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The modelling and optimization of a manufacturing systems in the context of sustainable production under uncertainty remain a pivotal focus in control theory. The goal of this research is to develop a robust decision-making framework for a production-inventory system characterised by imperfect production with reworking processes, and interval valued non-linear demand rate which is dependent on green level, selling price, warranty period, and time. This study also considers the impact of carbon emission regulation taxes to demonstrate how CO2 emission control influences the best-found policy of the proposed system. To fulfil the goal, an interval-valued optimal control problem (IVOCP) is constructed using generalised variational principle and corresponding highly nonlinear interval maximization problem is obtained. To tackle this interval optimisation problem, an improved c-r optimisation technique and the meta-heuristic algorithm Sparrow Search algorithm (SSA) are employed. The best-found solution for the corresponding problem is numerically illustrated through four distinct scenarios based on the presence of green investment levels and warranty periods in the demand rate. The obtained best found results are compared by some other metaheuristic algorithms. Additionally, statistical tests and non-parametric tests are conducted to assess the effectiveness, consistency, and stability of the algorithms. Furthermore, sensitivity analyses have been made to observe how inventory system parameters impact the optimal policy. Based on these analyses, managerial insights are derived to aid in decision-making processes.

This study develops a comprehensive inventory model for deteriorating items by incorporating preservation technology and addressing sustainability-driven customer behavior. Demand is modeled as a nonlinear function influenced by three key factors: selling price, green level (reflecting the environmental friendliness of the product and its production), and available inventory level. Recognizing rising environmental consciousness, the green level directly shapes consumer demand, while preservation investment reduces deterioration and extends the shelf life of perishable goods. The objective of the model is to maximize the total profit by jointly optimizing five decision variables: selling price, green level investment, preservation effort, cycle length, and replenishment quantity. The resulting objective function is highly nonlinear and complex. To solve it efficiently, this study employs the Marine Predators Algorithm (MPA)—a newly developed metaheuristic algorithm well-suited for continuous, nonlinear optimization. Model authenticity is established through a combination of sensitivity analysis, convergence behavior examination, and validation against benchmark test problems from existing literature. The robustness of the solution method is further demonstrated by comparing the MPA’s performance with other optimization techniques in terms of solution quality and computational efficiency. Although the study is theoretical in nature, data assumptions are grounded in real-world parameter ranges drawn from validated case studies and academic sources. Parameters such as deterioration rates, green investment cost coefficients, and preservation effectiveness are selected to reflect practical supply chain conditions. This ensures the credibility of the model output and applicability in realistic scenarios. The study offers critical managerial insights, including how to balance sustainability initiatives, pricing decisions, and preservation investments for optimal inventory control. These insights are particularly valuable for supply chains dealing with environmentally sensitive, perishable products, helping businesses enhance operational efficiency while supporting green objectives.

Due to the current environmental situation and human health, a green manufacturing system is very essential in the manufacturing world. Several researchers have developed various types of green manufacturing models by considering green products, green investments, carbon emission taxes, etc. Motivated by this topic, a green production model is formulated by considering selling price, time, warranty period and green level dependent demand with a carbon emission tax policy. Also, the production rate of the system is an unknown function of time. Per unit production cost of the products is taken as increasing function of production rate and green level of the products. In our proposed model, carbon emission rate is taken as linear function of time. Then, an optimization problem of the production model is constructed. To validate of our proposed model, a numerical example is considered and solved it by AHA. Further, other five metaheuristics algorithms (AEFA, FA, GWOA, WOA and EOA) are taken to compare the results obtained from AHA. Also, concavity of the average profit function and convergence graph of different metaheuristics algorithms are presented. Finally, a sensitivity analysis is carried out to investigate the impact of different system parameters on our optimal policy and reach a fruitful conclusion from this study.

There has been a lot of research on pricing and lot-sizing practices for different payment methods; however, the majority has focused on the buyer’s perspective. While accepting buyers’ credit conditions positively impacts sales, requesting advance payments from purchasers tends to have a negative effect. Additionally, requiring a down payment has been found to generate interest revenue for the supplier without introducing default risk. However, extending the credit period, along with offering delayed payment options, has the potential to increase sales volume, albeit with an elevated risk of defaults. Taking these payment schemes into account, this study investigates and compares the per-unit profit for sellers across three distinct payment methods: advance payment, cash payment, and credit payment. The consumption rate of the product varies non-linearly not only with the time duration of different payment options but also with the price and the level of greenness of the product. The utmost objective of this work is to determine the optimal duration associated with payment schemes, selling price, green level, and replenishment period to maximize the seller’s profit. The Teaching Learning Based Optimization Algorithm (TLBOA) is applied to address and solve three numerical examples, each corresponding to a distinct scenario of the considered payment schemes. Sensitivity analyses confirm that the seller’s profit is markedly influenced by the environmental sustainability level of the product. Furthermore, the seller’s profitability is more significantly affected by the selling price index compared to the indices of the payment scheme duration and the green level in the demand structure.

In contemporary times, the environment is being progressively polluted by non-eco-friendly products from manufacturing sectors. Therefore, it is vital for individuals to be aware of the necessity of employing environmentally friendly items as a means to mitigate pollution. This consciousness, in return, drives an instant increase in the desire for environmentally friendly products, greatly improving their ecological sustainability. In this context, this study proposes a novel perishable inventory model that incorporates environmental attributes into demand and cost functions, which contributes to sustainable inventory management research. The maximum potential lifespan of a product is a crucial aspect of inventory management, especially when considering its suitability for reuse. One notable challenge in the connection between suppliers/manufacturers and merchants for products accessible during seasonal periods with high demand pertains to the issue of payment in advance. Integrating these multifaceted elements results in a perishable commodity inventory model characterized by a customer demand rate depending on the product’s green level and price, an interval-valued holding cost, and a linearly time-dependent holding cost. A partial backlog of shortages with interval values is incorporated in this model. The associated optimization problem is characterized as a maximization problem, wherein the objective function exhibits values throughout an interval. To assess the accuracy and reliability of the proposed model, the Arctic Puffin Optimization (APO) algorithm is employed to analyze and solve a specific numerical illustration. Furthermore, seven other algorithms (Dandelion Optimizer (DO), Grey wolf optimizer (GWO), The whale optimization algorithm (WOA), Artificial electric field algorithm (AEFA), Harris hawks optimization (HHO), Multi-verse optimizer (MVO) and Slime mould algorithm (SMA)) are used to compare the obtained solution from APO. Quantitatively, the APO and DO algorithms provid the same solution for the given example. However, during the statistical test for review the performance of the algorithms, it is observed that APO is outperformed among all other algorithms. Subsequently, a post-optimality analysis examines the quantitative effects of changes made to different inventory parameters, which results in an insightful conclusion. This study not only contributes to the theoretical framework of perishable commodity inventory modeling but also provides practical implications for sustainable inventory management in response to environmental concerns.