Evaluation of the Effectiveness of Fuzzy Logic Sensitivity Analysis in Matlab Works for Evaluating the EOQ Production Inventory Model with Variable Demand with the Lagrangian and Kuhn-Tucker Methods

Abstract

To mirror the real world, the various inventory cost characteristics are also shown as interval numbers. The assumption is that the relationship between the product\'s demand and selling price is linearly descending. The supply chain has been optimized in this article using these two techniques with random demand. These two approaches have been compared, and a potential machine-learning strategy combining these two approaches has also been offered. The demand is thought to be random. Crisp and fuzzy models were utilized in this study to fix perishable products in the manufacturing process. The proposed model is solved using both the nonlinear mathematical Programming Lagrangian and Kuhn-tucker Methods. The Grade Mean Integration Representation technique is used to defuzzify data in the Fuzzy Inventory Model, which uses a Trapezoidal Fuzzy Number to determine the lowest prices. To support the solution process, a numerical example that includes sensitivity analysis is done at the end. Lagrangian, Kuhn-Tucker, and fuzzy logic analysis are used to analyze the Economic Order Quantity (EOQ) for changeable demand in this study. This research compares and contrasts their approaches, and the findings demonstrate the superiority of fuzzy logic over traditional approaches. To explore the price-dependent coefficients with variable demand and unit purchase cost over variable demand, trapezoidal fuzzy numbers are used in this research. The outcomes closely resemble the clean output. To validate the model, sensitivity analysis in Matlab was additionally carried out.

Introduction

I. INTRODUCTION

Industries and businesses are focusing their supply chains on environmental performance by increasing service and cost. For a company or an industry, the most important factor is lot sizing or ordering quantity. Due to stronger and more frequent extreme weather events, global warming and the greenhouse effect have received a lot of attention. This was known as the Kyoto Protocol, which aimed to reduce the greenhouse impact. Three flexible procedures were also proposed by the protocol: international emissions trading, cooperative implementat0ion, and clean development mechanism. Trading emissions is one of the most efficient market-based strategies under the Kyoto Protocol (also known as Cap-and-Trade). With the help of this mechanism, all industries are forced to adhere to a cap on their carbon emissions, and they are also given the option to purchase or sell emission rights. Several developed nations have taken either regulatory action or other steps to reduce their emissions to meet the targets for the emissions decrease established by the Kyoto Protocol. Since emission is a fundamental component of fossil fuels, reducing emissions results in cost savings. The three main greenhouse gases—Carbon Dioxide (CO2), Methane (CH4), and Nitrous Oxide (N2O)—are responsible for both atmospheric emissions and removals. Human activities including the usage of automobiles, the production of energy, and the burning of fossil fuels during industrialization are the main causes of greenhouse gas emissions.

From an international economic perspective, the industry directly affects the economy. As a result, carbon emissions cannot be eliminated. The biggest challenge for any industry is to invest in green technologies to decrease emissions and combat global warming.

Green technology may help to minimize emissions. A sustainable technology, sometimes known as "green technology," has a "green" application. Nature refers to the color green, but in general, "green technology" refers to any innovation that considers both an invention's immediate and long-term effects on the environment. Due to its simplicity, the EPQ (Economic Production Quantity) model has been widely used in exercises. The classic EPQ model does, however, make certain additional assumptions, and several academics have attempted to develop it from various angles. The conventional EPQ model has recently been expanded in several ways. A different partial back-ordering example for a deterministic EPQ formula was addressed by Pentico et al. in 2009. With their unique EPQ formula in their model, they analyzed and studied the prior literature on EPQ models. By taking into account a partial back ordering example under how the effects of advance payments in profit operate, Taleizadeh (2014) extends the work of Pentico et al. (2009) after more than five years. They developed the single-objective function of carbon emissions as it relates to sustainable development. They then used multi-criteria decision analysis to expand their model to a multi-echelon sustainable order quantity. To create an inventory model, Benjaafar et al. (2013) linked several decision variables under the cost function and carbon footprint to various carbon emission metrics. They looked at the impact of emission restrictions on the price of emissions. By making some operational improvements, such as investing in carbon-reducing technologies, they expanded their model to account for carbon reduction. With the aid of order quantities, Chen et al. (2013) created an EOQ model for lower emissions. Then, they analyzed issues affecting emission reduction and overall cost increase while assuming some conditions for the decrease in carbon emissions. Hu and Zhou (2014) investigated the manufacturer's shared price and carbon emission reduction strategy under a carbon emission trade. They created their model utilizing the Stackelberg game method for the best price and pollution reduction effort. To maximize profit, they looked into the effects of a carbon emission policy. Sarkar et al. created a single-stage production model with reworking (2014). They suggested the backorder and random defective rate in his study. A multi-stage production system was enhanced by Kim and Sarkar (2017) using a quality improvement policy and lead time-dependent ordering costs. A production model with quality improvement and variable backorder costs was created by Sarkar and Moon in 2014. They demonstrated how crucial the setup cost cut was for long-term production. In a sustainable EPQ or non-sustainable EPQ situation, taking into account controllable or uncontrollable carbon emissions and various shortage cases led to the development of a new model that is more applicable and useful in a real-world setting. Additionally, optimization and machine learning are closely related since many learning problems are phrased as the minimization of a loss function on a training set of samples. The gap between the model's predictions and the actual problem occurrences is expressed by loss functions.

Conclusion

The Kuhn-Tucker and Lagrange methods are both taken into account in this work. When the ordering amount, reorder point, and quantity of shipments are all maximized, the supply chain\'s overall expected cost is decreased. Production and inventory including defectives have both been considered. According to carbon policies, it has been found that both the cost and defectives can be under control with a few operational adjustments. This model could help businesses choose the appropriate order quantity, reorder point, and number of shipments. The similarities and numerical results have both been examined. From an economic and environmental perspective, the study has shown that the right Matlab contour plot between surface plots of this strategy is valid. According to the mentioned earlier research, a fuzzy solution offers the more accurate answer for the perfect order amount compared to a crisp one for both the Lagrangian as well as Kuhn-Tucker methods. The suitable order amount is more effectively addressed by a trapezoidal method compared with the alternatives approach, and both procedures also produce similar results. The Matlab program graph shows the minimal order quantity as the ideal order quantity.

References

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Copyright

Copyright © 2023 S. Swathi, K. Kalaiarasi, N. Sindhuja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.