to compute so they rank the pareto front elements and they evaluate only the individuals that have higher ranks. In [START_REF] León | Hyperheuristics for a dynamic-mapped multi-objective island-based model[END_REF], the authors have proposed an hyper-heuristic that relies on the hypervolume calculation to improve computational results. These approaches consider only the Pareto front set evaluation to improve MOEA, whereas our approach evaluates operators contribution in improving fitness and thus injects mutation operators that are eligible to make MOEA converge faster. In [START_REF] Yuan | Statistical racing techniques for improved empirical evaluation of evolutionary algorithms[END_REF], the authors have shown that racing algorithms can be used to reduce the computational resources inherent from using evolutionary algorithms in large scale experimental studies, their approach automates solutions selection and discards solutions that can not come up with results improvement. Whereas racing techniques eliminate worst solutions candidates to speed up the search, in our approach we keep considering worst ranked candidates to maintain operators diversity. In [START_REF] Drake | Controlling crossover in a selection hyper-heuristic framework[END_REF], the authors have explored the advantages of using a controlled crossover on top of single-point search based hyper-heuristics. They maintain the best solutions obtained during the search and update crossover operator accordingly. The authors rely on a process focused on crossover as a biological selective breeding. This breeding assumes that fittest genes are already present in the initial population. Unlike cited approaches, Sputnik focuses on artificial mutation selection, therefore mimicking the process used to produce genetically modified organisms. As far as we know, there is no other hyper-heuristics that proposes artificial mutation at mutators level.

CONCLUSION

In this paper, we have introduced a novel hyper-heuristic breaking the random natural selection of classical MOEA to leverage instead an elitist artificial mutation inspired by biological studies [START_REF] Plaskett | Artificial transmutationof the gene[END_REF] supported by a continuous learning of mutations impact. Sputnik, relies on a mutation operator selection based on a continuous learning of past effect on fitness functions. The overall goal of Sputnik is to enhance the optimization algorithm itself, and to guide the search towards faster trade-off achievement to finally save generation cycle and time. Integrated in a model-based optimization framework, our approach has been validated on the construction of a cloud reasoning engine prototype. Experimentally, we provide evidence of the effectiveness of artificial guided mutation to reduce significantly the number of necessary generations to find acceptable trade-offs. In the future, we plan to evaluate the relevancy of our heuristic on crossover operations. Also we plan to classify elitist strategies to analyze their impact on solution diversity.

Figure 1 : 1

 11 Figure 1: Sputnik Workflow Ini$al popula$on Ρ

Figure 2 :

 2 Figure 2: Hypervolume: Sputnik (Elitist & Caste) vs Random of the result in terms of degree of trade-off achieved. Moreover the caste strategy improves the hypervolume score.For RQ 3 , we set up common MOEA algorithms with Sputnik. The results shown in Table1, are hypervolume values after 200 generations compared to MOEA without Sputnik. We conclude that Sputnik (both with caste and elitist configurations) is effective in achieving a better trade-off faster than current MOEA.

Table 1 ,

 1 are hypervolume values after 200 generations compared to MOEA without Sputnik. We conclude that Sputnik (both with caste and elitist configurations) is effective in achieving a better trade-off faster than current MOEA.

		NSGAII	ε-NSGA II	ε-MOEA	Hyper-MOEA
	Elitist	0.72	0.75	0.51	0.47
	Caste	0.70	0.73	0.52	0.47
	Random	0.67	0.66	0.43	0.44

Table 1 :

 1 Sputnik (Elitist & Caste) hypervolume on MOEA

http://www.genetics.org/content/111/1/147.short

https://github.com/dukeboard/kevoree-genetic

://en.wikipedia.org/wiki/


Keywords: Customer attractiveness, supplier satisfaction, preferred customer, social exchange theory, industrial marketing, purchasing

Industrial markets are frequently characterized by an oligopolistic market structure. As a result, suppliers may become highly selective with respect to decisions that involve collaborating with certain customers. Buying firms must therefore be more attractive than their rivals to obtain opportunities to collaborate with these selective suppliers. This apparently counterintuitive inversion of the classical marketing approach (that is, relationships that involve buyers competing for suppliers rather than the other way round) constitutes the foundation of the special issue that is introduced in this paper. In this paper, we present key terms and propose a model of preferred customership that uses a social exchange perspective to link customer attractiveness, supplier satisfaction and preferred customer status. The papers that contribute to this special issue are introduced within the context of this framework. Finally, this paper concludes with suggestions for future research directions.

1 Researching the "other side": shifting the burden of attractiveness from the supplier to the customer Commonly, both academics as well as practitioners approach buyer-supplier relations with the assumption that to successfully sell products or services, suppliers attempt to become as attractive as possible to (potential) buyers. In the current special issue, we explore another perspective, namely, the phenomenon of buyers that attempt to obtain the best resources from sellers by striving to become more attractive to suppliers. This scenario represents a counterintuitive inversion of the classical marketing approach (that is, in this scenario, buyers are competing for suppliers, rather than the converse interactions). The ultimate objective of this exploration is to provide firms with insights regarding how they can achieve preferred customer status with their core suppliers and thereby gain competitive advantages relative to competing buyers by deriving greater benefits from suppliers' resources and capabilities. "A firm has preferred customer status with a supplier, if the supplier offers the buyer preferential resource allocation. This can be accomplished in several ways. A supplier may dedicate its best personnel to joint new product development, customise its products according to the customer's wishes, offer innovations or even enter into an exclusivity agreement. The supplier might also ensure privileged treatment if bottlenecks occur due to constraints in production capacity" (Steinle & Schiele, 2008, p. 11). The key issue with respect to firms competing not only on the sales market but also on the supply market is that "really good" suppliers are in short supply [START_REF] Cordón | The Power of Two: How Smart Companies Create Win: Win Customer-Supplier Partnerships that Outperform the Competition[END_REF].

At least two primary motives may have driven the recent increase in research that addresses customer attractiveness: 1) a fundamental change in supply chain organization that allocates increasing responsibilities to suppliers, which has coincided with 2) a reduction of suppliers in many business-to-business markets, i.e., supplier scarcity. The core competence movement has caused many activities that were formerly performed in-house to be outsourced to suppliers [START_REF] Prahalad | The Core Competence of the Corporation[END_REF]. The 1990s also saw a shift in the typical process of innovation generation from a closed, laboratory-centered model to an open, networkembedded model for innovation. A panel study that surveyed top R&D-intensive firms found that only 22% of these firms relied heavily on external partners for innovation in the early 1990s but that this share had grown to 85% by the end of that decade [START_REF] Roberts | Benchmarking Global Strategic Management of Technology. Survey of the word's largest r&d performers reveals, among other trends, a greater reliance upon external sources of technology[END_REF]. Since the turn of the century, open innovation has become a buzz word. The growth of this model has been propelled, among others, by the increasing competence levels of suppliers [START_REF] Chesbrough | Open innovation: the new imperative for creating and profiting from technology[END_REF]. Given this phenomenon, to increase the scope of possible innovation, it has become increasingly important for firms to secure the best suppliers for collaborative development projects [START_REF] Brem | Introduction[END_REF]. However, actors have constraints on the resources that they can devote to any particular endeavor and "may only have the time and resources to form and satisfy the expectations of a limited number of alliances. By making choices to ally with some partners, others are ipso facto excluded" (Gulati, et al., 2000, p. 210). Firms may not wish to belong to that group of "ipso facto excluded" customers.

Moreover, in 2011, several events occurred that disrupted supply chains, stimulating further research into this topic; in particular, these events included a tsunami that damaged many coastal production facilities in Japan, a flood in Thailand and the "Arab spring", i.e., political turmoil in several countries that affected supply security. During these types of events, questions arose regarding which customers would obtain the remaining stores of scarce materials that suppliers had sequestered in safe locations and which customers would be the first to obtain new supplies as production slowly ramped up following the initial disruption. A similar situation of allocation, i.e., a situation in which suppliers have the opportunity to select customers, occurs during boom phases. Once again, it has been demonstrated that preferred customers are the beneficiary of these types of situations and are able to take advantage of their status to achieve market share gains [START_REF] Schiele | Accessing Supplier Innovation By Being Their Preferred Customer[END_REF]. Extreme situations, such as environmental risks that interrupt the supply chain or boom phases that create a seller's market, reveal an underlying challenge of certain markets: the presence of a low number of suppliers. In these markets, each supplier must make decisions regarding which customers to serve and to what extent. Supplier scarcity has been reported in several industries, such as the luxury car industry, in which producers rely on the same 30 suppliers for components of Mercedez E-class, Audi A6 and BMW 5 automobiles [START_REF] Wagner | A Credit Risk Modeling Approach to Assess Supplier Default Risk[END_REF]; the biotech field [START_REF] Powell | Interorganizational collaboration and the locus of innovation: Networks of learning in biotechnology[END_REF]; software production [START_REF] Lavie | Alliance portfolios and firm performance: A study of value creation and appropriation in the US software industry[END_REF]; or the railway industry [START_REF] Schiele | Location, location: the geography of industry clusters[END_REF]. For many types of industrial materials, no more than two or three leading suppliers remain in the market. As a result, these suppliers often become highly selective and do not dedicate their resources equally to all of their customers. [START_REF] Williamson | Supplier strategy and customer responsiveness: Managing the links[END_REF] argues that a supplier generally "responds first to the needs of his preferred customers" (p. 83), whereas less preferred customers are "forced to wait in a queue" (p. 81). In cases of uncertainty, suppliers first attend to their strategically important preferred customers and only subsequently conduct business with their regular customers.

The contributions of Baxter (this issue) and Ellis et al. (this issue) provide large-scale empirical evidence of the relevance of this phenomenon.

As early as 1970, Hottenstein noted that "most businesses have a preferred customer's list, which may be based on past orders or expectations of future business." (1970, p. 46) Thus, buying firms are faced with the challenge of rising to the top of an important supplier's preferred customer list. The primary research question that arises from observations of competition in the supply market is how a buyer can eventually become a preferred customer of leading suppliers. To address this issue, various sub-questions must be resolved; for instance, the antecedents to preferential resource allocation must be identified, metrics for measuring a buyer's status with a supplier must be developed, and methods of influencing suppliers must be characterized.

The traditional perspective, which is more focused on supplier attractiveness than on customer attractiveness, fails to provide satisfactory explanations for the aforementioned phenomena of the relationships on "the other side". As a consequence, to date, little information to guide firms with respect to managing their attractiveness and reaching preferred customer status has been provided in the extant literature. There have been some first practitioner books that have touched this issue [START_REF] Cordón | The Power of Two: How Smart Companies Create Win: Win Customer-Supplier Partnerships that Outperform the Competition[END_REF][START_REF] Rudzki | Next Level Supply Management Excellence: Your Straight to the Bottom Line Roadmap[END_REF][START_REF] Schumacher | Die 3 Faktoren des Einkaufs: Einkauf und Lieferanten strategisch positionieren[END_REF]; however, as emphasized by the literature reviews in this special issue (Hüttinger, et al., this issue; Mortensen, this issue), research has only begun to provide reliable answers to the questions that were posed above. It appears clear, though, that one condition for firms to achieve preferential treatment is to have satisfied suppliers. Moving one step earlier in the chain of buyer-supplier interactions, the buying firm may need to be sufficiently attractive in the first place to induce a supplier to start a business relationship at all. The distinction between the three steps of (1.) customer attractiveness, (2.) supplier satisfaction and eventually (3.) preferred customer status can be embedded in the context of social exchange theory, which is widely used as a foundation of work that addresses attractiveness.

In the following section, we briefly elaborate on the "cycle of preferred customership", which links the three stages of customer attractiveness, supplier satisfaction and preferred customer status and served as a guideline for selecting contributions to this special issue.

Concepts will be defined in ways that reflect the insights that have been gleaned from the latest contributions in this field. Subsequently, the papers of this special issue will briefly be introduced, distinguishing between conceptual and review papers and between case studies and quantitative empirical work. Finally, we will summarize what we know and what remains uncertain with respect to attractiveness research.

The cycle of preferred customership: defining and linking the core concepts of this cycle using a social exchange perspective

In the extant literature, several researchers have occasionally discussed topics that relate to the preferred customer situation. Relevant published investigations include the simulation study by [START_REF] Hottenstein | Expediting in job-order-control systems: a simulation study[END_REF], which marginally addressed the idea that firms may use preferred customer lists to make decisions that relate to expediting. The work of [START_REF] Brokaw | Positioning a Company as a Preferred Customer[END_REF] suggested that purchasers should apply marketing tools to sell their firm to the supplier. Ten years later, the idea of "reverse marketing" once again arose in the work of [START_REF] Leenders | Reverse marketing: the new buyer-supplier relationship[END_REF], although these researchers used a different framework. In case studies, [START_REF] Williamson | Supplier strategy and customer responsiveness: Managing the links[END_REF] and [START_REF] Moody | Customer supplier integration: why being an excellent customer counts[END_REF] emphasized the importance of a firm's role as a good customer for its suppliers. Notably, these sporadic publications did not reference each other; moreover, they have apparently gone unnoticed by many other researchers. For instance, according to the "Google Scholar" database, Brokaw and Davidsson's (1978) work, which appears to be the first research paper that was fully dedicated to exploring the logic underlying the preferred customer concept, was cited only three times as of 2012. Assuming that scientific progress is a cumulative process that involves each researcher building upon the findings of previous investigators [START_REF] Amundson | Relationships between theory-driven empirical research in operations management and other disciplines[END_REF], the dearth of connections to previous studies that address the preferred customer idea may explain why this notion has been largely neglected in the research community until relatively recently. In addition, the lack of a common theoretical basis may have slowed progress in this field. Recent findings comparing citation incidences have indicated that a common theoretical basis may foster the exchange of ideas [START_REF] Chicksand | Theoretical perspectives in purchasing and supply chain management: an analysis of the literature[END_REF].

Social exchange theory is frequently used as a theoretical harbor for attractiveness studies (Hüttinger, et al., this issue; Mortensen, this issue). In this special issue, for instance, six out of the eight published papers use elements of social exchange theory as a conceptual basis (Nollet et al.; Hüttinger et al.; Ellegaard; Hald; La Rocca et al. and Ellis et al.). Social exchange theory may well become a dominant theory in attractiveness studies, complementing resource-based arguments. The resource-based view is well suited for the discussion of consequences of resource allocation issues, particularly if an extended approach is adopted that addresses the resource environment external to the firm [START_REF] Dyer | The relational view: cooperative strategy and sources of interorganizational competitive advantage[END_REF][START_REF] Sanchez | Reinventing Strategic Management: New Theory and Practice for Competence-based Competition[END_REF]; in contrast, social exchange theory is better suited for discussing relationship continuation issues. One reason for the popularity of social exchange theory, and the choice of this theory here, is that the core issues that are discussed by social exchange theory include questions of relationship initiation, termination and continuation [START_REF] Kelley | Interpersonal relations: A theory of interdependence[END_REF]. This issue is central to the process of becoming a preferred customer or, in the worst case scenario, suffering from relationship discontinuation.

In fact, one of social exchange theory's pioneers emphasized the vital importance of attraction in social exchanges, stating that "processes of social attraction, without which associations among men would not occur, give rise to processes of exchange" [START_REF] Blau | Exchange and power in social life[END_REF]

p. 7)

A social exchange theory perspective

Social exchange theory has its origins in sociology [START_REF] Blau | Exchange and power in social life[END_REF][START_REF] Emerson | Social Exchange Theory[END_REF] and psychology [START_REF] Thibaut | The Social Psychology of Groups[END_REF] but also draws on concepts from economics, such as the use of "resources", which encompass any material or immaterial good that is exchanged in an interaction between different actors [START_REF] Foa | Resource theory: Interpersonal behavior as exchange[END_REF][START_REF] Homans | Social behavior as exchange[END_REF]. The core explanatory mechanism of social exchange theory revolves around the relational interdependence that develops over time through the interactions of the resource exchange partners; thus, this theory is particularly suited to a business-to-business context [START_REF] Cropanzano | Social exchange theory: An interdisciplinary review[END_REF][START_REF] Dwyer | Developing buyer-supplier relationships[END_REF][START_REF] Hallen | Interfirm adaptation in business relationships[END_REF][START_REF] Lambe | Social exchange theory and research on business-to-business relational exchange[END_REF].

The theory builds upon three core elements that can be linked into a cycle of preferred customership [START_REF] Schiele | Customer attractiveness, supplier satisfaction and preferred customer status: review, concept and research agenda[END_REF][START_REF] Schiele | Towards a social exchange theory perspective on preferred customership -concept and practice[END_REF]: (1.) expectations (E), which lead to the initiation of an exchange relationship; (2.) the "comparison level" (Cl), which is the standard that is used to judge the outcome of the exchange, producing satisfaction with the relationship after the minimum criteria have been attained; and (3.) the concept known as the "comparison level of alternatives" (Cl alt ), which refers to the assumption, first stated by [START_REF] Thibaut | The Social Psychology of Groups[END_REF], that actors will use not only absolute but also relative criteria to evaluate the outcome of an exchange relationship. This third step implies that to eventually decide upon whether a relationship should be continued, actors are influenced by the availability of alternatives. In the framework presented here, we expand on classical social exchange theory by differentiating between two levels of continuing industrial exchange relationships: as a regular customer or as a preferred customer.

Based on the assumption that buyer-supplier relationships are social exchange processes, it can be argued that customer attractiveness is based on the expectations that a supplier has towards the buyer at the moment of initiating or intensifying a business relationship. Thus, the comparison level describes an evaluation of the supplier's satisfaction with the relationship; this satisfaction reflects the outcome of the exchange relative to previously established expectations. The construction of the comparison level of alternatives (Cl alt ) refers to the decision of the supplier to award preferred status to a customer, assign a regular status to the customer or discontinue supplying the customer. Actors are expected to have a portfolio of relationships and compare their satisfaction with one relationship to each other exchange relationship that they possess. Based on a social exchange perspective, the three related concepts of customer attractiveness, supplier satisfaction and preferred customer status can thus be linked to each other in a logical way, and consistent definitions of these terms can be derived (see figure 1).

insert Figure 1 about here

Customer attractiveness: inducing relationship initiation and intensification

Attractiveness issues have been discussed in terms of mutual attraction in the buyer-supplier relationship development, customer attractiveness and the strategic positioning of buyers and suppliers in portfolio models (Mortensen, this issue). This topic is a recently emerging research field; consequently, most papers that have addressed attractiveness are either theoretical in nature or based on case studies. Very few surveys have been conducted in this field; to date, these surveys have underscored the relevance of the existence of alternative relationships [START_REF] Ping | Does satisfaction moderate the association between alternative attractiveness and exit intention in a marketing channel[END_REF], tested the attractiveness of one sales and distribution channel [START_REF] Anderson | A model of the distributor's perspective of distributormanufacturer working relationships[END_REF] and generated the recommendation that firms should concentrate on a limited number of suppliers [START_REF] Eggert | Benchmarking the impact of customer share in key-supplier relationships[END_REF].

In social exchange theory, attractiveness plays an important role. It is assumed that the perception of initial attraction is particularly based on beliefs and expectations. [START_REF] Blau | Exchange and power in social life[END_REF] stated that an individual is attracted to another if he expects an association with this other individual to be a rewarding experience. On a more operational level, [START_REF] Homans | Social behavior as exchange[END_REF] and [START_REF] Thibaut | The Social Psychology of Groups[END_REF] explained that the attractiveness of another entity is determined by the difference between the expected rewards from a relationship and the costs of being involved in this putative relationship. Thus, attractiveness involves a forward-looking orientation. In this context, [START_REF] Wilkinson | Business mating: Who chooses and who gets chosen?[END_REF] and [START_REF] Mortensen | Attractiveness in supply chains: A process and matureness perspective[END_REF] emphasized that a relationship will only be initiated and developed if actors on both the supplier and buyer sides perceive the attractiveness of this relationship. We therefore argue the following claim:

A customer is perceived as attractive by a supplier if the supplier in question has a positive expectation towards the relationship with this customer. The conditions for this perception of the supplier include an awareness of the existence of the customer and knowledge of the customer's needs.

Although the task of signaling one's needs to the market might sound trivial, this undertaking can be a challenge for many firms, particularly -but not only -for small buyers that might not even be known a priori to their potential business partners. Increasingly, instead of finished products, firms offer competences to solve problems; which adds further complexity to the development of buyer-supplier relationships [START_REF] Golfetto | Marketing competencies and the sources of customer value in business markets[END_REF]. In relationship literature, the need for sufficient awareness has been discussed [START_REF] Dwyer | Developing buyer-supplier relationships[END_REF].

However, awareness alone is not sufficient. A well-known customer can nonetheless be unattractive if there are negative expectations (and/or a lack of positive expectations) that are associated with this well-established organization. However, if the two conditions of awareness of the customer and positive expectations towards a relationship with this putative customer are met, customer attractiveness can be discussed. Mortensen (this issue) emphasized that customer attractiveness is an ex-ante construct that is based on expectations to start and to subsequently develop an exchange relationship. The ex-post evaluation of a relationship, which occurs after an exchange event has taken place, determines satisfaction. Customer attractiveness and supplier satisfaction are two distinct constructs; however, these constructs are sequentially linked to each other.

Supplier satisfaction: comparing outcomes with expectations

Research on supplier satisfaction in buyer-supplier relationships is scarce and is primarily conceptual in nature [START_REF] Benton | The influence of power driven buyer/seller relationships on supply chain satisfaction[END_REF]. Satisfaction has been marginally addressed by several authors, but few publications have focused on the satisfaction that is experienced by suppliers and tried to measure this. The first of these scarce publications, a dissertation, proposed a tool for measuring supplier satisfaction [START_REF] Maunu | Supplier Satisfaction: The Concept and a Measurement System: A Study to Define the Supplier Satisfaction Elements and Usage as a Management Tool[END_REF]. Another paper developed and tested a supplier satisfaction index [START_REF] Essig | Supplier satisfaction: Conceptual basics and explorative findings[END_REF], Nyga et al. ( 2010) tested buyer and supplier models, though with very few variables, whereas [START_REF] Ghijsen | Supplier satisfaction and commitment: The role of influence strategies and supplier development[END_REF] tested techniques that buyers can use to influence supplier satisfaction. These reports often were not linked to a clear theoretical foundation; as a result, they regarded satisfaction as a stand-alone construct and did not relate it to its potential antecedents and consequences of attractiveness and preferred customer status, respectively. A social exchange perspective can establish links between these concepts.

According to [START_REF] Thibaut | The Social Psychology of Groups[END_REF], a relationship is evaluated by comparing its expected value to the actual quality of the outcomes that it achieves, i.e., the quantities of rewards and costs that a supplier faces during the course of an interaction. The discrepancies between the supplier's expectations and the value that is actually obtained through an exchange relationship determine the level of satisfaction that is experienced by the supplier [START_REF] Wilson | An integrated model of buyer-seller relationships[END_REF]. Because there are costs that are associated with participating in an exchange relationship, social exchange theory suggests that parties will only remain in the relationship as long as satisfactory rewards continue to surpass a minimum comparison level [START_REF] Homans | Social behavior as exchange[END_REF][START_REF] Lambe | Social exchange theory and research on business-to-business relational exchange[END_REF]. In accordance with this reasoning, the importance of supplier satisfaction in the discussion of what factors determine the suppliers' decisionmaking processes should be emphasized. If the quality of outcomes of a relationship remains below expectations, the supplier will be dissatisfied. In contrast, if the supplier feels that a relationship produces outcomes that are equal to or exceed expectations, the supplier will be satisfied. Therefore, supplier satisfaction is a condition that is achieved if the quality of outcomes from a buyer-supplier relationship meets or exceeds the supplier's expectations.

The exact nature of the expectations may vary; as long as these expectations are met, satisfaction is the outcome. This definition includes previous definitions that are based on a notion of fairness [START_REF] Benton | The influence of power driven buyer/seller relationships on supply chain satisfaction[END_REF][START_REF] Essig | Supplier satisfaction: Conceptual basics and explorative findings[END_REF]; this notion may or may not be an expectation of the supplier. Important constructs in supplier evaluative judgments include expectations with respect to customer attractiveness, the degree to which these expectations are fulfilled and the resulting level of supplier satisfaction (see figure 1).

Although a minimum level of satisfaction may be required to maintain a relationship, satisfaction can rise gradually during the course of a relationship. "The assessment of outcomes is essential, since it helps parties in making decisions regarding upgrading or downgrading their relationships" (Wilson & Mummalaneni, 1986, p. 51). Thus, suppliers can upgrade customers with whom they are particularly satisfied to preferred status and assign a regular status to the remaining customers that provide adequate satisfaction.

Preferred customer status: differentiating customers

The idea of supplier selectiveness in business-to-business markets has gained little attention in academic literature; however, in recent years, several practitioner papers regarding customer of choice have appeared [START_REF] Bew | The new customer of choice imperative: ensuring supply availability, productivity gains, and supplier innovation[END_REF][START_REF] Day | How to be a customer of choice[END_REF]. With respect to empirical evidence, two case studies were presented in the early 1990s [START_REF] Moody | Customer supplier integration: why being an excellent customer counts[END_REF][START_REF] Williamson | Supplier strategy and customer responsiveness: Managing the links[END_REF], and another case study was reported more than a decade later [START_REF] Steinle | Limits to global sourcing? Strategic consequences of dependency on international suppliers: cluster theory, resource-based view and case studies[END_REF]. The first survey results regarding this topic appear to confirm the assumption that preferred customer status can be an antecedent to supplier innovativeness and at the same time have a positive impact on supplier pricing behavior [START_REF] Schiele | Supplier innovativeness and supplier pricing: the role of preferred customer status[END_REF]. Two additional quantitative studies appear in this special issue, exposing the role that preferred customer status plays in technology access (Ellis, et al., this issue) and revealing the connections between attractiveness, satisfaction and preferential treatment (Baxter, this issue).

According to social exchange theory, there is an interesting construct that sellers use to analyze and evaluate exchange relationships with buyers; this construct, which explains preferential resource allocation to customers rather well, is the comparison level for alternatives (Cl alt ). The comparison level for alternatives is a standard that represents the average quality of outcomes that are available from the best alternative exchange relationship [START_REF] Thibaut | The Social Psychology of Groups[END_REF]. Both Cl and Cl alt must be considered with respect to the development and maintenance of sound relationships, as the outcomes of a relationship (considered as a whole) must be superior to the outcomes that are available from alternative partners [START_REF] Anderson | A model of the distributor's perspective of distributormanufacturer working relationships[END_REF]. Over time, each party in the exchange relationship compares the outcomes from their interactions to the outcomes that are available from exchange alternatives [START_REF] Lambe | Social exchange theory and research on business-to-business relational exchange[END_REF]. Thus, supplier satisfaction is revealed as a necessary but not sufficient condition for the determination of the customer's status. Although a supplier may, in principle, be satisfied by a relationship because the value that it creates matches expectations, this supplier could still discontinue the exchange if a better alternative arises and if constraints impede serving both potential customers in similar ways.

Conversely, even dissatisfied suppliers may remain in a relationship if there is an absence of available alternatives, although possibly with reduced commitment. The consideration of alternatives is an important extension of the classical satisfaction literature [START_REF] Essig | Supplier satisfaction: Conceptual basics and explorative findings[END_REF][START_REF] Ghijsen | Supplier satisfaction and commitment: The role of influence strategies and supplier development[END_REF] and requires a shift from dyadic-level analysis to network-level analysis. In essence, buyers must know which other customers their supplier is serving. A supplier's designation of a buyer as either a preferred or regular customer is dependent on the supplier's perception of the buyer's attractiveness and its satisfaction with this customer; these factors are contingent on the status of alternative players. A supplier awards a buyer with preferred customer status if this customer is perceived as attractive and if the supplier is currently more satisfied with this customer than with alternative customers. As a consequence of this satisfaction, a supplier reacts by providing privileged resource allocation to this preferred customer.

The implication is that the status that is assigned to each customer is directly linked to the supplier's intention. In particular, although the supplier's investment in a relationship with a regular customer may be low, the preferred customer is fostered and awarded favorable treatment. Thus, customer attractiveness and supplier satisfaction are the necessary conditions for achieving preferred customer status; a benevolent strategic prioritization by the supplier is the sufficient condition for attaining this status.

The circularity of attractiveness, satisfaction and resulting partner status

Ellegaard (this issue) concludes his analysis by emphasizing the circular character of attractiveness. Attractiveness is posited to grow as interactions increase between a supplier and buyer through stages of the relationship development process [START_REF] Byrne | Magnitude of positive and negative reinforcements as a determinant of attraction[END_REF][START_REF] Dwyer | Developing buyer-supplier relationships[END_REF]. Clearly, this growth assumes not to discuss spot purchases but instead considers a continuous exchange, which is typical for a business-to-business relationship. It can be expected that because preferred customer status positively influences customer attractiveness -an effect that may occur because the supplier acquires a better knowledge of the customer's needs -suppliers may opt to continue or even expand the relationship with their customer of choice. A circular relationship between customer attractiveness, supplier satisfaction and preferred customer status can hence be expected. "Therefore, relationship development is not a matter of a single stimulus-response. It is more analogous to climbing a ladder." (Cropanzano & Mitchell, 2005, p. 890) If the hypothesis of circularity holds true, it has substantial consequences: [START_REF] Dwyer | Developing buyer-supplier relationships[END_REF] noted that eventually, "the exchange partners have achieved a level of satisfaction from the exchange process that virtually precludes other primary exchange partners" (p. 19). Using arguments that related to comparison levels, [START_REF] Johnson | Resisting temptation: Devaluation of alternative partners as a means of maintaining commitment in close relationships[END_REF] also implied that the hypothesis of circularity should hold, as these researchers proposed that there is a tendency to devalue alternative relationships due to the high level of satisfaction that relationship participants experience in their present relationship: "Alternatives should appear less attractive because the subject's comparison level for alternatives has been increased as a consequence of involvement in the present satisfying relationship" (Ping, 2003, p. 239).

In summary, the logical progression depicted in figure 1 involves the following aspects. In the early stages of a business relationship, the buyer must be sufficiently attractive to the supplier to begin an exchange relationship. Once this business relationship is active, the supplier will evaluate its satisfaction with the relationship, i.e., the supplier's satisfaction with the customer. It is important for buyers to understand their supplier's satisfaction levels, in particular as the supplier has a choice to discontinue the relationship or de-emphasize its efforts. The supplier's assessment of the buyer can induce the former to either discontinue the relationship, continue with a regular degree of emphasis or award preferred customer status. The intensification of the relationship that occurs after preferred customer status is awarded creates additional expectations and may further increase the attractiveness of the customer, restarting the relationship cycle between the supplier and buyer. Of course, also a vicious circle of continuously deteriorating attractiveness can be imagined. It must be noted that a regular or "discontinued" customer could again attempt to increase its attractiveness to eventually reach preferred customer status. Moreover, an analogous cycle might occur on the supplier's side, although in this paper and in the papers constituting this special issue, the perspective of the buyer is taken.

In the following section, we will briefly introduce the papers of this special issue, which are spread across the dimensions of the cycle of preferred customership.

Introducing the contributions to this special issue: Concepts, reviews, cases and quantitative tests

The papers for this special issue were selected based on their methodological rigor, relevance and contribution to theory development, with the objective of achieving balanced contributions across the entire cycle of preferred customership. In total, 25 papers were received; 16 of these papers were subjected to a double-blind review process, 10 of these papers then received a second review, and eight eventually could be accepted. The papers that appear in this special issue begin from conceptual and review papers and transition to reports on theory testing.

The first paper, which is by Nollet, Rebolledo and Popel (this issue), provides a complete conceptual model of how preferred customer status could be achieved and proposes several tactics for achieving this purpose. A particular feature of the model that is presented in this paper is the addition of a "sustainability loop", which reminds both scholars and practitioners that preferred customer status, once achieved, must continuously be maintained and "reearned". Each of the four steps in this paper's model is accompanied by a checklist of practical uses that compiles various suggestions regarding how to progress forward. The next contribution, which is by Hüttinger, Schiele and Veldman (this issue) also addresses the full cycle of attractiveness but provides a literature review of customer attractiveness, supplier satisfaction and papers that elaborate on preferred customer status. Through their review process, the authors isolate the drivers that are antecedents of preferred customership and demonstrate how the achievement of attractiveness requires a crossfunctional effort of the buying firms.

Given that one purpose of special issues is to provide interested scholars with the chance to quickly obtain knowledge regarding the state-of-the-art in a field, reviews are an almost obligatory element of these issues. The aforementioned first review in this special issue is complemented by a more specialized review by Mortensen (this issue) who presents a "complete literature review on attractiveness". In addition to reviewing customer attractiveness to the supplier, Mortensen further addresses attraction not only with respect to buyer-supplier relationship development but also in the context of the management of portfolios and key accounts. He advocates for treating (ex-ante) attractiveness as a concept of its own that clearly differs from the (ex-post) satisfaction that may occur in a business relationship once an exchange has taken place.

One revelation of Mortensen's literature review is that in attractiveness studies, there is a predominance of meso-approaches at the firm level and a relative neglect of microapproaches, i.e., between individual actors in the dyad. This special issue contributes to addressing this deficiency: the next two papers, which include one article by Ellegaard (this issue) and one article by Hald (this issue), examine attractiveness on a micro-level.

Ellegaard's conceptual contribution highlights the cyclical character of attractiveness and thereby suggests that attractiveness forms in an evolutionary way. In contrast, Hald's case study stresses the importance of major events for shaping perceptions of attractiveness and satisfaction. Future research may provide the interesting opportunity to observe which of these different models better explains the underlying phenomenon. In particular, the practical implications of these models could differ. If attractiveness and satisfaction are predominantly influenced by events, then these events should be planned and managed. However, if an evolutionary approach prevails, then organizations may have to devote greater attention both to the day-to-day behavior of the employees who interact with suppliers and to operational excellence.

The final block of papers consists of research that is based on quantitative empirical work. In contrast to previously published studies, these papers do not ask for a purchaser's perceptions but instead survey the suppliers. La Rocca, Caruana and Snehota (this issue) investigate various facets of customer attractiveness among suppliers and develop and test a scale that comprises four factors called "development potential", "intimacy", "relational fit" and "profitability". Given the scarcity of empirical research in this field, these constructs could facilitate further investigations of this topic by providing appropriate measurement instruments. The next paper, by Baxter (this issue), also relies in part on new measurements, such as its preferred customer construct. To the best of our knowledge, this study by Baxter is the first large-scale test that jointly addresses attractiveness, satisfaction and preferred customer treatment. Interestingly, in Baxter's study, supplier satisfaction is not directly linked to preferred customer treatment; instead, this relationship is fully mediated by supplier commitment. Notably, Baxter further provides the first empirical evidence for the difference between commitment (which could even be an aspect of corporate culture, i.e., it could be assumed that a customer-centric firm demonstrates a higher commitment to all of its clients than a more inward-oriented organization) and preferred customer treatment (which results from a comparison between a customer of interest and diverse other customers that a vendor may have). The last paper, by Ellis, Henke and Kull (this issue), is the only study in this issue to provide empirical evidence of the benefits that preferred customer status may generate. In particular, these researchers reveal preferred customer status as an antecedent to technology access. Surprisingly, they did not find support for the hypothesis that a high share of sales with a supplier automatically makes the buyer a preferred customer. This finding encourages small-and medium-sized firms to strive to achieve preferred customer status and simultaneously alerts large corporations that their size alone may not be sufficient to ensure privileged treatment.

By providing these insights, this special issue has inventoried the state-of-the-art in the field through reviews, contributed to the structure of investigations into this field through conceptual contributions and advanced our understanding regarding the empirical content of the phenomenon of preferred customership. However, this exploration may be regarded as only the beginning of a journey. Therefore, the last section of this paper will discuss certain avenues for the further development of this field.

Conclusions and research directions: a phenomenon requiring purposeful management

What do we know about "the other side"? First and foremost, it is evident that attractiveness issues are real and measurable phenomena in business-to-business relationships rather than merely theoretical constructs. Baxter (this issue) and Ellis et al. (this issue) provide evidence for the assumption that suppliers differentiate between their customers and that this choice affects the performance level that a customer can expect from its supplier. Thus, further enquiries expanding our understanding of attractiveness are likely to be rewarding.

A finding that clearly emerges is that three different stages can be distinguished in the cycle of preferred customership: customer attractiveness, supplier satisfaction and preferred customership itself. Each of these stages has its own logical considerations and empirical manifestations, but these stages are clearly sequentially linked to each other. It is thus apparent that three streams of literature that had previously been largely uncoupled are actually supportive of each other and can be linked.

One striking finding from the research in this issue with respect to the findings and gaps in the current knowledge of supplier satisfaction is that selling firms may benefit from better tools to categorize their (potential) customers; to date, only a small number of portfolio models for this type of categorization have been proposed (Mortensen, this issue). In supplier satisfaction research, thus, a clear target would be to proceed with the development of theoretically and empirically validated instruments for customer evaluation [START_REF] Le Dain | Proposition of a tool to evaluate customer's performance in collaborative product development with suppliers[END_REF]. In addition, a new set of management practices to influence supplier satisfaction must be developed. The analysis of both failures to achieve supplier satisfaction, which could proceed in accordance with the typology of mismatches that Hald (this issue) proposes, and the dissolution of relationships [START_REF] Helm | Suppliers' Willingness to End Unprofitable Customer Relationships: An Exploratory Investigation in the German Mechanical Engineering Sector[END_REF][START_REF] Yang | Dissolution intention in channel relationships: An examination of contributing factors[END_REF] could also prove to be a rewarding path for future research.

The preferred customer logic requires at least an indirect shift from an analytical perspective of dyads to the assessment of networks of customers that compete in supply markets for the prime attention of the same set of suppliers. The acquisition of a better understanding of the dynamics in supply markets is a challenging task; however, this investigation could prove useful, supporting the recent growth of interest in the field of competitive dynamics.

Competitive dynamics is a field of strategic management research that analyzes the actions that specific firms take during competitions with specific rivals [START_REF] Chen | Competitive Dynamics: Themes, Trends, and a Prospective Research Platform[END_REF].

Attractiveness research can be conducted at three levels of analysis: the micro (individual actors), meso (firm and portfolio level) and macro level (entire networks and countries) [START_REF] Dopfer | Micro-meso-macro[END_REF][START_REF] Steinle | Ganzheitliches Management: Eine mehrdimensionale Sichtweise integrierter Unternehmungsführung[END_REF]. One enduring question is to determine the explanatory power of each level of analysis. For instance, one issue that could be addressed is whether individuals in their micro-dyads establish the policies of firms towards each other or whether preferred customers are defined by corporate planning and discussions of portfolio issues.

We would like to emphasize that to date, the macro level has been relatively unexamined in attractiveness studies. However, cross-cultural studies of supplier evaluation suggest that better evaluations are received by domestic suppliers than by international suppliers [START_REF] Callahan | Comparisons of the Competitive Position of Canadian, Mexican, and U.S. Suppliers[END_REF][START_REF] Homburg | Customer satisfaction in transnational buyer-supplier relationships[END_REF][START_REF] Schiele | The role of domestic and international external cluster linkages explored on the example of buyer-supplier relations in learning regions: a cross-functional assessment[END_REF]). It appears reasonable to postulate that the converse relationship might also hold; in other words, firms might find it easier to become a preferred customer of their domestic suppliers because suppliers may evaluate domestic customers more favorably than international customers.

Most of the contributions that have been discussed above and in previously published research elaborate on ways for buyers to be attractive, achieve supplier satisfaction and become a preferred customer; however, these studies do not particularly focus on the purpose of this effort (Hüttinger, et al., this issue). Certain research has been performed to examine the contribution of preferred customership to accessing the technologies and innovation initiatives of suppliers (Ellis, et al., this issue;[START_REF] Schiele | Supplier innovativeness and supplier pricing: the role of preferred customer status[END_REF]. However, preferred customership is also expected to generate benefits in production and logistics.

Similarly, with respect to risk management and quality, the expectation would be that compared to regular customers, preferred customers receive higher quality supplies or quicker repairs from suppliers. We did not find conclusive studies that tested these assumptions.

Last, but not least, strategic benefits, such as the outcome of achieving preferred customer status, could overcome "purchasing's strategic irrelevance" (Ramsay, 2001a). There are nearly continual attempts to elucidate the strategic relevance of the purchasing function. However, often "important" in the sense of "big" is mistaken for "strategic" in the sense of "competitive advantage". A preferred customer from a supplier that is desirable to other buyers also achieves competitive advantages by securing maximum exclusivity with respect to access to the supplier in question. This phenomenon is particularly relevant if relational rents [START_REF] Dyer | The relational view: cooperative strategy and sources of interorganizational competitive advantage[END_REF] can only be achieved with this supplier. The further development of this reasoning could eventually reveal an avenue for demonstrating and operationalizing the strategic relevance of purchasing [START_REF] Ramsay | The resource based perspective, rents, and purchasing's contribution to sustainable competitive advantage[END_REF].

With respect to the sketch of research avenues that is presented above, one final methodological feature appears noteworthy: attractiveness research can be categorized according to the cycle stage that an investigation examines (customer attractiveness, supplier satisfaction or preferred customer status), the level of analysis that a study employs (micro, meso or macro) and the benefits that a study elucidates (e.g., innovation, production/logistics, strategic). Future research could benefit from clear positioning with respect to all of these categories; for instance, among other combinations, a supplier satisfaction study could be conducted at the meso level that targets logistics benefits.

Through this type of classification, conceptually problematic redundancies may be avoided, and the scope of enquiry may be clarified. The clear positioning of research work in accordance with particular categories prevents researchers from mixing their levels of analysis unless they seek to purposefully include the investigation of the interfaces between these levels as their research proposition.

In conclusion, it is clear that customer attractiveness, supplier satisfaction and preferred customer status are delineating an emerging field of enquiry, which has demonstrated its phenomenal existence and managerial relevance; however, this field remains in its infancy with respect to its depth of understanding, its knowledge regarding contingencies, its set of tools and the guidance that it provides for managerial actions. Given the relevance of this field, the multitude of avenues for future studies that are sketched out above may encourage further promising research investigations.

Figure 1 :

 1 Figure 1: The cycle of preferred customership

  Figure 1