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Supplier Evaluation using Data Envelopment Analysis

Rajashekar Govindarajan Student, ECET, ASU [email protected] Abstract

In any organization, for an effective supply chain management to operate, the purchasing function is very essential to perform effectively. It is the responsibility of purchasing managers to choose suppliers to purchase the required products for their company. Thus, it is very common for purchasing managers to conduct supplier evaluation techniques effectively to choose the best supplier amongst all suppliers. This project focuses on the Data Envelopment Analysis technique (DEA) to measure the relative efficiency of the suppliers by implementing the DEA algorithm and explains the lack of subjectivity involved in DEA contrast to the weighted cost algorithm. This paper also deals with the pros and cons of both weighted cost and DEA algorithm. The criteria that were mentioned on supplier selection have focused on quantifiable measures such as cost, quality, delivery, and other related factors. These are important factors that should be considered in almost any supplier selection decision. However, under partnership sourcing, it becomes not a task of supplier selection but rather a question of identifying the best partner for a longterm relationship. In this situation, a new set of supplier selection criteria come into consideration, equally as important as some of the criteria mentioned above. The factors that are considered for supplier evaluation in this project are Input factors: Technological capability, financial stability, Number of employees and Quality assurance system. Output factors: Delivery performance, quality, service and price. The paper develops as follows. The next section explains how supplier selection gets complicated in a multi-criteria problem and explains about the algorithm that will be adopted to solve such problems. The following section gives a little information on Background and Related work to DEA; some of the other common approaches to supplier selection and explains the implementation of DEA and weighted cost approach. Section 4 deals with the methodology for the implementation of the whole project and section 5 explains a high level architecture that is used for implementation. Then the following section explains the functionalities and results of the project.

1. Introduction

One of the most important objectives in the purchasing process is that of the selection and maintenance of an effective supply base. Supplier selection is becoming increasingly critical as companies continue to develop more collaborative and long-term relationships with their suppliers. With the purchasing function playing a more strategic role, supplier selection has now become a strategic decision, particularly in relation to strategic purchased items. When a supplier selection decision needs to be made, the buyer establishes a set of evaluation criteria that can be used to compare the potential sources. These evaluation factors are classified into input and output factors. A study carried out by Dickson surveyed buyers to identify the factors they considered in awarding contracts to suppliers [9]. Although some supplier selection criteria were found to vary in different situations, in addition to price three common criteria emerged as important, regardless of the type of purchased product. These were quality, on-time delivery, and supplier performance history along these criteria. Another study carried out by Lehman and O'Shaughnessy, found that, the key factors generally thought to affect supplier selection decisions were price, quality, delivery, and service [9].

2. Problem Statement

Supplier selection is a multi-criteria problem and there are not a lot of efficient techniques or algorithms that addresses this problem. The conventional methods that are being used for supplier evaluation like categorical or keyfactor rating method, cost ratio method, weighted-cost method, etc., are very subjective in nature. They are subjective because the buyer assigns values to various factors that are involved in selection of suppliers and the values vary from one buyer to another for the same supplier. So the need for methods/algorithms that are more objective in nature, that involves assigning common set of values to the selection criteria, is to be used. Over

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the past two decades, Data Envelopment Analysis (DEA) has emerged as an important tool in the field of efficiency measurement. DEA focuses on calculating the overall operational efficiency of the suppliers and thus a supplier could be considered to have a relative efficiency of 1 if he produces a set of output factors that is not produced by other suppliers with a given set of input factors. Full (100%) efficiency is attained by any DMU if and only if none of its inputs or outputs can be improved without worsening some of its other inputs or outputs. DEA is used to compare Decision Making Units (DMUs) such as bank branches, sales outlets, individuals or groups of individuals, which use one or more inputs and one or more outputs to calculate relative efficiency. Inputs are the factors that are considered to influence in producing the chosen output factors. It is difficult to evaluate an organization's performance when there are multiple inputs and multiple outputs to the system. The difficulties are further enhanced when the relationships between the inputs and the outputs are complex and involve unknown tradeoffs. Thus DEA is used to calculate the relative efficiencies of multiple decision-making units (DMU's), in our case suppliers, based on multiple inputs and outputs. This relative efficiency calculation can provide benchmarking data for reducing the number of suppliers, which in turn would result in effective supply chain management. Thus, for validating that DEA is more suitable for supplier selection than weighted cost approach, a system is built that implements both the algorithm. Numerical values are assigned to the supplier selection criteria factors and both the algorithms are run to compare the results. Changes for the weights associated with selection criteria factors are done to see the consistency associated with DEA algorithm and subjectivity associated with weighted cost approach algorithm. Using DEA, improvement targets will be calculated for units who have efficiency less than 1.

decisions. Weber identified several basic techniques or models that have appeared in studies over the previous 25 years and found that the majority were linear weighting models, mathematical models such as Economical Order Quantity (EOQ) and a few probabilistic models [10]. DEA measure has been used to evaluate and compare educational departments (schools, colleges and universities), health care sector, agricultural production, banking, armed forces, sports, market research, transportation sector etc. The methodology for calculating efficiency using both the algorithms is explained in the following sections.

3.1 Weighted Cost approach

The efficiency of the supplier is calculated by dividing weighted sum of output by weighted sum of input. The efficiency for the set of suppliers is calculated and then the efficiency is divided by the maximum efficiency found to calculate the relative efficiency. The relative efficiency is calculated because it would be logical to compare the result with that of DEA as relative efficiency is found in DEA. In the weighted cost approach, same weight is applied to all the suppliers.

3.2 Data Envelopment Analysis

In contrast to weighted cost approach, DEA allows units in the system to choose their own weights in the way, which is most advantageous to them. If a unit is inefficient even with the set of weights, which is most favorable to it, then there are serious grounds for investigating further. Each unit is considered in turn and its most favorable weights are selected. The efficiency of all other units is computed using this set of weights. The result is that for each unit we obtain a series of relative efficiencies both using those weights most favorable to itself and those most favorable to other units. Algebraic model like this can be framed with the given inputs and outputs. Maximize efficiency s1 = r UrYrjs1 / i ViXijs1 Where s1 = the supplier that we choose. Ur, Vi = weight of outputs and inputs respectively. Yr, Xi = value of outputs and inputs respectively The U's and V's are variables of the problem that can be determined by solving the model. The above model is converted into a linear programming model and solving the linear program gives the relative efficiency of the suppliers. To obtain the efficiency of all the suppliers, it is necessary to solve a linear program focusing on each supplier in turn. As the objective function varies from

3. Background and Related work

DEA was originally developed by Charnes, Cooper, Rhodes with Constant returns to scale and was extended by Banker, Charnes, Cooper to include variable returns to scale [1]. If inputs are increased by m units and as a result if output increases by exactly m unit, it is constant returns to scale. If there are varied results in output, it is termed as variable returns to scale. Since 1978, many books and dissertations have been published and DEA has rapidly extended to returns to scale, dummy or categorical variables, discretionary and non-discretionary variables. Various supplier selection models and techniques thus have been developed supporting supplier selection

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problem to problem, the weights obtained for each target unit may be different.

support system environment where multiple conflicting criteria have to be considered in a Just in Time environment. Multi-Attribute Utility Theory (MAUT): Use of MAUT can help purchasing professionals to formulate viable sourcing strategies, as it is capable of handling multiple conflicting attributes inherent in international supplier selection.

3.3 The data envelope

An "Efficient frontier" could be established based on the outputs produced by each supplier and could be depicted as something like this.

S1 Output1 S3 S4 Output2

Figure 1. Data Envelope

4. Methodology

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This involves execution of the following steps. 4.1. Identification of inputs and outputs:

Identify the inputs and outputs that are strategically important or critical to the buyer. The inputs and outputs are used as the selection criteria for the suppliers.

4.2 Numerical data for inputs and outputs

The numerical data for all the inputs and outputs for all decision making units is fed into the system. In the weighted cost approach algorithm, the buyer is given the option of entering the weights by himself for the input and output factors considered. The administrator in the system is responsible for entering the numerical data for the input and output factors.

The positions on the graph represented by supplier 1, supplier 2 and supplier 4 demonstrate a level of performance, which is superior to all other suppliers. Supplier 3 is not on the efficient frontier and this means that he needs to improve upon some measure to reach the performance level of other suppliers. This line is called the efficient frontier. It represents the standard of performance that the other suppliers who are not on the efficient frontier would try to achieve

4.3 Calculation of efficiency by weighted cost approach

Calculation for efficiency is done for the weighted cost approach of supplier selection. This involves calculating the weighted sum of output and weighted sum of input and dividing the weighted sum of output and input. The input and output data is being normalized with respect to the maximum value of the factors entered by the user.

3.4 Other approaches in Supplier Selection:

Though cost is the primary concern to most of the buyers, more interactive and interdependent selection criteria are being increasingly used in the industry. Selection criteria and measures that are used are changing and will continue to change as Information technology advancements and applications in the industry are realized. [6] Some of the approaches that are commonly applied in the industries are Total Cost Ownership (TCO): TCO is a methodology and philosophy, which looks beyond the price of a purchase to include many other purchase related costs. This approach has become increasingly important as organizations look for ways to better understand and manage their costs. Multi-Objective Programming: The use of a multiobjective programming approach is generally used in the just-in-time scenarios. The analysis occurs in a decision

4.4 Calculation of efficiency by DEA

Calculate the relative efficiencies of each decision-making unit by employing the Data Envelopment Analysis algorithm. LINDO API program is used to solve the linear problem that is formed using the data. The steps involved in integration of Java code with LINDO API are given below. Formation of model: The objective direction is given as maximization; the constant terms in the objective function

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are stored in a double scalar, and the objective coefficients are placed into an array. The number of constraints, the constraint right hand sides, the constraint types (Greater than, less than, etc.), the number of non zero coefficients in the constraint matrix, the length of each column in the constraint matrix, the non-zero coefficients, column start indices, and the row indices of the non-zero coefficients are put into arrays. The details about the variables such as the number of variables, upper and lower bounds, and the variable types are also loaded into the model. Create an Environment and model: A LINDO environment object is created which resides at the LINDO API's internal object oriented data structure. Also a model object is being created and is associated with the environment object. Load the Model: The next step is to set up the LP data and load it to LINDO API. This is generally the most involved of all the steps discussed here. Solve: Since the model is an LP, a linear solver, such as the primal simplex method, can be used. The model is solved with the call to the LINDO API with parameters having the details of all the loaded numbers. Retrieve the solution: The next step is to retrieve the solution using solution query functions. Using the LINDO API, the objective function, the primal solution, the dual solution and the slacks are obtained. The size of the array that retrieves the solution should have sufficient memory and otherwise, the system would crash. Clear Memory: A last step is to release the LINDO API memory by deleting the LINDO environment. This frees up all data structures LINDO API allocated to the environment and all of the environment's associated models.

with respect to the highest numerical value given for the input factors, output factors and weights. The data for the set of suppliers from manufacturing industries are input in the system initially to calculate the efficiency using both the algorithms. Then the data set is manipulated by giving lower inputs and higher outputs to see the change in the result of the efficiencies by both algorithms. Also, higher inputs and lower outputs are given for the same set of data to see the changes in the efficiency values by both the algorithms.

5. Architecture of the application

The picture in the next page represents a high level architecture of the entire application. The application is built as a three-tier architecture that has the application components into three logical tiers: the user interface tier, the business logic tier, and the database access tier. In this system, the user interface tier communicates only with the business logic tier, never directly with the database access tier. The business logic tier communicates both with the user interface tier and the database access tier. The HTML layer has text boxes and dropdown menus that prompt the user for input. The user-input data are taken as variables that are declared in the Java Server pages The JSP creates objects for the Java classes that are required. These objects are used to access the methods inside those Java classes. Thus, the variables received as input from the HTML files are sent as parameters to those methods and the business logic is called. The Java class in the business logic, after executing the method, returns a value. JSP file receives this returned value and gives the output to the presentation layer either as HTML The JSP code communicates with various components of the Java code as shown in the picture. The Algorithm component that implements the DEA algorithm communicates with the LINDO API and solves the linear program. LINDO API acts as a server by residing in the tomcat server and communicates back and forth with the client by taking input and returning output. The other

4.5 Validation

A system is being built which calculates the efficiency both by weighted cost approach and DEA algorithm. The system provides options for the user to run both the algorithms and view the results. The data is normalized

Presentation Layer

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Tier Boundary

JSP Code

Quote Component

Product Search Component Order

Product, Factors and Weights Entry

Algorithm Component

LINDO API

Database Driver Tier Boundary

Database Layer

Figure2. Architectural Overview

redistributed if any changes are made to it. The tools and materials used for the project are given below. components are used to implement the functionalities like placing quotes and orders, searching products, entry of product, factors and weights into the database. A Postgres database is used as a backend and it is run on cywgin, which is a Linux-like environment for Windows Some of the interesting characteristics of the model are · The user interface tier is a client only, in that it only makes requests to the business logic tier. · The database access tier is a server only, in that it only responds to requests from the business logic tier. · The business logic tier acts as both a client and a server: a server relative to the user interface tier, because it process its request, and a client to the database access tier, because it sends a request to it. The ability to separate logical components of an application ensures that applications are easy to manage. Because communication can be controlled between each logical tier of an application, changes in one tier, for example, the database access tier, do not have to affect the client component tier, which would have to be

Tools Java Server Pages HTML / JavaScript Tomcat 5.2 DreamWeaver Postgres Cygwin

Application Used for Server side scripting Used for Customer web interface, used for client side interactivity Servlet container for hosting the application Used to generate HTML files for the customer Interface Database used Used to run postgres on windows environment

Table1. Tools and Materials used

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6. Functionality of the Application

Some of the functionalities of the system in addition to the implementation of algorithm are described below.

Negotiation between buyers and suppliers can take place back and forth for a quote given by the buyer. A supplier has the ability to view the orders that are being placed by a buyer for him and he can change the status from "Order placed" to "Order processed". After the algorithm is run by the buyer while selecting suppliers, improvement targets for the suppliers who have an efficiency of less than 1 is calculated and the supplier is given an option of viewing his improvement targets by selecting a factor.

6.1 Login

As an approved user, the user could log onto the system either as a buyer or as a supplier. The administrator could also log onto the system and can enter the values for the input and output factors of a company.

6.3 Buyer Module

Buyer is given the option of searching for the product that he wishes to buy. Then he is listed with the list of suppliers who supply that product. He could select a list of suppliers using the check box and run either the weighted cost approach algorithm or DEA algorithm.

6.2 Supplier Module

The supplier is given the option of entering products into the system, viewing the Request for Quote (RFQ), sending quote, negotiating with the buyers, view order status and edit profile, etc.

He can enter the price, quantity and delivery date by which he could send the product as shown below

He is the given option of entering or editing the weights for the selected supplier in the weighted cost approach and the algorithm calculates the efficiency of all the suppliers. If DEA algorithm is selected, the relative efficiency is calculated by calling the LINDO API and then option is given for the buyer to select the improvement target value on the input and output factors for the suppliers who have an efficiency of less than 100%.

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The buyer could view the improvement targets for the suppliers by selecting the factor for improvement. As shown in the following picture, he is able to see the reference group for the selected supplier which shows the suppliers who are performing better than him.

Delivery Predictability Quality Service Price Supplier NCR corporation Auto Ventshade George Pacific Ricoh Paragon Inc Solarcom

20 10 10 20

25 15 20 5 Efficiency1 % Efficiency2% 82 92 80 75 72 70 70 88 76 89 91 75

Table 2. Weights for weighted cost approach

Table 3. Efficiency for Weighted Cost approach

Then the buyer could view overall performance of the suppliers and send quotes for one or more suppliers by entering the price, quantity needed and delivery date expected. The buyer also has the option of viewing the proposal after the quote is being sent by the supplier and he can negotiate with the supplier by entering the quote details again. If the buyer runs the weighted cost approach algorithm, he must be given option to enter the weight for all the input and output factors.

7.2 DEA Algorithm

The relative efficiency of a target unit can be obtained by solving the linear program that is formed for a selected supplier. The primal solution gives the weights leading to that solution and these weights are the most favorable ones from the point of view of the target unit. As the objective function is varying from supplier to supplier, the weights obtained for each target unit may be different. The result of efficiency obtained by running the DEA algorithm is listed below. It can be noticed that it is a lot different than that calculated using weighted cost algorithm. Supplier NCR Corporation Auto Ventshade George Pacific Ricoh Paragon Inc SolarCom Efficiency % 92 90 88 85 78 78

7. Results and Validation 7.1 Weighted Cost approach algorithm

The efficiency of all selected suppliers is calculated using the weighted cost algorithm and it could be seen that the efficiency produced by this algorithm is not a good performance measure for suppliers because the buyer induces subjectivity by entering his own weights. It could be seen that, by giving different weights, the efficiency calculated by the algorithm has widely varied results. The table below indicates the change in weights entered for all the suppliers and it is evident from the next table that the change in efficiency is erratic.

Table4. Efficiency for DEA

Factor Technologica l Capability Financial Stability Number of Employees QA system

Weight1 10 20 20 15

Weight2 15 25 25 20

DEA calculates the improvement targets for the suppliers who have an efficiency of less than 1. The results of the application on peer groups and improvement targets are given in the following section.

7.3 Peer Groups and Improvement Targets

DEA does peer group comparison in which efficient units will form the efficient frontier and inefficient units will be enveloped by this frontier. For units enveloped

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by the frontier, the inefficient units, DEA compares the unit with a combination of units located on the frontier and enables the analyst to indicate the sources and the level of inefficiency for each of its inputs and outputs. The indicated targets, which are shown to the inefficient units as models, are their actual peer units. Thus for each inefficient unit that has an efficiency of less than 1, DEA guarantees a reference set that sets target values to its input and output. In our application, we have a supplier NCR Corporation who performs at 82% efficiency when compared with other suppliers. The improvement targets for the output factors of NCR Corporation are found by increasing one factor and by keeping other factors constant till an efficiency of 100% is obtained. The graph is shown below.

Im provement Targets for Output Factors for NCR Corporation Factor Values 60 40 20 0 Delivery Predictabili Service

the efficiency varies erratically. The subjectivity induced by the buyer by assigning weights is seen by the fact that the efficiency varies erratically and the efficiency does not remain to be high when weight for one factor is reduced. High input and low output: If the input factors are given high and outputs are given lower values, it is seen that the efficiency is lesser comparatively in both the algorithms. For the same values, if the weights are altered, no proper pattern is found in the weighted cost approach. DEA maintains the same relative efficiency because it does not have the subjectivity introduced by the buyer. Thus it is seen that DEA produces a standardized and consistent set of relative efficiencies for the suppliers considered in contrast to the weighted cost approach algorithm, which varies the efficiency drastically, based on the buyer's input to the weights.

Efficiency - 82% Efficiency - 100%

8. Strengths and Limitations 8.1 Advantages of DEA

· · DEA can handle multiple input and multiple output models. DEA identifies possible peers as role models who have an efficiency of 1 and sets improvement targets for them. By providing improvement targets, DEA acts as an important tool for benchmarking. Possible sources of inefficiency can be determined using DEA.

Output Factors

Figure 3. Improvement Targets

7.4 Validation

The system is being run with many different data sets to analyze the comparison of results produced by both the algorithms. The input and output factor values for a set of 20 suppliers in the manufacturing industries are fed into the system and the efficiency is calculated using both the algorithms. The initial set of numerical values given for the input and output factors are chosen to be less than 100. Similarly, the weights given by the buyer for running the weighted cost algorithm is kept below 100. The data is normalized with respect to the highest value for the factor that is entered by the user. The data is being manipulated in many ways to analyze the change in result of both the algorithms and some of the manipulation in the data sets for the suppliers is given below. Low input and high output: If the input factors are given lesser numerical values and outputs are given higher, and then the efficiency is found to be higher in both the algorithms. For the same values, the weights are reduced for the input and output factors separately and found that

·

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8.2 Limitations of DEA

· Being a deterministic rather than statistical technique, DEA produces results that are particularly sensitive to measurement error. If one organization's inputs are understated or its outputs overstated, then that organization can become an outlier that significantly distorts the shape of the frontier and reduces the efficiency scores of nearby organizations. DEA scores are sensitive to input and output specification and the size of the sample. Increasing the sample size will tend to reduce the average efficiency score, because including more organizations provides greater scope for DEA to find similar comparison partners. Conversely, including too few organizations relative to the number of outputs and inputs can artificially inflate the efficiency scores.

·

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Since a standard formulation of DEA creates a separate linear program for each DMU, large problems can be computationally intensive.

the required result, more real time data is needed to further validate the model and analyze the results more efficiently. More advanced methods can be implemented that alleviates the limitations carried by DEA algorithm.

8.3 Limitations in the application

· Calculation of improvement target for the suppliers tries to increase only one factor until an efficiency of 1 is achieved by keeping other factors constant. This cannot be done in real world because improving just one factor without varying other factors is not possible in all cases. Though the buyer has the option of placing an order with more than one supplier for a product, he can only place order for one product at a time.

References

[1] http://www.deazone.com "Ali Emrouznejad's Data Envelopment Analysis Home Page". [2] http://www.emp.pdx.edu/dea/wvedea.html "DEA Tutorial by Dr.Tim Anderson" [3] Robert Simons April (1995), "MP in Action", The Newsletter of Mathematical Programming in Industry and Commerce. [4] John Blake Feb (2000), "An Introduction to Data Envelopment Analysis", IENG 4564, Design and Optimization of Service Systems [5] [Andersen, P., Petersen, N.C. (1993). A procedure for ranking efficient units in data envelopment analysis. [6] Kalakota, R, Robinson, M., Tapscott, E-Business: Roadmap for Success [7] Narasimhan, R., Talluri, S., and Mendex, D. (2001), Supplier evaluation and rationalization via data envelopment analysis: an empirical examination. Journal of Supply Chain Management. [8] Erin, M. Burke, Nichol, L. Jenkins and Valerie, J. Stueland. Supplier evaluation: analysis of formal supplier evaluation processes and a method for creating your own process. Journal of Supply Chain Management. [9] Dickson Nov(1966). An Analysis of Vendor Selection: systems and decisions. Journal of Purchasing, Vol. 1, N 2 [10] Weber, C.A., Current, J.R. and Benton, W.C. (1991). Vendor selection criteria and methods. European Journal of Operational Research, Vol. 50 [11] http://www.lindo.com/table/dllhelpt.html "Lindo API documentation".

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9. Future Work

· The input and output factors are fixed in this application and the user can be given the facility to choose additional input and output factors. Bar charts can be drawn to show the improvement target values for all the factors for a chosen supplier. Other algorithms like Augmented DEA algorithm can be implemented which provide better results than DEA because it solves the drawbacks considered in DEA. Weight restrictions could be identified and included as constraints to attain better results. If output1 is at least twice as important as output2, then a constraint v1 > 2v2 can be added to the existing constraints.

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10. Conclusion

This project is an implementation of DEA and weighted cost approach algorithm that helps supplier selection for managers in a purchasing environment. It can be concluded from the results that DEA produces standardized and consistent set of relative efficiencies in contrast to weighted cost approach, which shows drastic changes in efficiency as the weights are allowed to change by the buyer. There are some critical factors to be considered in the application of DEA models. The efficiency scores could be very sensitive to changes in the data and depend heavily on the number and type of input and output factors considered. Also the size of the data set is an important factor when using the DEA model. Even though the DEA algorithm provides us with

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