A measure of perceived performance to assess resource allocation


Performance measurement is a key issue when a company is designing new strategies to improve resource allocation. This paper offers a new methodology inspired by classic importance–performance analysis (IPA) that provides a global index of importance versus performance for firms. This index compares two rankings of the same set of features regarding importance and performance, taking into account underperforming features. The marginal contribution of each feature to the proposed global index defines a set of iso-curves that represents an improvement in the IPA diagram. The defined index, together with the new version of the diagram, will enable the assessment of a firm’s overall performance and, therefore, enhance decision making in the allocation of resources. The proposed methodology has been applied to a Taiwanese multi-format retailer and managerial perceptions of performance and importance are compared to assess the firm’s overall performance.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. Abalo J, Varela J, Manzano V (2007) Importance values for importance-performance analysis: a formula for spreading out values derived from preference rankings. J Bus Res 60(2):115–121

    Article  Google Scholar 

  2. Agell N, Sánchez M, Prats F, Roselló L (2012) Ranking multi-attribute alternatives on the basis of linguistic labels in group decisions. Inf Sci 209:49–60

    MathSciNet  Article  Google Scholar 

  3. Ainin S, Hisham NH (2008) Applying importance–performance analysis to information systems: an exploratory case study. J Inf Inf Technol Organ 3(2):95–103

    Google Scholar 

  4. Bacon DR (2003) A comparison of approaches to importance–performance analysis. Int J Mark Res 45(1):55–72

    MathSciNet  Google Scholar 

  5. Braz RGF, Scavarda LF, Martins RA (2011) Reviewing and improving performance measurement systems: an action research. Int J Prod Econ 133(2):751–760

    Article  Google Scholar 

  6. Burns AC (1986) Generating marketing strategy priorities based on relative competitive position. J Consum Mark 3(4):49–56

    Article  Google Scholar 

  7. Butler J, Morrice DJ, Mullarkey PW (2001) A multiple attribute utility theory approach to ranking and selection. Manag Sci 47(6):800–816

    MATH  Article  Google Scholar 

  8. Chen Y-C (2002) An application of fuzzy set theory to the external performance evaluation of distribution centers in logistics. Soft Comput 6(1):64–70

    MATH  Article  Google Scholar 

  9. Chiclana F, Herrera-Viedma E, Herrera F, Alonso S (2007) Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. Eur J Oper Res 182(1):383–399

    MATH  Article  Google Scholar 

  10. Chini TC (2004) Effective knowledge transfer in multinational corporations. Palgrave Macmillan, Basingstoke

  11. Danaher PJ, Mattsson J (1994) Customer satisfaction during the service delivery process. Eur J Mark 28(5):5–16

    Article  Google Scholar 

  12. de Andrés R, García-Lapresta JL, Martínez L (2010) A multi-granular linguistic model for management decision-making in performance appraisal. Soft Comput 14(1):21–34

    Article  Google Scholar 

  13. de Soto AR (2011) A hierarchical model of a linguistic variable. Inf Sci 181(20):4394–4408

    Article  Google Scholar 

  14. Deng W (2007) Using a revised importance–performance analysis approach: the case of taiwanese hot springs tourism. Tour Manag 28(5):1274–1284

    Article  Google Scholar 

  15. Dolinsky AL (1991) Considering the competition in strategy development: an extension of importance–performance analysis. J Health Care Mark 11(1):31–36

    Google Scholar 

  16. Ennew CT, Reed GV, Binks MR (1993) Importance-performance analysis and the measurement of service quality. Eur J Mark 27(2):59–70

    Article  Google Scholar 

  17. Eskildsen JK, Kristensen K (2006) Enhancing importance–performance analysis. Int J Product Perform Manag 55(1):40–60

    Article  Google Scholar 

  18. Fornell C, Johnson MD, Anderson EW, Cha J, Bryant BE (1996) The American customer satisfaction index: nature, purpose, and findings. J Mark 60(4):7–18

    Article  Google Scholar 

  19. Gherardi S (2009) Organizational knowledge: the texture of workplace learning. Wiley, New York

    Google Scholar 

  20. Globerson S (1985) Issues in developing a performance criteria system for an organization. Int J Prod Res 23(4):639–646

    Article  Google Scholar 

  21. Glover WJ, Farris JA, Van Aken EM, Doolen TL (2011) Critical success factors for the sustainability of kaizen event human resource outcomes: an empirical study. Int J Prod Econ 132(2):197–213

    Article  Google Scholar 

  22. Gunasekaran A, Patel C, McGaughey RE (2004) A framework for supply chain performance measurement. Int J Prod Econ 87(3):333–347

    Article  Google Scholar 

  23. Hansen E, Bush RJ (1999) Understanding customer quality requirements: model and application. Ind Mark Manag 28(2):119–130

    Article  Google Scholar 

  24. Herrera F, Herrera-Viedma E (1997) Aggregation operators for linguistic weighted information. IEEE Trans Syst Man Cybern Part A Syst Hum 27(5):646–656

    Article  Google Scholar 

  25. Herrera F, Herrera-Viedma E, Martínez L (2008) A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans Fuzzy Syst 16(2):354–370

    Article  Google Scholar 

  26. Herrera-Viedma E, Pasi G, Lopez-Herrera AG, Porcel C (2006) Evaluating the information quality of web sites: a methodology based on fuzzy computing with words. J Am Soc Inf Sci Technol 57(4):538–549

    Article  Google Scholar 

  27. Hochbaum DS, Levin A (2006) Methodologies and algorithms for group-rankings decision. Manag Sci 52(9):1394–1408

    Article  Google Scholar 

  28. Kale S, Karaman EA (2011) Evaluating the knowledge management practices of construction firms by using importance–comparative performance analysis maps. J Constr Eng Manag 137(12):1142–1152

    Article  Google Scholar 

  29. Kendall MG (1948) Rank correlation method, 3rd edn. Griffin, London

  30. Keyt JC, Yavas U, Riecken G (1994) Importance–performance analysis: a case study in restaurant positioning. Int J Retail Distrib Manag 22(5):35–40

    Article  Google Scholar 

  31. Kim B-Y, Oh H (2001) An extended application of importance–performance analysis. J Hosp Leis Mark 9(3–4):107–125

    Article  Google Scholar 

  32. Lapata M (2006) Automatic evaluation of information ordering: Kendall’s tau. Comput Linguist 32(4):471–484

    MATH  Article  Google Scholar 

  33. Liu H-C, Mai Y-T, Jheng Y-D, Liang W-L, Chen S-M, Lee S-J (2011) A novel discrimination index of importance–performance analysis model. In: International conference on machine learning and cybernetics (ICMLC’11), vol 3. IEEE, pp 938–942

  34. Martilla JA, James JC (1977) Importance–performance analysis. J Mark 41(1):77–79

    Article  Google Scholar 

  35. Motta G, Zanga E, D’agnone P (2006) Process performances and process stakeholders: a case study in the health care. WSEAS Trans Bus Econ 3(3):208–212

    Google Scholar 

  36. Neely A, Gregory M, Platts K (2005) Performance measurement system design: a literature review and research agenda. Int J Oper Prod Manag 25(12):1228–1263

    Article  Google Scholar 

  37. Nonaka I, Teece DJ (2001) Managing industrial knowledge: creation, transfer and utilization. Sage, USA

  38. ONeill MA, Palmer A (2004) Importance–performance analysis: a useful tool for directing continuous quality improvement in higher education. Qual Assur Educ 12(1):39–52

    Article  Google Scholar 

  39. Ortinau DJ, Bush AJ, Bush RP, Twible JL (1989) The use of importance–performance analysis for improving the quality of marketing education: interpreting faculty-course evaluations. J Mark Educ 11(2):78–86

    Article  Google Scholar 

  40. Park Y-J, Heo P-S, Rim M-H, Park D-S (2008) Customer satisfaction index measurement and importance–performance analysis for improvement of the mobile rfid services in korea. In: Portland international conference on management of engineering and technology (PICMET’08). IEEE, pp 2657–2665

  41. Sharma MK, Bhagwat R, Dangayach GS (2005) Practice of performance measurement: experience from Indian SMEs. Int J Glob Small Bus 1(2):183–213

    Article  Google Scholar 

  42. Taticchi P, Tonelli F, Cagnazzo L (2010) Performance measurement and management: a literature review and a research agenda. Meas Bus Excell 14(1):4–18

    Article  Google Scholar 

  43. Teece DJ (2000) Managing intellectual capital: organizational, strategic, and policy dimensions: organizational, strategic, and policy dimensions. Oxford University Press, Oxford

    Google Scholar 

  44. Travé-Massuyès L, Dague P (2003) Modèles et raisonnements qualitatifs. Lavoisier

  45. Wittink DR, Bayer LR (1994) The measurement imperative. Mark Res 6(4):14–23

    Google Scholar 

  46. Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans Syst Man Cybern 18(1):183–190

    MathSciNet  MATH  Article  Google Scholar 

  47. Yager RR (2008) Prioritized aggregation operators. Int J Approx Reason 48(1):263–274

    MathSciNet  MATH  Article  Google Scholar 

  48. Yager RR, Filev DP (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern Part B Cybern 29(2):141–150

    Article  Google Scholar 

Download references


This work was partially supported by the SENSORIAL Research Project (TIN2010-20966-C02-01, 02), funded by the Spanish Ministry of Science and Information Technology.

Author information



Corresponding author

Correspondence to Núria Agell.

Additional information

Communicated by V. Loia.


Appendix A: The qualitative absolute order-of-magnitude model

Qualitative reasoning techniques, specifically order-of-magnitude models, are considered an appropriate mathematical framework to represent expert opinions or preferences through a hierarchical model with linguistic labels (Andrés et al. 2010; Soto 2011; Herrera et al. 2008).

The one-dimensional absolute order-of-magnitude qualitative model (Agell et al. 2012; Travé-Massuyès and Dague 2003) works with a finite number of qualitative labels corresponding to an ordinal scale of measurement. The number of labels chosen to describe a real problem is not fixed, but depends on the characteristics of each represented variable.

Let us consider an ordered finite set of basic labels \(S_m^*=\{B_1,\ldots ,B_m\}\), which is totally ordered as a chain: \(B_1<\cdots < B_m\), each basic label corresponding to a linguistic term, for instance, “very bad” \(<\) “bad” \(<\) “acceptable” \(<\) “good” \(<\) “very good”. The complete universe of description for the order-of-magnitude space OM(\(m\)), with granularity \(m\), is the set \({\mathbb {S}}_m={\mathbb {S}}^*_m \cup \{[B_i,B_j] \;| B_i,B_j \in S^*_m, i<j\},\) where the labels \([B_i,B_j]\) with \(i < j\) are defined \([B_i,B_j]=\{B_i,B_{i+1},\ldots ,B_j\}\) and named non-basic labels (see Fig. 9).

Fig. 9

The complete universe of description \({\mathbb {S}}_m\)

The order considered in the set of basic labels \(S_m^*\) induces a partial order \(\le \) in \({\mathbb {S}}_m\) defined as:

$$\begin{aligned} \le [B_r,B_s]\Longleftrightarrow \left( B_i\le B_r\;\text {and}\; B_j\le B_s\right) , \end{aligned}$$

considering the convention \([B_i,B_i]=B_i\).

This relation is trivially an order relation in \({\mathbb {S}}_m\), but a partial order, since there are pairs of non-comparable labels. Moreover, as Fig. 9 shows, there is another partial order relation in \({\mathbb {S}}_m\) “to be more precise than”; given two qualitative labels \(X_1\) and \( X_2\) in \({\mathbb {S}}_m\), we say that \(X_1\) is more precise than \(X_2\) if \(X_1\varsubsetneq X_2\). The least precise label (most abstract description) is \(?=[B_1,B_m]\) and basic labels are the most precise labels.

Appendix B: A ranking method using qualitative linguistic descriptions

In the proposed ranking method, each feature is characterized by the judgments of \(k\) evaluators, and each evaluator makes his/her judgements by means of qualitative labels belonging to an order-of-magnitude space \({\mathbb {S}}_{m_h}\) with granularity \(m_h\) for \(h=1,\ldots ,k\). The evaluations are then synthesized by means of the distance to a reference \(k\)-dimensional vector of labels. This reference \(k\)-dimensional label is given by the supreme of the sets of evaluations of each feature. The distances between evaluations and their supreme give the ranking of features directly. In this way, the process considered for ranking features assessed by \(k\) expert evaluators can be split in the following four steps:

  1. 1.

    Representing features as \(k\)-dimensional vectors of labels.

  2. 2.

    Defining a distance \(d\) between \(k\)-dimensional vectors of labels.

  3. 3.

    Building a reference \(k\)-dimensional vector of labels \(\mathbf X ^\mathrm{sup}\).

  4. 4.

    Obtaining the ranking of the features from the values \(d(\mathbf X , \mathbf X ^{\mathrm{sup}} )\).

The subsections below describe each of the above steps.

B.1. Feature representation as \(k\)-dimensional vectors of labels

Features are represented by a \(k\)-dimensional vectors of labels belonging to the set \({\mathbb {X}}\), which is defined as:

$$\begin{aligned} {\mathbb {X}}= & {} {\mathbb {S}}_{m_1}\times \cdots \times {\mathbb {S}}_{m_k} =\left\{ \mathbf X =(X_1,\ldots ,X_k) {\mid } X_i\in {\mathbb {S}}_{m_h} \; \right. \nonumber \\&\left. \forall h=1,\ldots , k\right\} . \end{aligned}$$

For every component, monotonicity is assumed, i.e., \(X_{h}\le X'_{h}\) indicates that the evaluation made by the evaluator \(h\) corresponding to the feature \(X'\) is better or equal to the one corresponding to \(X\). The order relation defined in each \({\mathbb {S}}_{m_h}\) is extended to the Cartesian product \({\mathbb {X}} \):

$$\begin{aligned} \mathbf X= & {} (X_1,\ldots ,X_k)\le \mathbf X '=(X'_1,\ldots ,X'_k) \Longleftrightarrow X_h\le X_h'\, \nonumber \\&\forall h=1,\ldots ,k. \end{aligned}$$

This order relation in \({\mathbb {X}} \) is partial, since there are pairs of non-comparable \(k\)-dimensional vectors of labels. And \(\mathbf X < \mathbf X '\), that is to say, \(\mathbf X \le \mathbf X '\) and \(\mathbf X \ne \mathbf X '\), means that feature \(\mathbf X \) is preferred to feature \(\mathbf X '\) by all the evaluators.

B.2. A distance between \(k\)-dimensional vectors of labels

A method for computing distances between \(k\)-dimensional vectors of labels is presented in Agell et al. (2012) via a codification of the labels in each \({\mathbb {S}}_{m_h}\) given by a location function. The location function codifies each element \(X_h =[B_i,B_j]\) in \({\mathbb {S}}_{m_h}\) by a pair of integers \((l_1(X_h), l_2(X_h))\), where \(l_1(X_h)\) is the opposite of the number of basic elements in \({\mathbb {S}}_{m_h}\) that are “between” \(B_1\) and \(B_i\), that is, \(l_1(X_h) = -(i-1)\), and \(l_2(X_h)\) is the number of basic elements in \({\mathbb {S}}_{m_h}\) that are “between” \(B_j\) and \(B_{m_h}\), i.e., \(l_2(X_h) = m_h-j\).

The extension of the location function to the set \({\mathbb {X}}\) of \(k\)-dimensional vectors of labels is defined in the following way:

$$\begin{aligned} L(\mathbf X )= & {} L(X_1,\ldots ,X_k)\nonumber \\= & {} (l_1(X_1), l_2(X_1), \ldots ,l_1(X_k), l_2(X_k)). \end{aligned}$$

A distance \(d\) between labels \(\mathbf X , \mathbf X '\) in \({\mathbb {X}}\) is then defined via a weighted Euclidian distance in \({\mathbb {R}}^{2k}\) between their codifications:

$$\begin{aligned}&\!\! d(\mathbf X ,\mathbf X ') \nonumber \\&= \sqrt{\sum ^k_{h=1}w_h[((l_1(X_h)-l_1(X'_h))^2+(l_2(X_h)-l_2(X'_h))^2]}.\nonumber \\ \end{aligned}$$

where \(w_i\) are considered to be the weights assigned to the \(k\) evaluators and \(\sum ^k_{h=1}w_h=1\). This function inherits all the properties of the weighted Euclidian distance in \({\mathbb {R}}^{2k}\).

B.3. Building a reference \(k\)-dimensional vector of labels

The reference \(k\)-dimensional vector of labels considered in this ranking method is the supreme with respect to the order relation \(\le \) of the set of feature representations.

Let \(\{\mathbf{X }^1,\ldots ,\mathbf{X }^n\}\subset {\mathbb {X}}\) be the set of \(n\) features representations to be ranked, then the supreme of the set \(\mathbf X ^\mathrm{sup}\), i.e., the minimum label in \({\mathbb {X}}\) which satisfies \(\mathbf{X }^r \le \mathbf X ^\mathrm{sup}, r = 1, \ldots , n,\) is computed as follows:

Given \(\mathbf X ^r=(X_1^r,\ldots ,X_k^r)\), with \(X_h^r=[B_{i_h}^r,B_{j_h}^r]\) for all \(h=1,\ldots ,k\), and for all \(r=1,\ldots ,n\), then,

$$\begin{aligned} \mathbf X ^\mathrm{sup}=\sup \{\mathbf{X }^1,\ldots ,\mathbf{X }^n\}=(\tilde{X}_1,\ldots ,\tilde{X}_k), \end{aligned}$$


$$\begin{aligned} \tilde{X}_h= [\max \{B_{i_h}^1,\ldots ,B_{i_h}^n\}, \max \{B_{j_h}^1,\ldots ,B_{j_h}^n\}]. \end{aligned}$$

B.4. Obtaining the features ranking from the values \(d(\mathbf X , \mathbf X _{\mathrm{sup}} )\)

Let \(d\) be the distance defined in \({\mathbb {X}}\) in Formula (5) and \(\mathbf X ^\mathrm{sup}\) the reference label defined in Formula (6). Then, the following binary relation in \({\mathbb {X}}\):

$$\begin{aligned} \mathbf X \ll \mathbf X ' \Longleftrightarrow d(\mathbf X ',\mathbf X ^\mathrm{sup}) \le d(\mathbf X ,\mathbf X ^\mathrm{sup}) \end{aligned}$$

is a pre-order, i.e., it is reflexive and transitive. This pre-order relation induces an equivalence relation \(\equiv \) in \({\mathbb {X}}\) by means of:

$$\begin{aligned} \mathbf X\equiv & {} \mathbf X ' \Longleftrightarrow [\mathbf X \ll \mathbf X ' \;,\; \mathbf X '\ll \mathbf X ] \nonumber \\\Longleftrightarrow & {} d(\mathbf X ',\mathbf X ^\mathrm{sup}) =d(\mathbf X ,\mathbf X ^\mathrm{sup}). \end{aligned}$$

In the quotient set \({\mathbb {X}}/\!\!\equiv \), the following relation between equivalence classes is:

$$\begin{aligned} \text {class}\,(\mathbf X )&\unlhd \text {class}\,(\mathbf X ') \nonumber \\&\Longleftrightarrow \mathbf X \ll \mathbf X ' \Longleftrightarrow d(\mathbf X ',\mathbf X ^\mathrm{sup}) \le d(\mathbf X ,\mathbf X ^\mathrm{sup})\nonumber \\ \end{aligned}$$

is an order relation. It is trivially a total order.

In this way, a set of features \(\mathbf X ^1,\ldots ,\mathbf X ^n\) can be ordered as a chain with respect to their proximity to the supreme: \(\text {class}\,(\mathbf X ^{i_1})\unlhd \cdots \unlhd \,\text {class}\, (\mathbf X ^{i_n})\).

If each \(\text {class}\, (\mathbf X ^{i_j}), j=1,\ldots n\), contains only a feature representation \(\mathbf X ^{i_j}\), the process is finished and we obtain the ranking   \(\mathbf X ^{i_1}\unlhd \cdots \unlhd \,\mathbf X ^{i_n}\). If there is some \(\text {class}\, (\mathbf X ^{i_j})\) with more than one feature representation, then the same ranking process is applied to the set of the feature representations belonging to \(\text {class}\, (\mathbf X ^{i_j})\), and continued until an iteration of the process gives the same ranking as the previous iteration. The final ranking \(\mathbf X ^{m_1}\unlhd \cdots \unlhd \,\mathbf X ^{m_n}\) is then obtained.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sayeras, J.M., Agell, N., Rovira, X. et al. A measure of perceived performance to assess resource allocation. Soft Comput 20, 3201–3214 (2016). https://doi.org/10.1007/s00500-015-1696-3

Download citation


  • Performance evaluation
  • Reasoning under uncertainty
  • Fuzzy operator
  • Similarity index