Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 594 https://internationalpubls.com Optimization of END -OF -LIFE strategies- Air conditioners Jonnagiri Sowmya1*, Govada Rambabu2 1 Senior lecturer at Govt. Polytechnic for Minorities, Kurnool, Part time PhD Scholar, Department of Mechanical Engineering, College of Engineering(A), Andhra University, Visakhapatnam, India. 2 Associate Professor, Department of Mechanical Engineering, College of Engineering(A), Andhra University, Visakhapatnam, India. * Email: sowmya.jonnagiri@gmail.com Article History: Received: 26-10-2024 Revised:10-11-2024 Accepted:18-12-2024 Abstract: Circular economy is a concept developed to seek sustainable development and resource usage optimization for sustaining the green environment.it is a deviation from the practice of manufacture, consume and dispose, reverse logistics is an activity that moves goods from customers back to sellers or manufacturers after their end-of life for repair and disposal.One common misconception about the circular economy is that it is an expensive and difficult endeavor. Its goal is to regenerate natural systems and ensure materials are reused rather than discarded, encompassing reverse logistics. Product recovery includes actions such as restoration, repair, refurbishment, manufacturing again, and recycling, all of which need an effective reverse logistics system.This network yields economic advantages by decreasing raw material acquisition, enhancing inventory management, and lowering the disposal of waste. A mixed-integer linear programming model for a multi-stage reverse logistics system is suggested to improve product recovery. optimization of refurbishment of air conditioners is considered in the paper. Keywords: circular economy,air conditioning,environment,optimization. 1. Introduction Society has traditionally followed a linear manufacturing and utilization paradigm termed the “take- make-dispose” strategy. This approach includes the extraction of raw materials, their transformation into items utilization by consumer, and their disposal into environment after post-utilization (Esposito et al., 2017). This method promoted industrial progress and the expansion of consumer markets, but it also resulted in considerable issues relating to environment and issues relating to society (Andrews, 2015). The inappropriate waste disposal and unsustainable exploitation of scarce resources, whether as raw materials or energy sources, highlight the constraints of this paradigm (Prieto-Sandoval et al., 2018). This linear approach leads to significant economic losses along the value chain, eventually compromising the competitiveness of enterprises (Schroeder et al., 2018). The economy which is circular in nature aims to improve resource efficiency by reducing utilities available in nature and their exploitation. Thus avoiding the generation of non useful items ,which will result in increasing issues relating to society in different angles. The fundamental tenets of the circular economy, as articulated by several writers [MacArthur, E. (2013); Murray et al. (2017); Geng (2019); Velenturf et al. (2021)], highlight sustainable resource use, minimization of waste, and increase of value . 1. The notion of a circular economy places an emphasis on prolonging the usable life of items, which is intended to reduce the frequency with which replacements are required. The use of high- quality materials, modular designs, and an emphasis on repairability and upgradability are the main means by which this objective is accomplished. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 595 https://internationalpubls.com 2. Product lifespans may be greatly extended by the implementation of methods like re-use, refurbishment, remanufacturing, and repurposing, which in turn drastically decreases the need for new resources. 3. Recycling recovers materials from items at the final stage of their life cycle, enabling the creation of new items. Effective waste management, sorting, and reprocessing are critical components of the recycling process. 4. By optimizing utilization of fossil fuels, the circular economy minimizes waste generation and reduces environmental impacts. 5. The circular economy is inspired by nature’s regenerative systems, offering several benefits: a. Reduced extraction of new materials, preservation of earth's resources, and reduction of environmental effect are all goals of this strategy. b. Reduce the amount of trash produced by recycling, refurbishing, and reusing items, which helps reduce the size of garbage which is ultimately useful in filling up low lying areas there by reducing the unnecessary damage to environment. c. The transition to an economic system that is both regenerative and sustainable, has a beneficial influence not only on the economy but also on society and the environment. Fig. 1: Circular economy circles The economy which is circular in nature is illustrated in the Fig. 1. The "outer circle" focuses on recycling, recovery, and remanufacturing to create a closed-loop system. For instance, recovering precious metals from electronic gadgets requires advanced technology, significant investment, and scale, which are typically managed by medium to large companies. The "inner circle" prioritizes repair, refurbishment, and reuse, promoting a shift away from single- use, disposable culture. By extending product lifespans, the inner circle benefits individuals and supports small businesses. While both approaches are essential, the central focus should be on reducing, redesigning, and avoiding waste, aligning closely with sustainable consumption practices. 1.1 Air Cooling Cycle Air cooling is a major energy-consuming process, as shown in Figure 2. Fig. 2: Circular Production flow chart of cooling Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 596 https://internationalpubls.com – adapted from (Khosla et al., 2022) 1.2 motivation The present study is motivated by the application of circular economy concepts, which hold significant.There is a substantial possibility of lowering the amount of carbon released and consumption of energy that occur during the production of new units. 2. Literature Review Marwan et al. (2023) explored energy optimization in air conditioning by modifying wall features, such as temperature and material composition, using materials like Styrofoam, soil, calcium carbonate, wood, and iron to design cost-effective buildings. Li et al. introduced a technique for improving the efficiency of energy when it is used for HVAC systems via load forecasting and energy flexibility. Their methodology integrates a penalty coefficient attuned to thermal comfort, making it more efficient for energy conservation compared to static air temperature settings for comfort. A feedforward control approach is used to improve efficiency. Baghoolizadeh et al. (2023) highlighted the threat of environmental air pollutants to human health and applied genetic algorithm optimization to improve occupant thermal comfort. Chaturvedi et al. (2022) minimized yearly cooling energy use by determining optimum building envelope designs and air conditioner sizes using stochasticalgorithmsGA and PSO. Akyuz et al. (2023) conducted research on a air conditioning systemwhich is solar-assisted, examining its performance in terms of energy consumption and climate during its whole life cycle. Their results highlight the need of developing effective ways to minimize the amount of energy that is used by such systems as well as the influence that they have on the environment while simultaneously enhancing their efficiency. Source: Adapted from Wemba (2017) The CE definition proposed by Sandoval et al. (2018), which emphasizes its close relationship with society's innovation processes and evolves on the flow of energy in circular path .The utilization of resources while attempting to reduce demand and utilization of waste which is generated when attempting to put the resources in the system as per with the framework offered by Wemba (2017). The information given by Wemba (2017) and Sandoval et al. (2018) is in agreement with the circular supply chain paradigm evolved by Barbosa et al. (2018). A circular supply chain was proposed by Barbosa et al. (2018). Using a genetic algorithm to determine the best possible configurations for each component, a design technique was introduced by Hapuwatte et al. (2022) that optimizes the closed-loop dynamic product sustainability performance. There is no real-time validity to its application. Degradation model for DC motor reliability evaluation by Yang et al., 2023 Return to manufacturer (RDM) was the subject of research by Zhang et al. (2021). Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 597 https://internationalpubls.com Literature gap:Identifying suitable end-of-life (EOL) destinations for abandoned items is an increasing difficulty, especially considering the implication f issues relating to environment and over filling of low lying areas.. To resolve these difficulties, the product design must be optimized to include an ecologically sustainable end-of-life scenario that adheres to economic and statutory limitations.(Marie 2012) There has been abrupt increase of trend towards CE as compared with linear economy. This change represents an all-encompassing strategy for sustainability, as it affects components as well as products and processes. In order for CE to become standard practice, the end-of-life of the product has to be rethought to include visual health tool evaluation of each component state (Waqua et al., 2024). End of life strategies are made during design stage of products which is evident in the literature2012 on wards. The concept of circular economy extending to component level is critically examined by Waqua et al (2024). Here an effort is made to bridge the component level suitability for assessing the end of life strategy to be adopted along with optimization of cost. The objectives of the study Minimisation of various costs and carbon emission in an air conditioning industry 3. Methodology • Study of the system • Formulation of model • Computation of component level calculation • Ascessing the composition of rejection, recycle, re manufacturing rates • Computation of cost and carbon emissions. Fig 3.rpc 3.1 considered: 1. Price and Quality Variance: The variance in price and quality between both refurbished and new goods drives deterministic the need for remanufactured goods. Spare parts often hold a higher unit value. Holding costs are not considered in the collection center (CC). Dismantling operations are conducted at the Reprocessing Center (RPC). 2. Transportation Costs: Transportation costs are assumed to be based on full truckloads, calculated considering distance and overhead costs, including the cost of new products. 3. Fixed Costs: The CC, Remanufacturing Center (RMP), and Recycling Operation Center (ROC) incur fixed monthly costs. For the Reprocessing Center (RPC), a new setup operates on a fixed-cost rental sharing model. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 598 https://internationalpubls.com 4. Disposition of Returned Products: o x% of returned products are disposed of. o The rest of the rejected modules are allocated for remanufacturing in manufacturing plants or sent to the serviceable market. o y% of articles undergo remanufacturing. o Thirty percent of tested goods are delivered to the service component market. o Zero percent of rejected modules are sent for recycling. The values of x, y, and z are calculated at the component level. 3.1.1 fuzzy linear programming The Linear Programming as proposed by Zimmermann is shown below (1-3): Minimize Z= Cx (1) Subject to. Ax ≤ b (2) x ≥ 0 (3) The equation modifies after fuzzification to (4-6). Cx≾Z⊝ (4) Ax ≾b (5) x ≥ 0 (6) Here ≾ indicates "smaller than or equal to," allowing the model to attain a certain level of aspiration . Here C and A indicate the values which are fuzzy in nature. The fuzzy set A in X is defined as: A = {x, μA(x)/xϵX}. Where μA(x) :x→[0, 1] is termed as the function of membership of A and μA(x) indicates the degree of membership of x extending upto A. The Z Xò which representing a Fuzzy Objective is a fuzzy subset of X indicated by its membership function μA(x) :x→ [0, 1]. The membership functions which are linear in nature for minimization and maximization objectives were given as: min max min max max min max 1 if ( ) ( ) ( ) if ( ) 0 if ( ) j j j j j j j j j j j j Z x Z Z Z x z x Z Z x Z Z Z Z x Z     − =   −   (7) where j = 1,2,…,j (for maximization). Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 599 https://internationalpubls.com min min min max max min max 0 if ( ) ( ) ( ) if ( ) 1 if ( ) j j j j j j j j j j j j Z x Z Z x Z z x Z Z x Z Z Z Z x Z     − =   −   (8) where j = 1,2,…,j (for maximization). In Eqs. (7)-(8), min jZ is minjZj(x*) and max jZ is maxiZj(x*) and x* is the maximum solution. min max j j jZ Z Z  for all j, j = 1,2,…,J (9) Maximize J j j j w  (10) Subject to, j ≤ zj for all j j = 1,2,…,J (11) Ax ≤ b constant which is deterministic in nature (12) 1 J j j w = (13) wj, x ≥ 0 and integer, for all j, j = 1,2,…,J (14) 0 ≤  ≤ 1. (15) here wjrepresents the relative importance of fuzzy goals. 3.2 Best Worst Method (BWM) The BWM is applied to ascertain the relative importance of factors and alternatives using fewer comparisons and achieving higher consistency. The steps include: 1. Defining the decision problem and its elements. 2. Identifying the most important (best) and least important (worst) elements. 3. Comparing the best element against all others using the Saaty scale (1–9). 4. Comparing all elements against the worst element using the same scale. 5. Checking consistency. 6. Calculating weight scores. Using the Saaty scale, rank the components from 1 to 9 and choose the most essential one from the set (e1, e2,..., en) (1-9). As a result, the most essential element for the r vectors will be Ea = (eal, ea2,..., ean), with eaa = 1 being the obvious collection center. Eb = (e1b. e2b,...,enb)T, on the other hand, would be the least significant element to other vectors if we used the same scale. Consistency is verified using the consistency ratio calculated as: * Consistency Index CR  = (6) The values of Consistency index are shown in Table-3 below Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 600 https://internationalpubls.com Table-3: eab 1 2 3 4 5 6 7 8 9 Consistency index (max) 0.0 0.44 1.0 1.63 2.3 3.0 3.73 4.47 5.23 To determine the maximum weight for all elements, the highest absolute differences are a aj j w e w − and j jb b w e w − , these differences are minimized across all criteria. The following is the formulation of the problem, which assumes that the total of the weights is positive.: min max , ja j aj jb j b ww e e w w    − −     s.t. 1j j b = (7) bj ≥ 0, for entire values of j. There is thus the possibility of transforming the problem into the following optimization model for resolution: min  s.t. ,a aj j w e w −  for all j , j jb b w e w −  for all j 1j j b = (8 bj ≥ 0, for all. 4. Mathematical Model Formulation 4.1 component level calculation The fuzzy inference model, which is used to estimate the quality of items that have attained the End phase of life (EoL), comprises the following steps: Step-1:Determine the parameters relating to input and output: The parameter representing output is expressed in the form of number, Fuzzy Quality Level, ranging from 0 to 1, denoting the FQL of an EoL component. Three input parameters are essential for computing the FQL: 1. Usage Condition (UC): This metric considers elements like use frequency, operational practices, staff proficiency, working conditions (e.g., moisture, humidity, and temperature cleanliness), and maintenance standards. Suboptimal consumption practices may result in degraded end-of-life situations. The UC is calculated as: UC = UFUF + EFEF + MLML + WSWS (1) Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 601 https://internationalpubls.com where UFUF, WSWS, EFEF + MLMLre weights assigned by experts (on a scale of 1–10). Scores for sub-indices {UF, EF, ML, WS}are determined using: 1 ( ) ( ) s i ij ij j X u h p h = =  (2) Herep(hij) is the statistical probability of a component belonging to partitionhij, andu(hij)is the evaluation score (1–5). 2) EoL component Reliability (ER): By determining the chance that a component will perform its function once the product attains its end-of-life (EoL), reliability may be measured. It is expressed as: ER = P{T ≥ t}, Here component’s lifespan is represented by Tis the and the mean usage age is represented by tis. Using the Weibull model. ER can be calculated exp k k k k t ER     = −      (3) Here mean usage age of k, is represented by tk , hk and bk are Weibull parameters derived from failure data. 3) Component Performance (CP): Since reliability alone cannot fully reflect EoL conditions, CP assesses component performance using lifecycle data: CP = PD(1 – PDk) + PM(1 – PMk) (4) 1 (defective | age )ku uu k P PD  ==   (5) Here the probability of a component being defective is represented by PDk and . PMk is the probability of it absence.PD and PM are weights( 0PD, PM1 and PD + PM= 1). Eq. (5) shows a technique to collective PDk, Here size of the sample space is represented by u the, the actual usage life of product u is exhibited by ageu and finally Pku is a conditional probability that provides the chance of component k being defective under a given usage life ageuk. Step-2: Fuzzification: This process results in the transformation of clear assessment values into fuzzy linguistic variables. For every input, there are three fuzzy sets that are used: low, medium, and high. On the other hand, the output (FQL) is specified with five levels, varying from very low to very high sensitivity. Figure 2 depicts the functions that are associated with membership. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 7s (2025) 602 https://internationalpubls.com Fig. 2: A diagrammatic representation of the functions representing membership for both the input and the output Step-3: Fuzzy inference: . “IF-THEN” criteria delineate input premises and output conclusions, for instance, “If UC, ER, and CP are elevated, then FQL is significantly high.” For three inputs and three fuzzy levels , a total of 27 criteria (3^3) is required. General rules include: 1. All inputs elevated (diminished): FQL is exceedingly high (remarkably low). 2. The condition that FQL is medium is possible only when l inputs are all medium: 3. The condition that FQL is medium(high) is possible only Two at high (medium) and one at medium (high); 4. The condition that FQL is low is possible only If both inputs are low Certain circumstances are unfeasible. (e.g., poor UC and low ER with high CP) and marked as N/A. Rules can be refined through expert feedback. Step-4: Defuzzification: The centroid defuzzification method is used to transform fuzzy outputs into precise values: ( ) ( ) a zb a zb x xdx FQL x dx  =    (6) Here the membership function of the fuzzy set Z on the interval [a,b] is represented by z(x) ]Recovery Decisions Based on the calculated FQL, components are assigned recovery options: 1) Reuse or Resale: If FQLik ≥Qh,k, ECikS3. 2) Remanufacture or Refurbish: If Qik≤ FQLik