Emission reduction strategies are crucial not only for environmental sustainability but also for ensuring economic viability in today’s highly competitive business environment. For the first time, this study explores how government subsidies can enhance the economic viability of sustainable practices, enabling companies to pursue green technology investments while managing inventory. The proposed model incorporates perishable products, integrates both partial downstream delayed payments and partial upstream advance payments, and is developed within an economic order quantity (EOQ) framework to align business performance with broader global sustainability objectives. The analysis evaluates the retailer’s operational decisions under four scenarios: (i) no investment, (ii) investment without subsidy, (iii) investment with base subsidy support (IBS), and (iv) performance-based subsidy (PBS) schemes. Taking into account the feasibility of the investment practice, optimal decisions are achieved by investigating cost functions analytically under all scenarios. To evaluate the monetary advantage of reducing emissions, a new metric, normalized Cost Saving per Unit of Reduced Emission (CSURE), is introduced. The findings highlight a dual advantage, enhancing retailer cost efficiency while advancing environmental sustainability. Among the scenarios, based on the numerical example, the PBS scheme achieves the best outcomes, reducing emissions by 14.01

Government subsidies are critical for promoting green technology adoption in supply chains. Simultaneously, retail operations are influenced by complex financing structures such as prepayment discounts and delayed payments. This study develops an integrated framework that combines environmental policy measures-Investment-Based Subsidies (IBS), Performance-Based Subsidies (PBS), and an emission tax (ET)-with financial structuring mechanisms in retail supply chains. The model examines retailers' optimal strategies for emission-control investment and inventory replenishment across three scenarios: (i) no green investment, (ii) green investment without subsidies, and (iii) green investment under IBS and PBS. Closed-form analytical solutions are derived for both full and partial prepayment settings, with convexity analysis confirming global optimality. To evaluate the financial efficiency of emission reduction, a new performance metric, Cost Saving per Unit Reduced Emission (CSURE), is introduced. Numerical experiments and sensitivity analyses demonstrate that with a fixed subsidy budget, PBS delivers greater cost savings, while IBS encourages larger emission reductions. Specifically, adopting green technology under IBS and PBS reduces total annual costs by up to 5.8% and 7.2%, respectively, and lowers emissions by approximately 18-20% in both prepayment contexts. These findings highlight the importance of aligning subsidy design with financing structures: IBS is more suitable for enforcing stricter emission controls in high-emission, developed industries, whereas PBS provides stronger incentives for cost-effective sustainability in emerging markets. This study advances the literature by integrating policy-driven subsidies with realistic payment mechanisms, offering both theoretical contributions and actionable insights for policymakers and practitioners.

Emission reduction investment is a crucial business policy not only to ensure environmental sustainability but also to maintain economic viability for companies in today’s highly competitive business environment. For the first time, this paper identifies the optimal emission-controlling investment decision under government subsidy frameworks for a company dealing with deteriorating items within prepayment and delay payment mechanisms. Employing the upstream partial prepayment, the retailer remits payments to the supplier in installments, whereas employing the downstream partial delayed payment, the retailer receives a fraction of the selling price from customers after the sale. Integrating payment mechanisms, partial backordering, and investment practices for deteriorating items, this study establishes one of the initial comprehensive inventory systems to address both environmental and financial challenges concurrently. Furthermore, this study employs two distinct government subsidy schemes, investment-based subsidies (IBS) and performance-based subsidies (PBS), to investigate how government subsidies impact green technology investment aimed at promoting environmentally sustainable practices. After developing three different models under both subsidized and unsubsidized conditions, optimal decisions are derived analytically, which are then integrated into the development of effective solution algorithms. The numerical results reveal that green investment substantially improves cost efficiency, achieving savings of 3.85

The highly competitive and volatile nature of the current marketing environment makes it challenging to predict demand and other uncertain costs. To address this uncertainty, this study employs an interval-valued optimization technique. We propose an economic order quantity (EOQ) model within an interval framework, where the demand rate is represented as an interval-valued power function dependent on the green level, selling price, and time. Furthermore, the retailer’s purchasing and holding costs are treated as interval values; the purchasing cost is dependent on the green level, while the holding cost varies over time. The model also permits fully backlogged shortages, which are considered interval values. A parametric method is utilized to convert the differential equation for the inventory level from its interval form into a crisp equivalent. The resulting maximization problem is then solved using the Teaching-learning-based optimizer algorithm (TLBOA), after being converted to a crisp problem using interval order relations and the center-radius optimization approach. Finally, a numerical example is provided to illustrate and validate the proposed model, followed by a post-optimality analysis to examine the impact of various parameters on the optimal policy. (AMS classification code: 90B05, 49M37, 90C70, 90C59)

Emissions reduction strategies are essential for sustaining both economic competitiveness and environmental responsibility. This study develops an optimization model for inventory management in Bangladesh's refrigerator retail sector, integrating profitability with sustainability objectives. The proposed model uniquely incorporates defective items, bulk purchase discounts, and multiple carbon regulation schemes, namely carbon tax (CT), cap-and-trade (CAT), cap-and-price (CAP), and carbon offset (CAO). It determines the optimal replenishment cycle and investment level in emissions control technologies that maximize annual profit under regulatory constraints. The inventory system is formulated as a constrained nonlinear optimization problem and is analytically solved using Karush-Kuhn-Tucker (KKT) conditions to obtain closed-form solutions. A customized algorithm is developed to identify the global optimum under an all-units discount (AUD) pricing scheme. A case study based on realistic parameters from the Bangladeshi refrigerator market validates the proposed model. Sensitivity analyses reveal that holding costs and transportation fuel consumption significantly influence both profit and emissions. Green investments improve performance under strict regulatory environments; however, diminishing returns indicate inherent technological limitations. Notably, a 50% reduction in holding costs increases profit by 2.72% and extends the optimal cycle by 29.42%. The findings underscore the importance of advancing green technologies and aligning inventory policies with environmental objectives.

Balancing sustainability with operational efficiency is a significant challenge in high-precision industries, including aerospace, pharmaceuticals, and electronics. Traditional Economic Production Quantity (EPQ) models often overlook factors such as the integrality of produced items, defective products, strict inspection, remanufacturing, and government-supported green investments, which limit their relevance in situations with inspection bottlenecks. This study develops EPQ models that integrate 100

This study develops an integrated optimization framework for designing a source-segregated municipal solid waste management network. A mixed-integer linear programming model is proposed to determine the optimal configuration of collection stations, assignment of waste generation points, installation of smart monitoring systems, and allocation of waste flows to treatment and recycling facilities within a multi-echelon municipal logistics network. The model minimizes total system cost while satisfying capacity, budget, and recycling constraints. A numerical experiment based on a representative case study of Tabuk city, Saudi Arabia, is conducted to demonstrate the applicability of the model. The results show that the optimal network opens three collection stations and allocates waste efficiently across treatment facilities, achieving a diversion rate of approximately 72% from landfill. The comparative and sensitivity analyses indicate that integrating source segregation with monitoring-enabled operational coordination, optimized infrastructure utilization, and resource recovery can significantly improve economic performance while reducing landfill dependency. Sensitivity analysis reveals that segregation participation, recycling revenue, and disposal cost are key drivers of system performance. Increased participation in source segregation leads to higher recovery rates and improved economic outcomes, while higher recycling revenues and disposal costs promote waste diversion from landfill. The findings highlight the importance of coordinated planning, economic incentives, operational coordination, and public participation in developing sustainable waste management systems. The proposed framework provides a practical decision-support tool for municipalities seeking to transition toward circular economy practices and improve resource efficiency in urban waste management.

Manufacturing companies are increasingly adopting green transformation through government innovation subsidy policies to incentivize it, and artificial intelligence (AI) to handle specific tasks, reducing dependence on human labor. This study, for the first time, integrates the impacts of green technology implementation within a hybrid subsidy policy, based on both the input and output of green technology investment, and the adoption of AI technologies in an energy-economy-environment (3E) conscious production system. The model defines a flexible manufacturing and remanufacturing system under limited floor-space capacity and thereby formulates a constrained optimization problem within a cap-and-trade (CAT) regulation. As a result, the Karush–Kuhn–Tucker (KKT) conditions are applied after examining the cost function’s curvature, and closed-form optimal solutions are derived to minimize the manufacturer’s total annual cost. Furthermore, this study provides practical implications for authorities in setting an appropriate emission cap to ensure effective CAT regulation across different scenarios. A numerical illustration highlights that the proposed hybrid subsidy policy, combining input- and output-based incentives, achieves the best overall performance. AI efficiency in controlling production-stage emissions plays a critical role in determining both technological investment and system cost. Under the baseline numerical parameter setting, AI technology significantly reduces operational costs and energy consumption, resulting in an 18

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.

Advance payment for replenishment and the lifetime of an item are the most vital issues in the business sector. With the consideration of these issues, the formulation of a non-deterministic inventory model in the interval environment is of great importance. In this work, two different non-deterministic inventory models are formulated along with a variable holding cost, variable demand, and advertisement frequency under an advance payment policy in the interval environment. In the first inventory model, a no-shortage situation is discussed, whereas in the second model, a stock-out scenario is adopted by partially backordering during modelling. The modelling framework for both problems is accomplished based on interval differential equations. The interval optimization problems related to both models are obtained utilizing parametric approach and interval mathematics. Then, using interval order relations and different types of quantum particle swarm optimization, both interval optimization problems are solved. By means of two examples, the authentication of both models is examined and the benefits of the proposed approach are demonstrated. The impact of deviations of various parameters on optimality is studied graphically through the performance of sensitivity analyses, and the work is concluded by providing potential management insights and future scopes.

Investment in reducing emissions for many diverse companies is a practical strategy to achieve the emissions objectives as outlined by the United Nations Framework Convention on Climate Change. Livestock-producing farms often fall short of sustainability goals, even though many businesses have already adopted an investment strategy towards sustainability with success. Thereby, livestock-producing farms come under increasing responsibility to reduce their environmental impact, and it is now crucial to make simultaneous decision-making of inventory replenishment and emissions reduction investment to ensure the livestock farming industry's sustainability. In this study, a new path towards sustainable development is designed for livestock-producing farms by investigating the optimal investment plan for controlling emissions under carbon tax (CT) and cap-and-trade (C&T) environmental emissions guidelines. Taking into account both edible and non-edible parts of slaughtering mature growing items (GIs), as well as a non-linear holding cost structure and a power demand pattern for edible components, a comprehensive analytical approach implementing mathematical modeling methodology, economic evaluation, and carbon accounting approaches is accomplished. The most economical investment level that not only improves the environment but also adds to the farm's financial stability is identified by examining the interplay between the investments in emissions reduction and replenishment carried out by the farm. The numerical studies demonstrate that implementing an emission reduction strategy under both CT and C&T guidelines results in a 2.45% reduction in carbon emissions for a tax rate of $4.5. In order to further highlight the impacts of investment accessibility and emission parameters, several outcomes of a numerical analysis are reported. The findings demonstrate that implementation of investment strategy is always beneficial in achieving sustainability goals of the farm by lowering emissions under both CT and C&T emissions regulations.

Supply chains and other complex systems can be effectively managed and optimised with the help of optimal control techniques. Optimal control, as used in supply chain management, is the process of using mathematical optimisation techniques to identify the best course of action for controlling a given objective function over time. Modeling the supply chain’s dynamics, which include elements like production rates, inventory levels, demand trends, and transportation constraints, is the best control strategy when applied to a supply chain. In this study, we have considered that production rate is an unknown function of time, which is a controlling function. The demand for the product is taken as a function of price and time. The emission of carbon is taken as a linear function of the production rate of the system. To solve the suggested supply chain system, we have used an optimal control approach for determining the unknown production rate. To find the optimal values of the objective function as well as the decision variables, we have used different meta-heuristic algorithms and compared their results. It is observed that the equilibrium optimizer algorithm performed better than other algorithms used. Finally, a sensitivity analysis is performed, which is presented graphically in order to choose the best course of action.

Rapid growth of the greenhouse, nursery, and flower industry, fueled by advancements in sustainability, technology, and innovative farming techniques, necessitates detailed exploration of sustainable production practices. This study delves into the complex dynamics of greenhouse flower-plant production (GFPP), focusing on strategies to minimize system costs while reducing environmental impacts. The production process is segmented into four critical stages: seed germination, development, maturation, and decline. Throughout the germination phase, no sales occur. In the development phase, trays are allocated for individual plants in preparation for marketing. As plants mature, demand rises, stabilizes, and gradually declines, following a trapezoidal demand pattern (TDP). Greenhouse farming operates in controlled environments, relying on heating, cooling, artificial lighting, and fertilizers, which contribute to emissions. These emissions are regulated under various frameworks, including carbon tax (CT), cap-and-trade (CAT), and cap-and-price (CAP) schemes, each imposing different cost and compliance requirements on the producer. Flower plant mortality is modeled as a continuous probability distribution function, adding further complexity to production planning. This research aims to identify the optimal stocking time that minimizes the producer’s costs while adhering to emission regulations. Analytical insights are developed and validated through multiple numerical scenarios. Findings demonstrate that sustainable GFPP can achieve balance between economic efficiency and environmental responsibility. By adopting proposed strategies, producers can enhance operational sustainability, contribute to ecological preservation, and strengthen flower industry resilience.

The requirement for adopting sustainable techniques for flower cultivation in greenhouses is escalating due to heightened environmental awareness and the increasing market demand for environmentally friendly products. Conventional flower cultivation typically entails substantial water usage, energy consumption, and chemical inputs, which contribute significantly to environmental degradation and climate change. Greenhouse flower producers may greatly diminish their ecological impact, preserve natural resources, and support biodiversity by implementing sustainable techniques. With a focus on reducing system costs and minimizing environmental impacts, this study examines the complex dynamics of sustainable flower-plant production within a greenhouse environment under carbon tax (CT), cap-and-trade (CAT), and cap-and-price (CAP) emission rules. To represent the variation in demand throughout their life cycle, the demand structure for flower plants is characterised by a trapezoidal demand pattern. Shortages of flower plants are allowed, with unsatisfied demand being backlogged. The percentage of backordered shortages is directly related to the waiting time for fulfillment. Furthermore, greenhouse farming is associated with emissions because of the greenhouse’s internal lighting, heating, and cooling systems, as well as the use of artificial fertilisers. Consequently, the farming operations are governed by several environmental regulations. The aim of this study is to identify the most favourable timing for stocking that minimises expenses while adhering to emission regulations. To achieve this goal, a range of analytical insights is obtained and demonstrated through the solution of various numerical scenarios. The results show that raising greenhouse system cost parameters increases the producer’s minimum overall cost while decreasing flower plant positive stocking period and emissions.

Uncertainty refers to a lack of precise knowledge or information about a particular event, situation, or outcome. It is an inherent characteristic of many real-world phenomena and is often associated with the presence of risk or ambiguity. Uncertainty can arise due to various factors, such as incomplete information, unpredictability, complexity, or variability of a system or process. In many cases, uncertainty can lead to difficulties in decision-making and pose challenges in planning, forecasting, and managing risks. There are different types of uncertainty, including epistemic uncertainty, which arises from the inherent randomness or variability of a system or process. This study encompasses the inclusion of all inventory parameters as uncertainty parameters, which are expressed in the form of intervals. Furthermore, demand for the product is taken into account in interval form. The conversion of the differential equation into an interval differential equation is carried out in order to account for the variability in demand within a certain interval. The utilisation of the centre-radius technique leads to the derivation of the related optimisation problem under a ‘buy now, pay later’ (BNPL) payment scheme. In order to demonstrate the concept, a numerical case is selected and solved with the MATHEMATICA software and interval order relations. In the end, a comprehensive sensitivity analysis has been conducted to derive insightful conclusions pertaining to this study.

Installment in the prepayment mechanism has emerged as a significant decision for many companies due to rising capital costs and increasing pressures from suppliers for various products. To motivate the companies about the prepayment mechanism, suppliers allow the frequency of installment of advance payment as a decision variable for the company and the per unit acquisition cost as a step-down function in exchange for an order-based prepayment regulation allowing the stepwise decreasing prepayment portion and duration as well. This paper investigates the optimal joint decision-making of a company’s prepayment, pricing, and stocking policies to maximize profits in the context of an order-based prepayment and discount regulation. A realistic approach is adopted in the study by considering the clients’ demand as a multiplicatively separable power function that accounts for both the price and the storage time of products. Theoretical expressions are derived to check when multiple or single installments are more profitable for the company. To achieve the maximum profit, a solution approach is introduced based on all the derived theoretical outcomes. The results of three numerical studies are documented and then the effects of order-based prepayment and discount regulation on optimal policies and maximum profit are further studied. The results of the study indicate that the profitability of the company can be enhanced through an increase in the frequency of installments, particularly in situations where the rate of interest charged is high. Finally, to draw up effective guidelines, a sensitivity investigation is conducted for all cost parameters.

Numerous studies have explored pricing and lot-sizing strategies for various payment methods, but most have focused primarily on the buyer’s perspective. This study, however, approaches these strategies from a different perspective, incorporating key and relevant factors often overlooked. The volume of sales increases when a seller accepts a buyer’s credit. However, it reduces sales volume when a seller requests a buyer make a payment in advance. To boost sales and profitability, a vendor occasionally provides a price reduction in exchange for a down payment. Demanding a down payment from a customer earns interest and carries without any risk of default. When a vendor offers customers the option to pay with credit, a higher delay payment period facility plan may boost sales volume, but it also increases the risk of default. To maximize profit per unit of time, the vendor aims to simultaneously determine the optimal selling price, replenishment schedule, and payment method. This is achieved by comparing and calculating the vendor’s profit per time unit for credit, cash, and advance payment options. This is done by comparing and calculating the seller’s profit for each piece of time for credit, cash, and advance payments. The following managerial impacts are highlighted by means of numerical analyses: (1) A particular payment type, among the three available options, yields the seller’s highest profit under certain conditions. (2) It is vitally crucial for a vendor to provide a price reduction if an advance payment is required. (3) Advance payment results in higher profit than delayed payment if sales volume does not significantly fall while switching from credit to advance payments, or vice versa. To solve the optimization problem, a popular metaheuristic algorithm (viz., Grey Wolf Optimizer) is used and finally performed a post optimality analysis for making a fruitful conclusion.

Regulators’ increasingly stringent carbon rules to protect the environment are encouraging practitioners to modify their operational activities that are accountable for releasing emissions into the atmosphere. Thereby, practitioners dealing with product inventory planning are seeking proper management strategies not only to increase profits but also to reduce released carbons from operations. In addition, increasing uncertainty in supply operations has motivated suppliers to impose prepayment mechanisms in recent decades. This study examines the best prepayment installment policy for a practitioner for the first time, where the consumption behavior of consumers changes as a result of the combined effects of unit selling price and storage time. Moreover, to make the present inventory planning more realistic, the unit holding cost function is adopted as a power function of the inventory unit's storage period. The goal of this study is to provide the best combined installment for advance payment, price, and replenishment strategies for a practitioner under cap-and-price, cap-and-trade, and carbon tax environmental guidelines by ensuring maximum profit. For this purpose, an algorithm is created by combining all derived theoretical results from the analytical study, whereas the efficacy of the algorithm is assessed through the examination of five illustrative numerical instances. A plethora of noteworthy management insights for the practitioner are obtained by investigating the dynamic shifts in optimal strategies resulting from fluctuations in system parameters. The results reveal that if the demand is low in the nascent phases of the business cycle, then the prudent approach for the practitioner entails procuring a comparatively smaller lot-size using a modest number of payment frequencies and then setting a relatively small unit selling price to increase profits.

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.