Improved Upper Bound to Product Rate Variation Problem

The sequencing problem which minimizes the deviation between the actual (integral) and the ideal (rational) cumulative production of a variety of models of a common base product is called the product rate variation problem. If the objective is to minimize the maximum deviation, the problem is bottleneck product rate variation problem and the problem with the objective of minimizing all the deviations is the total product rate variation problem. The problem has been widely studied with several pseudo-polynomial time exact algorithms and heurism-tics. The lower bound of a feasible solution to the problem has been investigated to be tight. However, the upper bound of a feasible solution had been established in the literature which could further be improved. In this paper, we propose the improved upper bound for BPRVP and TPRVP.

Download Full-text

Estimation of the Largest and the Smallest Function Values of a Feasible Solution for the Total Product Rate Variation Problem

Journal of Institute of Science and Technology ◽

10.3126/jist.v19i1.13824 ◽

2015 ◽

Vol 19 (1) ◽

pp. 35-38

Author(s):

Shree Ram Khadka

Keyword(s):

Mixed Model ◽

Feasible Solution ◽

Production Systems ◽

Exact Algorithms ◽

Just In Time ◽

Rate Variation ◽

Variation Problem ◽

Total Product ◽

Cumulative Production ◽

The Ideal

The problem of minimizing the total deviations between the actual and the ideal cumulative production of a variety of models of a common base product arises as a sequencing problem in mixed-model just-in-time production systems. This is called the total product rate variation problem. Several pseudo-polynomial exact algorithms and heuristics have been derived for this problem. In this paper, we estimate the largest and the smallest function values of a feasible solution for the problem when the m-th power of the total deviations between the actual and the ideal cumulative productions has to be minimizedJournal of Institute of Science and Technology, 2014, 19(1): 35-38

Download Full-text

On Upper Bound for the Bottleneck Product Rate Variation Problem

Dynamics in Logistics - Lecture Notes in Logistics ◽

10.1007/978-3-319-45117-6_34 ◽

2016 ◽

pp. 391-399

Author(s):

Shree Ram Khadka ◽

Till Becker

Keyword(s):

Upper Bound ◽

Rate Variation ◽

Variation Problem

Download Full-text

Bottlenecks to product rate variation problem with batching

BIBECHANA ◽

10.3126/bibechana.v8i0.4876 ◽

2012 ◽

Vol 8 ◽

pp. 53-58

Author(s):

Shree Ram Khadka

Keyword(s):

Optimal Solution ◽

Rate Variation ◽

Assembly Lines ◽

Sequencing Problem ◽

Variation Problem ◽

Processing Times ◽

Common Base

The product rate variation problem with batching minimizes the variation in the rate at which different models of a common base product are produced on the assembly lines with the assumption of significant setup and arbitrary processing times for each copy of each model. Establishment of bottlenecks to the problem is important for the feasible and the optimal solution to the problem. In this paper, the lower and the upper bottlenecks to the problem are established. Moreover, small bottlenecks that lead to optimality to some instances are investigated.Keywords: Product rate variation problem; batching; sequencing problem; nonlinear integer programmingDOI: http://dx.doi.org/10.3126/bibechana.v8i0.4876BIBECHANA 8 (2012) 53-58

Download Full-text

Sequencing Time Window for the Total Product Rate Variation Problem

Journal of Institute of Science and Technology ◽

10.3126/jist.v19i2.13847 ◽

2015 ◽

Vol 19 (2) ◽

pp. 14-18

Author(s):

Shree Ram Khadka

Keyword(s):

Time Window ◽

Science And Technology ◽

Rate Variation ◽

Variation Problem ◽

Total Product

Abstract on the PDFJournal of Institute of Science and Technology, 2014, 19(2): 20-23

Download Full-text

A Viable Approach to Mitigating Irreproducibility

Stats ◽

10.3390/stats4010015 ◽

2021 ◽

Vol 4 (1) ◽

pp. 205-215

Author(s):

David Trafimow ◽

Tonghui Wang ◽

Cong Wang

Keyword(s):

Upper Bound ◽

Influence of Dental Composite Viscosity in Attachment Reproduction: An Experimental in Vitro Study

Materials ◽

10.3390/ma12234001 ◽

2019 ◽

Vol 12 (23) ◽

pp. 4001

Author(s):

Vincenzo D’Antò ◽

Simone Muraglie ◽

Beatrice Castellano ◽

Ettore Candida ◽

Maria Francesca Sfondrini ◽

...

Keyword(s):

In Vitro Study ◽

Dental Composite ◽

Maximum Deviation ◽

Force System ◽

Maximum Value ◽

Significant Difference ◽

The Difference ◽

Level Of Significance ◽

The Ideal

Background: Attachments are composite auxiliaries that are used during a clear aligner orthodontic therapy to achieve difficult tooth movements. Two important factors are the planned configuration and the actual position of these auxiliary elements to obtain the desired force system. The aim of the present study was to evaluate the role of different composite materials in the correct reproduction of attachment shape and position. Methods: The materials that were considered in the study were a flowable resin, a dental restorative material, and an orthodontic composite. The attachments were created on three models of extracted teeth. Once the impressions were performed, 25 attachments of different shapes were added onto each virtual model to obtain the necessary templates to make the attachments. Each tested material was used to create a set of 25 attachments that were then scanned with an accuracy of 10μm. The resultant STL (stereolithography) files were superimposed onto the ones from the initial virtual plan, through Geomagic software, and the aligned scans were then compared while using a color map. The parameters that were calculated to make a comparison between the created attachments and the ideal ones were the maximum deviation in defect and in excess, the overflow, and the volume’s difference. In addition to these measurements comparing the three above-mentioned groups, the difference in volume between all the ideal and realized samples were analyzed. To test for differences among the three groups, a one-way Analysis of variance (ANOVA) was used with a Bonferroni post-hoc test. The level of significance was set at p < 0.05. Results: No statistically significant results were found between the three groups regarding the maximum value in defect, the maximum value in excess, and the minimum value as control, while a statistically significant difference was found between the overflow of orthodontic resin when compared to the flowable composite. Conclusions: The three materials that were used in this study were appropriate for attachment fabrication. The fidelity of attachment reproduction was similar when using the three different composites. The orthodontic composite showed more overflow when compared with the flowable one.

Download Full-text

Nilpotent Ideals in Alternative Rings

Canadian Mathematical Bulletin ◽

10.4153/cmb-1980-041-9 ◽

1980 ◽

Vol 23 (3) ◽

pp. 299-303 ◽

Cited By ~ 1

Author(s):

Michael Rich

Keyword(s):

Upper Bound ◽

Associative Ring ◽

Analogous Result ◽

Alternative Ring ◽

Locally Nilpotent ◽

Open Question ◽

The Ideal

It is well known and immediate that in an associative ring a nilpotent one-sided ideal generates a nilpotent two-sided ideal. The corresponding open question for alternative rings was raised by M. Slater [6, p. 476]. Hitherto the question has been answered only in the case of a trivial one-sided ideal J (i.e., in case J2 = 0) [5]. In this note we solve the question in its entirety by showing that a nilpotent one-sided ideal K of an alternative ring generates a nilpotent two-sided ideal. In the process we find an upper bound for the index of nilpotency of the ideal generated. The main theorem provides another proof of the fact that a semiprime alternative ring contains no nilpotent one-sided ideals. Finally we note the analogous result for locally nilpotent one-sided ideals.

Download Full-text

A New Upper Bound Based on Vertex Partitioning for the Maximum K-plex Problem

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2021/233 ◽

2021 ◽

Author(s):

Hua Jiang ◽

Dongming Zhu ◽

Zhichao Xie ◽

Shaowen Yao ◽

Zhang-Hua Fu

Keyword(s):

Branch And Bound ◽

Upper Bound ◽

Undirected Graph ◽

State Of The Art ◽

Search Space ◽

Exact Algorithms ◽

Induced Subgraph ◽

Massive Graphs ◽

Vertex Set ◽

Number Of Branches

Given an undirected graph, the Maximum k-plex Problem (MKP) is to find a largest induced subgraph in which each vertex has at most k−1 non-adjacent vertices. The problem arises in social network analysis and has found applications in many important areas employing graph-based data mining. Existing exact algorithms usually implement a branch-and-bound approach that requires a tight upper bound to reduce the search space. In this paper, we propose a new upper bound for MKP, which is a partitioning of the candidate vertex set with respect to the constructing solution. We implement a new branch-and-bound algorithm that employs the upper bound to reduce the number of branches. Experimental results show that the upper bound is very effective in reducing the search space. The new algorithm outperforms the state-of-the-art algorithms significantly on real-world massive graphs, DIMACS graphs and random graphs.

Download Full-text