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294 M. Mahdiloo et al.Maxs.t.n∑j = 1∑ s + ∑ sr∈OU+ U+ Drrr∈ODU + U Uλ y + s = y , r∈O,j rj r roUnD + D D∑ λjyrj + sr = yr ,,o I∈OD(5)j = 1n∑j = 1λ = 1, j = 1, ..., n,jλ j ≥ 0,j = 1, ..., n+ Us ≥0, I∈U,r+ Ds ≥0, r∈D,rwhere ë is the intensity vector, determining the ‘best practice’ for the DMU o . Subscript‘o’ refers to the DMU under evaluation. The variable s + Drexpresses shortages indesirable outputs and s + Urcorresponds to excesses in undesirable outputs. In thepresence of undesirable outputs and lack of inputs, DMU o is the additive efficient, if andonly ifD∑ s + ∑ s = 0.r∈OU+ U+rrr∈OD4 Case studyIn this section, we present a case study at SAIPA (Societe Annonyme Iranienne deProduction Automobile), Iran’s second-largest car maker, to demonstrate the applicabilityof the proposed framework and exhibit the efficacy of the procedures and algorithms.Saipa was established in 1966 to assemble Citroëns under license for the Iranian market.Over the past four decades, SAIPA has implemented a joint venture with CITROENand RENAULT of France, NISSAN of Japan and KIA of Korea. A 2008 data set is usedin this study. Suppliers of engine cylinder heads are evaluated based on seven criteriapresented in Table 1.Table 2 presents the original data set for 36 suppliers. To meet the strictly positivityrequirement of the data set, zero values are eliminated by adding a unity. The translationinvariance property of the developed model guarantees that the efficiency scores of thesuppliers using the original and translated data are the same. Table 3 presents thetranslated data set for the 36 suppliers under evaluation.
A novel DEA model for solving supplier selection problems 295Table 1The suppliers’ evaluation criteriaCriteriaDescriptionDy Standardisation certificate:1• suppliers with no standardisation certificates (receiving a score of 0)• suppliers with ‘in progress’ standardisation certificates (receiving a scoreof 16)• suppliers with standardisation certificates (receiving a score of 40)Dy Process and the product audit: the process and product audit score with a 70–30%2split for process and product audit, respectivelyDy Price gap: the ratio of the target price to the price proposed by the supplier3Dy Order fulfilment: the ratio of the delivered items by suppliers to the ordered items4Dy On time delivery: the percentage of the delivered parts that have met the5predetermined delivery scheduleDy Oversupply: the ratio of the delivered parts in out-of- the program orders to the6number of parts which are ordered out-of- the program 1Uy1Defective parts: the number of defective Parts Per Million (PPM) detected in thequality control department1 Since some of the variables of our empirical illustration are ratio variables (see,comments and considerations should be added in relation to the developedmodel. Hollingsworth and Smith (2003) argue that it is often necessary to useratios rather than absolute numbers as inputs and outputs in DEA. This may benecessary in order to reflect accurately the underlying production function, orbecause of the nature of the data available. They prove that in the presence ofratio variables, use of the standard CCR model with the CRS assumption istechnically incorrect, and should be rejected in favour of the BCC model.They argue that this advantage of DEA is due to its VRS assumption.Therefore, while our proposed model is a VRS model, it does not suffer fromthe problem discussed in Hollingsworth and Smith (2003).Table 2The original data set for the 36 suppliersSuppliersDDDDDDUy1y2y3y4y5y6y11 40 51.6 80 47 49.29 20.4 02 40 51.6 71.43 47 45.58 22.08 03 40 51.6 67.3 47 53 0 04 40 51.6 67.38 47 53 24 305 40 51.6 67.38 47 53 24 306 40 36 80 47 53 3.12 307 40 36 80 47 53 3.12 308 0 18 80 46 48.23 24 13.89 40 0 80 47 53 0 010 40 51.6 70.56 47 53 0 3011 0 18 80 47 47.7 24 26.412 16 18 80 47 53 3.6 25.8
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