Minimum Number Of Units Research Articles

РАЗРАБОТКА ОПТИМИЗАЦИОННОЙ ИМИТАЦИОННОЙ МОДЕЛИ ПРИОЗВОДСТВЕННОГО ПРОЦЕССА

The article discusses the optimization of the production process based on simulation modeling in the Arena Rockwell software product. A simulation model of the current "AS-IS" process has been developed. Based on optimization parameters - maximum equipment load, minimum number of units, a target model of the "TO-BE" process was developed. As a result of simulation modeling, when considering processes, the following parameters were established: the utilization rate of machine tools, the average duration of stay of parts in the production process, the average number of parts in the queue, the average time of stay of parts in the queue, profit and loss during the implementation of the production process. The obtained modeling results made it possible to recommend a production line based on a group technological process for processing parts. This will increase the economic efficiency of the production process by 1.36 times while reducing the number of equipment used by 16 units compared to individual (single) technological processes for processing parts.

Energy Integration of Crude Distillation Unit of a Refining and Petrochemical Company in Northern Nigeria

Most Nigerian refineries were constructed before pinch technology was developed, hence, the design were not optimal, leading to high energy loss. The objective of this work is to evaluate energy integration of crude distillation unit (CDU) of a refining and petrochemical company in Northern Nigeria using pinch analysis by utilising HINT software. Minimum heating and cooling demand of 32251.1 kW and 29637.9 kW at the pinch point of 506.5 K was evaluated from the composite curve, grand composite curve and the cascade diagram. The region of overlap in the composite curve indicates a total of 108,945 kW as the possible energy that can be recovered in the process. Existing utility demand of the unit was 96,873.5 kW, after heat integration it reduces to 61,889 kW, this showed 36.11 % energy saving with a total operating cost of US$4,560,766.5 that could be saved (annually). Minimum approach temperature (DTmin) analysis results showed an optimum DTmin of 15 K which resulted in a total annual cost of US$6,715,700. Furthermore, the analysis showed the effect of DTmin on energy, area, minimum number of units and cost targets. The design objective of the retrofit heat exchanger network (HEN) was set toward maximum energy recovery. A total of twenty (20) heat exchangers made up the new network, which comprises of twelve (12) process to process heat exchangers, two (2) heaters and six (6) coolers.

An Analytical, Numerical, and Experimental Investigation on Transverse Vibrations of a Finite Locally Resonant Beam

An analytical, numerical, and experimental investigation on the transverse vibrations of a finite beam with periodically arrayed beam-like resonators was carried out. A continuous-discrete model of the finite locally resonant beam was established by employing the “mass-spring- mass” subsystem. The analytical solution of the coupling vibration equations was derived based on the modal superposition method, and the analytical expression of average velocity response and vibration transmissibility were given. Then, the minimum periodic number of different units which could result in a bandgap was determined. Finally, the bandgap of a finite locally resonant beam was confirmed by a vibration experiment on a simply supported beam with twelve uniformly distributed beam-like resonators. The numerical and experimental results show that finite locally resonant beams have low-frequency bandgaps like infinite locally resonant beams, and the bandgap position is close to the resonance frequency of resonators. In addition, for a beam with a different type of locally resonant units, the minimum number of units that can generate the bandgap is nearly the same. Within considered frequency ranges, the experimental results are consistent with the theoretical results, meaning that the transverse vibration in locally resonant beams could be substantially attenuated. The conclusions may be supported to the application of locally resonant theory to control low-frequency vibration and radiation noise.

Influence of Inter- and Intra-Batch Variability on the Sample Size Required for Demonstration of Equivalent Microstructure of Semisolid Dosage Forms

Inter- and intra-batch variability of the quality attributes contribute to the uncertainty for demonstrating equivalent microstructure of post-approval changes and generic/hybrids of semisolid topical products. Selecting a representative sample size to describe accurately the in vitro properties of semisolids and to reach enough statistical power to demonstrate similarity between two semisolid topical products is currently challenging. The objective of this work is to establish the number of batches and units per batch to be compared based on different inter-batch and intra-batch variability to demonstrate equivalence in the physical characteristics of the products that ensure a similar microstructure of the semisolid. This investigation shows that the minimum number of batches to be compared of each product is 3 and the minimum number of units per batch could be 6 in the case of low intra- and inter-batch variability. If the products are not identical, i.e., 2.5–5% differences that are expected due to differences in the manufacturing process or the suppliers of excipients, 12 units and 6 batches are needed. If intra- or inter-batch variability is larger than 10%, the number of batches and/or the number of units needs to be increased. As the interplay between inter- and intra-batch variability is complex, the sample size required for each combination of inter- and intra-batch variability and expected difference between products can be obtained in the attached tables.

Multi-period Heat Exchanger Network Synthesis with Temperature Intervals and Uncertain Disturbances

High energy consumption is a major challenge currently threatening many industrial processes. This has made industrial processes such as absorptive CO2 capture expensive and energy intensive. However, research has shown that the application of Heat Exchanger Networks has the potential of minimizing energy demands in many industrial processes due to its energy recovery advantage. In this study, a sequential procedure is presented for the synthesis of heat exchanger network for multi-period operations with specified uncertainties in flow rates and variations in inlet and outlet temperatures of process streams. The synthesis task in this study was sequentially decomposed into three stages. Temperature interval method was used to determine the loads and minimum utilities required by the network in the first stage. Determination of the minimum number of units was considered in the second stage while the third stage was dedicated to the derivation of a network configuration and sizing of heat exchangers to determine the capital cost using area targeting technique. Efficacy of the proposed methodology was tested using an example from literature. A new heuristic rule was established and the network topologies obtained using the proposed approach testifies to the applicability of HENs for energy minimization during absorptive CO2 capture.

A heat- and mass-integrated design of hydrothermal liquefaction process co-located with a Kraft pulp mill

This paper aims to establish a new standard process for heat and mass integration of hydrothermal liquefaction, co-located with an existing Kraft pulp mill, to produce bio-crude. Hydrothermal liquefaction is an energy-intensive process that operates at high temperature and pressure and produces a biocrude similar to conventional crude oil. The key advantages of installing hydrothermal liquefaction in proximity with a Kraft Mills enables the use of black liquor as a feed to hydrothermal liquefaction, asset repurposing and optimisation, as well as supply chain and logistics integration. This work follows a design process to increase the energy efficiency of the hydrothermal liquefaction process by using an iterative mass and heat integration procedure to optimise mass and energy flows and assets of the hydrothermal liquefaction process. The method uses process simulation tools, Pinch Analysis, heat exchanger network design tool, and the understanding of the process constraints to develop a heat exchanger network for the hydrothermal liquefaction process with maximum energy recovery, minimum number of units and enhanced mass integration. The number of heat exchangers in the network reduced from 14 to 7 when the proposed method was applied. Substituting bio-crude from the new integration hydrothermal liquefaction process for conventional fuels has the potential to decarbonise transport fuels by 11.3 kg CO2-e/GJ of fuel.

A linear relation between input and first layer in neural networks

Artificial neural networks grow on the number of applications and complexity, which require a minimization on the number of units for some practical implementations. A particular problem is the minimum number of units that a feed forward neural network needs on its first layer. In order to study this problem, it is defined a family of classification problems following a continuity hypothesis, where inputs that are close to some set of points may share the same category. Given a set S of k −dimensional inputs and let $\mathcal {N}$ be a feed forward neural network that classifies any input in S within a fixed error, there is proved that $\mathcal {N}$ requires ${\Theta } \left (k \right )$ units in the first layer, if $\mathcal {N}$ can solve any instance from the given family of classification problems. Furthermore, this asymptotic result is optimal.

Patient blood management programs: how to spread the word?

Red blood cell (RBC) transfusions save lives and improve health; however, unnecessary transfusion practice exposes patients to immediate and long-term negative consequences. Indirect consequences of unnecessary transfusions are the reduced availability of RBC units for patients who are in need. Accumulating evidence shows that restricting RBC transfusions improves outcomes and current guidelines suggest limiting RBC transfusion to the minimum number of units required to relieve symptoms of anemia or to return the patient to a safe hemoglobin range (7–8 g/dl in stable, non-cardiac inpatients). Still, studies show that there is over-utilization of RBC transfusion, partly due to low level of knowledge of physicians regarding restrictive RBC transfusion policy across a broad range of professions and specialties. Patient blood management (PBM) programs have been developed to promote clear hospital transfusion guidelines, strive for optimization of patient hemoglobin and iron stores and, most importantly, improve education regarding restrictive RBC policy. Understanding what and where the gaps of knowledge are, as was done in the study by Dr. Koren and his colleagues, is an important step for developing effective PBM programs.

Synthesis of indirect work exchange networks considering both isothermal and adiabatic process together with exergy analysis

Abstract In this paper, an efficient methodology for synthesizing the indirect work exchange networks (WEN) considering isothermal process and adiabatic process respectively based on transshipment model is first proposed. In contrast with superstructure method, the transshipment model is easier to obtain the minimum utility consumption taken as the objective function and more convenient for us to attain the optimal network configuration for further minimizing the number of units. Different from division of temperature intervals in heat exchange networks, different pressure intervals are gained according to the maximum compression/expansion ratio in consideration of operating principles of indirect work exchangers and the characteristics of no pressure constraints for stream matches. The presented approach for WEN synthesis is a linear programming model applied to the isothermal process, but for indirect work exchange networks with adiabatic process, a nonlinear programming model needs establishing. Additionally, temperatures should be regarded as decision variables limited to the range between inlet and outlet temperatures in each sub-network. The constructed transshipment model can be solved first to get the minimum utility consumption and further to determine the minimum number of units by merging the adjacent pressure intervals on the basis of the proposed merging methods, which is proved to be effective through exergy analysis at the level of units structures. Finally, two cases are calculated to confirm it is dramatically feasible and effective that the optimal WEN configuration can be gained by the proposed method.

Multiproduct Cost-Volume-Profit Model: A Resource Reallocation Approach for Decision Making

This work addresses the problem of reallocating productive resources to maximize profit. Most contributions to the topic focus on developing or improving the Cost-Volume-Profit model to obtain solutions that provide an ideal mix of products before the data is given. In particular, some algorithms are available for the problem, such as the ones proposed by Kakumanu and Shao and Feng. However, these proposals do not consider the minimum number of units to be produced, and the reallocation of productive resources for each product is a problem found in these studies. Bearing this in mind, a new algorithm based on individual financial revenue is proposed. Computational results indicate that the proposed method can be utilized as a decision support system.

Automatic Impairment-aware Optical Path Switching in Multi-core Fiber Link Based on Multi-ring Structure

We developed a novel multicore fiber (MCF) link based on a multiring structure composed of field programmable gate array (FPGA)-based optical switching units for highly reliable networks. The switching algorithm implemented on the FPGA in the unit has five high-functioning processes capable of coping with multiple link failures in the network. To verify the operations of this MCF link, we experimentally demonstrated automatic impairment-aware optical path switching when a failure occurred in an MCF link based on a two-ring structure. We were able to perform path recovery by switching within a relatively short period of time, 7.6 ms, which is sufficiently less than that required by ITU-T. The restoration path that substitutes for the failed working path was also optimized for low-loss transmissions by selecting the path having the minimum number of units through which a signal passes. These results indicate that the link will be useful for optical network designs that simultaneously need to ensure high capacity and reliable transmissions in businesses such as data centers.

On the Minimum Number of Units in Heat Exchanger Networks

The minimum number of units in a network has been proposed to be obtained using a very simple formula using graph theory (Hohmann, E. C. Ph.D. Thesis, University of Southern California, Los Angeles, CA, 1971.; Linnhoff, B. et al. Comput. Chem. Eng. 1979, 3, 295). This is done, usually, assuming that thermodynamic feasibility holds, especially in Pinch technology, where it is applied above and below the pinch, but also for cases where the pinch is ignored. While the failure of this formula is informally known in the community, to our knowledge no realistic counterexample was presented before. We provide such an industrial counterexample. In addition, we propose to use a recently developed MILP model (Barbaro, A., and Bagajewicz, M. Comput. Chem. Eng. 2005, 29, 1945) that guarantees finding the global minimum number of exchangers. Finally, we point out the large number of alternative solutions that real industrial problems may exhibit.

Solving the Impediment Induced Variable Shape Covering Problem

Given finite resources, organizations are in a constant struggle to satisfy conflicting demands for resource allocation. Finding the right number of response units needed to respond to an incident in a given area is one such problem. Different geographical areas have different characteristics that further complicate the problem. For example, Canada’s Arctic waters is a large area with many islands and where varying ice coverage conditions are the norm. These impediments complicate what would otherwise be a straightforward application of the Circle Packing or Circle Covering Problem. The authors propose to call such a problem the Impediment Induced Variable Shape Covering Problem and present the Incident Response Model that determines the minimum number of units needed to respond to an incident anywhere in a given Area of Interest within a predetermined response time while avoiding or accounting for impediments.

Worst-Case Diagnosis Completeness in Regular Graphs under the PMC Model

System-level diagnosis aims at the identification of faulty units in a system by the analysis of the system syndrome, that is, the outcomes of a set of interunit tests. For any given syndrome, it is possible to produce a correct (although possibly incomplete) diagnosis of the system if the number of faults is below a syndrome-dependent bound and the degree of diagnosis completeness, that is, the number of correctly diagnosed units, is also dependent on the actual syndrome sigma. The worst-case diagnosis completeness is a syndrome-independent bound that represents the minimum number of units that the diagnosis algorithm correctly diagnoses for any syndrome. This paper provides a lower bound to the worst-case diagnosis completeness for regular graphs for which vertex- isoperimetric inequalities are known and it shows how this bound can be applied to toroidal grids. These results prove a previous hypothesis about the influence of two topological parameters of the diagnostic graph, that is, the bisection width and the diameter, on the degree of diagnosis completeness.

An algorithm for the (r,s)-domination number of a tree

Suppose that at most r units of some commodity may be positioned at any vertex of a graph G = (V,E) while at least s (>= r) units must be present in the vicinity (i.e. closed neighbourhood) of each vertex. Suppose that the function f : V -> {0,...,r}, whose values are the numbers of units stationed at vertices, satisfies the above requirement. Then f is called an s-dominating r-function. We present an algorithm which finds the minimum number of units required in such a function and a function which attains this minimum, for any tree.

Two-dimensional packing problems: A survey

We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there is a single standardized unit of given width, and the objective is to pack all the items within the minimum height. We discuss mathematical models, and survey lower bounds, classical approximation algorithms, recent heuristic and metaheuristic methods and exact enumerative approaches. The relevant special cases where the items have to be packed into rows forming levels are also discussed in detail.

The Muqarnas Pre-designed Erecting Units: Analysis, Definition of the Generic Set of Units, and a System of Unit-Creation as a New Evolutionary Step

The muqarnas is an architectural form developed and used in Islamic architecture over the last millennium. In short it can be defined as: a three-dimensional form, whose visual function is the gradual transition between two levels, two sizes, and or two shapes. One of the methods of its production, which prevailed in the Islamic western lands, involved the use of certain sets of pre-designed units, that when combined in different ways generate a very wide range of alternatives. The plans of these units are based on shapes of 45-, 90-, 135- degrees. Thus, they are limited in their final output; and their innovativeness was long lost accordingly. The main objective of this paper is to create a new set (or sets) of units that belong to the same logic of these described but overcome their limitations. The method is first to analyze the available units, second to reach the minimum number of units that can be considered as the generic units, third to synthesize their origin of creation (as it is not found in any literature) and thus creating a system of unit-generation, and finally to create the new sets of units. These sets can be considered as a new evolutionary step of the muqarnas of this type. Accordingly, a computer program for the unit creation was created to test and evaluate the concepts presented in the paper.

Capital and total cost targets for mass exchange networks: Part 1: Simple capital cost models

This paper presents a method for targeting the capital and total cost of a mass exchange network. This part of the paper considers stagewise systems and uses a simplified capital cost correlation in order to convey the fundamentals. The method starts by determining the number of stages required, using the y− x composite curve plot presented previously, and then converts this to a capital cost. This target is combined with utility targets to give a target for the total annual cost. Simple design guidelines are presented, which allow these targets to be approached to within a few percent. The method is applied to a coke-oven gas sweetening example, which is a case involving two mass separating agents (MSAs) which do not overlap. It is also applied to an example involving phenol removal, in which there are overlapping MSAs. A final example deals with multicomponent transfer by extending the coke-oven gas problem. The paper introduces a new graphical tool, the y− y* composite curve plot, for handling systems with overlapping MSAs. The paper demonstrates that, contrary to previous belief, using the minimum number of units does not necessarily lead to a minimum cost design.

A New Method To Determine the Best Units for Breaking Heat Load Loops of Heat Exchanger Networks

For a heat exchanger network that contains more than the minimum number of units, it is often required to simplify the network by removing extra units. A new method is proposed to find the best units for breaking loops involved in the network. The energy penalty incurred by deleting a unit from a loop depends not only on the heat loads of all units but also on the structure of the network. To take into account the effects of heat loads and interactions of units on energy relaxation, the constrained units that cannot absorb any transferred energy and the redistribution of {Delta}t{sub min} are discussed. The constrained units make the evaluation of energy penalties of some units simple and straightforward. When the redistribution of {Delta}t{sub min} caused by deleting a unit is examined, the lower bound of the energy penalty of the unit can be easily estimated. When the lower bound is compared with the heat loads of other units, it can be decided whether the unit should be deleted or not. The proposed method is reliable and efficient. It considers effects of both the heat loads and the interactions of units and avoids calculations of the accurate energy penaltiesmore » of all units. A common testing example is used to demonstrate the effectiveness of the proposed method.« less

A designer-controlled framework for the synthesis of heat exchanger networks involving non-isothermal mixers and multiple units over split streams

A general MINLP algorithmic approach to the optimal synthesis of heat exchanger networks reaching specified topology targets is presented. The approach regards the network structure as composed of two types of primary components: individual units and parallel arrangements of heat matches, all connected in series over each process stream. Proper sets of decision variables are introduced to stand for the existence and relative location of (a) the primary components in the network and (b) the individual units within each parallel arrangement. In this manner, the designer can gain control on the network structure synthesis task by specifying some desired topological features. Nonlinearities are just confined to parallel sub-structures involving non-isothermal mixers and/or multiple units in series over a split stream. Topology targets normally lowering the problem size are taken into account from the beginning to compute both the least utility usage and the minimum number of units. Application of the new synthesis method to the widely known 4SP2 example problem provides an optimal network configuration not reported before.