iosr-Jm   Volume-16 ~ Issue-6 ~ Nov. – Dec. 2020

Abstract: From the start the problem solution was designed to allow the design of the superconductive magnets using mathematical optimization techniques. Due to the principle of features, the complex coil assemblies can be generated in 2 and 3 dimensions using just a limited amount of engineering data that can then be viewed as optimization design variables. The development of operating research has been motivated by mathematical optimization, including numerical methods such as linear and nonlinear programming, integer programming, theory of network flow and dynamic optimization. Most real-world problem optimization involves multiple competing goals, and so-called vector optimization problems must be taken into account simultaneously. The solution cycle is three times based on decision-making methods, nonlinear constraint methods and algorithms of optimization to minimize objective function.

Keywords: Optimization Problems, Numerical Methods, Solution, mathematical optimization, techniques, programming, network, nonlinear programming, algorithms

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Abstract: In this paper, we generalize the topological results of the convergence of convex – sequences in the epigraphical sense to the convex–concave sequences in Mosco – epi \ hypo graphical sense. We actually prove
that if two convex – concave sequences are convergent in Mosco – epi \ hypo graphical sense, then the sequence of epi \ hypo graphical – sum of the two sequences is convergent in Mosco – epi \ hypo graphical
sense.Also, we useour result to study the convergence of a sequence of Moreau – Yosida functions for convex – concave functions.

Keywords:convex-concave function, epi-graph, epi\hypo-graph, epi\hypo-sum, epi\hypomultiplication, parent convex function, parent concave function, Mosco's epi \ hypo graphical convergence

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Abstract: In the economic-business, trade credit is a very useful promotional tool for contractors to increase productivity through motivating extra sales and an exclusive prospect for the traders to lessen demand improbability. In this planned study we have formulated and analyzed an inventory model for perishable products under permissible delay in payments. Learning effect is incorporated on holding cost and ordering cost. To minimize the retailer's total cost is the main goal of the presented model. The results are illustrated with the help of some hypothetical numerical values to the parameters for two different cases. The sensitivity of the solution with the changing values of the parameters associated with the model is discussed.

Keywords: infation;Inventory;learningeffect;deteriorationrate;EOQ;creditfinancing;

[1]. Aggarwal, A., Sangal, I., and Singh, S. R. (2017). Optimal policy for non-instantaneous decaying inventory model with learning effect with partial shortages. Int J Comput Appl, 161(10), 13-18.
[2]. Aliyu, I., and Sani, B. (2018). An inventory model for deteriorating items with generalised exponential decreasing demand, constant holding cost and time-varying deterioration rate. American Journal of Operations Research, 8(1), 1-16.
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Abstract: Inventories are unrefined supplies, work-in-process commodities and finally completed merchandise that are measured to be the segment of business's material goods that are ready or will be equipped for trade. Formulation of an appropriate inventory model is one of the foremost concerns for a business organization. In the present work, a deteriorating inventory model for constant demand having shortages is developed where shortages are partially backlogged. Two parameter Weibull distribution is assumed as deterioration rate. Permissible delay in payments is considered in two different cases with replenishment cycle. Supplier and retailer both got some profit during the permissible period. The concept of learning and salvage value is also highlighted in the present study. A simple method is used to find out the optimal solution of the total cost. Finally, a numerical example is provided and sensitivity examination of the optimal solution with respect to the parameters is carried out.

Keywords: Inventory; shortages; Weibull deterioration; constant demand rate; salvage value; partial backlogging; learning effect; permissible delayed payments.

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[4]. Hsu, C. I. and Li, H. C. (2006). Optimal delivery service strategy for Internet shopping with time-dependent consumer demand. Transportation Research Part E: Logistics and Transportation Review, 42(6), 473-497.
[5]. Jayaswal, M. K., Sangal, I. and Mittal, M. (2019). Learning Effect on Stock-policies with Imperfect Quality and Deteriorating Items under Trade Credit. In 2019 Amity International Conference on Artificial Intelligence (AICAI) (pp. 499-504). IEEE..