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An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus on enumerative algorithms for the computation of the equitable coloring number and propose a general scheme to derive pruning rules for them: We show how the extendability of a partial coloring into an equitable coloring can be modeled via network flows. Thus, we obtain pruning rules which can be checked via flow algorithms. Computational experiments show that the search tree of enumerative algorithms can be significantly reduced in size by these rules and, in most instances, such naive approach even yields a faster algorithm. Moreover, the stability, i.e., the number of solved instances within a given time limit, is greatly improved.
Since the execution of flow algorithms at each node of a search tree is time consuming, we derive arithmetic pruning rules (generalized Hall-conditions) from the network model. Adding these rules to an enumerative algorithm yields an even larger runtime improvement.
There is a growing demand for more flexibility in manufacturing to counter the volatility and unpredictability of the markets and provide more individualization for customers. However, the design and implementation of flexibility within manufacturing systems are costly and only economically viable if applicable to actual demand fluctuations. To this end, companies are considering additive manufacturing (AM) to make production more flexible. This paper develops a conceptual model for the impact quantification of AM on volume and mix flexibility within production systems in the early stages of the factory-planning process. Together with the model, an application guideline is presented to help planners with the flexibility quantification and the factory design process. Following the development of the model and guideline, a case study is presented to indicate the potential impact additive technologies can have on manufacturing flexibility Within the case study, various scenarios with different production system configurations and production programs are analyzed, and the impact of the additive technologies on volume and mix flexibility is calculated. This work will allow factory planners to determine the potential impacts of AM on manufacturing flexibility in an early planning stage and design their production systems accordingly.
Manufacturing companies across multiple industries face an increasingly dynamic and unpredictable environment. This development can be seen on both the market and supply side. To respond to these challenges, manufacturing companies must implement smart manufacturing systems and become more flexible and agile. The flexibility in operational planning regarding the scheduling and sequencing of customer orders needs to be increased and new structures must be implemented in manufacturing systems’ fundamental design as they constitute much of the operational flexibility available. To this end, smart and more flexible solutions for production planning and control (PPC) are developed. However, scheduling or sequencing is often only considered isolated in a predefined stable environment. Moreover, their orientation on the fundamental logic of the existing IT solutions and their applicability in a dynamic environment is limited. This paper presents a conceptual model for a task-based description logic that can be applied to factory planning, technology planning, and operational control. By using service-oriented architectures, the goal is to generate smart manufacturing systems. The logic is designed to allow for easy and automated maintenance. It is compatible with the existing resource and process allocation logic across operational and strategic factory and production planning.
75 Jahre Vereinsgeschichte
(2010)
3D-Freiformflächenmessung
(2003)