Decision making over the production system life cycle: MOORA method

Abstract

Decisions in robust and flexible production systems are made in an environment often characterized by complexity, need for flexibility, and inclusion of a decision-maker’s subjectivity. Typically in production system life cycle, decisions on the product design, facility location, facility layout, supplier, material, technology, and so forth has to be made in an efficient and timely manner. These decisions are more complex as the decision makers have to assess a wide range of alternatives based on a set of conflicting criteria. In this paper, application of multi-objective optimization on the basis of ratio analysis approach is explored to solve such type of decision making problems. Moreover performance of the reference point approach is also tested for the considered decision making problems.

1 Introduction

As in product life cycle, the product goes through several distinct stages: introduction, growth, maturity, decline and death. The marketing decisions at each stage of the product life cycle are typical. The same concept is extended to a production system as a whole. In the introduction stage of production, product and its design is selected. The manufacture has to provide facilities to manufacture it. All these decisions are major strategic decisions, taken by the promoters of an industry. Immediately thereafter, the production system becomes steady as most on-going organizations are. Here the decisions are short term tactical decisions. Here the system is influenced slightly by internal and external environmental changes. When there are radical changes in external environment, and the production system finds it difficult to adopt those changes, the system comes to end (Attri and Grover 2012; Chunawalla and Patel 2009).

The life cycle of production system shows the progress of production system from the inception to the termination of system. Bellgran and Säfsten (2010) and Attri and Grover (2013a) have discussed that the main activities within the production system are often described based on the products life-cycle such as (i) market activity places demands on the product delivered from the production system, engineering activity controls the product development; (ii) production activity creates the product in the production system; (iii) distribution activity makes sure that the product is delivered under the right conditions to the customer; (iv) service activity targets at eliminating and inhibiting defects which might appear in the product; and (v) recycling activity objects at saving resources and handles worn-out material. Figure 1 shows the key activities to be performed in different stages of a production system life cycle.

Fig. 1

Production system life cycle (Attri and Grover 2012)

In each stage of the production system life-cycle, certain decisions have to be taken. For example, in the first stage i.e. initiation of the system, decision on product is to be taken. In design stage, several strategic decisions such as selection of product design, material, facility location, facility layout, process and technology has to be made. While in operation stage, decision on machine selection, manpower selection, vendor selection, job design etc. is to be made. In revision stage, there may be decision on the change of technology in the light of the environment change. In last stage, decision on the termination of the system is to be taken.

Yamada et al. (2010) have predicted the product quality on the basis of software process data. Singh et al. (2011) have applied the graph theoretic approach (GTA) to judge the best manufacturing process among various manufacturing processes for manufacturing any product. Attri and Grover (2013b) have applied VIKOR method (compromise ranking method) for decision making over the design stage of the production system life cycle. Rao et al. (2010) have applied stochastic programming in graded manpower systems for the development of optimal manpower recruitment. Although, a number of multi-attribute decision making (MADM) techniques are available in literature to assist the decision makers in making good judgments. This paper endeavours to explore the applicability of a novel MADM method, i.e. multi-objective optimization on the basis of ratio analysis (MOORA) method to deal with the decision making problems in the production system life cycle.

2 MOORA approach

Multi-objective optimization on the basis of ratio analysis (MOORA) is also known as multi-criteria or multi-attribute optimization. It is defined as the process of simultaneously optimizing two or more conflicting attributes subject to some constraints (Chakraborty 2011; Karande and Chakraborty 2012). Multi-criteria problem can be found in different stages of production system life cycle such as product design, process design, material selection, machine tool or cutting tool selection, material handling system selection, advanced manufacturing system selection. This approach was introduced by Brauers (2004).

This approach starts with a matrix consisting of performance measures of different alternatives with respect to various criteria.

$$ X = \left\{ {\begin{array}{*{20}c} {x_{11}} \hfill & {x_{12}} \hfill & \ldots \hfill & \ldots \hfill & {x_{1n}} \hfill \\ {x_{21}} \hfill & {x_{21}} \hfill & \ldots \hfill & \ldots \hfill & {x_{2n}} \hfill \\ \ldots \hfill & \ldots \hfill & \ldots \hfill & \ldots \hfill & \ldots \hfill \\ \ldots \hfill & \ldots \hfill & \ldots \hfill & \ldots \hfill & \ldots \hfill \\ {x_{m1}} \hfill &{x_{m2}} \hfill & \ldots \hfill & \ldots \hfill & {x_{mn}} \hfill \\ \end{array} } \right\} $$

(1)

where x _ij is the performance measure of the ith alternative on the jth attribute, m is the number of alternatives and n is the number of the attributes.

MOORA approach consists of two parts namely ratio system approach, the reference point approach.

2.1 Ratio system approach

In the ratio system approach, the initial data in the decision matrix is normalized. The reason behind the normalization is to make the decision matrix dimensionless. This makes all the elements of the decision matrix comparable. For normalization, different procedures are suggested by the authors Karande and Chakraborty (2012) and Brauers et al. (2010).

According to Karande and Chakraborty (2012), normalization can be done by comparing the performance of an alternative on a criterion to a denominator which is a representative for all the alternatives concerning that criterion.

$$ X_{ij}^{*} = \frac{X_{ij}}{{\sum\limits_{i = 1}^{m} {X_{ij}} }} $$

(2)

where X ^* _ij is a dimensionless number in the [0, 1] interval, which represents the normalized performance of the ith alternative on the jth criterion. The elements of the matrix are normalized without considering the type of the attribute i.e. beneficial attribute or non-beneficial attribute. Beneficial attributes are those attributes whose higher values are required, while for non-beneficial attributes, lower values are required.

For optimization based on ratio system approach of MOORA method, normalized performances are added in case of beneficial attributes (maximization) and subtracted in case of non-beneficial attributes (minimization), which can be expressed by following expression:

$$ y_{i}^{*} = \sum\limits_{j = 1}^{g} {X_{ij}^{*} } - \sum\limits_{j = g + 1}^{n} {X_{ij}^{*} } $$

(3)

where y ^* _i is the assessment value of the ith alternative with respect to all the criteria, g is the number of criteria to be maximized, and (n − g) is the number of the criteria to be minimized.

Furthermore the value of y ^* _i can be positive or negative depending on the totals of beneficial and non-beneficial attributes in the matrix. The alternative with highest value of y ^* _i would be the best alternative. An ordinal ranking of y ^* _i shows the final preference.

In some cases, some attributes are more significant than others. In these cases attribute weight is taken into deliberation. The weights of the attribute can be determined by applying entropy method and analytical hierarchy process (AHP). When weights of the attributes are considered, Eq. (3) becomes as follows:

$$ y_{i}^{*} = \sum\limits_{j = 1}^{g} {w_iX_{ij}^{*} } - \sum\limits_{j = g + 1}^{n} {w_iX_{ij}^{*} } $$

(4)

where w _i is the weight of the jth attribute.

2.2 Reference Point Approach

In the reference point theory a maximal objective reference point is deduced from the ratios found in Eq. (2). This approach is also known as realistic and non-subjective when the coordinates (r _i ) selected for the reference point are realized in one of the candidate alternatives (Brauers et al. 2008).

The set of reference point series is obtained on the basis of the beneficial and non-beneficial attributes. It will consist of maximum value in case of beneficial attribute and minimum value in case of non-beneficial attribute. The deviation of a criterion value from the set reference point (r _i ) is computed as:

$$ r_i - X_{ij}^{*} $$

(5)

From the reference point approach of MOORA, best alternative is one which would possess the maximum values in all of its beneficial attributes and minimum values in its non-beneficial attributes. It is not possible all the times that a specific alternative having all of the maximum values in its beneficial attributes and minimum values in its non-beneficial attributes. In such cases, there will be deviation from the set of reference point series.

Karlin and Studden (1966); Brauers and Zavadskas (2006) have proposed following formula for optimization based on reference point approach:

$$ P_i = \mathop {Min}\limits_{(i)} \left\{ {\begin{array}{*{20}c} {\mathop {Max}\limits_{(j)} } \hfill & {|r_{i} - X_{ij}^{*} |} \hfill \\ \end{array} } \right\} $$

(6)

where P _i is the performance index.

The best alternative would be one which has the total minimum deviation from the set of reference point series. In other words, it will have the minimum value of P _i .

3 Illustrative examples

To demonstrate the applicability, accuracy and potentiality of the MOORA method in decision making over the different stages of production system life cycle, the following five problems are cited here.

3.1 Product design selection

This problem deals with the selection of the most appropriate product design for the power electronic device (Besharati et al. 2006). This product design selection problem consists of ten design alternatives and three performance attributes i.e. manufacturing cost (MC), junction temperature, and thermal cycles to failure, as shown in Table 1. Among these three attributes thermal cycles to failure is a beneficial attribute and MC, junction temperature are non-beneficial attribute.

Table 1 Qualitative data for example 1 (Besharati et al. 2006)

The decision matrix for the product design selection problem is shown in Table 1. Applying Eq. (2), the normalized decision matrix is obtained, as shown in Table 2.

Table 2 Normalized decision matrix for example 1

Rao (2007) solved the same product design selection problem using AHP approach. Rao (2007) determined the criteria weights as W_JT = 0.1047, W_TCF = 0.2582, and W_MC = 0.6371 using the same method. In the current problem same weights are used here for subsequent analysis. After this, normalized assessment values (y_i) of all the considered alternatives are computed using Eq. (4) as shown in Table 3. Moreover, Table 3 also exhibits the value of performance indices.

Table 3 Ranking of the alternative for example 1

This MOORA method based analysis gives a comparative ranking of 5–10–2–4–7–3–6–9–8–1 when arranged according to the descending order of their assessment values. For this problem, product design 5 is the best choice among the considered ten product designs for the given power electronic device. Besharati et al. (2006) obtained the ranking for the product design alternatives as 5–10–4–3–7–6–2–8–9–1, while Rao (2007) obtained ranking 5–4–10–2–3–7–6–8–9–1. Here, alternative five is also observed as the best choice in both cases. In all the cases, the worst choice is product design 1. The ranking performance of MOORA method with respect to those derived by Besharati et al. (2006) and Rao (2007) are exhibited in Fig. 2.

Fig. 2

Comparative ranking for example 1

3.2 Facility layout design selection

Rao and Singh (2012) applied weighted euclidean distance based approach (WEDBA) to select plant layout design for a chemical packaging industry situated in the western part of India. This problem consists of four alternative plant layout design and five attributes i.e. interaction with existing facility distance, area available for each assembly group, material quantity flow, accessibility for fire fighting and comfort of crew, as shown in Table 4. Among these three attributes interaction with existing facility distance is a beneficial attribute and remaining ones are non-beneficial attributes.

Table 4 Qualitative data for example 2 (Rao and Singh 2012)

Using Eq. (2), the quantitative data for the facility layout design selection problem are first normalized, as given in Table 5.

Table 5 Normalized decision matrix for example 2

Rao and Singh (2012) determined the criteria weights as W_IEFD = 0.2491, W_AAG = 0.0995, W_MQF = 0.1068, W_AFF = 0.2022, W_COC = 0.3423 using AHP method which are subsequently used here for the MOORA method based analysis. Then, normalized assessment values (y_i) of all alternatives are computed using Eq. (4) as shown in Table 6.

Table 6 Ranking of the alternative for example 2

Table 6 also exhibits the value of performance indices. A ranking of 2–3–4–1 is derived when the assessment values are sorted in ascending order. Rao and Singh (2012) derived a ranking of the considered alternatives as 2–3–1–4. In both the cases, first ranked facility layout exactly match. The ranking performance of MOORA method with respect to those derived by Rao and Singh (2012) is exhibited in Fig. 3.

Fig. 3

Comparative ranking for example 2

3.3 Flexible manufacturing system selection

Kulak and Kahraman (2005) proposed axiomatic design (AD) principles for multiple attribute comparison of advanced manufacturing systems. This flexible manufacturing system selection problem consists of four alternative flexible manufacturing systems and six attributes. Decision matrix for the flexible manufacturing system (FMS) selection problem is shown in Table 7. The attributes considered are annual depreciation and maintenance costs), quality of results, ease of use, competitiveness, adaptability and expandability. In the current problem, annual depreciation and maintenance cost is the non-beneficial attribute and the remaining ones are the beneficial attributes.

Table 7 Qualitative data for example 3 (Kulak and Kahraman 2005)

On applying Eq. (2), the normalized decision matrix is obtained, as shown in Table 8.

Table 8 Normalized decision matrix for example 3

Rao and Parnichkun (2009) solved the same problem using the combinatorial mathematics based method. Rao and Parnichkun (2009) determined the criteria weights as W_ADM = 0.4188, W_Q = 0.1873, W_E = 0.0688, W_C = 0.1873, W_A = 0.0688, W_X = 0.0688 using AHP method. The weights as derived by Rao and Parnichkun (2009) are used here for subsequent analysis. Values of normalized assessment (y_i) and performance indices (P_i) are shown in Table 9.

Table 9 Ranking of the alternative for example 3

A ranking of 2–4–3–1 is derived when the assessment values are sorted in ascending order. Rao and Parnichkun (2009) derived a ranking of the considered alternatives as 2–1–3–4. In both the cases, first ranked facility layout exactly match. The ranking performance of MOORA method with respect to those derived by Rao and Parnichkun (2009) is exhibited in Fig. 4.

Fig. 4

Comparative ranking for example 3

3.4 Welding process selection

This example is related with the selection of a suitable arc welding process to join mild steel (0.2 % C) of 6 mm thickness (Rao 2007). This welding process selection problem consists of three alternate arc welding processes i.e. shielded metal arc welding, gas tungsten arc welding, and gas metal arc welding. The attributes considered are: weld quality, operator fatigue, skill required, cleaning required after welding, availability of consumables and initial preparation required. Among these attributes weld quality and availability of consumables are the beneficial attributes while the remaining ones are the non-beneficial attributes.

The decision matrix for the welding process selection problem is shown in Table 10. Applying Eq. (2), the normalized decision matrix is obtained, as shown in Table 11.

Table 10 Qualitative data for example 4 (Rao 2007)

Table 11 Normalized decision matrix for example 4

Rao (2007) determined the criteria weights as W_WQ = 0.3534, W_OF = 0.2526, W_SR = 0.1669, W_CR = 0.1103, W_AC = 0.0695, and W_IP = 0.0473 using AHP method. Same weights are used here for subsequent analysis. Normalized assessment values (y_i) and performance indices of the considered alternatives are shown in Table 12.

Table 12 Ranking of the alternative for example 4

From the Table 12, a ranking of SMAW–GTAW–GMAW is derived. Rao (2007) obtained ranking of SMAW–GTAW–GMAW. The result exactly matches with that of the Rao (2007).

3.5 Supplier selection

This example deals with the supplier performance evaluation using data envelopment analysis (DEA) in an agricultural and construction equipment manufacturing organization (Liu et al. 2000). Liu et al. (2000) considered five criteria, i.e. price, quality, delivery performance, distance and supply variety while evaluating the performance of 18 alternative suppliers engaged in supplying hydraulic valves. Among the five criteria considered in the present problem, quality, delivery performance and supply variety are the beneficial attributes, and price and distance are the non-beneficial attributes. Decision matrix of the problem consisting of 18 suppliers and five evaluation criteria, is shown in Table 13.

Table 13 Qualitative data for example 5 (Liu et al. 2000)

The corresponding normalized decision matrix is given in Table 14.

Table 14 Normalized decision matrix for example 5

Rao (2007) solved the same problem using TOPSIS method. Rao (2007) determined the criteria weights as W_P = 0.1361, W_Q = 0.4829, W_DP = 0.2591, W_D = 0.0438, and W_SV = 0.0782 using AHP method. Same weights are used here for subsequent analysis. Table 15 shows the normalized assessment values (y_i) and performance indices.

Table 15 Ranking of the alternative for example 5

From the Table 15, a ranking of 10–17–15–6–5–8–13–11–12–9–2–1–16–3–18–14–7–4 is derived. Rao (2007) obtained ranking of 10–17–15–6–5–8–13–11–12–9–2–1–16–14–3–18–4–7. The first ranking exactly matches with that of the Rao (2007). The ranking performance of MOORA method with respect to those derived by Rao (2007) is exhibited in Fig. 5.

Fig. 5

Comparative ranking for example 5

Table 16 shows the comparative performance of MOORA method with other MADM methods on the basis of their computational time, simplicity and calculation involved (Chakraborty 2011; Ginevičius and Podvezko 2008).

Table 16 Comparative performance of MOORA method with other MADM methods

It is observed from the Table 16 that MOORA method involves less mathematical calculations as it is based on the simple ratio analysis (as explained in Sect. 2). So, MOORA method is very simple to understand and easy to apply, when it is compared to other MADM techniques. Chakraborty (2011) have listed the following advantages of MOORA over the other MADM methods:

• Less computational time required for performing mathematical calculations.

• No extra parameters are required in this approach such as ν in VIKOR method and ξ in GRA method.

These advantages of MOORA method has made it more favourable to the decision making problems. Moreover, Brauers and Zavadskas (2009) have identified the MOORA method as the robust method which provides the stable result as compared to other MADM methods.

4 Conclusion

In the production system life cycle, numerous decisions are to be taken in each stage. These decisions are more complex as the decision makers has to assess a wide range of alternatives based on a set of conflicting criteria. In view of this, a novel multiple decision making MOORA method is suggested in this paper for decision making in different stages of production system life cycle. For the demonstration of proposed method, five examples have been cited from the literature. In all the cases, it is observed that best alternative exactly matches with those derived by the past researchers. MOORA method can consider all the attributes along with their relative importance which results in better evaluation of alternatives. MOORA method is very simple to comprehend and easy to apply. The proposed method is a general method and can consider any number of quantitative and qualitative attributes simultaneously and offers a more objective and simple decision making approach. Furthermore, this method can be extended to any type of selection problems.

MOORA method can be effectively used by the management or decision makers to make accurate decisions in different areas of manufacturing environment such as product design, material, manufacturing system, facility location, facility layout, material, and technology, supplier in an efficient and timely manner. However, this method is based on manual mathematical calculations, which has necessitated the development of computer program, which in turn will reduce the computational time. In future, computer program may be developed by using C++ language.