iosr-Jm   Volume-19 ~ Issue-1 ~ Jan. – Feb. 2023

Abstract : In this paper, we have analysed an inventory model for deteriorating items with time dependent quadratic demand rate and time dependent holding cost. Two parameter Weibull distribution is considered for time to deterioration and shortages are not allowed to occur.The objective is to minimize the average total inventory cost.The solution of the discussed model is illustrated by a numerical example and sensitivity analysis is carried out to understand the effect of change of the significant parameters. The aim of this paper is to derive optimum results to help the retailer to take inventory management decisions for an economic order quantity model..

Key Word: Inventory model, deteriorating items, quadratic demand, Weibull distribution

[1]. Bhunia, A. K., and Shaikh, A. A. (2016). Investigation of two-warehouse inventory problems in interval environment under inflation via particle swarm optimization. Mathematical and Computer Modelling of Dynamical Systems, 22(2), 160-179.
[2]. Dutta, D., and Kumar, P. (2015a). Application of fuzzy goal programming approach to multi- objective linear fractional inventory model. International Journal of Systems Science, 46(12), 2269- 2278.
[3]. Dutta, D., and Kumar, P. (2015b). A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost: An interval number approach. Croatian Operational Research Review, 6(2), 321-334.
[4]. Gothi U. B. & Kirtan Parmar (2015), "Order level lot size inventory model for deteriorating items under quadratic demand with time dependent IHC and partial backlogging", Research Hub - International Multidisciplinary Research Journal IMRRHJ), Vol 2, Issue 2.
[5]. Hwang H, and Shinn S. W. (1997). Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments. Computers and Operations Research, Vol. 24, Issue 6. pp 539-547.

Abstract : By introducing parameters into the hypergeometric summation formula, and applying differential method to the summation formula, two new infinite summation formulae are obtained, which are closely related to central binomial coefficients and harmonic numbers. More similar identities can be obtained by applying this method,
which illustrates the important role of hypergeometric series summation formulas in solving the problem of infinite series summation involving central binomial coefficients and harmonic numbers.

Key Word: Hypergeometricseries; Central binomials coefficients; Harmonic numbers; Identities

[1]. BoyadzhievW, Series with central binomial coefficients, Catalan numbers, and harmonic numbers. Journal of Integer Sequences.
2011, 15(1).
[2]. Liu H, Wang W, Gauss's Theorem and Harmonic Number Summation Formulae with Certain Mathematical Constants. Journal of
Difference Equations and Applications, 2019, 24(1/4):313-330.
[3]. Choi J, Summation Formulas Involving Binomial Coefficients, Harmonic Numbers, and Generalized Harmonic Numbers. Journal
of Inequalities and Applications, 2013.
[4]. CantarinM.,D'AurizioJ.,On the interplay between hypergeometric series, Fourier–Legendre expansions and Euler sums.Bollettino
dell'Unione Matematica Italiana. 2019, 12:623–656.
[5]. FerrettiF, GambiniA.,RitelliD.,Identities for Catalan's Constant Arising from Integrals Depending on a Parameter. Acta Math. Sin.
(Engl. Ser.). 2020, 36(10):1083--1093.

Abstract : Background: Innovative teaching is one of the highlights of mathematics education in the twenty-first century. In this context, the study examined how Man's approach, an innovative teaching approach, affected the partial fraction decomposition performance (PFD) of engineering students enrolled in the Differential Equations course at the Jose Rizal Memorial State University's Main Campus in Dapitan City, Zamboanga del Norte, during the first semester of the academic year 2022–2023. Materials and Methods: The Pretest - Posttest Nonequivalent Group Design was used in the study as a quasi-experimental method. The traditional PFD approach, which is the method of undetermined coefficients, was presented to the control group, the BSCE-II Block B class......

Key Word: Innovative Teaching; Teaching Approaches; Partial Fraction Decomposition

[1]. Agarwal, B., Buccioni, F., von Manteuffel, A., &Tancredi, L. (2021). Two-loop leading colour QCD corrections to qq¯ $$ q\overline {q} $$→ γγg and qg→ γγq. Journal of High Energy Physics, 2021(4), 1-22. Retrieved from https://link.springer.com/content/pdf/10.1007/JHEP04(2021)201.pdf
[2]. Bauldry, W. C. (2018). Partial fractions via calculus. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 28(5), 425-437. DOI: 10.1080/10511970.2017.1388312. Retrieved from https://www.tandfonline.com/doi/abs/10.1080/10511970.2017.1388312
[3]. Bentley, B., &Bossé, M. J. (2018). College students' understanding of fraction operations. International Electronic Journal of Mathematics Education, 13(3), 233-247. Retrieved from https://doi.org/10.12973/iejme/3881.
[4]. Cohen, J. (1988). Statistical power analysis for the behavioral sciences(2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.
[5]. Ignacio, A. G. (2016). Students' viewpoints on mathematics courses in engineering: A basis for improvement. Asia Pacific Journal of Multidisciplinary Research, 4(3), 111-118. Retrieved from https://www.researchgate.net/profile/Avelino-Ignacio-Jr-2/publication/329084932_Students'_Viewpoints_on_Mathematics_Courses_in_Engineering_A_Basis_for_Improvement/links/5c346f8392851c22a3639eeb/Students-Viewpoints-on-Mathematics-Courses-in-Engineering-A-Basis-for-Improvement.pdf

Abstract : The selection of strategic facility locations is a very important aspect to minimize the distance and total allocation costs. This study aims to locate the optimal facility location to serve a number of customers with a minimum total distance. TSP is used to find facility routes to serve a number of customers. An illustrative example is presented to implement the proposed method. The illustrative results show that the proposed method can provide a good solution to this problem.

Key Word: facility location, location-allocation problem, traveling salesman problems

[1] L. Cooper, "Location-Allocation Problems," Oper. Res., vol. 11, no. 3, pp. 331–343, 1963.
[2] A. Ghaderi, M. S. Jabalameli, F. Barzinpour, and R. Rahmaniani, "An Efficient Hybrid Particle Swarm Optimization Algorithm for Solving the Uncapacitated Continuous Location-Allocation Problem," Networks Spat. Econ., vol. 12, pp. 421–439, 2012.
[3] M. D. H. Gamal and S. Salhi, "Constructive Heuristics for The Uncapacitated Continuous Location-Allocation Problem," J. Oper. Res. Soc., vol. 52, pp. 821–829, 2001.
[4] M. D. H. Gamal, Zulkarnain, and M. Imran, "Rotary Heuristic for Uncapacitated Continuous Location-Allocation Problems," Int. J. Oper. Res., vol. 39, no. 3, pp. 406–415, 2020.
[5] Firmansyah and R. Aprilia, "Algoritma Model Penentuan Lokasi Fasilitas Tunggal dengan Program Dinamik," Algoritm. J. Ilmu Komput. dan Inform., vol. 02, no. 01, pp. 31–39, 2018

Abstract : The problem of cutting two-dimensional stock is a problem where the cutting pattern considers the length and width of a rectangular stock. The objective is to minimize the wastage which is equivalent to minimizing the number of stocks used. This article discusses the solution to the problem of cutting two-dimensional stocks assuming that the supply is unlimited, and demands requested when cutting cannot be rotated. Then, the column generating technique is implemented to obtain a knapsack problem, and the knapsack is solved by dynamic programming method. The result obtained is a best combination of cutting patterns, so it minimizes the cutting wastages.

Key Word: Column generating; Cutting pattern; Knapsack problem; Rectangular stock; Two dimensional cutting-stock.

[1] P. C. Gilmore and R. E. Gomory, "A linear programming approach to the cutting-stock problem," Oper. Res., vol. 9, pp. 849–859, 1961.
[2] W. L. Winston, Operations Research: Applications and Algorithms, 4th ed. Belmont: Thomson Brooks/ Cole, 2004.
[3] S. Wongprakornkul and P. Charnsethikul, "Solving one-dimensional cutting stock problem with discrete demands and capacitated planning objective," J. Math. Stat., vol. 6, pp. 79–83, 2010.
[4] F. Furini, E. Malaguti, R. Medina Durán, A. Persiani, and P. Toth, "A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size," Eur. J. Oper. Res., vol. 218, pp. 251–260, 2012.
[5] S. Juttijudata and P. Sudjarittham, "Two-dimensional cutting stock problems with a modified column generation method," Curr. Appl. Sci. Technol., vol. 20, pp. 217–225, 2020..

Abstract : In this paper, a hypernetwork model is constructed by taking human proteins as nodes and protein complexes formed by protein interactions as hyperedges. By calculating and analyzing the related indexes of the hypernetwork, it is found that it has the nature of small world, and the node's hyperdegree presents the scale-free characteristic, but its hyperedge hyperdegree does not meet the scale-free characteristic. Considering the cross-linking of three hyperedges in the hypernetwork, the hypergraph motif is used to analyze the structure of the human protein complex hypernetwork.

Key Word: Hypernetwork; Protein complex; Topological property analysis; Hypergraph motifs.

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[3]. Yonghao S, Jinli G. Topology and robustness analysis of airline hypernetwork[J]. Intelligent Computer and Applications, 2021, 11(12): 87-92+96.
[4]. Haixiu L, Haixing Z,Yuzhi X, et al. A hypergraph-based analysis of the topology and robustness of bus hypernetworks[J]. Journal of Southwest University (Natural Science Edition), 2021, 43(10): 181-191.
[5]. Ruiming L, Jinli G. Topological characteristics and robustness analysis of shanghai bus hypernetwork[J]. Mathematics in Practice and Theory, 2018, 48(20): 129-137.