Selection of supplier is very critical problem in supply chain management (SCM). In the recent years, selection of suppliers in the supply chain has become very decisive to mould a trade-off between the qualitative and quantitative criteria. These criteria are considered for making final decisions on supplier selection advertently and comprehensively. However, these decisions usually in- volve in various criteria or objectives to compromise among all possible conflicting parameters. This study deals with the uncertain issue of the supplier selection using integrated TOPSIS model for multi criteria decision making(MCDM). The advantage is that it distinguishes between the cost (less the better) and benefit (more the better) criteria and select the solutions which are closest and farthest from the positive and negative ideal solution. Sensitivity analysis is carried out to investigate the effect of criteria weights on the supplier selection. A computative model is illustrated for a small scale steel manufacturing unit in India.
Selection of supplier is very critical aspect in SCM where firms expend minimum 60 percent of its total sales on purchasing items like parts, components and raw materials . Further, manufacturers procure services and goods us- ing upto 70 percent of product cost . Supplier selection is a region of enormous significance and must be considered as a tactical aspect in effectual SCM.
During 1990s, manufacturers attempted to develop strategic partnerships to improve their management’s preference and competitiveness . Supplier selection and evaluation are complex tasks for decision makers as they required to consider various criteria. Dickson  recognized 23 criteria for the selection of supplier based on which Weber et al.  measured supplier performance considering the criteria of price, delivery, quality, location, technical capability, productive capability, industry position, reputation, financial stability, maintainability and history. Evans  studied various key criteria for the selection of supplier such as price, quality and delivery.
Recently, the marketing management literature has been paid considerable attention to the supplier selection pro- cess. Few important criteria are: suppliers’ profitability, technological capabilities, relationship closeness, conflict resolution and performance quality. Lin and Chang  emphasized that reputation, customer responsiveness, com- munication, relationship closeness and industry position are necessary in vendor selection. Due to inexact, imprecise, vague and uncertain nature of data, modeling of many situations may be insufficient or inexact .
The one of the most important business function is strategic sourcing (SS). Under the expanded heading of logistics, now SS is an essential segment of the firm program to cover the purchasing schemes. Companies are interested to find out how they can provide facilities to the customers rapidly with reasonable pricing compared to their competitors. So, managers realized that they should work in a mutual system with the best corporation in their logistics networks containing warehouses, suppliers, customers undoubtedly,production units and the distribution centers. The long-term viability of the company is determined on the selection of supplier decision .
Liao and Kao  analyzed issues related to selection of supplier in SCM. Both qualitative and quantitative criteria make multi criteria for selection of supplier problem more complex . Methods are developed for decision makers in a suitable way to deal with the problem related to the selection of supplier more effectively . The applications of various type fuzzy models are explored in the context of decision making problems . Liao and Kao  presented MCGP and fuzzy TOPSIS approaches simultaneously for selection of supplier problems using trapezoidal fuzzy number. Asamoah et al.  reported an AHP approach in a pharmaceutical manufacturing unit in Ghana for evaluation and selection of suppliers. Kumar and Roy  studied factors which are qualitatively important to obtain suitable suppliers. Wang et al.  presented preemptive goal programming (PGP) and analytic hierarchy process (AHP) jointly for selection of supplier. The linguistic terms or vague concepts are represented in crisp value to formulate the model for real-life situations . Amid et al.  proposed a multi objective linear model using fuzzy theory to overcome the blurriness of the information. Amid et al.  defined the supplier selection problems using fuzzy weighted max-min model to solve a problem effectively. Chen  studied about the elaboration of each criterion weight and each alternative by linguistic values which could be framed in triangular fuzzy numbers (TFN). Chang et al.  implemented a new method of MCGP to evaluate the houses in order to help home buyers to find a suitable house. Luthra et al.  analyzed the ecological pressure from markets, customer knowledge and various stakeholders. It helps managers and business professionals to assess the most effective supplier for sustainability in supply chain. Sureeyatanapas et al.  analyzed the TOPSIS method to make easy for practitioners to logically select a supplier even when unavailability and /or uncertainty of the estimation information emerge. Cheraghalipour and Farsad  proposed a decision making tool to solve the sustainable order allocation and selection of supplier problem in multi-item, multi-supplier and multi-period environment considering bulk rebate under disruption risks.
In this current study, multi supplier selection problem is addressed using fuzzy TOPSIS model. In the first case, linguistic terms are framed in TFN to compute rating and criteria weights for the selection of a supplier. In the second case, fuzzy TOPSIS model is applied to get the supplier closeness coefficients. Finally, sensitivity analysis is carried out for evaluating the possible effect of criteria weights on the performance estimation of suppliers.
2. Fuzzy TOPSIS
Zadeh  introduced fuzzy theory as an augmentation of the classical notation of set. A positive TFN can be expressed using three points such as: B˜ = (n, o, p) which is depicted in Fig. 1.