Analysis of How Selecting Simplified Models of Different Variability Affects Ranking for Ordinal Optimization: Re-entrant Line Capacity Allocation Case
Date Issued
2015
Date
2015
Author(s)
Chang, Chun-Ming
Abstract
Ordinal optimization (OO) focuses on “ranking” in performances among designs instead of their “values” and exploits a goal softening strategy aiming at “good enough” designs with high probability as opposed to an optimal design for sure. Ordinal transformation (OT) is an OO technique that utilizes a simplified model for perform evaluation and ranking to further reduce computational effort. There are often multiple choices of simplified models for a system that capture different levels of details or aspects. The selection of an appropriate simplified model is a key factor for the effectiveness of OT and OO. Thus, how to select simplified models for ranking and how to analyze the goodness of simplified models are significant and challenging problems for OT and OO. However, there is little literature to theoretically explore the influences of different simplified models on ranking largely because the comparison among various simplified models is often difficult in lack of a common ground. In addition, ranking is a relative index instead of an absolute index. The goodness of ranking is not straight forward to quantify let alone to analyze. In this thesis, machine capacity allocation for re-entrant lines, an important engineering optimization problem, is adopted as the conveyor problem to investigate the selection of an appropriate simplified model. In particular, Jackson network approximation (JNA) and queueing network analyzer (QNA), two commonly used queueing network approximation models, are studied with the mean cycle time as the performance index. Both models are developed based on parametric decomposition, but JNA has unity SCVs due to its exponential time assumptions while QNA has heterogeneous SCVs. Thus, we compare between QNA and JNA to investigate how selecting simplified models of different variability affects ranking and analyze the goodness of a simplified model with consideration of heterogeneous SCVs. A key step in the investigation is the quantification of the goodness of rankings by simplified models. This is difficult since “ranking” is a relative index, not an absolute index. A bound and ranking analysis (BRA) is innovatively developed to quantify and analyze the goodness of rankings by simplified models. BRA consists of two innovations: i) Analyze the upper and lower bounds of simplified models, ii) Derive the probability of correct ranking under the assumption of actual cycle time being uniformly distributed between its upper and lower bounds. The probability of correct ranking between a pair of designs for a single GI/G/m queue is first studied. With the variation of two QNA approximations, the least variation of their upper bound is derived and this helps obtain a higher probability of correct ranking α. The results and insights from BRA are as follow. i) Showed that QNA approximation is bounded by known upper and lower bounds proposed by Kingman, Brumelle and Marshall respectively. ii) Compared with existing literature results, QNA captures the variations of true expected cycle time well because of heterogeneous SCVs but JNA does not. iii) Obtained a valuable insight from derived α that capturing heterogeneous SCVs benefits the ranking of top designs and improves probability of correct ranking because variability has greater impacts on cycle time while lower utilization. Based on the above for a single GI/G/m queue, BRA is then extended to general re-entrant lines with multiple workstations. Rank correlation, which measures the concordance of pair-wise comparisons in two quantitative indices, is adopted to quantify the goodness of ranking. Simulation studies over a five-station re-entrant line demonstrated that rank correlation of QNA always outperforms that of JNA, and the difference is especially significant for top designs. This is consistent with the insight iii) obtained from BRA. Then, in order to investigate the effects of heterogeneous SCVs, the original design space is transformed using true ranking, and in this ordinal space each thirty designs are clustered into a group. After grouping, we found that heterogeneous SCVs contribute to improve differentiation between groups and also make designs in a group better separated, which benefit raise the probability of correct ranking. This is why heterogeneous SCVs benefit rank correlation of a simplified model. In summary, the contributions of this thesis are as follows. i) Adopted re-entrant line capacity allocation as the conveyor problem to meaningfully compare two simplified models: JNA has unity SCVs while QNA has heterogeneous SCVs, ii) Established theoretical foundations, BRA, to analyze the probability of correct ranking and quantify the goodness of different simplified models, iii) Derived the probability of correct ranking between a pair of designs α, and a valuable insight is that heterogeneous SCVs have greater impacts on top designs, iv) Simulation studies demonstrated that heterogeneous SCVs contribute to improve differentiation between groups and make designs in a group better separated, v) Because of iv), QNA always outperforms JNA in terms of rank correlation, and the difference is especially significant for top designs. It is consistent with iii), vi) Investigate in aspects of both theory and experiment how selecting simplified models of different variability affects ranking for OO and OT.
Subjects
Model selection
ordinal optimization
heterogeneous variability
ranking analysis
re-entrant line capacity allocation
Type
thesis
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