Complexity Results on a Paint Shop Problem

Motivated by an application in the automobile industry, we present results and conjectures on a new combinatorial problem: Given a word w and restricted reservoirs of colored letters, synthesize w with a minimal number of color changes. We present a dynamic program that solves this problem and runs in polynomial time if we bound both, the number of different letters and colors. Otherwise, the problem is shown to be NP-complete. Additionally, we focus on upper bounds on the minimal number of color changes, simultaneously giving results for special instances, and posing open questions

Fair Correlation Clustering in Forests

The study of algorithmic fairness received growing attention recently. This stems from the awareness that bias in the input data for machine learning systems may result in discriminatory outputs. For clustering tasks, one of the most central notions of fairness is the formalization by Chierichetti, Kumar, Lattanzi, and Vassilvitskii [NeurIPS 2017]. A clustering is said to be fair, if each cluster has the same distribution of manifestations of a sensitive attribute as the whole input set. This is motivated by various applications where the objects to be clustered have sensitive attributes that should not be over- or underrepresented. Most research on this version of fair clustering has focused on centriod-based objectives. In contrast, we discuss the applicability of this fairness notion to Correlation Clustering. The existing literature on the resulting Fair Correlation Clustering problem either presents approximation algorithms with poor approximation guarantees or severely limits the possible distributions of the sensitive attribute (often only two manifestations with a 1:1 ratio are considered). Our goal is to understand if there is hope for better results in between these two extremes. To this end, we consider restricted graph classes which allow us to characterize the distributions of sensitive attributes for which this form of fairness is tractable from a complexity point of view. While existing work on Fair Correlation Clustering gives approximation algorithms, we focus on exact solutions and investigate whether there are efficiently solvable instances. The unfair version of Correlation Clustering is trivial on forests, but adding fairness creates a surprisingly rich picture of complexities. We give an overview of the distributions and types of forests where Fair Correlation Clustering turns from tractable to intractable. As the most surprising insight, we consider the fact that the cause of the hardness of Fair Correlation Clustering is not the strictness of the fairness condition. We lift most of our results to also hold for the relaxed version of the fairness condition. Instead, the source of hardness seems to be the distribution of the sensitive attribute. On the positive side, we identify some reasonable distributions that are indeed tractable. While this tractability is only shown for forests, it may open an avenue to design reasonable approximations for larger graph classes

A Quantum Optimization Case Study for a Transport Robot Scheduling Problem

We present a comprehensive case study comparing the performance of D-Waves' quantum-classical hybrid framework, Fujitsu's quantum-inspired digital annealer, and Gurobi's state-of-the-art classical solver in solving a transport robot scheduling problem. This problem originates from an industrially relevant real-world scenario. We provide three different models for our problem following different design philosophies. In our benchmark, we focus on the solution quality and end-to-end runtime of different model and solver combinations. We find promising results for the digital annealer and some opportunities for the hybrid quantum annealer in direct comparison with Gurobi. Our study provides insights into the workflow for solving an application-oriented optimization problem with different strategies, and can be useful for evaluating the strengths and weaknesses of different approaches

Plan effectiveness monitoring: Built heritage, Wellington City District Plan

The goal of this project has been to assess the effectiveness of the built heritage provisions in the Wellington City District Plan. To this end, sixty nine buildings were chosen from the Plan’s Heritage List: Buildings (a sample size of around 14%), which include: 55 buildings that have had at least one resource consent granted under the District Plan. A total of 80 consents were assessed for these buildings as part of this project; 14 buildings that have had no resource consents granted. Each building was visited and an evaluation was undertaken regarding the effects of consented activities on heritage values. The effects of permitted activities (i.e. repair and maintenance) were assessed for the buildings that have no consent history. The evaluation relates only to the effects that could be viewed from the street

A Mathematical Approach to Paint Production Process Optimization

As the global paint market steadily grows, finding the most effective processing model to increase production capacity will be the best way to enhance competitiveness. Therefore, this study proposes two production environments commonly used in the paint industry: build-to-order (BTO) and the variation of a configuration-to-order (CTO), called group production, to schedule paint production. Mixed-Integer Linear Program (MILP) was solved using genetic algorithms (GA) to analyze two production environments with various products, different set-up times, and different average demand for each product. The models determine the number of batches, the size and product of each batch, and the batch sequence such that the makespan is minimized. Several numerical instances are presented to analyze the proposed models. The experimental results show that BTO production completes products faster than group production when products are simple (low variety). However, group production is more applicable to manufacturing diverse products (high variety) and mass production (high volume). Finally, the number of colors has the most significant impact on the two models, followed by the number of product types, and finally the average demand

The delayed transformation: restructuring in the automobile, chemical, clothing and machine tool industries.

In this paper, we focus on the results of the Belgian Trend Study. The intention of this study was to examine the prevalence of new production concepts within the widest possible range of companies in the automobile, the machine-tool, the chemical and the clothing industries. The Trend Study aimed to answer the following questions : is the Taylorist division of labour a thing of the past ? What are the alternatives ? Are shifts in the division of labour accompanied by another type of personnel policy, and do traditional relations have to make way for this new approach ? The methodological concept used had to guarantee that the findings at the level of each industry could be generalized. Though the picture emerging from the empirical data collected in the four industrial sectors is inevitably diverse, the data make it possible merely to suggest a 'neo' rather than a 'post' Taylorist or Fordist concept.

Class Size Neo-Piagetian Testing: Theory, Results, and Implications

The main thrust of this study, therefore, revolved around the scale-up of the Case Instructional Sequence into a classroom size application able to be implemented by instructors with little additional practice in employing thistype of instructional sequence. Specifically, the purpose of this study was to determine the effect of the Case type treatment on the performance of two successive ninth grade physical science classes at a private, college-preparatory, secondary school in northeast Florida. These groups were to be assessed using the Tobin and Capie Test of Logical Thinking, a measure which could help assess their respective Piagetian stage