The innovative logistics strategy of cross-docking enables the offloading of goods from incoming vehicles at the receiving dock, followed by loading the products into outgoing trucks, eliminating the need for prolonged product storage. The brisk movement of products within the cross-docking strategy has made this an uncompromisable approach for transporting staples, groceries, and perishable items. Although the goal is to maintain a stable environment within the cross-dock centres and vehicles, the loading and unloading process often fails to achieve this. Exposure to an unstable environment affects the quality of goods and initiates their deterioration. The inclusion of the pre-emption technique in the unloading or loading process leads to frequent exposure to an unstable environment, thereby accelerating deterioration. This study explores how pre-emption affects the deterioration rate variation risk coefficient of the products when a limited number of interruptions in the unloading process is considered. A non-linear programming model that considers pre-emption is developed for this problem, and the optimization is performed using an interior-point algorithm to minimize the deterioration rate variation risk coefficient. Results obtain highlight that the inclusion of the pre-emption technique increases the accumulated deterioration rate variation coefficient by nearly 265%, while an increase in the number of product types and their quantities heavily influences the accumulated deterioration rate variation coefficient value, showing a whopping rise of nearly 152%.

Products can be sold in two ways: online and offline. The traditional procedure is to sell through offline mode. However, based on the necessity, customers prefer online mode to save time and cost. But which mode is time and cost saving? This is a big question to be asked by the researchers. In this direction, this study considers a three-echelon supply chain management with dual channels, considering the significant effect on pricing in both online and offline modes and the quality of products. This study utilizes the benefit of a third party in managing a cost-reduction strategy. The manufacturer is cautious about the reputation of the supply chain because the goodwill lost cost is utilized within the management system. The model is solved analytically with the help of a classical optimization approach. The theoretical results provide the global optimum results for the supply chain model. Numerical experiments are conducted based on the existing data and it is found the global optimum profit for the chain. Some graphical representations of optimality and sensitivity have been drawn, and several conclusions are obtained from them. Finally, the numerical results prove that the online mode is much better than the offline if the customer if the customer is aware of both modes at the time of order, purchasing, or others.

Market demand in today's global environment is highly dynamic, shaped by globalization, evolving consumer preferences, and shifting priorities. To address these challenges, firms increasingly adopt dual-channel supply chain systems that integrate both online and offline channels. The integration of sales data across these channels provides valuable insights into consumer behavior, enabling effective resource allocation during peak seasons and periods of demand uncertainty. In this study, an integrated dual-channel supply chain model is developed under a stochastic lead time and variable demand, incorporating investment in lead time reduction and setup costs reduction. Demand is considered as a function of the selling price, the advertisement cost, and the consumer service cost for both channels. The model allows shortages and treats the reorder point as a decision variable, jointly determining the optimal selling price, order quantity, reorder point, lead time, machine failure rate, and cost allocations. A global solution is obtained analytically, and an iterative algorithm provides optimal numerical results. The analytical results show that dual-channel facilities significantly boost profitability. Profit decreases by 62.90% and 43.18% when the offline and online facilities are absent, Similarly, profit decreases by 7.65% in the absence of advertisement facilities and by 3.70% when setup costs reduction is not considered. The findings also indicate that the absence of free delivery reduces profit by 2.25%.

Electric vehicle production has recently gained popularity due to increasing emissions. The research on electric vehicle production concerning technical, economic, and environmental aspects is very less compared to the traditional vehicle. This research studies a mixed-type electric vehicle production system that produces spare parts and finally assembles all spare parts for the vehicle. The spare parts production combines in-line production with returnable items and outsourcing. An automated inspection for both spare parts and vehicles is included within the system. Two different types of machines work for the production process: Machine 1 for spare parts and Machine 2 for vehicles. As the basic purpose is to provide an ecofriendly logistics facility, the manufacturing company takes care of carbon emissions from the system, customer satisfaction, and the green quality of vehicles. Necessary and sufficient conditions of classical optimization find global optimum solutions. Results show that green technology and customer satisfaction are two important factors for vehicle production. Comparative discussions, sensitivity, and robust analysis are provided to validate the theoretical contributions. The proposed mixed-type production model earns 85.32% more profit than a traditional production model. The electric vehicle provides a 96% customer satisfaction with an increase of 68.97% profit without customer satisfaction.

With the available internet and its facility, even physical stores rely on digital systems for transactions and storing data digitally. Therefore, there is a risk of cyberattacks leading to data breaches and customer identity theft from physical stores. Cyberattacks have devastating effects on both customers and retail stores, as both may face financial losses. Further, the retail store loses customers’ trust, reducing demand and total profit. Based on this, the study formulates a mathematical model to mathematically and numerically show the importance of cybersecurity investment for a profitable retail business by keeping data and transactions safe. A supply chain model is formulated with a retailer as a downstream player and two manufacturers as an upstream player, where manufacturers produce a single type of deteriorated product. This study finds an optimal cybersecurity investment for the retailer under a variable pricing strategy and advertisement policy to get the maximum profit. The formulated profit function is a highly nonlinear, unconstrained function solved using a classical optimization technique. The robustness of the result is tested through sensitivity analysis of input parameters. Results indicate that the cybersecurity investment increases the total profit by 3.95

Nowadays, every sector opens a hybrid retail channel to sell their products to customers in the market to serve customers easily, and to provide the best satisfaction. In a supply chain management model, the manufacturer produces deteriorating-type products and sends these products to the retailer through an offline channel. The retailer sells those products to customers through three different retailing channels, namely online, offline, and buy online and pick up in-store, with different selling prices. The competition between the manufacturer and retailer is demonstrated through the leader–follower Stackelberg game policy. From the results, it is found that the centralized system provides better outcomes than the decentralized system. Comparing the beta distribution, uniform distribution, and triangular distribution, the triangular distribution yields more profit for the centralized system. For the case of uniform distribution, the centralized system provides 19.57 % more profit than the original system under manufacturer leadership.

Dual-channel retailing empowers the manufacturer to benefit from market opportunities by producing customized items that fulfill client requirements. The manufacturer and retailer sell customized products, which allow customers to express their chosen style to increase both the likelihood of customers making a purchase and their level of satisfaction with the product. This trend is demonstrated by the current study, in which customized consumer items are considered through online and offline channels. On the other hand, cybersecurity has become a crucial aspect of the digital era, ensuring the protection of sensitive data, networks, and systems from cyberattacks and unauthorized access. This study develops with a modern cybersecurity framework to protect against cyberattacks and increase customer trust. This model is based on customized product design, cybersecurity investment, advertisement investment, and increasing the green level of customized products. The model is solved using both centralized policy and vertical Nash policy. Numerical results indicate that centralized profit is 2.37% more than the decentralized profit. Without investing in customized products and cybersecurity, the profit of the supply chain decreases by 2.33% and 1.99% for the centralized method, 1.28% and 1.15% for the vertical Nash method for the retailer, and 1.85% and 1.38% for the vertical Nash method for the manufacturer.

Within supply chain members, data sharing is an exceptionally significant issue for global biofuel supply chain management. Based on these, an advanced biofuel dual-channel supply chain with a single manufacturer and single retailer is established within the asymmetric data sharing, bullwhip effect, and autonomation policy. The retailer provides asymmetric information to the manufacturer regarding demand to increase their profit. In these circumstances, measuring the bullwhip effect is essential in the supply chain. To increase the satisfaction level of customers, the manufacturer sells products only offline, while the retailer sells products through both online-to-offline and offline channels. Considering the sustainable development goals, an advanced transportation policy is considered together with carbon emissions reduction. By both analytical and numerical methods, a biofuel supply chain management is formulated with consideration of centralized and decentralized profit scenarios. The study is solved numerically by the classical optimization technique and an integer programming. To validate the model, several numerical examples and special cases are observed. The applicability and efficiency of the proposed model are finally demonstrated through a case study in India. It is clear from the findings that information sharing among the players in the centralized case provides 3.77% more profit compared to the decentralized case. Due to asymmetric information, which leads to the bullwhip effect, the retailing system faces a loss. As a result, information sharing among supply chain players is 2.86% beneficial for dual-channel selling.

In real-world situations, the human-based inspection process often involves errors in detecting defective products, affecting the quality of products. When the production system enters an out-of-control state in a long-run process, it produces faulty products at a random rate. Based on this, the model introduces an autonomation inspection technology in an imperfect smart complex production system to separate faulty items using a machine-based inspection strategy. The manufacturer reworks the separated faulty items to control their quality. The manufacturer sells new quality and reworked quality products at variable prices and offers service for sold products. The model introduces variable demand and formulates it mathematically by incorporating space and budget constraints. The formulated nonlinear function is solved using the Karush-Kuhn-Tucker method. A numerical example and sensitivity analysis are provided to illustrate the model. Results show that autonomous inspection, quality, and service improve the profit of the proposed model.

In the realm of circular economy, effective product life cycle management necessitates decision support systems capable of adapting to the dynamic and stage-specific variations in product demand and return rates. Current literature often assumes identical replenishment cycles throughout a product’s life, overlooking that demand and return rates fluctuate significantly across different life cycle stages. This paper addresses this critical gap by introducing a novel decision support system that integrates adaptive replenishment strategies tailored to each phase of the product lifecycle. Unlike traditional approaches, which reset demand rates at the beginning of each cycle of every stage, this study ensures continuity and reflects the practical progression of demand within and across planning horizons. A fuzzy modeling approach accommodates uncertainties inherent in finite planning horizons, enhancing the system’s robustness. Analytical findings reveal that during the growth stage, production periods must increase in arithmetic progression with successive replenishment cycles. Conversely, the maturity stage requires a longer remanufacturing period and shorter production cycles, with adjustments proportionate to return rates and inversely related to remanufacturing rates. Numerical results emphasize that indiscriminately accepting all returned items during the decline stage is suboptimal and should be strategically limited. This study’s innovative framework bridges the gap between theoretical assumptions and practical realities, providing actionable insights for production and remanufacturing planning in finite and uncertain planning horizons. By incorporating dynamic demand and return rates, this work offers a pioneering contribution to sustainable product life cycle management, paving the way for more realistic and effective strategies in circular economy settings.

This study introduces predictive modeling based on Extreme Gradient Boosting (XGBoost), which utilizes Optuna for hyperparameter optimization and evaluates performance against GridSearchCV and RandomizedSearchCV using a 500-day dataset. To ensure statistical reliability of the findings, a bootstrapping with 1000 iterations is used to calculate 95% confidence intervals for all performance measures. Although GridSearchCV and RandomizedSearchCV achieve consistent performance, their average R-squared test performances are 0.81677 and 0.85538, respectively. In contrast, Optuna outperforms both methods by identifying better regions of optimal parameters, with an average R-squared of 0.94146. Furthermore, the computational efficiency analysis shows that Optuna’s average execution time of 28.31 s is a practical trade-off for running on consumer-grade hardware. Model interpretability is confirmed through Shapley Additive Explanations (SHAP) analysis, which identified the 3-day rolling average as the most important driving factor of demand.

Reducing setup costs and improving product quality are critical objectives in a sustainable production processes. The significance of these goals lies in their direct impact on efficiency. It affects competitiveness and customer satisfaction. Businesses can reduce setup costs to maximize resource usage. It can reduce downtime between production runs and improve overall operational agility. Sustained performance and expansion in contemporary manufacturing environments focus on setup cost reduction and product quality improvement. The present paper discusses a production inventory model for the product, which produces by-products as secondary products from the same manufacturing process. Setup cost is reduced for the setup of production and refining processes. A production process may change from being under control to an uncontrolled one. As a result of this, imperfect products are formed. This paper considers product quality improvement for both produced and processed items. The outcome shows that dealing with by-products helps make the system more profitable. Sensitivity analysis is performed for various costs and parameters. Mathematica 11 software was used for calculation and graphical work.

Live products have some unique features which are different from the conventional products. Because of that, managing live products, especially imperfect efficiency management, is the most important decision. Imperfect efficiency control of live products has not received sufficient attention, a major research gap in deteriorating products. Live products, such as chicken and pork, are living creatures that grow during a certain cycle. That cycle can be customized within a certain time to reduce cost with a time cap. This implies that quality assurance for live products is essential even when controlling imperfect efficiency. However, live deteriorating products lose their usefulness over time, which is frequently an important factor in decision-making. This study investigates a four-layer supply chain’s interconnected live product control scheme through breeding, processing, testing, and buyer operations. The processor supplies a fixed number of evenly sized bunches of high-quality managed stock to the buyer, influencing the time-dependent demand for the high-quality processed stock. Although most fully developed products are imperfect, they are thoroughly tested, followed by realistic implementations. Consequently, the key purpose of this work is to minimize the overall expense of the supply chain in terms of the number of replenishments of high quality during the planning horizon and cycle time. Furthermore, an algorithmic rule is established for optimality, and a numerical illustration is discussed to explain the results. The impacts of key parameters are analyzed using sensitivity analysis, and the important managerial implications are identified, enabling the supply chain to minimize the overall expense.

In response to complex retail challenges, the elasticity of production and logistic efficacy can minimize expenses, which always meets consumer satisfaction. The approach evolves by implementing a retail logistics strategy to integrate advanced production information under diverse trading modes. The research promotes a high level of consumer service, and on the other hand, the remanufacturing establishes a significant retail insight by holistically defining the prime pillar in the success of reverse e-commerce platforms. In reality, the advent of strategy actualizes quantifying success components in retail logistics practices with an adequate understanding of consumer preferences. The approach intensifies consumer expectations to trigger retailing efforts and ensures effective interaction, which is a prominent challenge to retailers. In this context, consumer-centric retail strategy is reshaped under the robust paradigm to facilitate the impact of the retail economy in the logistics framework. The study proposes a comprehensive mathematical framework with multiple objectives following restrictions to implement the marketing operations under two distinct retail scenarios. The findings demonstrate consumer loyalty and outline the logistics experiences with declining total costs and delivery time by looking at cooperative interaction methodology. An excellent measure reveals a consumer service goal of reducing the 34% expenses and 25% delivery time of the product by expanding a 20% green advantage into logistics retailing. The empirical analysis revamps the conceptual underpinnings of the reverse logistics business and extends a novel opportunity in marketing. More specifically, the trend has led to anticipating the subject’s intention under the logistics operational services.

Buying inventory on a credit basis is an effective pricing plan, and trade credit is a popular component of market transactions that increase demand. In a dynamic situation, most businesses offer different rewards and services to their consumers under certain terms and conditions during commodity sales. The accompanying companies provide a warranty period facility to increase consumer demand for products. The holding cost often increases over time. This study determines a production model wherein the production rate is proportionate to the price-warranty period based on the demand rate with time- dependent holding cost and trade credit policy. This work leads to three vital conventions: (I) the rate of product demand is considered to be price-warranty period dependent; (II) the non-linear function is considered for the rate of replacement failure, wherein the capital of the manufacturer depends on the warranty period; and (III) the rate of inflation is constant; moreover, the present time value of money measured. This study aims to find the selling price, cycle time, and warranty period by using an algorithm to maximize the total profit function of the manufacturer. The results are validated by solving three numerical examples with their graphical representation based on different situations and the major parameters, and sensitivity analysis is analyzed with important decision-making implications.

Dynamic pricing in the newsboy problem within the context of dual-channel retailing significantly impacts inventory management strategies, allowing retailers to optimize pricing decisions based on real-time demand fluctuations across multiple sales channels. By dynamically adjusting prices, retailers can better balance inventory levels between online and offline channels, maximizing profit margins while minimizing stockouts or excess inventory. Effective implementation requires careful consideration of consumer behavior, competitive dynamics, and channel-specific constraints to achieve desired outcomes and maintain customer satisfaction. This study explores the application of the Black-Scholes equation in solving the newsboy problem with dynamic pricing, investigating its effectiveness in optimizing inventory management decisions. It delves into the concept of risk transfer within this framework, examining how it impacts decision-making processes. Additionally, the study evaluates the incorporation of green considerations at the product level, analyzing its implications for sustainability and market positioning. Furthermore, it scrutinizes the pros and cons of online marketing strategies, highlighting their impact on brand visibility, customer engagement, and market reach. Finally, the paper explores the concept of dual-channel retailing, assessing its role in enhancing customer experience and optimizing sales channels. Sales effort initiatives and consideration of green level of the product provide a 34.75% enhance profit compare to the traditional retailing system without sales effort and green level of the products.

Retailing strategy can be considered as the most critical factor for the success of industries. Managing deteriorating products in retail demands a strategic approach aimed at mitigating losses while maximizing profitability. This entails a proactive stance towards identifying products nearing expiration, becoming obsolete or showing signs of deterioration. Offering discounts or promotions can stimulate consumer interest and clear out inventory. The promotion of products within the context of retail management involves a multifaceted approach aimed at increasing awareness, generating interest, and ultimately driving sales. Sustainability helps retailers to develop social as well as economic consistency. Every country and their respective governments are currently working towards sustainable development. New technologies in this direction have been introduced. The present paper introduces a retailing model considering green technology as it is becoming popular to lower environmental risks. The items considered in this study are perishable in nature. As product prices and the promotion of products highly influence demand, a demand pattern dependent on price and promotion is therefore considered. This paper presents a sustainable retail-based inventory model that considers preservation technology to lower the rate of deterioration and increase product shelf life. As carbon emissions is currently the biggest threat to the environment, enforcing a penalty may lower its emissions. Carbon emissions costs due to storage, transportation, and preservation are considered herein. This model studies the effect of various cost parameters on the model. A numerical analysis is performed to validate the result. The results of this study show that the implementation of preservation technology not only increases cycle time but also significantly reduces total cost, hence increasing profit. Sensitivity analysis is performed to show the behaviors of different cost parameters on total cost and decision variables. Mathematica 11 and Maple 18 software are used for graphical representation.

Multi-stage production systems produce a severe amount of defective items as a result of an irregular quota of defectiveness. It is very important to remanufacture those imperfect pieces that are wasted and try to keep the model as reality close as possible. Two different models are developed in this study: a smart production system with numerous stages and with only one cycle and a smart production system with numerous stages and numerous cycles. The essential objective of this study is to scale down the overall waste and lower the final total cost in both models at the same time by optimizing the planned batch size, investments in each stage, and the production rate based on the demand. The remanufacturing of the defective products occurs in two ways. While the remanufacturing process in the smart multi-stage production system with a single cycle occurs within the cycle, the reworking in the case of a smart multi-stage production system with numerous cycles occurs in different cycles. Numerical examples are conducted and compared to illustrate the model quantitatively. It is found that in both scenarios of both models, the total cost is minimized.

The aim of almost every production firm is to gain maximum profit along with customer satisfaction. The formation of imperfect products is an obvious process in a production system, which is not a good thing from a business point of view. This paper considers an inventory model for an imperfect production system. All the imperfect products are assumed to be reworkable. An investment occurs for in-process inspection to reduce the rate of formation of imperfect items. A comparison is performed with a production system without in-process inspection to demonstrate the effectiveness of the model. The study shows that the implementation of in-process inspection significantly reduces the total cost of the system as compared to a production system without in-process inspection. The results obtained show that the use of in-process inspection can reduce the total cost by up to 9.3%. Moreover, reducing the formation of defective items saves energy as well as resources. In addition, to reduce carbon emissions, a penalty is implemented on carbon emissions caused by manufacturing, reworking, disposal, and indirect emissions caused by the transportation of disposed items to the treatment facility. As everyone should now be concerned about the environment, green technology is implemented to reduce the amount of carbon emissions to some extent. A classical optimization technique is used to achieve decision variables, i.e., optimal production quantity (Q), fraction of profit invested in in-process inspection (Pf), and green technology investment (G), such that the total cost of the system is minimized. A sensitivity analysis is performed to determine the effects of various parameters on the decision variables and total cost. Maple 18 and Mathematica 11 software are used for mathematical work and graphical representation.

Even if a new product is launched, that is a deteriorating type; there is a chance of imperfect production due to its deteriorating nature. Then, the producer faces trouble since the production starts and the trouble is the deteriorating rate of those products. One sure fact is that the longer a deteriorating product stays in the production unit or warehouse, the lesser its shelf-life will be when it reaches the retailer and, finally, consumers. During this entire process, one of the most troublesome things is the uncertain nature of the deterioration rate of the product. This study examines the above-stated scenario when the deterioration rate affects the newly launched products from the production of the product to the selling of the product. In this process, the product loses its shelf-life gradually, where inflation exists in the market. This implies that inflation happens for the time value of money but with the depreciating value of the shelf-life of a product. Because of the depreciating shelf-life, the retailer faces a shortage of the products in the market. As it is a newly launched product, an increasing demand happens over time, and a ramp-type demand pattern justifies the market demand for this type of product. To ensure the minimum cost of the supply chain, two different types of deteriorating rates are tested in this study: crisp deterioration rate and uncertain deterioration rate. A fuzzy and cloudy fuzzy sets are used to check the uncertain deterioration rates. A global minimum cost is found using the classical optimization methods. Results show that the cloudy fuzzy environment for a deterioration rate obtains the global minimum supply chain cost. The global minimum cost of the supply chain in the cloudy fuzzy environment is 2.54% less than the fuzzy environment and 1.95% less than the crisp environment. The optimal time is minimal in the cloudy fuzzy environment, followed by the crisp and fuzzy environments. Sensitivity analysis and managerial insights are discussed for generating insights from this study.