Samir Adly
email: adly@unilim.fr

AND Emil Ernst
email: emil.ernst@univ.u-3mrs.fr

Michel Th Éra
email: michel.thera@unilim.fr

NORM-CLOSURE OF THE BARRIER CONE IN NORMED LINEAR SPACES

The aim of this note is to characterize the norm-closure of the barrier cone of a closed convex set in an arbitrary normed linear space by means of a new geometric object, the temperate cone.

Introduction and notation

Throughout the paper, we assume that X is a real normed linear space with continuous dual X * and we denote by • and • * the norms on X and X * , respectively. Let C be a convex subset of X, and let

B(C) = f ∈ X * : sup x∈C f, x < ∞
denote the barrier cone to C. As usual (see Rockafellar [START_REF] Rockafellar | Convex Analysis[END_REF] as a reference book for the finite-dimensional case), we use the notation C ∞ for the recession cone of the closed convex set C, that is,

C ∞ = {v ∈ X : ∀λ > 0, x 0 ∈ C, x 0 + λv ∈ C} .
Denoting by •, • the duality pairing between X * and X, we recall that the negative polar cone C • of a closed convex set C is

C • = {f ∈ X * : f, w ≤ 0 ∀w ∈ C}.
The main objective of this note is to give a direct characterization of the normclosure of the barrier cone for a closed convex set in a general normed linear space. It is well known (see for instance [START_REF] Zȃlinescu | Convex Analysis in General Vector Spaces[END_REF], Ex. 2.45) that the weak * -closure of the barrier cone of C is the polar of the recession cone of C,

weak * -cl(B(C)) = (C ∞ ) • .
When the underlying linear space X is reflexive, since the barrier cone of C is convex, its weak * -closure coincides with its norm-closure, and thus the norm-closure B(C) of B(C) is characterized in X * by the formula:

(1.1) B(C) = (C ∞ ) • .
When X is not a reflexive Banach space, the weak * -closure of B(C) may significantly be larger than its norm-closure, and thus relation (1.1) may fail. This situation occurs for instance when X = L 1 (0, 1) and

C = {f ∈ L 1 (0, 1) : 0 ≤ f (x) ≤ 1 x }. Then, obviously, C is a closed convex set and C ∞ = {0}. The sets K = {f ∈ X * = L ∞ (0, 1) : 1 ≤ f } and B(C) are disjoint; since the interior of K is non-void, it follows that B(C) = X * = (C ∞ ) • .
In order to characterize the norm-closure of the barrier cone in a general normed linear space, we introduce and study a new object that we call the temperate cone of a closed convex set. The main result, Theorem 2.1, states that the temperate cone of a closed convex set C is the norm-closure of the barrier cone of C for every closed and convex subset C of a normed linear space. This result leads to the description (Proposition 2.5) of the class of all closed and convex sets satisfying relation (1.1) in a general normed linear space.

In the sequel, the symbol B X is used to denote the closed unit ball in X, and a closed convex set is called linearly bounded if C ∞ = {0}.

The norm-closure of the barrier cone

Let C be a closed convex set in a normed linear space X. Along with the barrier cone B(C) of the set C, we define the temperate cone of C:

(2.1) T (C) = f ∈ X * : lim r→∞ inf x∈C, f,x ≥r x r = ∞ . Since inf x∈∅ x = ∞, it follows that B(C) ⊆ T (C).
The following theorem states the main result of this note.

Theorem 2.1. For every closed convex set C of a normed linear space X the temperate cone is the norm-closure of the barrier cone.

Let C be a given closed convex set. We recall that the indicator function of C is the functional ι C defined by

ι C (x) = 0 if x ∈ C, ∞ if x ∈ X \ C.
Given an extended real-valued function Ψ :

X → R ∪ {+∞}, recall that the Fenchel conjugate of Ψ is the function Ψ * : X * → R ∪ {+∞} given by Ψ * (f ) := sup x∈X { f, x -Ψ(x)}.
The barrier cone of a closed convex set C coincides with the effective domain of the Fenchel conjugate of its indicator function, i.e., the set of all the points where this Fenchel conjugate is finite. Since, obviously, the epigraph of ι C denoted by epi ι C coincides with C × [0, +∞), we have

B(epi ι C ) = B(C) × (-∞, 0] and therefore, (2.2) B(epi ι C ) ∩ X * × {-1} = B(C) × {-1}.
Obviously, the domain of Ψ * denoted by dom Ψ * is connected to the barrier cone of the epigraph of Ψ through the following equivalence:

g ∈ dom Ψ * ⇔ (g, -1) ∈ B(epi Ψ).
This yields that dom Ψ * × {-1} is the intersection of the barrier cone of epi Ψ with the hyperplane X * × {-1} of X * × R:

(2.3) dom Ψ * × {-1} = B(epi Ψ) ∩ X * × {-1} .
Finally, from relations (2.2) and (2.3) we deduce that

B(C) = dom ι * C .
Let us recall the following well-known characterization of the norm-closure of the domain of the Fenchel conjugate of an extended real-valued, proper, convex and lower semicontinuous functional. Theorem 2.2. Let Ψ : X → R ∪ {+∞} be an extended real-valued proper convex and lower semicontinuous functional. Then 0 ∈ dom (Ψ * ) if and only if the map x → (Ψ(x) + ε x ) is bounded from below for every ε > 0.

Remark 2.3. For the reflexive case, Theorem 2.2 goes back (in a slightly different form) to [START_REF] Rockafellar | Level Sets and Continuity of Conjugate Convex Functions[END_REF]. The non-reflexive setting has been considered for the first time in [START_REF] Borwein | Convergence of Lipschitz Regularizations of Convex Functions[END_REF] (the reader is invited to consult Example 25 in [START_REF] Zȃlinescu | Convex Analysis in General Vector Spaces[END_REF], where a clear, detailed and self-contained analysis is given).

From Theorem 2.2 we deduce that a given element f of X * belongs to the normclosure of B(C) if and only if the map x → ι C (x)f, x + ε x is bounded from below for every ε > 0.

Theorem 2.1 will thus be verified by proving that the above property characterizes the elements of the temperate cone of the closed convex set C.

For every f ∈ X * , let us use the notation C f for {x ∈ X : f, x ≥ x }. The proof of Theorem 2.1 relies on the following characterization of the temperate cone. Lemma 2.4. Let C be a closed convex set in a normed linear space X. A continuous linear functional f ∈ X * belongs to the temperate cone T (C) if and only if the set C ∩ C λf is bounded for every λ > 0.

Proof of Lemma 2.4. Let us first prove that for every f ∈ T (C) and λ > 0, the set C ∩ C λf is bounded. From relation (2.1) it follows that there is r > 0 such that (2.4) inf

x∈C, f,x ≥r x r ≥ (1 + λ) ∀r ≥ r. Let x ∈ C be such that f, x ≥ r. Applying relation (2.4) to r = f, x yields (2.5) x ≥ (1 + λ) f, x > λf, x ∀x ∈ C, f, x ≥ r. Let x ∈ C ∩ C λf , which means that x ∈ C and x ≤ λf, x . From relation (2.5)
it follows that f, x ≤ r. Accordingly, x ≤ λr, and so C ∩ C λf ⊆ λrB X .

In order to complete Lemma 2.4 it suffices to prove that

f ∈ T (C) provided that the set C ∩ C λf is bounded for every λ > 0. Pick M > 0. Since the set C ∩ C Mf is bounded, there is r > 0 such that (C ∩ C Mf ) ⊆ rB X . Accordingly, for every x ∈ C ∩ C Mf it follows that x ≤ r; since f, x ≤ f * x for every x from X, we deduce that f, x ≤ f * r for every x ∈ C ∩ C Mf . Thus, for every x ∈ C such that f, x > f * r we have x / ∈ C Mf ; that is, x > M f, x . Consequently, for every r > f * r and x ∈ C such that f, x ≥ r we have x r > M f, x r ≥ M. Hence, inf x∈C, f,x ≥r x r ≥ M ∀r > f * r,
and the conclusion of Lemma 2.4 follows.

Proof of Theorem 2.1. Remark that the map x → ι C (x)f, x + ε x is bounded from below if and only if

(2.6) ∃µ ∈ R such that f, x ≤ ε x + µ ε , ∀x ∈ C.
In view of Lemma 2.4, we have only to prove that relation (2.6) holds for every ε > 0 if and only if C ∩ C λf is bounded for every λ > 0.

Assume that for some f ∈ X * relation (2.6) holds for every ε > 0, and fix λ > 0.

Taking ε = 1 2λ in relation (2.6) yields ∃µ ∈ R such that f, x ≤ 1 2λ x + µ, ∀x ∈ C.
According to the definition of C λf , for every x ∈ C ∩ C λf we have

x ≤ λf, x .
From the two previous relations we deduce

x ≤ 1 2 x + λµ ∀x ∈ C ∩ C λf ,
and consequently we have

C ∩ C λf ⊆ 2λµB X . Thus, if the map x → ι C (x) -f, x + ε x is bounded from below for every ε > 0, then C ∩ C λf is bounded for every λ > 0.
Conversely, assume that C ∩ C λf is bounded for every λ > 0, and fix ε > 0. The set C ∩ C f/ε being bounded, there exists γ > 0 such that x ≤ γ for every

x ∈ C ∩ C f/ε . Let x ∈ C \ C f/ε ; accordingly, (2.7) f ε , x ≤ x .
On the other hand, for every

x ∈ C ∩ C f/ε it follows that (2.8) f ε , x ≤ f * ε x ≤ f * ε γ.
From relations (2.7) and (2.8) it follows that

f, x ≤ ε x + μ ∀x ∈ C,
where μ = γ f * . Thus, the map x → ι C (x)f, x + ε x is bounded from below for every ε > 0, and the proof of Theorem 2.1 is completed.

From Theorem 2.1 and Lemma 2.4 we obtain the following characterization of the family of all closed convex sets fulfilling condition (1.1). Proposition 2.5. For every closed convex set C of a normed linear space X, the following two facts are equivalent: i)

B(C) = (C ∞ ) • ; ii) C ∩ C f is bounded for every f ∈ (C ∞ ) • .
Remark 2.6. When C is linearly bounded, Proposition 2.5 states that B(C) = X * if and only if C ∩ C f is bounded for every f ∈ X * . Condition ii) from Proposition 2.5 defines the family of conically bounded sets, which is a subclass of the class of linearly bounded sets for which holds the property of density of the barrier cone in X * .

Acknowledgments

The authors gratefully acknowledge a referee for a careful reading of the manuscript and for useful suggestions concerning the proof of Theorem 2.1.


Robert Winter
email: robert.winter@unisg.ch

Using Empirical Foundations for Designing EIS Solutions

From a design science research perspective, enterprise information systems (EIS) are understood as artifacts intended to support organizations in achieving certain goals. Proper EIS design needs not only to be based on solid general foundations ('kernel theories') and valid construction processes, but also should incorporate domain related experience and expertise. One important aspect is to understand which design goals and context factors have lead to which variations in existing solutions in the real world. Another aspect is to understand which design variations can be empirically related to which design goals, and to derive respective design actions. Using examples from enterprise architecture management and process performance management for illustration purposes, we show that existing variations of EIS solutions can be transparently explained and that innovative EIS solutions can be systematically constructed.

Introduction

According to Hevner et al. [START_REF] Hevner | Design Science in Information Systems Research[END_REF] two scientific approaches characterize much of the research in the information systems discipline, namely behavioral science and design science. Behavioral science addresses research through the development and justification of theories that explain or predict existing phenomena in a domain. Design science addresses research through the building and evaluation of innovative artifacts that are intended to solve important, relevant design problems in the domain. Both types of research reflect the respective foundations and methodologies in order to provide guidance for researchers. The knowledge base, as defined in the information systems research framework of Hevner [START_REF] Hevner | A Three Cycle View of Design Science Research[END_REF] interfaces these approaches. It is composed of foundations and methodologies.

In the wide field of information systems, being concerned with people, task and technology [cf. e.g. [START_REF] Mason | A Program for Research on Management Information Systems[END_REF][START_REF] Keen | Information systems and organizational change[END_REF], different design science research approaches have been proposed over the years. Such approaches aim at constructing and testing various kinds of designed artifacts as solutions to certain classes of design problems in organizations. Since design proposals are often widely varying with regard to foundations, goals, and processes, Hevner [START_REF] Hevner | A Three Cycle View of Design Science Research[END_REF] introduced a general framework comprising three cycles -relevance, design and rigor cycles -, which should be present and clearly identifiable in every piece of design science research (see Fig. 1).

In the introduce in the en solving u existing d introduce derived fr cycle, wh activities

Foundational concepts

Common design artifacts produced by design science researchers in the information systems field are constructs, models, methods and instantiations [START_REF] March | Design and Natural Science Research on Information Technology[END_REF]. Hevner et al. describe these artifacts as follow: "Constructs provide the language in which problems and solutions are defined and communicated […]. Models use constructs to represent a real world situation -the design problem and its solution space […]. Methods define processes. They provide guidance on how to solve problems, that is, how to search the solution space. […] Instantiations show that constructs, models, or methods can be implemented in a working system." [START_REF] Hevner | Design Science in Information Systems Research[END_REF].

It is important to understand the artifact types of design science research in the information system field not as separate concepts, but as an interdependent system. Winter [START_REF] Winter | Design Science Research in Europe[END_REF] refers to Chmielewicz's [START_REF] Chmielewicz | Forschungskonzeptionen der Wirtschaftswissenschaften[END_REF] conceptualization of research in social sciences, which may serve as a foundation to explain such dependencies. Chmielewicz differentiates between ontological facts, theoretical statements, technological statements, and normative statements. These concepts are represented by the artifact types foundational concepts, cause-effect relations, means-ends relations and justifications (for choosing certain goals or preferring certain means to pursue a goal). Chmielewicz's concept system can therefore be easily matched to design science research artifacts.

Fig. 2. The interdependent system of concepts for design research

To illustrate the relationships between the concepts and artifacts, the pyramid metaphor can be used: Applicable ontology and meta models define constructs and constitute the foundation for formulating theories for analysis, explanation and/or prediction. Together with domain experience and expertise, valid explanatory and/or predictive theories then constitute the foundation for constructing effective technologies (e.g. reference models or methods). Since alternative means might be effective for the same ends, normative statements are needed to justify which goals to choose and which technologies to apply -Chmielewicz designates this layer "philosophy". At the top of the concept pyramid, concrete goal and technology choices lead to actual design instantiations. Fig. 2 illustrates the concept pyramid.

It is obvious that the presented concepts are fundamentally different regarding the extent they embody certain design goals and regarding their problem-solving power for specific design problems. Goal orientation (vs. neutrality) is strongly related to applicability (vs. generality): Although design artifacts of every type (except instantiations) can be defined on different levels of generality, the typical generality decreases when moving up in the concept hierarchy. In addition to utility, generality is an important quality of design science research artifacts [START_REF] Hevner | Design Science in Information Systems Research[END_REF]. Baskerville et al. [START_REF] Baskerville | Soft design science methodology[END_REF] demand a design science research artifact to "represent [.] a general solution to a class of problems."

In addition to applicability / goal orientation vs. generality / neutrality, design artifacts can be classified regarding the problem solution phase they support: While the same system of foundational concepts should be used both in the assessment and construction phases of a problem solution to ensure consistency, instantiations always relates to a specific phase. Certain theories might be used to explain assessment as well as justify design, while others are specific to one of these phases. Since the goals of assessment and construction are different, different technologies will be relevant, and different (yet coherent) justifications will be needed.

Assessment: Identifying contingencies of existing solutions

There is some, but not much, work on how to identify contingencies in design science research. For method engineering, "project size", "number of stakeholder groups" or "applied technology" have been suggested as general contingencies [e.g. [START_REF] Kornyshova | Method Chunks Selection by Multicriteria Techniques: an Extension of the Assembly-based Approach[END_REF][START_REF] Van Slooten | Characterizing IS Development Projects[END_REF]. Other authors recommend to identify and specify situations individually on a case-bycase basis [e.g . 15]. As a compromise between these positions, we recommend to identify specific contingencies for a domain, i.e. a class of similar design problems, by analyzing existing real-world solutions in that domain. This analysis is not restricted to methods; It is applicable to other problem solutions like (reference) models and constructs as well.

Based on earlier proposals by Winter [START_REF] Winter | Problem Analysis for Situational Artefact Construction in Information Systems[END_REF] and Bucher and Klesse [START_REF] Bucher | Contextual Method Engineering[END_REF], the following procedure is proposed in [START_REF] Winter | Design Solution Analysis for the Construction of Situational Design Methods[END_REF] to identify contingencies of existing problem solutions:

Step 1: Preliminary specification of the design problem class

A rough idea about the delineation of the design problem class is developed. Results of this step are definitions, a description of the system under analysis and ideas about design goals for the respective class of design problems.

After a while, EIS management practice develops a common understanding about the scope of relevant artifacts and about useful design goals for such problem classes. In the remainder of this section, enterprise architecture management (EAM) is used as an exemplary design problem class. In EAM, a considerable amount of consensus exists regarding which artifacts and relationships should be addressed by that approach. Furthermore, design goals like transparency, consistency, simplification or flexibility are established.

Step 2: Identification of contingency factor candidates

A literature analysis is conducted in order to identify contingency factor candidates for the respective class of design problems, i.e. factors which might have influence on how such design problems are solved in practice.

For EAM, such an analysis yields factors like 'EAM's main sponsor is IT or business', 'EAM's main deliverable is maps, analyses or project support', 'EAM's main goal is transparency, consistency, simplification, or flexibility', or 'EAM's role is active or passive'.

Step 3: Field study A field study is conducted in order to analyze how design solutions for this class of design problems in practice are actually related to which contingencies. Using principal component analysis on the field study data, the list of potential contingency factor candidates from step 2 is reduced and aggregated into a smaller set of relevant "design factors". Design factors are usually aggregates of several relevant contingency factors and therefore need to be semantically interpreted.

For EAM, principle component analysis on EAM practice solutions yielded eight design factors (like IT operations support, integrative role, business strategy support, or design impact) which aggregate 54 statistically relevant contingencies. E.g., the design factor 'integrative role of EAM' aggregates the contingencies 'EAM takes place in an interdisciplinary team', 'EAM team and business departments continuously exchange information (e.g. in architecture boards)' and 'EAM team and IT departments continuously exchange information (e.g. in architecture boards)'.

Step 4: Redefinition of the design problem class

Every surveyed real-world solution in the domain can be understood as a point in a multi-dimensional coordinate system where every dimension corresponds to a design factor. The design problem class now should be redefined by specifying value ranges for the design factors identified in step 3. This means that "outlier" solutions are excluded from further analysis in order to ensure a useful degree of solution homogeneity. For the EAM approaches in 94 companies, the optimal number of clusters is three [START_REF] Aier | Understanding Enterprise Architecture Management Design -An Empirical Analysis[END_REF]. This means that, for this observation, three different EAM 'approaches' with specific characteristics should be differentiated (see Fig. 4). With more and broader surveys, this kind of findings might be generalized to the respective design problem domain in general. Step 7: Specification of design situations For the level of solution description generality chosen in step 6, each cluster represents one design situation. The situations should not only be defined formally (i.e. by specifying value ranges of the respective design factors), but also should be interpreted semantically ("design problem types").

The three EAM clusters differ in particular with regard to their values for the design factors 'IT operations support', 'integrative role', 'design impact', 'enterprisewide focus' and 'IT strategy support'. These differences are used to characterize one cluster as 'balanced, active EAM', one as 'business analysis' and one as 'IT focused, passive EAM' [START_REF] Aier | Understanding Enterprise Architecture Management Design -An Empirical Analysis[END_REF]. In order to interpret the design situations, the cluster centroids have to be analyzed. These can be identified by the mean factor values within each cluster. The mean factor values for each cluster are depicted by the net diagram in fig. 4. The clusters can then be described as follows: [START_REF] Aier | Understanding Enterprise Architecture Management Design -An Empirical Analysis[END_REF] Design situation 1: Balanced, active EAM Cluster 1 (solid line in fig. 4) presents a rather balanced approach to EAM. For most factors this cluster shows the highest or at least average values. Especially the similar values for the factors 'IT operations support' and 'enterprise-wide focus' allow the conclusion that organizations within this cluster focus neither on IT support nor on management support. In contrast to the other clusters, the high support of 'IT operations management', 'IT strategy' as well as the focus on 'design impact', 'integrative role' and 'EAM governance' argue for a high degree of integration within the organization. In particular the values for 'design impact', 'integrative role' and 'EAM governance' are by far the highest between all three clusters. It can therefore be presumed that these organizations have a rather high level of maturity in their EAM approach. It should be noted that this cluster includes 53 out of 94 organizations, which lead to the supposition that this cluster represents a 'mainstream'

Design situation 2: Business analysis

The second cluster (dashed line in fig. 4) groups 22 organizations that have an apparent focus on business support in their EAM approach. The factors 'IT operations support' as well as 'IT strategy and IT governance support' are clearly assigned with comparatively low values. Comparing the mean factor values to those of cluster 1, the overall low values imply that the organizations in this cluster do not show a high degree of EAM implementation in any dimension. Two conclusions can be derived from this fact: First, the organizations could have decided to apply a minimalist EAM approach, focusing on management support without putting resources in EAM governance or an active role of EAM. Second, the introduction of EAM could only recently be initiated by management and is not very mature yet. For both cases, literature suggests that a sustainable EAM approach can only be established by realizing an effective EAM governance [START_REF] Aziz | Enterprise Architecture: A Governance Framework -Part I: Embedding Architecture into the Organization[END_REF][START_REF] Aziz | Enterprise Architecture: A Governance Framework -Part II: Making Enterprise Architecture Work within the Organization[END_REF].

Design situation 3: IT focused, passive approach

Organizations assigned to this cluster (dotted line in fig. 4) clearly emphasize the use of EAM for IT operations as well as the information supply by EAM. In contrast, values for 'management support' are by far the lowest compared to the other clusters. As the factors 'design impact' as well as 'integrative role' are not focused by this approach, it can be described as a passive approach that is most probably realized very locally within the organization. Obviously, this small cluster which includes only 19 of the 94 organizations represents a specialized, IT-centered EAM approach that primarily takes a documentation role. It can be presumed that the EAM approach was initiated by IT departments and has not been disseminated throughout the organization yet.

Examples like [START_REF] Baumöl | Strategic Agility through Situational Method Construction[END_REF][START_REF] Bucher | Taxonomy of Business Process Management Approaches: An Empirical Foundation for the Engineering of Situational Methods to Support BPM[END_REF][START_REF] Klesse | Organizational Forms of Data Warehousing: An Explorative Analysis[END_REF][START_REF] Lahrmann | Towards a Classification of Information Logistics Scenarios -An Exploratory Analysis[END_REF][START_REF] Leist | Methoden zur Unternehmensmodellierung -Vergleich, Anwendungen und Diskussionen der Integrationspotenziale[END_REF] show that, for typical design problem classes, between four and eight design factors can be identified which explain the variance of the observed design solutions sufficiently. These design factors span up a solution room where between three and six design situations can be differentiated.

Design: Relating design goals to solution variations

While identifying design situations is of utmost importance to understand the design problem class, the construction of innovative, useful solutions as the core phase of design science research has not been covered yet.

In contrast to as-is solutions that exist in the real world and can be analyzed using field studies or other methods in a descriptive way, to-be solutions need to be constructed and have a prescriptive character. It is therefore necessary to base the construction on (1) valid theories, (2) proven design products and processes, or on (3) domain experience and expertise.

• First, explanatory and/or predictive theories can provide important input for solution construction. E.g., indicators from valid success factor models of the domain at hand provide guidance which properties to-be solutions need to have. Such indicators can often be related to specific design activities. • Second, existing solutions in the domain can be evaluated, and high-performance existing solutions can be chosen as to-be (reference) solutions. This approach however requires that the design problem domain is already quite mature and highperformance solutions exist. When comparing low-performance as-is solutions with high-performance to-be solutions regarding their design factor values, 'elementary movements' can be determined. These 'movements' represent elementary design steps that need to be composed to construct a better solution -or to be more precise: to change existing design solutions in a way that promises to develop properties of a solution that has better performance. • If high-performance solutions do not exist or cannot be identified, a third way to determine to-be solutions is to use a field study to define desired solution characteristics. If an as-is solution characterization and a to-be characterization are available for all cases in the field study, solution 'paths' can be identified. These paths constitute the project types for situational artifact construction.

Empirical domain knowledge is essential regardless which approach is taken. Since "one size fits all" solutions cannot be expected to perform in all situations, theory application as well as as-is solution ranking and to-be solution surveys need to relate to the identified relevant contingencies, i.e. to be adapted to design situations. For each design situation, there is a different set of design activities (approach 1) or 'elementary movements' (approach 2) or a situation-specific to-be solution (approach 3). In the following, we illustrate approach 2 using the EAM example and approach 3 using an example from Process Performance Management (PPM).

Solution composition from elementary design actions (approach 2)

First, characterizing design factors have to be identified for every design situation. In the EAM example, only situation 'IT focused, passive EAM' is characterized by high values of the design factor 'IT operations support' and low values of the design factors 'enterprise-wide focus', 'integrative role' and 'design impact'. The situation 'balanced, active EAM', in contrast, exhibits much smaller values for 'IT operations support', but much higher values for 'enterprise-wide focus', 'integrative role' and 'design impact'. With regard to 'information supply', 'business support' and 'IT strategy and IT governance support', these two design situations are not much different, so that these factors are not useful to characterize them.

In a second step, characterizing design factors are linked to design problems. For the EAM example, the description of the clusters implies a characterization of the respective design problems:

• In situation 2 (Business analysis), EAM implementation and impact need to be addressed. Business is the main stakeholder and executor and implementation considerations are widely neglected.

• In situation 3 (IT focused, passive approach), EAM is too IT centric and has not disseminated through the entire organization yet. The characterizing design factors 'integrative role', 'enterprise-wide focus' and 'design impact' can be associated with an EAM setup where the main EAM sponsor is the CIO, the main EAM customer is the IT function, EAM is primarily performed within the IT function, and EAM is widely ignored by business units. • If EAM is not systematically addressed in the organization at all, either a balanced approach (very challenging) or an IT focused EAM or a business analysis approach can be followed.

Most EAM setups can be easily linked to major EAM challenges as often described in the literature. E.g., missing business involvement and missing business value creation of EAM correspond to the first EAM setup, while missing 'grounding'/'execution' and too much 'locality' of EAM correspond to the latter EAM setup. In a third step, elementary design actions are derived by comparing design solutions with design problems. Based on the design situation characteristics of the EAM example illustrated by Fig. 4, the following design actions can be derived:

• In situation 2 (Business analysis), 'IT operations support', 'IT strategy and IT governance support' as well as 'EAM governance' need to be strengthened. Since IT topics and EAM governance constitute widely different measures, two different design actions (designated as A and B) should be differentiated. • In situation 3 (IT focused, passive approach), 'design impact', 'integrative role' and 'enterprise-wide focus' need to be strengthened. Since design impact and IT/business alignment issues constitute widely different measures, design actions C and D should be differentiated. • If EAM is not systematically addressed yet and an IT focused approach is favoured, 'IT operations support', 'IT strategy and IT governance support', 'information supply' and 'business strategy support' need to be developed foremost. In addition to design action A, a design action E should be defined to address business strategy support and a design action F to address information supply. • If EAM is not systematically addressed yet and a business analysis approach is favoured, 'enterprise-wide focus' as well as 'information supply' and 'business strategy support' need to be developed foremost. As a consequence, the already defined design actions D, E and F are most relevant.

The final step is to define rules for combining the specified elementary design actions. The fewer characterizing design factors and the fewer design problems have been identified, the simpler the design action configuration will be -and vice versa. For the EAM example, four situated design solutions are configured from, depending on the design situation, up to four design actions out of a total number of six reusable design actions A...F:

• Situated solution I "from business analysis to balanced, active EAM" is comprised of design actions A and B • Situated solution II "from IT focused, passive to balanced, active EAM" is comprised of design actions C and D • Situated solution III "initial development of IT focused, passive EAM" is comprised of design actions A, E and F • Situated solution IV "initial development of business analysis" is comprised of design actions D, E and F

Although not advised because a big maturity leap is necessary, it is possible to combine EAM design methods III and IV to a fifth situated method "direct move to balanced, active EAM" that is composed of design actions A, D, E and F.

Survey-based solution path derivation (approach 3)

Although the above presented approach allows to systematically construct 'better' problem solutions, it (a) requires that such approaches can already be observed and (b) creates no useful solution in cases that already come close to the 'best' solution cluster.

As an alternative, to-be solutions (in the sense of information systems with certain desired properties) could be elicited by means of field studies, i.e. in the same way that is used to identify design situations. In addition to as-is properties of existing solutions, to-be properties of desired solutions are collected and undergo identical analyses.

Fig. 5.

As-is situations (left) vs. to-be situations (right) for process performance management [START_REF] Cleven | Process Performance Management -Illuminating Design Issues through a Systematic Problem Analysis[END_REF] Using PPM as an example, Fig. 5 illustrates that as-is situations differ significantly from to-be situations. One explanation could be that desired solution properties are more homogeneous than the existing variety of approaches so that cluster analysis generates situations that are less different. This would however require that companies' visions for 'ideal' solutions are very similar which is only true in very mature problem domains. In the majority of domains (including PPM) it can be expected that, if many contingencies exist, companies' PPM visions are quite different so that the variations of to-be solutions is not smaller than the variation of as-is solutions.

From the analysis of as-is and to-be situations, it is not immediately clear which project types result that need to be supported by suitable artifacts. If as-is and to-be data were obtained by the same survey, 'movements' can be analyzed because every case can be assigned to a specific as-is cluster as well as to a specific to-be cluster. Fig. 6 illustrates the aggregated 'movements' for the PPM survey. The number in the lower right corner of each of the boxes indicates the population of each cluster. The thickness of the lines is proportionate to the number of 'movements'. It becomes evident that, although there is a favorite to-be cluster ('full-scale PPM', 23 out of 42 companies), some companies also aim at alternative to-be solutions. Fig. 6. Project types derived from process performance management design situation analysis [START_REF] Cleven | Process Performance Management -Illuminating Design Issues through a Systematic Problem Analysis[END_REF] For solution construction, the most significant aggregate 'movements' can be defined as project types. For every project type, it is possible to specify design activities by matching to-be solution properties to as-is solution properties.

To this end a weighted adjacency matrix is used that is based on the items that are grouped by the to-be factors (cf. Table 1). The values represent the arithmetic means of the differences between the to-be and as-is item values across all movers per project type. This allows to identify the areas that require the most change when a company intends to reach a certain to-be PPM approach. Details of this analysis are documented in [START_REF] Cleven | Process Performance Management -Illuminating Design Issues through a Systematic Problem Analysis[END_REF]. rized by a nvergence towards another approach⎯be it "measurement-focused", "selective", or "full-scale" ⎯requires establishing a more sophisticated process orientation. In any case the measurement-biased organization must consistently design and model its processes and make them transparent beyond both functional and system borders so as to enable a comprehensive and successful PPM implementation. The last movement Cleven et al. [START_REF] Cleven | Process Performance Management -Illuminating Design Issues through a Systematic Problem Analysis[END_REF] analyzed in more detail leads from the "advanced" to the "full-scale approach". Due to the fact that the advanced approach already shows a comparatively high maturity, only minor adoptions are required. The analysis reveals that an improvement of the overall data quality becomes necessary. As the measurement level of production processes is already very high, the focus will be shifted to sales and purchasing processes. An increased use of the balanced scorecard and the plando-check-act cycle further fosters the holism of the approach.

Discussion and future research

We presented a generally applicable approach to systematically analyze the mutability of information system solutions and differentiate design situations for a domain. For relating design goals to solution variations, we presented two alternative approaches. While the first approach requires an evaluation of the as-is clusters and then helps to transform inferior solutions into superior ones by specifying respective design actions, the second approach is based on a separate set of as-is and to-be situation specifications which provide the foundation to define project types and then derive appropriate design activities. While the latter alternative provides a sufficient variation of to-be solutions for every domain, it requires surveyed organizations to specify their respective solution vision in great detail -which is not always possible in particular when a domain is immature. While many solution engineering approaches claim to incorporate situational factors, they do nearly never detail what these situational factors exactly are and how they can be incorporated into solution design and solution component configuration rules. This is the contribution of the empirical approach we presented here. It must however be conceded that every empirical foundation of solution design is only as general as the empirical base supports. Within a specific domain like EAM or PPM, we can reliably specify design factors, design situations, design actions and solution procedures. The less specific the domain is, the less useful the results, and the less effective their application will be. Several broad categories of research opportunities exist:

• First, the proposal needs to be further validated. Although a number of research projects have applied the proposed procedures and many case studies provide evidence that as-is situations, to-be situations, project types and respective design actions are meaningful and realistic in the respective domain, these claims might be invalidated by future studies. • Both the EAM example and the PPM example comprised several simplifications like the elimination of tradeoffs between design goals and design activities. E.g., the derivation of design actions was straightforward for EAM if implementation impact and business involvement can be achieved equally. If however tradeoffs have to be observed, solution design becomes much more complex. • An interesting feature of many design solution analyses that yield a larger number of design factors is that the first factor is often representing many and quite diverse problem aspects that are sometimes not easy to interpret qualitatively. With regard to design solution analysis and solution construction, we interpret this "technically" overloaded design factor as a problem independent aggregation of "generalized" properties and the respective solution component as a basic set of domain-independent problem solution activities like e.g. general project/transformation management. This aspect of our approach does certainly need additional research attention.

• In addition, our approach does not explicitly cover yet the adaptation of situated solutions to specific design problems in an organisation. On the one hand, we consider this extension not too problematic because there is a plethora of adaptation knowledge on reference models which promises to be transferrable to this approach. On the other hand, adaptation efforts might depend on problem properties and influence the 'optimal' level of solution generality that up to now is determined using 'technical' homogeneity/heterogeneity metrics in cluster analysis only.

• Another and probably the most important extension would be to include not only adaptation effort, but also other 'economic' properties like the number of problem instantiations of a type or the attractiveness of design problems in terms of economic gains into the identification procedure of design factors and in particular design situations. This is probably the most interesting -and challenging -avenue for further research.

Fig. 1

 1 Fig. 1. De The de from the to the rig investigat often ove reason m artifacts, also diffic This p for desig systems ( domain k solutions introduce analyzes and relev we prese respectiv Examples managem solutions systemati further re

Step 5 :

 5 Solution similarity analysis Now ultrametric distances can be computed that represent the similarity (or dissimilarity) of the relevant solutions. Metrics are usually based on Euclidian distance. The observations and their distances can be visualized by a dendrogram-like tree graph. The (dis)similarity of two design solutions corresponds to the generality level of represent their link Figure different axis. Cas and 104. compared

Fig. 3

 3 Fig. 3. Vis

Fig. 4 .

 4 Fig. 4. Problem class decomposition into design situations[START_REF] Aier | Understanding Enterprise Architecture Management Design -An Empirical Analysis[END_REF]

Table 1 .

 1 A

	Erro


ENGINEERINGA WOMAN:MARKETING OPPORTUNITIES AND CHALLENGES IN INDIA

Keywords: Gender, Women, Engineering Education, Selection, Marketing Services. I

Purpose and Motivation: Engineeringplays a key rolein supportingthe growth anddevelopmentof a country'seconomy as wellas in improving thequality of life forcitizens.Most of developed countries witnessed economic growth with the contribution of women in engineering field. In developing countries like India women remainedunder-utilized resource.

Women in engineering are probably the single best investment that can be made in the developing world.There is clearly room for improvementnot only in recruitingwomen into engineering, but also in retaining and promotingthose women who wish and do enter the profession. This study was designed to investigate a perception anddetermination of undergraduate womentowards accessing Engineering Education.The study has highlighted women's perceptions and experienceson accessing engineering education through institute's Marketing Mix strategies which enables women to take up strategic positions to enjoy success in engineering education and career. Findings of this study revealed that women students in engineering are better satisfied and act of referring services/program to others is higher than men students in terms of numbers for a particular set of marketing mix applied to gender.

Research Methodology:A qualitative research survey through a structured questionnaire for the students who arestudying or have recently completed their engineering educationfrom reputed engineering institutes affiliated to the North MaharashtraUniversity, Jalgaon was conducted.

Findings:The study discloseswomen's approach to engineering education in terms of marketing mix; program, price, place, promotion, people, physical evidence and process. Women tended to rate most the marketing criteria as having a higher level of importance than men.

Women needed morecommunalsupport while making decision making of selection of engineering education.

Research Limitations:The survey is delimited to the engineering education belonging to North Maharashtra University,Jalgaon and Khandesh region, a rural part of India.

Practical Implications:Findings of the studywill be useful for the institutes and direct and indirect service providers of engineering education in developing a communication program and should be utilized and integrated into all aspects of the marketing program to attract women in engineering.

INTRODUCTION

By educating a woman,we educate the whole family and directly or indirectly, we educate nation. Given that a woman has the responsibility of the whole family on herself, several studies proved that an educated woman is better capable of taking care of the health, nutrition and education of her children and family.Gender refers to the socially constructed roles, behaviors, activities and attributes that a given society considers appropriate for men and women [START_REF]Gender and Reproductive Rights: Working Definitions[END_REF].In virtually all but a handful of countries, there are severe constraints on women's entry into higher levels of education and their work in senior professional and managerial jobs [START_REF] Elson | Progress of the World's Women 2000[END_REF].The status of women in India has been subject to many great changes over the past few millennia [START_REF] Hindu | Rajya Sabha passes Women's Reservation Bill[END_REF]. With a decline in their status from the ancient to medieval times, to the promotion of equal rights by many reformers, the history of women in India has been eventful [START_REF] Jayapalan | Indian society and social institutions[END_REF] [START_REF]Women in History[END_REF].Women in India now participate fully in areas such as education, sports, politics, media, art and culture, service sectors, science and technology, etc. [START_REF]Women in History[END_REF]. Families of engineering students provide exceptional levels of support to their children. For women in engineering, this support is crucial from the pre-college levelonward. In particular, female engineers' parents tend to raise their daughters with fewergender stereotypes and place greater weight on education and learning [START_REF]Assessing Women in Engineering (AWE) Project[END_REF].Education of girls is vital not only on grounds of socialjustice but also because it accelerates social transformation and human resource development of the nation. Studies haveindicated that there is a strong correlation between female education and several developmentalindicators such as increased economic productivity, improvement in health, increased political participation and effective investments in the nextgeneration.There is also evidence that lower gender disparity in educational attainment for a developing country correlates with lower overall income disparity within society [START_REF] Hanushek | Schooling, Gender Equity, and Economic Outcomes[END_REF].Negative cultural and societalattitudes, different standards-roles for boys and girls, competing demands on the girls time,economic reasons like; lack of resources, distance from college, lack of facilities forgirls, lack of female teachers, lack of security both in and outside the college,curriculum notrelevant and flexible, gender stereotyping in curriculum,gender unfriendly classroomenvironment, early marriage and child bearing, absence of women role models, fear ofdeterioration of social structure are the most frequently quoted stumbling blocks to femaleeducation [START_REF] Singh | Higher Education for Women in India--Choices and Challenges[END_REF]. Which leads to a very limited presence of females in higher education and the high-wage labor market.Although women are given high respect in Indian society [START_REF] Budhwar | Doing business in India[END_REF], women working outside the home have been looked down upon. Reference [START_REF] Kulkarni | Women and professional competencya survey report[END_REF], found that traditional and cultural inhibitions acquired by women from childhood, nurtured by parents, and reinforced by their socialization was the key hurdle that inhibited their urge to be in an executive or leadership position. This is further supplemented by a lack of self-direction, independence and self-motivation to enter the male-dominated world. However, those who have reached higher echelons of organizations are seen as determined to stay, confront the barriers and secure the requisite familial support and personal drive [START_REF] Nath | Gently shattering the glass ceiling: experiences of Indian women managers[END_REF].Results of senior secondary school examinations regularly show the outstanding performance of girl students with many of them topping the merit list [START_REF] Budhwar | Women in Management in the New Economic Environment: The Case of India[END_REF], which is a good mark for the graduation of women. As per the article published in Times of India, girls' candidates carried a tradition of surpassed boys in the Higher Secondary Certificate (HSC) examination over the last few years [START_REF] Ganjapure | Women on top in HSC Results[END_REF].One notable success came in 2013, when the first two girls ever scored in the top 10 ranks of the entrance exam to the Indian Institutes of Technology (IITs) [START_REF]In a first, girls among IIT entrance test toppers[END_REF]. Unfortunately, due to a combination of factors including limited exposure and opportunities andlack of encouragement from role models and mentors, many qualified and talented young womendo not consider a nontraditional career choice such as engineering.

II. WOMENINENGINEERING

Engineering plays a key role in ensuring the growth and development of a country'seconomy as well as in improving the quality of life for citizens within the country. There is animportant link between a country's engineering capacity and its economic development [START_REF]Engineering and economic growth: a global view[END_REF].Engineering is viewed in the public sphere as masculine, competitive, objective, impersonal qualities that are at odds with our images of what women are. Because engineering is a traditionally male-dominated field, women may be less confident about their abilities, even when performing equally [START_REF] Jones | The impact of engineering identification and stereotypes on undergraduate women's achievement and persistence in engineering[END_REF].

Countries like; Myanmar (65%), Tunisia (42%) and Honduras (41%) lead the world in gender parityamong engineers, according to latest data on female engineering graduates from theUnited Nations Educational, Scientific and Cultural Organization (UNESCO) [START_REF]Engineering and economic growth: a global view[END_REF], followed by Denmark(35%), India (30%) and Sweden (29%). Women only make up 22% of engineering graduates in the UK. with Switzerland 14% and Japan12%.As per 2011 Censes of India, sex ratio was 943 females per 1000 male; female 48% of total population [17].In India, reservation for women cuts across all classes and communities and is a horizontal and not vertical reservation and counts 33.33% [START_REF] Dna | Gujarat increases women's reservation to 33% in government jobs[END_REF] in the state of Maharashtra and Gujrat. [START_REF]All India Council for technical Education[END_REF].Women have contributed to the diverse fields of engineering in modern and historical times. Women are often under-represented in the fields of engineering, both in academia and in the profession of engineering. A number of organizations and programs have been created to understand and overcome this tradition of gender disparity [START_REF]Women in Engineering[END_REF]. In India, women's presence is known to range between a high of 5.8 per cent [START_REF] Kulkarni | Women and professional competencya survey report[END_REF] to a low of roughly 3 per cent [START_REF] Singh | Women managers: perception vs. performance analysis[END_REF] of all administrative positions. They can be seen mainly in HR, IT and servicing activities.

As

III. MARKETING MIX AND WOMEN'S ACCESS TO ENGINEERING EDUCATION

Boys and girls differ in how they are involved in education and choice processes, illustrating changing forms of young people's gendered identities and subjectivity [START_REF] David | Gender Issues in Parental Involvement in Student Choices of Higher Education[END_REF]. There has also been research focusing on gender differences in decision-making processes [START_REF] Crow | Gender and values: What is the impact on decision making?[END_REF]. Reference [START_REF] Tashakkori | Gender, ethnicity, and the structure of self-esteem: An attitude theory approach[END_REF] found evidence to suggest that the attributes important in determining self-esteem for women and men are different. Due to biological factors, women and men show different behaviors in terms of mood, personality or natural inclination for some skills [START_REF] Saucier | Lateral and sex differences in manual gesture during conversation[END_REF]. In the decision-making process, women have a tendency to rely on emotion that can be presented by harmony, affiliation, and betterment of self and others [START_REF] Meyers-Levy | Influence of sex roles on judgment[END_REF]. Marketing mix is a set of controllable marketing tools that an Institutes uses to produce the responses it wants from its various target markets [START_REF] Ivy | A new higher education marketing mix: the 7Ps for MBA marketing[END_REF].Reference [START_REF] Ivy | A new higher education marketing mix: the 7Ps for MBA marketing[END_REF] & [START_REF] Gajić | Importance of marketing mix in higher education institutions[END_REF] had discussed 7P approach in order to satisfy the needs of the service provider'scustomers: product (program), price, place, promotion, people, physical facilities and processesare discussed below.

Program (Product):

When it comes to educational offers, Kotler firstlyrefers to curricula and services [START_REF] Gajić | Importance of marketing mix in higher education institutions[END_REF].Technical educational program like engineering, pharmacy etc. are the products/services of the technical educational institutes.The program and curriculum must be appropriately developed and adapted to meet the needsof the students [START_REF] Ivy | A new higher education marketing mix: the 7Ps for MBA marketing[END_REF].Brooks proposes that a career must be perceived as both attainable and attractive before a woman will be motivated to choose it [START_REF] Brooks | Encouraging women's motivations for nontraditional career and lifestyle options: A model for assessment and intervention[END_REF]. In adapting Vroom's (1964) [START_REF] Vroom | Work and motivation[END_REF] expectancy model of motivation to women's career choices, Brooks first describes three components of expectancy: career self-efficacy, perceived structure of opportunity and perceived social support. It is not only the course content which discourages women from doing engineering but also the selection criteria which is used to screen prospective students [START_REF] Beder | Towards a More Representative Engineering Education[END_REF].

Men prefer practical, physical or managerial occupations while women prefer supportive, clerical, and socially oriented occupations [START_REF] Chatterjee | Sex role attitudes of self and those inferred of peers, performance, and career opportunities as reported by women in nontraditional vs. traditional training programs[END_REF]. Reference [START_REF] Morgan | Focus Groups as Qualitative Research[END_REF] hypothesized that women at the college age perceive nontraditional fields to be incompatible with having a family. Indeed, women in nontraditional programs (like engineering) expect more difficulties than women in traditional programs [START_REF] Chatterjee | Sex role attitudes of self and those inferred of peers, performance, and career opportunities as reported by women in nontraditional vs. traditional training programs[END_REF]. Reference [START_REF] Goodman | A comprehensive evaluation of women in engineering programs[END_REF] found that there is a lack of Pre-College Experience and Knowledge in Engineering due to the absence of engineering awareness from the K-12 curriculum. A lack of interest was a factor for women not choosing careers in engineering or science [START_REF] Dick | Factors and influences on high school students' career choices[END_REF]. For women, having highly educated parents, a strong desire for control, prestige and influence and a desire for positive interaction with others are primary influencers on nontraditional occupational choice [START_REF] Ware | Undergraduate women: Who chooses a science major[END_REF]. Another construct commonly used to explain women's discomfort in engineering has been -math anxiety,‖ a profound fear of mathematics and the belief that only white men succeed in math [START_REF] Tobias | Ideology of recruitment of women in science and math[END_REF]. Findings of [START_REF] Sax | Origins of the Gender Gap: Pre-College and College Influences on Differences Between Men and Women[END_REF] suggest that women may be more likely than men to view education as a means to influence social change and improve race relations. Reference [START_REF] Sax | Origins of the Gender Gap: Pre-College and College Influences on Differences Between Men and Women[END_REF] also indicated that women tend to be more satisfied than men with their college courses and instruction. In a finding of reference [START_REF] Mansfield | Gender Differences in Students' and Parents' Evaluative Criteria When Selecting a College[END_REF], female students appear to be slightly more interested than male students in the overall reputation of the school and its degrees and what both can do for them after graduation. Studies of engineering students have also shown that women rate their abilities lower than men, despite higher GPAs [START_REF] Jackson | Engineering persistence: past, present, and future factors and gender differences[END_REF]. Some researchers have found that the lack of self confidence among female engineering students stems partly from their lack of technological experience and expertise, qualities deemed especially important in the engineering -culture of technical knowhow‖ [START_REF] Mcilwee | Women in engineering: Gender, power, and workplace culture[END_REF].

Price:

The price element of the services marketing mix is dominated by what is beingcharged for the degree or tuition fees that are required [START_REF] Ivy | A new higher education marketing mix: the 7Ps for MBA marketing[END_REF]. Tuition fee, fee concessions, scholarships, educational loan, cost of education, fee installments offered by the service providers (institutes) for the service delivered to the service receiver (students) includes in this category of service mix.

Because of social and economic reasons, parents may be unwilling to spend on education as well as the dowries of their daughters [START_REF] Singh | Higher Education for Women in India--Choices and Challenges[END_REF]. Parents of female students are less likely to save for college. This may be one reason why, once in school, freshman women were more likely than male freshman to report major concern about financing their education and were more likely to indicate low tuition was an important factor for them when selecting a college [START_REF] Jacobs | Gender and the Stratification of Colleges[END_REF].

Place:

Place is a measured in terms of accessibility, acceptability and convenience. This refers location of institutes & distance of institute from the targeted future students native place.The locationcan refer to the place where the institute is. Then, it can referto the characteristics of the area in which the instituteis located. Location can also have a relativemeaning, i.e. it can be viewed in relation to wherecurrent and future students and high school studentslive [START_REF] Gajić | Importance of marketing mix in higher education institutions[END_REF].

In the rural areas, the girl child is made to perform household and agricultural chores.

This is one of the many factors limiting girls' education. Physical safety of the girls, especially when they have to travel a long distance to school is the other reasons that impede girls' education [START_REF] Singh | Higher Education for Women in India--Choices and Challenges[END_REF]. Two studies, reference [START_REF] Shank | Gender Effects on the University Selection Process[END_REF] and reference [START_REF] Hayes | Promoting to Women: It's Not What You Think[END_REF] have measured differences in this college selection criterion between college men and women, the results, college women believed location was more important as a selection criterion than college men.

Promotion:

Promotion encompasses all the tools that institute can use to provide the marketwith information on its offerings: advertising, publicity, public relations and salespromotional efforts [START_REF] Ivy | A new higher education marketing mix: the 7Ps for MBA marketing[END_REF].Promotion is a process of communication between an institute and service user with an aim tocreate a positive attitude on products and services,leading to their favoring in the process of purchaseon the market [START_REF] Gajić | Importance of marketing mix in higher education institutions[END_REF].As per the reference [START_REF] Kotler | Strategic Marketing for Educational Institutions[END_REF], most educational institutions use public relations, marketing publications and to a lesser extent, advertising. The communication is made through presentations, print & visual advertisements, digital marketing, displays, internet & social media [START_REF] Kotler | Strategic Marketing for Educational Institutions[END_REF].

Women engage in a more complex information search process than men [START_REF] Richard | Selective versus Comprehensive Processors: Gender Differences in Web Consumer Behavior[END_REF]. Many studies have suggested that as a result of socialization pressures, the feminine personality emerges in terms of communion with others [START_REF] Chodorow | Family structure and feminine personality[END_REF] and as a result, women see relationships as more important in their lives than men do [START_REF] Hodgson | Gender-integrated management teams[END_REF]. Women appear to be more strongly motivated by affiliation needs [START_REF] Hoffman | Early childhood experiences and women's achievement motives[END_REF] and tend to express a higher degree of interest in person-oriented professions [START_REF] Weller | Birth order, sex, and occupational interest[END_REF]. Studies have also shown that women who enter engineering hold its extrinsic (i.e., social) value in higher regard than men do [START_REF] Frehill | Education and occupational sex segregation: The decision to major in engineering[END_REF].Social value is sought when individuals seek to shape the response of others [START_REF] Holbrook | Consumption experience, customer value, and subjective personal introspection: An illustrative photographic essay[END_REF]. For instance, when it comes to advertising on the web, males were found to have a more positive attitude than females [START_REF] Seock | The Influence of College Students' Shopping Orientations and Gender Differences on Online Information Searches and Purchase Behaviours[END_REF]. In online purchases, word of mouth is a more influential tool for women than for men in terms of reducing perceived risk and increasing willingness [START_REF] Garbarino | Gender differences in the perceived risk of buying online and the effects of receiving a site recommendation[END_REF].

People:

People is a key instrument in educational process. Because most services are provided by the people and experienced by the people by their motivation and behavioral characteristics, they make a huge difference in customer satisfaction [START_REF] Pike &kuh | First and second-generation college students: A comparison of their engagement and intellectual development[END_REF]. As per reference [58], Previous Teachers, Alumni, Current-Students, Parents, Siblings, Relatives, Management People and Prospective students themselves affect the decision of selection in technical education.

Career -modeling and mentoring‖ is essential for girls and women of all ages and races andat every developmental stage of the life span [58]. Girls in engineering perceive that they receive more parental support than their peers in any other discipline [START_REF] Ciccocioppo | Transitional Patterns of Adolescent Females in Non-traditional Career Paths[END_REF]. Studies have found that girls are advantaged in both non-academic areas such as parental, peer and teacher expectations and non-cognitive skills such as organization, self-discipline, attentiveness, dependability and seeking help from others [START_REF] Conger | Women students dominating in many countries[END_REF]. Social cues can also easily discredit women and dissuade them from pursuing a degree in a field where they are underrepresented [START_REF] Zeldin | Against the odds: Self-efficacy beliefs of women in mathematical, scientific, and technological careers[END_REF]. Women view their professors as advisors and role models [START_REF] Seymour | Talking about leaving: Factors contributing to high attrition rates among science, mathematics, and engineering undergraduate majors: Final report to the Alfred P. Sloan Foundation on the ethnographic inquiry at seven institutions[END_REF] and look to them to help them understand engineering. Some have found that institutional proportionality (a large percentage of women in faculty and administrative positions) may have a greater effect on women's persistence in a major than peer group proportionality (a large percentage of female peers) [63]. An awareness of others' feelings is a trait exhibited more strongly by women than men [START_REF] Rosenkrantz | Sexrole stereotypes and self-concepts in college students[END_REF]. In case of girls, parents generally take the decision regarding the academic stream to be pursued [START_REF] Singh | Higher Education for Women in India--Choices and Challenges[END_REF]. As per focus group discussions made by [START_REF] Sax | Origins of the Gender Gap: Pre-College and College Influences on Differences Between Men and Women[END_REF], The lack of female faculty members was discouraging to many of the young women. However, they wanted to find supportive, strong faculty advisors, regardless of gender. Parents were highly influential in students' decisions about the major, with others who influenced students were likely to be engineers or high school math or science teachers [START_REF] Sax | Origins of the Gender Gap: Pre-College and College Influences on Differences Between Men and Women[END_REF].Women are more likely than men to feel that their faculty provide them with personal and professional support, thus accounting for women's greater satisfaction with faculty, curriculum, and the overall sense of community on campus [START_REF] Sax | Origins of the Gender Gap: Pre-College and College Influences on Differences Between Men and Women[END_REF].

Process & Physical Evidence:

Educational services are personal andcharacterized by intensive, intellectual, emotionaland/or physical participation of students in a serviceprocess. Services are often realized in a numberof steps, which, basically, constitute the very serviceprocess. There are numerous other processes that needto be implemented concurrently (with the finance system, accommodation, time tablingand the library) to ensure the highest level of student satisfaction [START_REF] Ivy | A new higher education marketing mix: the 7Ps for MBA marketing[END_REF]. Reference [65] discussed several processes and physical evidence in the form of services to be delivered which Women tend to be influenced by service quality more strongly than men [65]. At college entry, women place more value than men on the educational benefits of college, a differential that predicts women's greater interest in social activism and to their stronger commitment to promoting racial understanding [START_REF] Sax | Origins of the Gender Gap: Pre-College and College Influences on Differences Between Men and Women[END_REF]. In another notable study, there is evidence to suggest that women display somewhat higher levels of computer anxiety [START_REF] Bozionelos | Psychology of computer use: XXXIX. Prevalence of computer anxiety in British managers and professionals[END_REF]. Women from social categories are the most affected by the stratification of disciplines, programs and institutions [START_REF] Singh | Higher Education for Women in India--Choices and Challenges[END_REF]. Women lag men in extracurricular engineering experiences [START_REF] Goodman | A comprehensive evaluation of women in engineering programs[END_REF]. However, boys more often engage in play activity that tends to exercise their spatial-visual skills, whereas girls tend to exercise their verbal skills [START_REF] Sadker | The issue of gender in elementary and secondary education[END_REF].As per the focus group discussions conducted by reference [START_REF] Goodman | A comprehensive evaluation of women in engineering programs[END_REF], a heavy workload, a restrictive curriculum, and the practice of grading on a curve were discouraging to many of the women. Who participated in social enrichment activities-were less likely to leave engineering [START_REF] Goodman | A comprehensive evaluation of women in engineering programs[END_REF]. The survey also found that Campus Life/ Climate and Policies are directly affiliated with the encouragement and satisfaction of women students. Participation in support activities is vital to women undergraduates, who need to feel that they are part of a larger caring community in engineering. Community allows students to build networks and to feel that their presence in engineering is important to others and valued. Networking can counteract the isolation that women feel-providing them with information, support, and the knowledge that they're not alone in the challenges they face [START_REF] Goodman | A comprehensive evaluation of women in engineering programs[END_REF]. The survey also found that different kinds of activities influence women's persistence differentially-those that promote social enrichment are most closely linked to women's persistence in engineering. Time is an important variable to use the Internet in which men use the Internet more frequently and for long hours while women are in the categories of moderate user [START_REF] Thanuskodi | Gender Differences in Internet Usage among College Students: A Comparative Study[END_REF].Females perceived Internet as a tool of maintaining social values. There is a slight variation in the usage pattern athome between men and women due to the influence of gender role [START_REF] Thanuskodi | Gender Differences in Internet Usage among College Students: A Comparative Study[END_REF]. (2) Women's perception on place:

Conceptual Framework:

To find out women's perception on place, gender-wise mean of responses on weightage given by the gender on distance of engineering institute from their native place while selecting an engineering institute were obtained and are presented in figure 3.

(Figure 3: Perception on place)

Women students (mean=2.8) have perceived more importance for a place/location of institute while selecting an engineering institute than men students (mean=2.62).

(3) Women's perception on price:

(Figure 4: Perception on price)

To find out women's perception on price, gender-wise mean of responses on weightage given by the gender on cost of engineering education while selecting an engineering institute were obtained and are presented in figure 3.Women students (mean=2.66) have perceived more importance for cost of education while selecting an engineering institute than men students (mean=2.51).

(4) Women's perception on people: (5) Women's perception on promotion:

(Figure 6: Perception on promotion) Like the ‗people' marketing mix, women students have collected information from all sources of institute's promotional activities. They perceived all such activities are important in making their decision of selecting engineering institute. Their selection is mostly supported by Social

Networking Site (mean=3.05), Institute Website (mean=3.15), Leaflet / Brochures (mean=2.89)

and Publicity (mean=2.85).

(6) Women's perception and experience on process and physical evidence:

(Figure 7: Perception on process and physical evidence) To find out women's perception and experience on process and physical evidence i.e services offered by the institute in which they are enrolled in or studied, gender-wise mean of responses on infrastructural facilities, operating services, supporting services and extension services of the institutes were obtained and their perceptions and experiences are presented in figure 7.

Women students have weighted more, on the services of institute experienced by them than men students. The research study revealed that for the same input of marketing mix activities of an engineering institute, 70.4% of women students are completely satisfied while 47.92% men students are completely satisfied. Also, dis-satisfaction level for the same marketing activities is higher (7.47+1.95=9.42%) for male students than women students (5.3+0.5=5.8%).89.41% of female will refer others for the admission while 63.71% of male students have shown their desire of referring their institute to others for admission.

VI. EMPIRICAL FINDINGS AND DISCUSSIONS

Challenges and Opportunities of marketing:This research study finds that females tended to rate the majority of the criteria ashaving a higher level of importance than did males while accessing marketing mix strategies of engineering institutes. Practitioners shouldbe aware that males and females look for differing levels of detail.

While accessing engineering marketing mix; program, place, price, promotion and people, women have rated high importance which indicates broader, intense and integrated marketing approach is needed to attract women. On the other hand, for the same strategies provided to gender, women perceived and experienced better services provided by institutes than men students for the services; physical evidence and process.

In terms of satisfaction, women are completely satisfied (70.4%) on their decision of selection of engineering institute than male students (47.92%) which is greater by46.9% in terms of numbers, for the same marketing approaches. This shows, if one male student is satisfied, 1.47 women students will be satisfied for the same marketing approach. Similarly, 89.41% women students and 63.71% male students will refer others for the admission to their respective engineering institute, which is greater by 40.34% in terms of numbers. If one male student act as a referral then, 1.40 women student will refer others for admissionon the same marketing services of institute.

VII. THE ROAD MAP TO WOMEN'S INCLUSIVITY TO ENGINEERING

Understanding the facts that women do have a more diverse set of responsibilities and often need to wear multiple hats should not compromise their chances of success or progress in any of the worlds in which they operate, the transformation process for gender inclusivity requires mapping the journey. An ideal state in a process of inclusion is one where minorities are totally empowered. In this case, it means that women are empowered to make choices in all spheres of life and that the same opportunities available to anyone else (especially men) are available to them. This is different from saying they are equal, for it is time to move away from the original claim of the equality movement and towards one that recognizes differences and tailors responses relevant to those differences. The success of this roadmap is dependent on increased levels of awareness, acceptance and partnership from both sexes, the government and the society. Therefore, at many levels and in many ways, both men and women need to recalibrate their roles and expectations for this to happen.

VIII. CONCLUSION

Equity does not just mean an equal number of women andmen; it means equal chances of success and career development; averagewomen will succeed as much as average men. The Indian governments initiatives like National Program for Education of Girls at Elementary Level (NPEGEL), RashtriyaMahilakosh (RMK), Kasturba Gandhi BalikaVidyalaya (KGBV), Working Women Hostels, National Mission for Empowerment of Women (NMEW), SarvaShikshaAbhiyanshall be extended and oriented further more towards engineering education for the dream come true of Digital India and Smart Cities with more encouragement of women in engineering. The strategic marketing aim must be to ‗normalize' engineering as a career choice for women, so that people inside and outside of engineering no longer presume that ‗the engineer' will be men.Marketing efforts to recruit more women into engineering must avoid appealing to gender which associate men and masculinity with ‗things technical' and women with ‗things social'. In sum, we must broaden the image and vision of engineering work from technical to techno-social if we are to attract and keep talented women in engineering.

Engineering has room for diverse ‗types' of people because it incorporates a wide variety of jobs and roles. Women engineering education is a multi-dimensional phenomenon;marketing efforts to attract women in engineering shall not be limited to the institutes/service providers, but it shall be responsibility of the government, NGOs and community as a whole, for India to be Super

Power.If engineering education is a signifier of development, it should incorporate a gender perspective to it. Perhaps then, we will see more women enjoying success and fully participating in engineering education.

Figure 1 :( 1 )(Figure 2 :

 112 Figure 1: Women's access on marketing mix of engineering education (Own creation through

[

62 (Figure 5 :

 625 Perception on people) Women students have taken support from all possible people resources while selecting an engineering institute. Their decision of selection is mostly supported by Parents (mean=3.36), Management People (mean=3.55) and Women themselves (mean=3.6).

  As per the report 2015-of All India Survey for Higher Education, out of 42.28 lakh students enrolled in Engineering and Technology,the share of female participation in this sector was relatively low; 11.84 lakh, 28% only[19]. As per the statistics available on the website of All India Council for Technical

Education (AICTE dashboard), female enrollment in Engineering and Technology undergraduate program during 2012-13, 2013-15, 2014-15 and 2015-16 was 33.83%, 27.77%, 27.71% and 28.28% respectively, which shows decline interest of women in engineering

Table 1 :

 1 They believed that Infrastructure and Technology (mean=3.72), Faculty and Gender-wise satisfaction on the decision of selection)

	Teaching Methodology (mean=3.6), Campus Life and Discipline (mean=3.6), Soft and Technical
	Shill service (mean=3.54), Library and Computational Facilities (mean=3.5), Placement
	Activities (mean=3.4), Alumni Interaction Program (mean=3.34), Accreditation, recognition and
	Affiliation (mean=3.31) and Amenities and Recreation (mean=3.32) are the better facilities and
	services of institutes offered to them. On the other hand, Institutes are lagging in services like
	Sports and Cultural activities (mean=2.94)and Research Activities (mean=2.94).
	(7) Women's satisfaction on the decision of selection of engineering institute and act of
	referral to others for admission:
	Gender-wise responses collected from the sample of 550 students on their satisfaction of
	decision of selection of engineering institute and their act of referring others for the engineering
	admission in an institute where they graduated or doing engineering are presented in Table 1 & 2
	respectively.
	Gender Completely Satisfied Some-what Satisfied Some-whatDis-satisfied Completely Dis-satisfied
	Female	133 (70.4%)	45 (23.8%)	10 (5.3%)	1 (0.5%)
	Male	173 (47.92%)	154 (42.66%)	27 (7.47%)	7 (1.95%)
	(Gender	Will prefer for admission	Can't say	Will not prefer for admission
	Female	169 (89.41%)	15 (7.94%)	5 (2.65%)
	Male	230 (63.71%)	116 (32.14%)	15 (4.15%)
	(

Table 2 :

 2 Gender-wise responses on the act of referring others for admission)

  Below is the proposal of what this will look like:

	Government	Government	Government
		 Back-up 
	Phase 1	Phase 2	Phase 3
	Pre-student Life	Student Life	Post-student Life
	(School Education)	(Engineering Education)	(On Job)
	Marketing Mix	Marketing Mix	Marketing Mix
		(Program, Price, Place,
	(Program, Place, People,	People, Process & Physical	(Process, People, Place,
	Promotion)	Evidence)	Promotion)
	Knowledge, Awareness	Gendered infrastructure,	Social connectivity,
	And creating importance	amenities and services	Memberships
	Involving Role Models	Retention and building confidence	Flexible work schedule or Time concession
	Career Counselling	Engaging women staff with women students	Safe and secured transportation and residence nearby work location.
		Financial support in terms of
	Family and social support	fee concession and	Awards and Rewards
		scholarships
	Proposals/Offers	Safe and secured residential facility	Adequate Reservation
	Equal treatments	Social activities	Grievance Management and lawful policies
	Active Participation	Special coaching classes and training	Ensure gender mix in top management
	Self-actualization	Adequate Reservation	Cross cultural exposure
		Grievance Management and
		lawful policies
	Family, Schools, Society,	Institutions, Society,	Industry, Society,