Penalty Cost Research Articles

From features to benefits: a data-driven approach for the economic design of adaptive quality control

The current economic design of control charts assumes specific quality distributions, limits parameter choices, and over-relies on historical samples, hindering companies from determining the most economical parameters accurately. Leveraging industrial big data, we propose a data-driven, mixed-integer linear programming model for the economic design of adaptive control charts. Control limits are dynamically designed as a function of features to minimise quality costs. Considering the trade-off between false alarms and penalty costs, we develop three models: a basic model incorporating big data, a model with cost-penalised features, and a model that uses regularisation to manage overfitting. We simulate the model using new performance measures. Our findings demonstrate the economic value of adaptive control limits strategies incorporating feature data compared to benchmarks. We expanded the model to an endogenous sample size and sampling interval framework, further demonstrating the superiority of our approach. We undertook a case study using real-world data from a casting company and revealed that employing our approach culminates in a 24.6% reduction in costs relative to the company's existing quality control protocols. Our approach enables manufacturers to make strategic decisions about quality control by operationalising big data, thereby proving advantageous in reducing quality costs.

Stochastic Vehicle Routing With Delivery Choice

ABSTRACTWe consider the problem of designing delivery routes for vehicles where the vendor has the choice of how much of the demand from a customer to fulfill. The customer demand is known a priori only as a probability distribution. Exact customer demand is known only after visiting the customer. Different customers are able to negotiate different prices for each unit of product with the vendor. Given a route, the objective is to decide at each customer location, how much demand to satisfy so as to maximize expected profit taking into account a linear penalty cost for unfulfilled demand and the vehicle routing costs. In this article, we develop several new structural results for this problem. We illustrate how these structural results can be embedded in different heuristic frameworks commonly used for deterministic vehicle routing problems. This helps develop efficient routes for a single vehicle as well as a multiple vehicle scenario for this stochastic variant. For small‐sized problems that allow for exhaustive enumeration, we demonstrate the effectiveness of the illustrated heuristic. For larger problem instances, based on structural results, we develop methods that allow the heuristic to run more efficiently than otherwise. Results are reported on instances based on benchmark instances drawn from literature for upward of 100 customers and vehicle capacity up to 600 units. Computational times needed to heuristically solve such problems are within 1 100 s.

Optimizing Multi-Echelon Delivery Routes for Perishable Goods with Time Constraints

As the logistics industry modernizes, living standards improve, and consumption patterns shift, the demand for fresh food continues to grow, making cold chain logistics for perishable goods a critical component in ensuring food quality and safety. However, the presence of both soft and hard time windows among demand nodes can complicate the single-network distribution of perishable goods. In response to these challenges, this paper proposes an optimization model for multi-distribution center perishable goods delivery, considering both one-echelon and two-echelon network joint distributions. The model aims to minimize total costs, including transportation, fixed, refrigeration, goods damage, and penalty costs, while measuring customer satisfaction by the start time of service at each demand node. A two-stage heuristic algorithm is designed to solve the model. In the first stage, an initial solution is constructed using a greedy approach based on the principles of the k-medoids clustering algorithm, which considers both spatial and temporal distances. In the second stage, the initial routing solution is optimized using a linear programming approach from the Ortools solver combined with an Improved Adaptive Large Neighborhood Search (IALNS) algorithm. The effectiveness of the proposed model and algorithm is validated through a case study analysis. The results demonstrate that the initial solutions obtained through the k-medoids clustering algorithm based on spatio-temporal distance improved the overall cost optimization by 1.85% and 4.74% compared to the other two algorithms. Among the three two-stage heuristic algorithms, the Ortools-IALNS proposed here showed enhancements in the overall cost optimization over the IALNS, with improvements of 3.24%, 1.12%, and 0.41%, respectively. The two-stage heuristic algorithm designed in this study also converged faster than the other two heuristic algorithms, with overall optimization improvements of 1.55% and 1.28%, further validating the superior performance of the proposed heuristic algorithm.

Optimization of Fresh Food Logistics Routes for Heterogeneous Fleets in Segmented Transshipment Mode

To address the challenges of environmental impact and distribution efficiency in fresh food logistics, a segmented transshipment model involving the coordinated operation of gasoline and electric vehicles is proposed. The model minimizes total distribution costs by considering transportation, refrigeration, product damage, carbon emissions, and penalties for time window violations. The k-means++ clustering algorithm is used to determine transshipment points, while an improved adaptive multi-objective ant colony optimization algorithm (IAMACO) is employed to optimize the delivery routes for the heterogeneous fleet. The case study results show that compared to the traditional model, the segmented transshipment mode reduces the total distribution costs, carbon emissions, and time window penalty costs by 22.13%, 28.32%, and 41.08%, respectively, providing a viable solution for fresh food logistics companies to achieve sustainable and efficient growth.

Enhancing Resilience and Coordination in Sustainable Logistics Service Supply Chains Through Integrated Investment Contracts

Within the logistics service supply chain, where logistics service integrators and providers collaborate, the role of integrators in orchestrating resources and enhancing supply chain efficiency is pivotal. To motivate logistics service providers to invest in logistics capacity, thereby maintaining supply chain resilience and achieving coordination, a joint contract incorporating cost and benefit sharing is proposed in a novel Stackelberg game model. By analyzing the behavior of various decision-making models—centralized, coordinated, and decentralized—in supply chains, we find that the proposed Stackelberg game model effectively correlates higher investment levels with increased supply chain resilience. The coordination mechanism significantly improves both the level of resilience and the investment amount, leading to enhanced overall profitability. Sensitivity analysis reveals the impact of market pricing, demand stockout penalty costs, and substitute demand prices on these outcomes. This research contributes a new theoretical framework and practical insights into supply chain coordination and investment strategies.

An adaptive genetic algorithm with neighborhood search for integrated O2O takeaway order assignment and delivery optimization by e-bikes with varied compartments

To improve the dining experiences, online-to-offline (O2O) takeaway services with warm-keeping or refrigerated requirements are quickly expanding and becoming popular. However, single-compartment e-bikes are commonly used in takeaway platforms, which can only meet one kind of requirements and may result in an inflexible delivery. Within this context, a new type of e-bikes, namely e-bikes with mixed compartments, is introduced. Thus, warm-keeping and refrigerated orders can be delivered by one bike, namely on one route. This paper considers an integrated order assignment and delivery problem by e-bikes with warm, refrigerated, and mixed compartments (AD-EBM). To solve the problem, we develop a novel integer programming formulation to minimize the total cost by determining order assignments and finding optimal routes, and then some properties of the solutions are provided from the view of mathematics. An algorithm is designed by combining the self-adaptive genetic algorithm with the neighborhood search method (SGA-NS). Numerical experiments are conducted based on simulated different-scale takeaway instances. The experimental results highlight the excellent performance of the SGA-NS and the results are quite encouraging compared with Gurobi solver, SGA, and NS. The results of the model comparison demonstrate that the AD-EBM offers 12.38% total cost savings on average, compared to using only single-compartment e-bikes. A sensitivity analysis is performed to explore the effects of the mixed compartment costs, the customer acceptable delay time, the penalty costs for delays, and the e-bike capacity for the platform’s daily operations. Some management insights are provided to facilitate the O2O takeaway delivery.

Blockchain-backed resilient strategies in a stochastic supply chain sourcing and distribution environment under disruption: implications for B2B sector

Purpose With the changing landscape of the globalised business world, business-to-business supply chains face a turbulent ocean of disruptions. Such is the effect that supply chains are disrupted to the point of failure, supply is halted and its adverse effect is seen on the consumer. While previous literature has extensively studied risk and resilience through mathematical modelling, this study aims to envision a novel supply chain model that integrates blockchain to support visibility and recovery resilience strategies. Design/methodology/approach The stochastic bi-objective (cost and shortage utility) optimisation-based mixed-integer linear programming model integrates blockchain through a binary variable, which activates at a particular threshold risk-averse level of the decision-maker. Findings Firstly, visibility is improved, as identified by the average reduction of penalties by 36% over the different scenarios. Secondly, the average sum of shortages over different scenarios is consequently reduced by 36% as the recovery of primary suppliers improves. Thirdly, the feeling of shortage unfairness between distributors is significantly reduced by applying blockchain. Fourthly, unreliable direct suppliers resume their supply due to the availability of timely information through blockchain. Lastly, reliance on backup suppliers is reduced as direct suppliers recover conveniently. Research limitations/implications The findings indicate that blockchain can enhance visibility and recovery even under high-impact disruption conditions. Furthermore, the study introduces a unique metric for measuring visibility, i.e. penalty costs (lower penalty costs indicate higher visibility and vice versa). The study also improves upon shortages and recoveries reported in prior literature by 6%. Finally, blockchain application caters to the literature on shortage unfairness by significantly reducing the feeling of shortage unfairness among distributors. Practical implications This study establishes blockchain as a pro-resilience technology. It advocates that organisations focus on investing in blockchain to enhance their visibility and recovery, as it effectively reduces absolute shortages and feelings of shortage unfairness while improving recovery and visibility. Originality/value To the best of the authors’ knowledge, this is a unique supply chain model study that integrates a technology such as blockchain directly as a binary variable in the model constraint equations while also focusing on resilience strategies, costs, risk aversion and shortage unfairness.

Optimization of storage yards in sustainable forest management in the amazon

In the management of native Amazonian forests, infrastructure, such as stockyards and skid trails, are costly attributes and are responsible for a large part of the environmental impacts, productivity, costs and performance in forest management operations. The objective of this study was to apply a mathematical optimization model for the allocation of storage yards in native forest. The study was carried out in a native forest, in a sustainable forest management located in the Brazilian Amazon. The analyzed area has 3556.27 ha, which involved 16,425 trees and 311 wood storage yards. The study area was subdivided into three smaller areas by the company, which helped to optimize the number and size of yards. The dimensions of the storage yards were 25 × 25 m, with the maximum skid distance of trees from the felling site to the prioritized storage yard being 250 m. Two models were analyzed using integer linear programming: Model A - without penalties and Model B - with cost penalties (fictional) for opening storage yards through integer linear programming. The cost penalty served to prevent the selection of an excessive number of yards and thus the initial need to open them. Among the models, area 3 had the fewest storage yard exclusions when adding the opening cost penalty and can be considered the one that best managed the distribution in terms of cost and environmental impact of this infrastructure in the exploration. The number of storage yards allocated by model B was reduced by 27.3%, proving to be efficient in reducing impacts (5.3 ha) and in the uniformity of the amount of wood to be stored. The answers found by the models are viable solutions that allow for better results in infrastructure planning, and they can certainly be adopted by companies engaged in sustainable forest management.

Accelerated bender’s decomposition algorithm and hybrid heuristics for multi-period planning of maternal healthcare facilities in India

This work addresses the challenge of improving availability and accessibility of maternal healthcare in India by presenting a multi-period planning problem of hierarchical and successively inclusive healthcare facilities. The problem is formulated as a mixed-integer linear programming model to minimize the overall cost, including the cost of establishing and upgrading the facilities, the cost of allocating/referring the mothers-to-be to the respective facilities and the penalty cost of demotivating the overburdening of the facilities in each time period. To solve the model effectively and efficiently, a Bender’s Decomposition Algorithm (BDA) with several acceleration strategies such as valid inequalities, disaggregated Benders cuts, rolling horizon heuristic and parallelism is developed. A Bender’s type heuristic is also tested by solving the master problem heuristically. Additionally, a Fix-and-Optimize (F&O) heuristic hybridized with Simulated Annealing (SA) enhanced by various search space reduction techniques is developed to obtain good quality solutions in a reasonable time for large instances. It is evident from the results of the computational experiments that the accelerated BDA and Bender type heuristic outperforms Gurobi. The hybrid F&O and SA is observed to be the most computationally efficient approach. A representative scenario in the Indian setting presents further evidence of the model’s applicability.

Optimizing floating crane operations for efficient bulk product transshipments on inland waterways

In the realm of global supply chains, the optimization of floating crane operations for bulk product transshipment via inland waterways emerges as a crucial necessity to address economic, operational, and environmental imperatives. This research identifies a significant gap in existing methodologies for the scheduling, routing, and assignment of floating cranes, which are essential for improving efficiency and sustainability in maritime logistics. To bridge this gap, we propose the Reinforcement Learning Variable Neighbourhood Strategy Adaptive Search (RL-VaNSAS) algorithm, a novel integration of reinforcement learning with variable neighbourhood search strategies. This advanced model aims to holistically minimize energy consumption, labor costs, and penalty costs, while simultaneously enhancing service efficiency. Through rigorous simulations, RL-VaNSAS was benchmarked against conventional methods such as Differential Evolution (DE), Genetic Algorithm (GA), and the original Variable Neighbourhood Search Adaptive Strategy (VaNSAS), revealing its superior capability in significantly reducing annual energy costs to $1,211,948, labor costs to $270,948, penalty costs to $19,948, and operational hours to 12,087. Demonstrating notable advancements in operational efficiency and cost reduction, RL-VaNSAS offers a sustainable solution to the dynamic challenges of maritime logistics, characterized by fluctuating vessel arrivals and diverse cargo requirements. The findings illuminate the critical need for innovative optimization techniques in enhancing the sustainability and efficiency of maritime logistics operations. RL-VaNSAS not only fills the identified research gap but also sets a new standard for future endeavors in global supply chain management, underlining the importance of adopting advanced optimization strategies for sustainable production and economic growth.

Decision-making optimization for post-disaster restoration of multimodal transport networks in terms of resilience

IntroductionPublic health emergencies can have a ripple effect on the resilience of multimodal transport network, which will lead to problems such as route disruptions or blockages, route selection change and information transmission delay spreading to the whole network, further hindering the transportation planning and operational efficiency of the network. MethodsThis study constructs a multimodal transport route optimization model under uncertainty with the objective of the sum of transportation cost, transshipment cost, penalty cost and carbon emission cost. To enhance the computational efficiency of the model, a novel invasive weed optimization with memory and encoding value clustering capabilities is proposed. In addition, by fusing the Q-learning algorithm in reinforcement learning with the novel invasive weed algorithm, the action-value function table obtained from the training facilitates the selection of optimal routes. Based on empirical data, explore the sensitivity analysis of node disruptions, time windows, and fuzzy demand on route decision-making under public health emergencies. ResultsThe transport network is affected by public health emergencies, which makes the optimal route deviate from the expected goal, resulting in an increase in the total cost. The proportion of total cost is determined by the position of nodes in the network, with critical nodes suffering more losses than ordinary nodes. Reasonable setting of time windows and fuzzy demand intervals is an effective way to improve the resilience and transportation efficiency of multimodal transport network. ConclusionsThis study provides more applicable decision-making references for enterprises to prevent the risk of supply chain disruptions caused by public health emergencies.

A Multi‐Trip Vehicle Routing Problem With Release Dates and Interrelated Periods

ABSTRACTThis article proposes a new multi‐trip vehicle routing problem variant, originally motivated by a practical application, namely a car components distribution to repair centers (warehouses). The problem is named the multi‐trip vehicle routing with release dates and interrelated periods (MTVRP‐RDIP). The routes may start at different pre‐defined periods, called departure periods, and may have different durations. Thus, two routes that start at different periods may be active at the same period, leading to the so‐called interrelated periods. Moreover, a route may only start at a period if a vehicle is available, and the availability of the vehicle depends not only on the existing vehicles but also on the active routes at that time period. The clients are classified according to their importance and represent warehouses that require car components that are made available throughout the time horizon, thus leading to the consideration of release dates. Delays in satisfying client orders and not serving orders in the time horizon result in penalty costs that must be minimized. The objective to minimize also includes routing costs and vehicle utilization costs. Two metrics are defined to compute an order's delay, each leading to a different mixed integer linear model. Computational results showed that one model clearly outperforms the other and even this one is only suited to address the smallest instances. A matheuristic based on a rolling‐horizon process that iteratively solves the better‐performing model with fewer periods was designed to tackle the largest instances. The matheuristic can provide feasible solutions for all test instances in an efficient manner that are, on average, better than the ones provided by the model in most of the compared key performance indicators.

Scale sensitivity of ethanol production via consolidated bioprocessing with consideration of feedstock cost

AbstractWe examine feedstock cost and minimum selling price for ethanol production from corn stover as a function of scale, stover yield, participation rate, and price incentives for two conversion technologies: a conventional base case featuring thermochemical pretreatment with added cellulase, and an advanced case featuring consolidated bioprocessing with cotreatment (C‐CBP). Delivered feedstock cost ranged from $85 Mg−1 at small (10 million gallons year−1 or ~38 million L year−1) scale with high yield and participation rates to $124 Mg−1 at large scale (60 million gallons year−1 or 227 million L year−1) and low yield and participation rates. The minimum ethanol selling price (MESP) was approximately twofold lower for the advanced case compared with the base case. The payback period was several times lower for the advanced case compared with the base case, with increasing disparity at smaller scales, and was highly sensitive to ethanol price supports. For both C‐CBP and the conventional processing paradigm, MESP decreased with increasing scale, indicating that the cost penalty due to higher feedstock transport distances was more than outweighed by lower capital costs. However, the cost penalty for operation at small scale, expressed in $ gallon−1 ethanol, is lower for C‐CBP than for the conventional paradigm by roughly twofold. Particularly for initial applications of C‐CBP, we speculate that this cost penalty will likely be modest compared with the anticipated benefits of small‐scale operation such as increased opportunity to use existing infrastructure, easier plant siting and supply chain establishment, and lower total investment required.

Based on improved crayfish optimization algorithm cooperative optimal scheduling of multi-microgrid system

In order to solve the influence of the complex interaction relationships among subjects on the system solution accuracy and speed of the Multi-Microgrid system under the high penetration rate of new energy. Firstly, the paper establishes the bi-level optimal scheduling Stackelberg game model based on shared energy storage, considering the inter-subject interaction in MMG. Subsequently, based on the four improvement methods of Chaotic Map, Quantum Behavior, Gaussian Distribution, and Nonlinear Control Strategy, the Chaotic Gaussian Quantum Crayfish Optimization Algorithm is proposed to solve the optimization scheduling model. The improved algorithm exhibits superior initial solutions and enhanced search capability. In comparison to the original algorithm, the relative errors of the CGQCOA optimization outcomes are 98%, 20.96%, 98.74% and 16.55%, respectively, enhancing the model-solving accuracy and the speed of convergence to the optimal solution. Finally, the simulation demonstrates that the revenue of Microgrid 1, Microgrid 2, and Microgrid 3 have increased by 0.73%, 1.17%, and 1.04%, respectively. Concurrently, the penalty cost of pollutant emission has decreased by 5.9%, 11.5%, and 12.68%, respectively. Furthermore, the revenue of the shared storage have increased by 1.91%. These findings validate the efficacy of the methodology proposed in enhancing the revenue of the various subjects and reducing pollutant gas emission.

Condition-based maintenance policy for shared service-oriented leased equipment

Due to growing consumer demands for immediacy, personalization, and high availability, equipment manufacturers are venturing into the sharing market with expanded shared leasing services. While selling usage rights of equipment, they provide additional services to the consumer in the role of equipment operators, such as free maintenance and swap. However, uncertain usage rates and return times in the shared model pose significant maintenance challenges. This paper proposes a personalized condition-based maintenance (CBM) policy accounting for these uncertainties and heterogeneous consumer usage patterns. By considering inspection, maintenance, and penalty costs, we minimize the long-run expected maintenance cost per unit of time for operators. In the numerical example, we compare our policy against fixed inspection interval CBM policy and non-fixed inspection interval CBM under average usage rate, demonstrating that personalized CBM reduces maintenance costs. Sensitivity analysis provides some managerial insights. Firstly, operators should adjust the number of free swaps strategically to manage the intensity of equipment swaps, and strike a balance between the increased maintenance costs due to the swap intensity enhancement and the improved user satisfaction and equipment availability resulting from the increased number of free swaps. Secondly, when the acceleration effect of imperfect maintenance on the degradation rate is strengthened, operators should prioritize reducing the frequency of imperfect maintenance and increasing the frequency of perfect preventive maintenance. Moreover, operators must make strategic investments in their maintenance actions, balancing maintenance costs and penalty costs to develop cost-effective imperfect maintenance improvement factors.

Does environmental regulation affect corporate environmental awareness? A quasi-natural experiment based on low-carbon city pilot policy

The low-carbon city pilot (LCCP) policy, as an important measure for China to achieve its "dual carbon" goals, has attracted widespread attention regarding its implementation effects. However, no studies have yet focused on the impact of the LCCP policy on corporate environmental awareness. This study, based on data from Chinese A-share listed companies from 2007 to 2020, employs a triple difference model to evaluate the impact of the LCCP policy on corporate environmental awareness, filling the aforementioned gap in the literature. The results indicate that the LCCP policy can significantly enhance corporate environmental awareness, particularly in non-state-owned enterprises, enterprises in the growth stage, and those located in the eastern regions. The LCCP policy will compel corporations to enhance their environmental awareness by increasing the costs of environmental penalty and environmental governance. However, the analysis of economic consequences reveals that although corporate environmental awareness has improved, it has not directly translated into significant economic benefits or substantial environmental benefits. This may be indicative of a scenario where, in the short term, the cost effect of the LCCP policy outweighs the compensation effect. Nevertheless, the improvement in the quality of information disclosure can significantly mitigate these adverse economic consequences. This research not only enriches the academic outcomes related to environmental regulatory policies but also contributes to ensuring the effective achievement of green, low-carbon objective and the sustainable development of the economy and society.

A novel two-stage optimal layout model of hydrogen refueling facility network based on green electricity hydrogen production: Beijing-Tianjin-Hebei region of China as case study

Green electricity hydrogen production(GEHP) is fundamental support for developing new-type power system (NPS) and achieving the green and low-carbon transformation in the transportation sector. It is key issue to build a hydrogen refueling facility network(HRFN) to link hydrogen production and consumption. Firstly, the framework of HRFN is proposed including hydrogen production points(HPP), hydrogen refueling stations(HRS) and hydrogen demand points(HDP). Secondly, a two-stage model is built. In the first stage, the siting model of HRS cluster is constructed considering the service capacity, service radius, and construction, operation and penalty costs. In the second stage, the bi-objective planning model of HRFN is constructed considering network stability, hydrogen storage and transportation forms and producing total costs. Finally, the Beijing-Tianjin-Hebei region of China(BTH) is taken as case study to verify the effectiveness. Sensitivity analyses are conducted on four factors:HRSs' service radius, service capacity, GEHP's efficiency and HDPs' scope. The key findings are: 1)the service radius and capacity of HRSs and HDPs' scope all affect the layout of HRSs, with HDPs' scope further influencing HPPs' number; 2)the construction and operation costs are more impacted by changes in GEHP's efficiency compared to network stability; 3)the network should be strengthened to cover the whole processes from hydrogen production to consumption.

Asymptotic optimality of base-stock policies for lost-sales inventory systems with stochastic lead times

We consider the lost-sales inventory systems with stochastic lead times and establish the asymptotic optimality of base-stock policies for such systems. Specifically, we prove that as the per-unit lost-sales penalty cost becomes large compared to the per-unit holding cost, the ratio of the optimal base-stock policy's cost to the optimal cost converges to one. Our paper provides a theoretical guarantee of the widely adopted base-stock policies in lost-sales inventory systems with stochastic lead times for the first time.

Research on multi-time scale Volt/VAR optimization in active distribution networks based on NSDBO and MPC approach

To explore the potential of all-round and multiangle voltage and reactive power control to reduce losses in a new power system with a high proportion of distributed resources connected to a distribution network, this study proposes a Volt/VAR optimization method for distribution networks using a nondominated sorting dung beetle optimizer (NSDBO) and model predictive control (MPC). According to the characteristics of the various adjustable resources in the network, they are divided into day-ahead and intraday optimizations. The optimization process in the day-ahead stage uses the NSDBO to create a discrete equipment scheduling plan. The optimization process in the intraday stage combines the discrete equipment scheduling plan with the MPC to create the scheduling plan for photovoltaics, energy storage, and vehicle charging stations. Two-stage optimization scheduling is achieved with the lowest discrete equipment regulation cost and minimization of network loss and node voltage deviation penalty cost as the optimization goal. The feasibility of this method for coordinating various resources in the network, processing discrete and continuous variables, and coping with the volatility and uncertainty of high-proportion distributed resources is verified through case analysis. The effectiveness of this method in improving the security and economy of distribution networks is demonstrated. The superiority of the solution speed and quality is also confirmed.

Intelligent location-routing for sustainable reverse supply chain of end-of-life vehicles considering awareness cost and carbon penalty

This paper presents a comprehensive investigation into optimizing the reverse supply chain for end-of-life vehicles (ELVs) with a focus on sustainability considerations, including awareness cost and carbon penalty. A novel three-objective mathematical model is developed, leveraging fuzzy logic to address the complex nature of the problem. Two multi-objective algorithms, the Grey Wolf Optimizer (GWO) based on the Pareto boundary and the NSGA-II algorithm, are deployed to solve the model. A case study in China is conducted to validate the proposed model, with results compared against the outcomes of the algorithms. Additionally, a sensitivity analysis approach is employed to assess the impact of awareness cost and carbon penalty parameters. Furthermore, the Taguchi experimental design method is utilized to identify the optimal combination of parameter values. The findings reveal that the GWO algorithm surpasses NSGA-II in terms of solution quality and diversity, although NSGA-II demonstrates superior performance in uniformity and computational time. The sensitivity analysis highlights the positive correlation between increased awareness cost and various performance metrics, such as the number of collected vehicles, economic profit, and social profit, while also indicating a reduction in environmental impacts. Conversely, escalating carbon penalties leads to a decrease in the acceptance and processing of vehicles within the supply chain, resulting in diminished chain and social profits, despite the decrease in carbon penalties.