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One goal of Artificial Intelligence is to develop and understand computational mechanisms for solving difficult real-world problems. Unfortunately, domains traditionally used in general problem-solving research lack important characteristics of real-world domains, making it difficult to apply the techniques developed. Most classic AI domains require satisfying a set of Boolean constraints. Real-world problems require finding a solution that meets a set of Boolean constraints and performs well on a set of real-valued constraints. In addition, most classic domains are static while domains from the real world change. In this paper we demonstrate that SteppingStone, a general learning problem solver, is capable of solving problems with these characteristics. SteppingStone heuristically decomposes a problem into simpler subproblems, and then learns to deal with the interactions that arise between the subproblems. In lieu of an agreed upon metric for problem difficulty, we choose significant problems that are difficult for both people and programs as good candidates for evaluating progress. Consequently we adopt the domain of logic synthesis from VLSI design to demonstrate SteppingStone’s capabilities.

Today's supply chains increasingly involve complex sets of processes, objectives and constraints, and therefore agent-based architectures for supply chain management (SCM) become much more difficult to implement and maintain. The paper presents a multi-agent architecture for specifying, analyzing and developing SCM systems, in which asynchronous teams (A-Team) of problem solving agents exchange results within populations that provide effective management of information flows in supply chains, and cooperate to produce sets of non-dominated solutions that show the tradeoffs between objectives. Our approach distinguishes itself by improving problem-solving efficiency based on a diverse set of algorithms without complicated synthesis efforts, removing the focus from agent communication and coordination details, and improving reusability, flexibility and extensibility by supporting object-oriented and component-based programming style. We examine the effectiveness of the architecture through a real-world case study and experimental results.

An AI tool called the Quantitative Problem Solver (QPS) has been developed for building knowledge based systems which can solve quantitative problems in science and engineering. QPS can store and manipulate quantitative knowledge comprising numerical data and scientific laws represented by formulas. The human interface is based on the symbols commonly used by scientists and engineers. All knowledge is represented as objects and classes in an object-oriented knowledge base. QPS employs the familiar Problem Decomposition strategy for selecting the correct sequence of equations needed for solving problems and it has been tested by the building of knowledge based systems to solve several simple problems in Engineering and Physics.

IT business value research examines the organizational performance impacts of information technology. In this paper, we apply the value configuration of the value shop to describe and measure organizational performance. The value shop consists of the five primary activities of problem understanding, solutions to problems, decisions on actions, implementation of actions, and evaluations of actions in an iterative problem-solving cycle. Police investigation work is defined as value shop activities. Our empirical study of Norwegian police results in significant relationships between information technology use and investigation performance for all primary activities. The most important primary activities for IT use are problem understanding and implementation of actions, as both significantly improve value shop performance.

Purpose — The aim of this paper is to provide answers to two significant questions. The first question is "what is the comprehensive action for the Big 3 to overtake Toyota Company?" The second question is "Can TOC (Theory of Constraints) really deal with this kind of complicated problem effectively?"

Design/methodology/approach — In order to address this question and come out with a reasonable answer, this study uses the Theory of Constraints to discover the root causes and countermeasures for the Big 3 to break through their paradigms.

Findings — It is worthwhile to highlight that we have demonstrated that a sophisticated case in global competition of the motor market can provide solutions with only four TOC logic trees. Furthermore, it is interesting to note that the four TOC logic trees fit perfectly well with each of the four problem solving steps in two aspects: (1) It provides a shortcut through mirror imaging process and (2) It enhances the clarity of the thinking process.

Research limitations/implications — However, there remains some issues open for further exploration: (1) How can we make sure that the appropriate core problem(s) or root cause(s) has been identified in CRT (Current Reality Tree) and it is indeed the most meaningful one? (2) How can we proceed from CRT to FRT (Future Reality Tree) & further from FRT to PT (Prerequisites Tree) more effectively? (3) How can we discover key obstacles from PT and how to develop action plans from TT (Transition Tree) smoothly? (4) How to refine and integrate these feasible solution sets coming out from TT into the optimal solution scheme to be adapted in the real world?

Originality/value — This study demonstrates how TOC problem solving can help to solve the core problems and root causes of "can the Big 3 overtake Toyota?" It not only gives managerial insights for the Big 3 to break through their paradigms to fight back Toyota; but also identify how a complex problem beyond production field can be analyzed and dealt with effectively.

Paper type–Case study paper.

The Japanese carmaker Toyota has long been regarded as the pinnacle of Japanese innovation, manufacturing quality and industrial strength — particularly since it overtook General Motors in 2008 to become the world's biggest carmaker. Its "lean" manufacturing techniques and culture of continuous improvement were the envy of the business world. Companies sent delegations to tour Toyota's factories in the hope that some of its magic would rub off on them.

But within a few weeks all this has changed. Problems with "unintended acceleration" of its cars which the firm has belatedly taken seriously, has resulted in a crisis within the company. Toyota's woes were compounded on 9 February 2009 when it said it would also recall 440,000 hybrid vehicles, including the celebrated Prius, to fix a problem with their brakes. The firm's reputation for quality, on which the business was built, is shattered. Its market capitalization has dropped by an amount roughly equal to the entire value of Ford. But the greatest damage has been done by its misreading and mishandling of the crisis.

Surrounding this current problem, we came with an interesting question: Can the Toyota Way bring back Toyota to the lead? The aim of this paper has the intention to answer two significant questions. The first question is "Is the Toyota Way safe enough to prevent problems brewing outside its factories?" In order to address this question and get reasonable answer, this study tries to use the Theory of Constraints (TOC) to discover the root causes and countermeasures of how Toyota's Way can bring back Toyota to the lead. The second question is "Can TOC deal with this kind of complicated problem effectively?" From the case study, we successfully answered the two preceding questions, presenting some findings about TOC problem solving strategy.

This paper identifies four major types of technological capabilities of firms developing multi-technology products: integrative, absorptive, coordinative, and generative. Using an in-depth case study of a high technology sub-system, the paper focuses on a firm's generative capabilities. The paper illustrates that a firm's generative capabilities enables it to (a) frame a particular problem, (b) enact an innovative vision, and (c) solve the problem by developing new manufacturing techniques. The triad frame-enact-solve is argued to be the primary feature of a firm's generative capability.

Complaints that new product development projects frequently encounter problems keep occurring, despite the availability of a considerable body of literature and a large and still increasing set of tools to guide such projects. Against the wider background of managerial problem-solving in general and NPD-literature more specifically, we present and analyse two NPD-projects within the same financial services firm. These show a marked contrast in success. The reasons for this difference are explored and conclusions are drawn about the usefulness of NPD-literature and tools.

Intermediaries are an inherent part of value creation in open innovation. They connect organisations seeking external solutions for an innovation-related problem (seekers) with potential solution providers (solvers). To bridge between the innovation problem and external knowledge sources, intermediaries deploy different search strategies. This study compares the cost of using two prevalent approaches: direct versus delegated search. Direct search corresponds to the conventional understanding of search by screening a pre-identified set of solution providers that the intermediary has identified as potentially relevant contributors. Delegated search comprises more indirect search such as problem broadcasting or crowdsourcing. Here, the innovation problem is distributed to a large external network of potential solvers, allowing even unobvious outsiders to contribute to its solution. An empirical study of 53 open innovation intermediaries indicates that delegated search outperforms direct search in terms effectiveness. The lower overall effort for intermediation in delegated search mainly arises from decoupling the effort to coordinate the search process by shifting it towards the solution provider.

This study examines the construction of each search strategy that combines search space, depth and network into innovation. It approaches a search as a problem-discovery process, which occurs during all phases of a problem-solving process. It selects three cases of LG Household and Healthcare’s product and process innovation, which typically occur in the cosmetics industry, where many cosmetic firms have conducted problem discoveries of oriental knowledge for product and process innovation. Knowledge of oriental medicine and fermentation are called, as oriental knowledge is traditionally rooted in Asian culture and practices. Through a qualitative multiple-case study, this study identifies the different combinations of the three components in each search strategy — in terms of core competences. It notices that searches in each innovation are conducted during all phases of each problem-solving process rather than being confined to the initial stage of problem-solving activities. Through discussions of each component, this study reveals that despite the importance of ambidexterity in a search, the value system and absorptive capacity can take an important role in an effective search by properly recognising and evaluating the value of knowledge and turning it into a problem. Secondly, the search depth influences the innovation proceedings and links different pieces of knowledge. Lastly, a search network can facilitate problem discoveries, reduce the risk and uncertainty of each problem formulation and lead to competence building, even though it can be subject to partner availability and strategic compatibility issues.

Creativity has been identified as a critical activity in distributed product development. Various methods and tools support distributed product development and distributed teams in general, but none with a focus on creative problem solving. To tackle this challenge, a systematic literature review has been conducted to gather the influencing factors on distributed creativity to be used as a starting point for supporting creativity in distributed product development teams. Within this submission, an impact model is developed, focusing on the success factors of creativity. Furthermore, the interconnection between the factors is modelled. Barriers to creative problem solving are included as well but will be the focus of a following publication.

Semantic Computing extends Semantic Web both in breadth and depth. It bridges, and integrates, several computing technologies into a complete and unified theme. This article discusses the essences of Semantic Computing with a description of SemanticServices.Net, a new paradigm that enables "Problem-driven" search that may offer a new story to the Internet.

For some topics in the Algebra strand, students are often taught procedures and rules and made to practise these skills to perfection with little understanding of “how” and “why” they work. Research in cognitive science and mathematics education suggests that having students explain contrasting examples leads to gains in problem solving, increased conceptual understanding and enhanced procedural flexibility. The contrasting examples (CE) instructional approach involves having students examine, compare and discuss the similarities and differences of alternative solution methods for a particular problem. These methods are presented side-by-side instead of one after another for students to conveniently notice critical features and abstract their common underlying structure. This chapter describes how two carefully crafted CE tasks were used to support robust understanding in Algebra in the topics of Simultaneous Linear Equations and Sketching of Quadratic Functions. Facilitation prompts and possible questions to illustrate how teachers assessed and advanced students’ understanding at different stages of the classroom discourse are shared.

Problem solving has been the central focus of the Singapore mathematics curriculum and it is supported by five inter-related components: Concepts, Skills, Processes, Metacognition and Attitude. Pólya’s Four Phases of Mathematical Problem Solving is a problem solving approach that Singapore teachers are familiar with, especially using heuristics such as ‘work backwards’, ‘look for a pattern’ to solve problems. Few teachers have related the Pólya’s approach to the development of metacognition in mathematical problem solving especially during the ‘understand the problem’ phase. This chapter discusses how this problem solving approach can enhance problem solving ability by helping students to be more conscious of their metacognitive processes such as awareness, monitoring and regulating of their thinking processes involved in problem solving.

An on-going emphasis of the Singapore mathematics curriculum has been the strengthening of mathematical processes (e.g. reasoning and communication). To develop these processes, research has shown that worthwhile mathematical tasks are important for enhancing students’ mathematical thinking and reasoning. However, teachers face challenges in implementing tasks with high cognitive demand in terms of mathematical reasoning and communication. Additionally, the affordances of such tasks may not be well-harnessed as teachers were often observed to have inadvertently transformed these into less-demanding tasks during instruction when they scaffold the learning. This chapter outlines a framework to design and implement lessons that promote the development of mathematical reasoning and communication in secondary school students. It also discusses how teachers can facilitate the learning to help students develop these processes (e.g. deciding what aspects of a task to highlight, teacher questioning to challenge students with varied levels of mathematical competencies and supporting students without taking over the process of thinking for them). An example of a task, designed using the framework, and implemented by a very experienced teacher is also presented. Lastly, considerations for designing such tasks and factors that enable the successful enactment of these tasks are discussed.

This report presents a summary of the content of the various presentation by the participants in ICME-14 under the Topical Study Group 17: Problem Posing and Solving in Mathematics Education. Some trends in the research on problem solving and problem posing are identified through this study. Other areas which were less explored were also highlighted

Mathematics is one of the oldest disciplines in the world. Bishop (1991) expressed its value regarding human relationships and social institutions as Openness — that is, mathematical constructs such as propositions and ideas are open to human deliberation. Even before such systematization, many problems were solved and simultaneously created since earliest civilizations. This effort became the foundation for further endeavors.

What is the “Problem” in problem-solving? It has various types. Especially, the open-ended approach (Shimada, 1977) has been developed in Japan as a method to evaluate and develop mathematical thinking. Furthermore, problem posing can be an extension of problem solving. While posing various problems we may notice the patterns among those problem variations. In this sense, problem posing itself can be a problem. What is “Solving” in the problem-solving? It is dependent on the type and characteristic of problem. For example, the open-ended problems provide more than one solution. Socially open-ended problems provide solutions together with values. Problem posing requires developing problems and such development itself can be a solution. Therefore, importantly, the meaning of solving a problem is extended beyond traditional problem solving.

This paper explores the idea of problem-solving in mathematics to appreciate the value of openness under the Open Science movement (OSF, 2021). Open science is a movement accommodating experts and non-experts to have access to the outputs of scientific research and can participate in the research activities. This is essential for future citizens and is related to the ethical dimension of mathematics education (Ernest, 2012).

Based on the findings from a number of cross-national comparative studies of US and Chinese students, we provided a retrospective review of these studies and presented a profile of Chinese learners' mathematical thinking in problem solving and problem posing. In particular, we identified several characteristics of Chinese learners' mathematical thinking in problem solving as well as pointed out some future directions to refine and extend this list of characteristics of Chinese learners. This chapter not only helps us understand the nature of Chinese students' mathematical thinking from a cross-national comparative perspective, but also provides information to refine instructional programs so that Chinese students' mathematical thinking can be better nurtured and developed.

This chapter presents a study which investigated how teachers and students used textbooks within and beyond Chinese mathematics classrooms. Data were collected from 36 mathematics teachers and 272 students in 12 secondary schools in Fuzhou and Kunming, two major cities in Mainland China, through questionnaires, classroom observations, and interviews. The study provided a general picture of the textbook use by Chinese teachers and students of mathematics. The results showed that textbooks were the main but not the only source for teachers to make decisions about what to teach and how to teach. For students, textbooks were their main learning resource for both in-class exercise and homework. No significant differences were found between teachers with different genders, experiences, from different regions and schools in their use of textbooks, though some significant differences were found between students in the two cities in their use of textbooks. Explanations for the results are offered in the chapter.

In this paper, it is shown that there is a common structure of algebraic algorithms and logical algorithms. Three examples of problem-solving are shown. Simultaneous equations for describing and solving the problem are used in one example, and congruence expressions are used in another example. Both of these problem are algebraic. Logical formulae and the resolution principle are used in the third problem, which is a logical problem. The three examples are formalized by using three basic concepts, a description of a given problem, an answer to the problem, and the relationship between these two. In the formalization, the algorithm always consists of a sequence of transformations of descriptions. When a description is transformed into another form, the algorithm is guaranteed to be correct, i.e., the correct answer is obtained, if the transformation keeps the answer not changed.