Automated two-stage continuous decision support model using exploratory factor analysis-MACBETH-SMART: an application of contractor selection in public sector construction

Abstract

Public sector client marks contractor selection decisions on technical and financial bid considerations where efficient use of public resources is never unheeded. A plethora of past studies has developed two-stage models; however, continuous assessment of contractors is disregarded, and the models compromise on the discontinuous progression that partially recognizes the prominence of the technical stage in the selection process. This research aims to develop a novel automated two-stage continuous decision model for contractors’ assessment and selection where each contractor would be assessed on corresponding performance assessment grading levels. Exploratory Factor Analysis (EFA) assimilated with MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) employed to assess the model criteria, whereas, criteria assessment stage is developed using a novel hybrid combination of SMART (Simple Multi-Attribute Rating Technique), which in turn entails the EFA-MACBETH-SMART triplet-combination. The model encompasses extensive model criteria; thus, 76 model criteria were investigated and evaluated. Final selection of a contractor is proposed on technical bid/financial bid ratio mechanisms based on performance levels such as R_T/F: 80/20; 75/25; 70/30; 65/35; and 60/40. A hypothetical case is encompassed to portray the operational mechanism of the automated assessment system. Findings from the model unveil that continuous progression of technical assessment stage in final selection make justice with the highly qualified contractors, and the likelihood of project success increases. The developed model further conclude that technically highest bidders may be awarded the contract if additionally offers a feasible bid. The developed model preserves the concept of efficient use of public resources alongside supporting the technically highest bidders.

Appendices

Appendix A:Preliminaries in MACBETH

Let S is a set of finite elements and ∀ i, j, k,l (∈ S) is a subset of another number Q [∀ Q ∈ {0, 1, 2, 3, 4, 5, 6}]. To rank the criteria, the set S must satisfy Condition 1 of the linear programming from classical MACBETH.

Condition 1: [For ranking the criteria].

Say, i, j, k, l represent the four different judgments on a seven-point semantic scale of differences such that i is more attractive than j, and k is more attractive than l, then the first condition can be followed as;

$$\forall {\text{ i}},{\text{ j}},{\text{ k}},{\text{ l }} \in {\text{S}}:{ }[{\text{i is more attractive than j }} \Leftrightarrow {\text{ i }} > {\text{j }}\Lambda {\text{ k is more attractive than l }} \Leftrightarrow {\text{ k }} > {\text{ l}}]{ }$$

(6)

e attractiveness can be found through semantic scale. Condition 1 in classical MACBETH satisfies through direct rating or swing weight method where the fundamental intention is to rank the criteria in decreasing order. This represents the ordinal information (ranking the criteria) from the DMs. However, the process of MACBETH is based on the assumption of converting the ordinal information into cardinal information (based on differences of attractiveness). This conversion can be satisfied by following Condition 2 of linear programming of MACBETH.

Condition 2 (i): [Relation as measure of attractiveness between two elements].

From Condition 1 we have the information about the order of criteria and say ∀ (i, j) ⇔ (k, l) ∈ Q (here Q denotes the measure of difference of attractiveness), then;

$$\forall {\text{ i}},{\text{ j}},{\text{ k}},{\text{ l }} \in {\text{S}}:{ }[{\text{iQj }} \Leftrightarrow {\text{ u}}\left( {\text{i}} \right){ } > {\text{ u}}\left( {\text{j}} \right){ }\Lambda {\text{ kQl }} \Leftrightarrow {\text{ u}}\left( {\text{k}} \right){ } > {\text{ u}}\left( {\text{l}} \right)]$$

(7)

Condition 2 (ii): [quantifying the level of attractiveness]

$$\forall {\text{ i}},{\text{ j}},{\text{ k}},{\text{ l }} \in {\text{S}}:{ }\left( {{\text{i}},{\text{ j}}} \right){ }\Lambda { }\left( {{\text{k}},{\text{l}}} \right){ } \in {\text{Q}}:{ }\left[ {{\text{u}}\left( {\text{i}} \right) - {\text{u}}\left( {\text{j}} \right)} \right]/\left[ {{\text{u}}\left( {\text{k}} \right) - {\text{u}}\left( {\text{l}} \right)} \right]$$

(8)

Further,

$$i <^{{Q_{i} }} j$$

(9)

$$k <^{{Q_{i} }} l$$

(10)

Eq. A4 and A5 describe the relation between elements such as i and j, and k and l respectively on the scale of Q such that j is Q times greater than i, and l is Q times greater than k. At the scale Q, if i is strongly attractive than j and similarly, k is extremely attractive than l; equation A4 and equation A5 turns to equation A6 and A7 respectively.

$$u\left( i \right) - u\left( j \right) = 5 \cap$$

(11)

$$u\left( k \right) - u\left( l \right) = 6 \cap$$

(12)

∀, ∩ must meet the necessary condition say u(i), u(j), u(k), u(l) ∈ [0,100].

Applying the Condition 1 and Condition 2 and solving the equation A6 and A7, the following additive value model would generate as mentioned in equation A8 and A9.

$$U\left( S \right) = \mathop \sum \limits_{m = 1}^{n} \left( {w_{m} } \right)\left( {u_{m} } \right)$$

(13)

$$\mathop \sum \limits_{m}^{n} w_{m} = 1 > 0$$

(14)

Appendix B:Preliminaries in SMART

SMART likewise MACBETH operates on the elementary principle of additive value model. The utility values in SMART can be calculated by multiplying the criteria weightage with their expected utility values. Hence the earliest step is to develop objective weightages. The weightage (w_α) can be calculated by the normalization process using Eq. B1. The normalization process produces the final criteria weightage, later on, the criteria value (performance values) (V_ak) can be computed.

$$V_{ak} = \mathop \sum \limits_{\alpha = i}^{\beta } \left( {w_{\alpha } } \right)*\left( {V_{k} } \right)$$

(15)

The utility value of each criterion can be calculated using Eq. B2, the value is normalized on a scale of 0–1.

$$V_{k} = \frac{\Delta \alpha \beta - \Delta min}{{\Delta max - \Delta min}}$$

(16)

where; w_α is the relative weightage of each criteria/sub-criteria (from 1 to 100). V_k is the utility value of each criteria/sub-criteria [0 to 1 scale; 1 = highest, 0 = lowest]. ∆min is the minimum scale value. ∆max is the highest scale value.