## 4 Further Analysis and Discussion
### Code Optimization: The Recursive Implementation of the Permanent Value Determination Algorithm
Eventually, eight alternatives remained after pre-processing by considering the agent's ability to issue local invoices and using the \"complete case study method\" (carrying no missing value for all criteria). This then formed a data warehouse that stored the 8 \(\times\) 7 \"source decision matrix\" that contains information on how each alternative performs and justified based on each selection criterion. An 8 \(\times\) 7 \"normalized performance matrix\" was obtained to serve as a base for later GTMA calculations. An AHP-style survey was then conducted. The \"source pairwise comparison matrix\", which is a 7 \(\times\) 7 matrix, was filled with the DM's opinions, and as a sub product of this phase, a criteria weight vector (CWV) that defines the priority of the attributes in the DM's mind, was obtained using an AHP. By spreading the elements in a row of the \"normalized performance matrix\" (1 \(\times\) 7, which is in fact the performance vector of an alternative) over the matrix diagonal of the \"source pairwise comparison matrix\", a square 7 \(\times\) 7 \"ASAM matrix\" (alternative selection attribute matrix) was obtained. The permanent value of this was regarded as the \"index score\" for an alternative. Repeating this process for all of the alternatives, the index scores for each were obtained, to form an 8 \(\times\) 1 \"final score vector\". As a final outcome, based on this vector, the alternatives were ranked, so the best (or winner) shredder(s) could be identified. ## Appendix B Code Segment in R for the Non-Parametric Test

* wilcox.test (ROV_AHPGTMA, ROV_AHPTOPSIS, paired = TRUE ) Wilcoxon signed rank test with continuity correction data: ROV_AHPGTMA and ROV_AHPTOPSIS V = 15, \(p\)-value = 0.9301 alternative hypothesis: true location shift is not equal to 0

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