Computer-aided machine-tool selection based on a Fuzzy-AHP approach

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Abstract

Investment evaluation methods play an important role in today’s competitive manufacturing environment. Shrinking profit margins and diversification require careful analysis of investments and decisions regarding these investments are crucial for the survival of the manufacturing industry. Both economic evaluation criterion and strategic criteria such as flexibility, quality improvement, which are not quantitative in nature, are considered for evaluation. Much has been written about the deficiencies of traditional models for justifying advanced manufacturing systems. The use of fuzzy set theory allows incorporating unquantifiable, incomplete and partially known information into the decision model. In this paper, an analytic hierarchical process (AHP) based on fuzzy numbers multi-attribute method is proposed for the evaluation and justification of an advanced manufacturing system. Finally, an example of machine tool selection is used to illustrate and validate the proposed approach.

Introduction

Advanced manufacturing technologies (AMT) is an important item in the design of a manufacturing system. Using proper manufacturing technology can enhance the production process, provide effective utilization of resources, increase productivity and improve system flexibility, repeatability and reliability. Therefore, given the wide range of advanced manufacturing technologies available today, the determination of the best equipment available for a given production scenario is not an easy task.

Economic justification methods of manufacturing investments have been discussed thoroughly in the past years. Economic analysis methods are the basic discounted cash flow (DCF) techniques such as present worth, annual worth, internal rate of return, etc., and other techniques such as payback period and return on investment, which ignore time value of money.

The conventional DCF methods do not appear to be suitable on their own for the evaluation of AMT investments due to the non-monetary impacts posed by the manufacturing system. The inadequacy of traditional financial justification measures lies on their deterministic nature.

The probabilistic cash flow analysis can be used if the probabilities distributions of the possible outcomes are known. However, when the frequency distribution of the possible outcomes is not known, as in revenues and expenses of a new production system, most decision-makers are reluctant to employ DCF methods during the evaluation phase. Table 1 shows an updated version of the classification of the justification methods for advanced manufacturing technologies.

Much has been written about the deficiencies of traditional engineering economic models for justifying AMT (Bozdag et al., 2003, Ordoobadi and Mulvaney, 2001, Shamsuzzaman et al., 2003). Most of the dissatisfaction revolves around the following points:

  • Short term returns are emphasized rather than long term strategy.

  • A variety of assumptions are made designed to deal with the uncertainty involved in predicting the future environment.

  • And, the range of benefits considered is diminished due to the difficulty in quantifying many important factors.

According to Shamsuzzaman et al. (2000), numerous tangible and intangible benefits are expected after the introduction of AMT. Among the intangible benefits one can mention reduced labor costs, high capital utilization, faster throughput times, better quality control, increased safety and a better response to unpredictable situations.

Sullivan and William (1986) points out the inadequacy of traditional financial justification measures of project worth such as return on investment, payback, and net present worth in considering the strategic merits of advanced manufacturing technologies.

According Karsak and Tolga (2001), DCF methods appear as the most popular economic justification methodology; however, determining cash flows (revenues, expenses) and discount rates as crisp values can lead to erroneous results in most real-life applications.

The results of the surveys conducted by Lefley (1994) for justification of advanced manufacturing technology (AMT) in the UK, and by Lefley and Sarkis (1997) for appraisal of AMT investments in the UK and US both support the difficulty in assessing AMT investments due to their non-quantifiable benefits. As a result of this difficulty, over 80% of the respondents in the US and UK point out that not all potential benefits of AMT investments are considered in the financial justification process. Furthermore, the results of the surveys state that subjective assessment of AMT investment with/without financial justification is observed in approximately 60% of the manufacturing firms responding the questionnaire.

In the justification process of advanced information or manufacturing systems, quantification of some of the revenue or quality improvements is often difficult if not impossible. Many managers have argued that accounting methodologies restrict the adoption and use of advanced technologies and are incapable of quantifying many of the benefits offered by these systems in many organizations.

The analytic hierarchy process (AHP) developed by Saaty (1980) is a decision-making tool that can handle unstructured or semistructured decisions with multiperson and multicriteria inputs. It is a decision-rule model that relaxes the measurement of related factors to subjective managerial inputs on multiple criteria. AHP has several advantages, including its acceptance of inconsistencies in managerial judgments/perceptions and its user friendliness because users may directly input judgment data without further requiring mathematical knowledge. It also allows users to structure complex problems in the form of a hierarchy or a set of integrated levels. AHP can also be combined with well-known operations research techniques to handle more difficult problems. One of the main advantages of this method is the relative ease with which it handles multiple criteria. In addition to this, AHP is easier to understand and can effectively handle both qualitative and quantitative data. The use of AHP does not involve cumbersome mathematics. AHP involves the principles of decomposition, pair wise comparisons, and priority vector generation and synthesis. The power of AHP has been validated by empirical application in diverse areas such as healthcare, politics, and urban planning (Karsak & Tolga, 2001). It has been used in making decisions that involve ranking, selection, evaluation, optimization, and prediction (Lee, Lau, Liu, & Tam, 2001).

Though the purpose of AHP is to capture the expert’s knowledge, the conventional AHP still cannot reflect the human thinking style. In spite of its popularity, this method is often criticized because of a series of pitfalls associated with the AHP technique which can be summarized as follows:

  • Its inability to adequately handle the inherent uncertainty and imprecision associated with the mapping of the decision-maker’s perception to exact numbers (Lefley & Sarkis, 1997).

  • In the traditional formulation of the AHP, human’s judgments are represented as exact (or crisp, according to the fuzzy logic terminology) numbers. However, in many practical cases the human preference model is uncertain and decision-makers might be reluctant or unable to assign exact numerical values to the comparison judgments.

  • Although the use of the discrete scale of 1–9 has the advantage of simplicity, the AHP does not take into account the uncertainty associated with the mapping of one’s judgment to a number.

In order to overcome the aforementioned shortcomings, a fuzzy extension of AHP, was developed to solve the hierarchical fuzzy problems. In the next sections a Fuzzy-AHP technique is proposed, and an example for the evaluation and justification of advanced manufacturing system is presented.

Section snippets

Fuzzy-AHP methodology

The Fuzzy-AHP methodology extends Saaty’s AHP by combining it with the fuzzy set theory. In the Fuzzy-AHP, fuzzy ratio scales are used to indicate the relative strength of the factors in the corresponding criteria. Therefore, a fuzzy judgment matrix can be constructed. The final scores of alternatives are also represented by fuzzy numbers. The optimum alternative is obtained by ranking the fuzzy numbers using special algebra operators.

The next three steps can summarize the procedure of applying

Case study

In this section, the proposed methodology is applied to a case study, in order to prove its applicability and validity. A new CNC turning center investment decision of a given manufacturer was taken into consideration. A triplet of decisions makers was asked to evaluate a set of three alternatives machine tools (MT1, MT2, MT3). After a set of interviews, a series of six qualitative attributes was selected to perform the analysis. The six attributes are: flexibility, operation easiness,

Proposed software

As can be easily seen, AHP with fuzzy numbers requires many time-consuming calculations. Depending on the number of attributes and alternatives taken into consideration, a lot of time is necessary to make all calculations in order to reach the final solution. As the number of attributes increases, the dimension of the problem expands. This could lead to a great number of mathematical and fuzzy operations. Therefore, software aid may be very useful to automatically carry out the Fuzzy-AHP

Conclusions

In this paper a Fuzzy-AHP based Software for selecting machine tools was proposed. In order to consider uncertainty and improving imprecision in ranking attributes and/or machine alternatives. The presented approach introduces triangular numbers into traditional AHP method. Adoption of fuzzy numbers allows decisions makers to achieve a better estimation flexibility regarding the overall importance of attributes and real alternatives. For the methodology of Fuzzy-AHP explained above a program

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