H. S. Shukla ¹, R. P. Tripathi ², A. Siddiqui ¹, Vivek Shukla ³

Affiliations
1 Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur - 273009, Uttar Pradesh, IN
2 Department of Mathematics, Graphic Era University, Dehradun - 248002, Uttara Khand, IN
3 Department of Mathematics, MMM Engineering College, Gorakhpur - 273001, Uttar Pradesh, IN

Abstract

In this paper, we develop an EOQ model for power demand under the condition of permissible delay in payment by considering four different situations. Mathematical formulation is derived under these four different situations. The main objective of this work is to obtain minimum total relevant cost. Next, we derive optimal solution optimal cycle time, order quantity and total relevant cost for the proposed model. The theoretical results are illustrated with numerical examples. The sensitivity analysis of the optimal solution is provided with respect to key parameters of the system. Mathematica 5.1 software is used for finding numerical results.

Keywords

Cash Discount, Demand Rate, EOQ Model, Permissible Delay, Total Relevant Cost

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H. S. Shukla ¹, R. P. Tripathi ², M. A. Siddiqui ¹

Affiliations
1 Department of Mathematics and Statistics, DDU, Gorakhpur University, Gorakhpur – 273009, Uttar Pradesh, IN
2 Department of Mathematics, Graphic Era University, Dehradun – 248002, Uttarakhand, IN

Abstract

Objective: In this paper, we consider time dependent demand under constant deterioration. The main objective of this paper is to obtain optimal cycle time which minimizes the total relevant cost. Methods/Statistical Analysis: We know that every business refers to the input- out relation. If the firm expands output by employing more and more the variable input, it alters the proportion between fixed and variable inputs. In this study, the truncated Taylor’s series approximations are used for exponential terms to find closed form numerical solution. The optimal value of cycle time is obtained by differentiating cost function. Findings: We compared all results with the optimal solution we also show that the total relevant cost function in minimum. Mathematical models are established to validate the proposed model considering four different situations i.e. case (1) T ≥ M1 Case (2) T < M1. Case (3) T ≥ M2 and case (4) T < M2. Application/Improvements: Capital is the most essential element of production process. At present inflation plays a crucial role in each type of business transaction. Numerical examples are given for four different situations, those show that the validity of the model. Sensitive analysis is included for different parameters. Cost is a factor which is directly related to production cost analysis helps in achieving high quality production at low cost.

Keywords

Credit Period, Deterioration, EOQ Model, Optimal, Time Discounting, Time Sensitive Demand

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