Supply Chain 3

A. Firmness loss models

The Boltzmann, Simple Exponential and Inverse Exponential models were fitted to the flesh firmness data collected during storage and transportation of kiwifruit along Supply Chain 3. The best model which characterised the data was the Simple Exponential model followed by the Boltzmann model and the Inverse Exponential Polynomial (Figure 5.29).

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Figure 5.29: Three firmness loss models fitted to the flesh firmness data of kiwifruit obtained during storage period and transportation along Supply Chain 3.

Simple Exponential model best described the data, as the AICc value was the lowest compared to that of the Boltzmann and the IEP models. The likelihood that the SE model was the better model compared to the Boltzmann model was 68.26%. The AICc value of the SE (-69.29) was lower than that of the Boltzmann model (-67.76). The Δi value (1.53) was < 2, further suggesting substantial evidence that the Boltzmann model was the second best model fitted to the flesh firmness data (Figure 5.30). The probability of the Boltzmann model being a better model compared to the SE model was 31.73%.

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Figure 5.30: Comparison of Simple Exponential and Boltzmann models fitted to the flesh firmness data collected during storage and transportation of kiwifruit along Supply Chain 3.

The likelihood that the SE model is the better model compared to the IEP model was 98.78%. The calculated AICc value for the SE model (-69.29) was lower than the IEP (- 60.49), indicating that the SE model was a better model than the IEP model. The Δi value (8.799) suggested that the IEP model had considerably less support in characterising the firmness loss data compared to the SE model. The probability of IEP model being a better model compared to SE model was only 1.21% (Figure 5.31).

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Figure 5.31: Comparison of Simple Exponential and Inverse Exponential Polynomial models fitted to the flesh firmness data collected during storage and transportation of kiwifruit along Supply Chain 3.

When comparing the IEP model and the Boltzmann models, the latter model showed to be a better fit for Supply Chain 3 dataset. The likelihood that the Boltzmann model was a better model as compared to the IEP model was 97.42%. The AICc value (-67.76) for the Boltzmann model was lower than the AICc value (-60.49) for the IEP model, further indicating that the Boltzmann model was a better fit for the data. The Δi value (7.26) was

greater than 7 indicating that the IEP model had considerably less support in characterising the flesh firmness data compared to the Boltzmann model. The probability of IEP model being better compared to the Boltzmann model was only 2.57% (Figure 5.32). Table 5.8 shows the equations of the three firmness loss models with their corresponding AICc values and standard errors.

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Figure 5.32: Comparison between Boltzmann and Inverse Exponential Polynomial models fitted to the flesh firmness data collected during storage and transportation along Supply Chain 3.

Table 5.8: Overview of firmness loss models for Supply Chain 3

Model AICc value Standard error Equation Simple Exponential -69.29 0.139 _{ܨܨ ൌ ܣ଴൅ܣଵ݁}ିఒ௧ Boltzmann -67.76 0.139 _{ܨܨ ൌ ܣ} ଴൅ οܣ ͳ ൅ ݁ሺ௧ି௧ೖሻȀఒ Inverse Exponential Polynomial -60.49 0.150 ܨܨ ൌ ߜ ͳ ൅ ݁ሺఉబାఉభ௧ାఉమ௧మାఉయ௧యሻ

B. Development of storage potential models

The three models (Reciprocal, Reciprocal Quadratic and Power) were fitted to the data on flesh firmness and core temperature collected along the Supply Chain 3. The best fitted

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model for this dataset was the Reciprocal model, followed by the Power and the Reciprocal Quadratic models (Figure 5.33). The likelihood that the Reciprocal model was a better fit compared to the Power model was 57.15% (Figure 5.34). The Power model had a higher AICc value (-63.30) compared to the Reciprocal model (-63.88), indicating the latter model to be a better fit. The difference in the AICc (Δi) value (0.57) indicated that the Power model

could be the second best fit for the flesh firmness and core temperature data (Figure 5.34).

Figure 5.33: Three non-linear models (Reciprocal, Power and Reciprocal Quadratic) fitted to the flesh firmness and core temperature data of kiwifruit collected along Supply Chain 3.

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Figure 5.34: Comparison of the Reciprocal and the Power models fitted to flesh firmness and core temperature data of kiwifruit collected along Supply Chain 3.

A comparison between the Reciprocal and the Reciprocal Quadratic models was obtained by conducting the AIC test. The Reciprocal model had an AICc value of -63.88, which was lower than the AICc value (-62.20) of the Reciprocal Quadratic model. This indicated that the Reciprocal model was a better fit compared to the Reciprocal Quadratic model (Figure 5.35). The Δi value being 0.16 (< 2), thus demonstrating the potential of the Reciprocal Quadratic model to be used as storage potential model for Supply Chain 3.

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Figure 5.35: Comparison of Reciprocal and Reciprocal Quadratic models fitted to the flesh firmness and core temperature data of kiwifruit collected along Supply Chain 3.

The second best model which fitted the Supply Chain 3 data was the Power model. The AIC test indicated that the likelihood that the Power model was a better model compared to the Reciprocal Quadratic was 63.42% (Figure 5.36). The AICc value of the Power model (- 63.30) was slightly lower than that of the Reciprocal Quadratic model (-62.20), indicating the Power model to be a better fit compared to the Reciprocal Quadratic model. The difference in AICc value (1.10) was lower than 2, which suggested substantial evidence that the Reciprocal Quadratic model could be used as the storage potential model for predicting kiwifruit shelf-life.

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Figure 5.36: Comparison of Power and Reciprocal Quadratic models fitted to the flesh firmness and core temperature data of kiwifruit collected along Supply Chain 3.

The AICc values and the standard error values indicated that the best fit model for Supply Chain 3 dataset was the Reciprocal model, followed by the Power and the Reciprocal Quadratic models. Table 5.9 shows the storage potential models with the calculated AICc values and standard errors.

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Table 5.9: Overview of storage potential models for Supply Chain 3 Model AICc value Standard error Equation Reciprocal -63.88 0.169 ܨܨ ൌ ͳ ܽ ൅ ܾܶ Power -63.30 0.170 ܨܨ ൌ ܽ ൈ ்ܾ Reciprocal Quadratic -62.20 0.170 ܨܨ ൌ_{ܽ ൅ ܾܶ ൅ ܿܶ}ͳ _ଶ

C. 3D modeling to describe the effect of core temperature and SSC on the flesh firmness

A non-linear model was fitted to the data of flesh firmness (kgf), Brix (% SSC) and core temperature (°C) of kiwifruit (Figure 5.37). This model helps to understand the effect of temperature and soluble solids content on the flesh firmness of the fruit. The flesh firmness reduced while the core temperature increased. As soluble solids content increased, the flesh firmness of the fruit decreased. The Linear Logarithm model was the best fit model to the data as the AICc value (-73.66) was the least for this model (Figure 5.37).

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Figure 5.37: Linear Logarithmic model fitted to the flesh firmness (kgf), Brix (% SSC) and core temperature (°C) data of kiwifruit collected along Supply Chain 3.

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