Data collection and analysis

This section completes the MADM approach by addressing the issue of data collection and analysis. The selection of decision makers and how to approach them is described in the data collection subsection. The calculations and final result of MADM technique is then revealed in the data analysis subsection.

Data collection- As discussed in the introductory section, this research applies a multiple decision makers approach. To eliminate the impacts of personal decisions and emotions, all the decision makers are selected from the industry. The experts are required to be experienced in the FFVs industry and able to compare and score alternatives associated with the attributes.

The experts, therefore, are selected from the FFVs retail shops and supermarkets because they are in direct relations with the consumers and deal with the wastage at the store levels. The experts were selected randomly from local stores and supermarkets. The shops are located in different parts of Melbourne in order to reduce the demographic influences on the experts’ opinions. Store managers of supermarkets, category managers of supermarkets, and local FFVs shop owners were asked to participate and four experts participated in the scoring process.

The experts were asked to weight each alternative for each attribute. The data has been collected by face to face questioning of the experts. After receiving the matrix table, they

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to 5, where 1 has the least relation and 5 the most. The interviews have been conducted in June and July 2012.

Data analysis- The decision making problem in this research is deterministic and a deterministic analysis approach was applied to find the top ranked produce as the case studies. The following subsection provides the general formulas used in data analysis. Weighted Sum Model- The Weighted Sum Model (WSM) has been used to analyse the data. WSM is one of the most commonly used approaches in the deterministic problems (Triantaphyllou et al. 1998). This method represents the preferences of decision makers by a linear additive function. WSM is used when the preferences are independent and separated (Tzhang & Huang 2011).

Table ‎5-2 shows the general MADM matrix with attributes weights, where 𝐴_𝑖 , 𝑖 = 1,2, … 𝑀 indicates the ith alternative;

𝐶_𝑗 , 𝑗 = 1,2, … 𝑁 indicates the jth attribute;

𝑊𝑗 , 𝑗 = 1,2, … 𝑁 indicates the weight for jth attribute;

𝑎𝑖𝑗 indicates the score of ith alternative for jth attribute.

Table ‎5-2 General MADM matrix with attributes weights

Attributes W1 W2 W3 … WN Alt. C1 C2 C3 … CN A1 a11 a12 a13 … a1N A2 a21 a22 a23 … a2N A3_… a31_… a32_… a33_… … a3N … AM aM1 aM2 aM3 … aMN

The total score of the ithalternative, scored by the kth expert (𝑇𝑆𝐴_𝑖𝑘) is calculated form the following equation:

Chapter Five

According to the equation 5.1, attributes in the WSM need to be weighted. The attribute weighting process is done by the researcher since the research aims and objectives have to be considered in this step. The most relevant attribute receives the highest score. The scoring scale, the same as for the alternative scoring, is from 1 to 5. Scores of alternatives multiplies to each associated weight to the attributes, and then 𝑇𝑆𝐴_𝑖𝑘 is calculated. The weight vector for the seven attributes in this problem is (5, 4, 4, 1, 5, 2, 3). According to the literature of WSM, it is suggested that normalised weights be used for the attributes. After normalising, the normalised weight vector becomes (0.208, 0.167, 0.167, 0.042, 0.208, 0.083, 0.125).

Equation 5.2 has been used to normalise the attributes weights, as follows: 𝑤_𝑗′= 𝑤𝑗

∑𝑁𝑗=1𝑤𝑗

(5.2)

It is assumed that each of the experts has the same weight in the ranking process. Therefore, the final score of alternatives equals to the average score of 𝑇𝑆𝐴_𝑖𝑘 given by each decision maker. Therefore, the final score for each alternative can be calculated by the following equation:

𝑇𝑆𝐴_𝑖 =∑𝑙𝑘=1𝑇𝑆𝐴𝑖𝑘

𝑙 (5.3)

where l stands for the number of experts in the decision making.

Table ‎5-3 provides a real example of the scored matrix by one of the experts. The weighted score of alternatives (𝑇𝑆𝐴_𝑖𝑘) associated to this table is shown in Table ‎5-4.

Table ‎5-3 Example of scored MADM matrix by one of the decision makers

seasonality wastage short life time demand fluctuations price fluctuations price sale volume Peach 5 4 5 5 5 5 3 Mandarin 4 1 2 3 2 2 3 Strawberry 2 3 5 2 2 2 4

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Mango 5 3 5 5 3 5 3 Avocado 1 2 3 2 2 1 3 Royal gala 2 1 2 5 2 2 4 Apricot 5 4 5 5 4 5 2 Cauliflower 1 1 1 3 2 1 2 Pear 1 1 2 3 2 1 2 Table Grape 4 4 5 2 5 5 5

Table ‎5-4 Weighted scores for alternatives (𝑻𝑺𝑨𝒊𝒌)

Alternatives Weighted scores Peach 4.583 Mandarin 2.417 Strawberry 2.917 Tomato 3.000 Orange 2.167 Banana 2.417 Mango 4.000 Avocado 2.000 Royal gala 2.208 Apricot 4.250 Cauliflower 1.417 Pear 1.583 Table Grape 4.500

The final results of the scoring (𝑇𝑆𝐴_𝑖) and sorted results are provided in Table ‎5-5. Table ‎5-5 𝑻𝑺𝑨𝒊 before and after sorting

Before Sorting After Sorting

Alternatives Alternatives

Chapter Five

Mandarin 2.635 Apricot 4.125 Strawberry 3.49 Table Grape 4.125

Tomato 2.802 Mango 3.76

Orange 2.031 Strawberry 3.49

Banana 2.406 Tomato 2.802

Mango 3.76 Mandarin 2.635

Avocado 2.24 Banana 2.406

Royal gala 2.073 Avocado 2.24 Apricot 4.125 Royal gala 2.073 Cauliflower 1.688 Orange 2.031

Pear 1.979 Pear 1.979

Table Grape 4.125 Cauliflower 1.688

According to the table, the first five alternatives have the highest weighted score significantly above the average. These products are peaches, apricots, table grapes, mangoes and strawberries. Peaches and apricots rank first and second, due to their similarities. Both of these sets of produce are within the stone fruits category, acting similar in the market. In addition, the score of apricots and table grapes is exactly the same. For these two reasons, apricots can be removed from the list of case studies without missing any future information. The top four produce are selected to be investigated as the case studies in this research- peaches, table grapes, mangoes and strawberries. The following section describes each fruit specification in the Australian context in details.

In document Option Contracts for Supermarket Fruit Supply Chains: Theory and Practice (Page 91-95)