Hierarchical Production Research Articles

Graph Rewriting Techniques in Engineering Design

Capturing human knowledge underlying the design and engineering of products has been among the main goals of computational engineering since its very beginning. Over the last decades, various approaches have been proposed to tackle this objective. Among the most promising approaches is the application of graph theory for representing product structures by defining nodes representing entities and edges representing relations among them. The concrete meaning of these structures ranges from geometry representations over hierarchical product breakdowns to functional descriptions and flows of information or resources. On top of these graph structures, graph rewriting techniques provide another powerful layer of technology. By enabling the formal definition of rules for transforming graph structures, they allow on the one hand side to formally capture the engineering development process. On the other hand, the assembly of rewriting rules into graph grammars allows for an exhaustive search of the solution space of the engineering problem at hand. In combination with search strategies, an automated optimization of the design under given constraints and objectives can be realized. The paper provides an overview of the current state-of-the-art in graph rewriting and its applications in engineering design, with a focus on the built environment. It concludes with a discussion of the progress achieved and the missing research gaps.

Color darkness and hierarchy perceptions: How consumers associate darker colors with higher hierarchy

AbstractThis study demonstrates that perceived hierarchy (high vs. low) from bundled products depend on the darkness of their color (darker vs. lighter). Results from 11 experiments show that consumers infer a darker‐colored product as a higher hierarchical product (HHP), relative to the otherwise identical lighter‐colored product of the same hue and saturation. We further establish that perceived dominance mediates this association: dark colors signal dominance. This study also demonstrates several downstream outcomes of the effect of darkness on hierarchy perceptions: consumers prefer product bundles where an HHP is colored darker than a lower hierarchical product. Furthermore, in the final study, we establish that this effect extends to three‐product bundles and is moderated by presentation mode.

Energy-Oriented Production Planning in Industry: A Systematic Literature Review and Classification Scheme

Scarcity of resources, structural change during the further development of renewable energy sources, and their corresponding costs, such as increasing resource costs or penalties due to dirty production, lead industrial firms to adapt ecological actions. In this regard, research on energy utilization in production planning has received increased attention in the last years, resulting in a large number of research articles so far. With the paper at hand, we review the literature on energy-oriented production planning. The aim of this study is to derive similar core issues and related properties along energy-oriented models within hierarchical production planning. For this, we carry out a systematic literature review and analyze and synthesize 375 research articles. We classify the underlying literature with a novel two-dimensional classification scheme and identify three key topics and five frequently found characteristics, which are presented in detail throughout this article. Based on these results, we state several potentials for further research.

Spray drying induced engineering a hierarchical reduced graphene oxide supported heterogeneous Tin dioxide and Zinc oxide for Lithium-ion storage

In this work, a hierarchical reduced graphene oxide (RGO) supportive matrix consisting of both larger two-dimensional RGO sheets and smaller three-dimensional RGO spheres was engineered with ZnO and SnO2 nanoparticles immobilized. The ZnO and SnO2 nanocrystals with controlled size were in sequence engineered on the surface of the RGO sheets during the deoxygenation of graphene oxide sample (GO), where the zinc-containing ZIF-8 sample and metal tin foil were used as precursors for ZnO and SnO2, respectively. After a spray drying treatment and calcination, the final ZnO@SnO2/RGO-H sample was obtained, which delivered an outstanding specific capacity of 982 mAh·g−1 under a high current density of 1000 mA·g−1 after 450 cycles. Benefitting from the unique hierarchical structure, the mechanical strength, ionic and electric conductivities of the ZnO@SnO2/RGO-H sample have been simultaneously promoted. The joint contributions from pseudocapacitive and battery behaviors in lithium-ion storage processes bring in both large specific capacity and good rate capability. The industrially mature spray drying method for synthesizing RGO based hierarchical products can be further developed for wider applications.

Surviving peace: Resilience and production decentralization in the Italian gun-making district, 1945–1970

This article analyzes the key resilience factors of the Italian firearms district after World War II structured around four main questions: resilience of what, to what, by what means, and with what outcome. This study aims to improve and expand knowledge about the capacity and difficulties of industrial districts to adapt to market changes and maintain their competitiveness. Our findings highlight that the successful recovery was based on the conquest of a new market segment and a novel decentralised and flexible—although hierarchical—production structure achieved through the reorganisation of know-how and resources accumulated in the district. The advantages of local clustering and elevated levels of specialisation provided the district with an effective short-term adaptation to the post-war crisis and a stable long-term growth path.

Using Machine Learning to Improve Public Reporting on U.S. Government Contracts

The U.S. government procures more than $500 billion annually in goods and services on public contracts, which it classifies using a hierarchical product and service taxonomy. Classification serves several purposes, including transparency in the use of taxpayer funding; reporting, tracing, and segmenting government expenditures; budgeting; and forecasting. Government acquisition personnel have historically performed these classifications manually, resulting in a process that is time-consuming and error-prone and offers limited visibility into government purchases. The problem faced is not unique to the public sector and is common across retail, manufacturing, and healthcare, among other settings. Using almost 4 million historical data records on governmental purchases, we fit a series of classifiers and demonstrate (a) superior performance when explicitly modeling the hierarchical structure of information domains through the use of top-down strategies and (b) the effectiveness of character-level convolutional neural networks when textual inputs are terse and contain irregularities such as abnormal character combinations and misspellings, which are common in government contracts. Our machine learning models are embedded in multiple software applications, including a web application that we developed, used by federal government personnel and other contracting professionals.

Star coloring under some graph operations

A star coloring of a graph [Formula: see text] is a proper coloring of [Formula: see text] such that no path of length [Formula: see text] in [Formula: see text] is bicolored. In this paper, the star chromatic number of join of graphs is computed. Some sharp bounds for the star chromatic number of corona, lexicographic, deleted lexicographic and hierarchical product of graphs together with a conjecture on the star chromatic number of lexicographic product of graphs are also presented.

Some binary products and integer linear programming for [formula omitted]-metric dimension of graphs

A sharp upper bound and a closed formula for the k-metric dimension of the hierarchical product of graphs is proved. Also, sharp lower bounds for the k-metric dimension of the splice and link products of graphs are presented. An integer linear programming model for computing the k-metric dimension as well as a k-metric basis of a given graph is proposed. These results are applied to bound or to compute the k-metric dimension of some classes of graphs that are of interest in mathematical chemistry.

A study of a new variant of the eccentric connectivity index for composite graphs

The eccentric connectivity index is a well-known graph invariant defined as the sum of contributions dependent on the eccentricities of adjacent vertices over all edges of a connected graph. Recently, a new variant of the eccentric connectivity index namely multiplicative eccentric connectivity index has been proposed. In this paper, we investigate the behavior of this new invariant under various families of composite graphs. Exact expressions for the values of the multiplicative eccentric connectivity index of sum, disjunction, symmetric difference, lexicographic product, and a special case of strong product, and upper and/or lower bounds for the multiplicative eccentric connectivity index of generalized hierarchical product, Cartesian product, rooted product, corona product, and strong product are presented.

Computation of Mostar index for some graph operations

AbstractVery recently, a novel bond‐additive topological descriptor named as the Mostar index has been proposed as a measure of peripherality in networks and graphs. In this article, we compute the Mostar index of generalized Hierarchical product, lexicographic product, Cartesian product, corona product, join, subdivision vertex‐edge join and Indu–Bala products of graphs and apply these results to determine the Mostar index of some types of nanostructures and chemical graphs. As an application, we give the explicit expressions for the Mostar index of various nanostructures and chemical graphs.

Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning

In hierarchical production planning, the consideration of interdependencies between superior top-level decisions and subordinate base-level decisions is essential. In this respect, the anticipation of base-level reactions is highly recommended. In this paper, we consider an example from the metal-processing industry: a serial-batch scheduling problem constitutes the top-level problem and a complex nesting problem constitutes the base-level problem. The top-level scheduling decision includes a batching decision, i.e., the determination of a set of small items to be cut out of a large slide. Thus, to evaluate the feasibility of a batch, the base-level nesting problem must be solved. Because solving nesting problems is time consuming even when applying heuristics, it is troublesome to solve it multiple times during solving the top-level scheduling problem. Instead, we propose an approximative anticipation of base-level reactions by machine learning to approximate batch feasibility. To that, we present a prediction framework to identify the most promising machine learning method for the prediction (regression) task. For applying these methods, we propose new feature vectors describing the characteristics of complex nesting problem instances. For training, validation, and testing, we present a new instance generation procedure that uses a set of 6,000 convex, concave, and complex shapes to generate 88,200 nesting instances. The testing results show that an artificial neural network achieves the lowest expected loss (root mean squared error). Depending on further assumptions, we can report that the approximate anticipation based on machine learning predictions leads to an appropriate batch feasibility decision for 98.8% of the nesting instances.

Perfect codes in some products of graphs

A r -perfect code in a graph G = ( V ( G ), E ( G )) is a subset C of V ( G ) for which the balls of radius r centered at the vertices of C form a partition of V ( G ). In this paper, we study the existence of perfect codes in corona product and generalized hierarchical product of graphs where the cardinality of U is equal to one or two. Also, we give some examples as applications of our results.

The average trapping time for a weight-dependent walk on a weighted hierarchical graph

A hierarchical graph is a kind of self-similar network, which is widely discussed and has a wide range of applications. In this paper, we introduce a class of weighted hierarchical graphs H (n, k), which is constructed using the hierarchical product of complete graphs. The weighted hierarchical graph depends on two parameters: the weighted factor r $$(0<r\le 1)$$ and the number k $$(k\ge 3)$$ of nodes of the complete graph $$K_k$$ . In addition, we also discuss the trapping problem and the average trapping time (ATT) for a weight-dependent walk on a weighted hierarchical graph. Based on the special structure of the weighted graph, we derived the exact expression of the ATT for a weighted hierarchical graph. The results show that the ATT obeys a power-law function with the exponent $$\frac{\mathrm{ln}(kr)}{\mathrm{ln}k}<1$$ , which is related to the factors k and r and indicate that for $$kr=k(r=1)$$ and $$1<kr<k$$ , the ATT has a linear and sublinear relationship with the network order, respectively. Therefore, the smaller kr is, the more efficient the trapping process of the weighted hierarchical graph is. Compared with the unweighted hierarchical graph, the weighted hierarchical graph has a higher efficiency in the trapping process.

Distinguishing number of hierarchical products of graphs

The distinguishing number D(G) of a graph G is the least number k such that G has a coloring with k colors that is only preserved by the trivial automorphism. In this paper, we study the distinguishing number of hierarchical products of graphs. The distinguishing number of hierarchical products of two complete graphs is determined. We obtain an upper bound for the distinguishing number of the hierarchical product of two connected graphs. Moreover, the distinguishing number is determined for the hierarchical product of an arbitrary graph by a special graph such as a complete graph, a hierarchical power of K2, or a tree.

Developing a Master Production Schedule Using Fuzzy Mixed Integer Linear Programming

This paper considers the hierarchical production planning (HPP) concept to solve a production planning problem in the process industry in a fuzzy environment. The adopted fuzzy HPP consists of two levels in which a fuzzy aggregate production planning (FAPP) model is developed in the first level, and then a fuzzy disaggregate production planning (FDPP) model is developed at the second level. The FAPP was reported by Omar et al. [1] and therefore, this research paper discusses the FDPP model. We formulated the disaggregate model as a fuzzy mixed-integer linear programming model that aims to develop a master production schedule in which numbers of optimal batches are developed in presence of setup time. In addition, we evaluate the performance of the FMILP by comparing its results with a previously reported approach. The findings indicate that significant cost savings were achieved by adopting the fuzzy mathematical programming approach.

Edge metric dimensions via hierarchical product and integer linear programming

If $$S=\{v_1,\ldots , v_k\}$$ is an ordered subset of vertices of a connected graph G and e is an edge of G, then the vector $$r_G(e|S) = (d_G(v_1,e), \ldots , d_G(v_k,e))$$ is the edge metric S-representation of e. If the vertices of G have pairwise different edge metric S-representations, then S is an edge metric generator for G. The cardinality of a smallest edge metric generator is the edge metric dimension $$\mathrm{edim}(G)$$ of G. A general sharp upper bound on the edge metric dimension of hierarchical products $$G(U)\sqcap H$$ is proved. Exact formula is derived for the case when $$|U| = 1$$ . An integer linear programming model for computing the edge metric dimension is proposed. Several examples are provided which demonstrate how these two methods can be applied to obtain the edge metric dimensions of some applicable graphs.

IMPROVING THE APPROACHES IN RESEARCH INTO THE SELF-DEVELOPMENT OF INDUSTRIAL AND ECONOMIC SYSTEMS

A new approach to the creation of a sustainable management mechanism for an industrial enterprise is proposed, which creates stimulating conditions and stimulates motives for self-development. Economic and mathematical modeling of the two-level hierarchical production and economic system, which is included as one of the elements in a larger hierarchical system. The state of the production and economic system according to the proposed stages is determined.The formal description of the production and economic system is divided into two parts: a description of its production model and a description of the decision-making model. Many acceptable solutions are determined by the production capabilities of the elements, its internal conditions of development and the balance of its relationships with other elements of the system and the external environment.

System principles in analysis of large-scale projects (on the example of high-speed traffic projects)

In the article it is described the large-scale projects as a hierarchical production and economic system. The connection of the stages of the projects analysis with the assessment of the level of implementation is presented.

Dominated and dominator colorings over (edge) corona and hierarchical products

Dominator coloring of a graph is a proper (vertex) coloring with the property that every vertex is either alone in its color class or adjacent to all vertices of at least one color class. A dominated coloring of a graph is a proper coloring such that every color class is dominated with at least one vertex. The dominator chromatic number of corona products and of edge corona products is determined. Sharp lower and upper bounds are given for the dominated chromatic number of edge corona products. The dominator chromatic number of hierarchical products is bounded from above and the dominated chromatic number of hierarchical products with two factors determined. An application of dominated colorings in genetic networks is also proposed.

MDAIC – a Six Sigma implementation strategy in big data environments

PurposeModern production facilities produce large amounts of data. The computational framework often referred to as big data analytics has greatly improved the capabilities of analyses of large data sets. Many manufacturing companies can now seize this opportunity to leverage their data to gain competitive advantages for continuous improvement. Six Sigma has been among the most popular approaches for continuous improvement. The data-driven nature of Six Sigma applied in a big data environment can provide competitive advantages. In the traditional Six Sigma implementation – define, measure, analyze, improve and control (DMAIC) problem-solving strategy where a human team defines a project ahead of data collection. This paper aims to propose a new Six Sigma approach that uses massive data generated to identify opportunities for continuous improvement projects in a manufacturing environment in addition to human input in a measure, define, analyze, improve and control (MDAIC) format.Design/methodology/approachThe proposed Six Sigma strategy called MDAIC starts with data collection and process monitoring in a manufacturing environment using system-wide monitoring that standardizes continuous, attribute and profile data into comparable metrics in terms of “traffic lights.” The classifications into green, yellow and red lights are based on pre-control charts depending on how far a measurement is from its target. The proposed method monitors both process parameters and product quality data throughout a hierarchical production system over time. An attribute control chart is used to monitor system performances. As the proposed method is capable of identifying changed variables with both spatial and temporal spaces, Six Sigma teams can easily pinpoint the areas in need to initiate Six Sigma projects.FindingsBased on a simulation study, the proposed method is capable of identifying variables that exhibit the biggest deviations from the target in the Measure step of a Six Sigma project. This provides suggestions of the candidates for the improvement section of the proposed MDAIC methodology.Originality/valueThis paper proposes a new approach for the identifications of projects for continuous improvement in a manufacturing environment. The proposed framework aims to monitor the entire production system that integrates all types of production variables and the product quality characteristics.