This study introduces a new discount policy in inventory management, called the Discount Order-Frequency Quantity (DOFQ). The proposed framework introduces a behavioral and coordination-oriented inventory incentive mechanism that rewards replenishment regularity instead of encouraging bulk purchasing behavior. Unlike traditional EOQ models that link discounts to order size, timing, or payment method, the DOFQ approach applies discounts based on the frequency of orders placed. The supplier grants a price reduction after a buyer completes a predetermined number of orders, thereby encouraging regular purchasing behavior. A mathematical model is developed to analyze the impact of this policy on total inventory costs. An exact solution method is proposed to determine the optimal order frequency that minimizes total costs. Numerical examples and sensitivity analyses demonstrate the efficiency and practical applicability of the model. The results highlight the benefits of frequency-based discounts for both suppliers and buyers, providing a cost-efficient and sustainable alternative to existing discount policies. This study fills an important gap in EOQ literature and opens avenues for further research on frequency-driven incentives.
This study presents a novel Shewhart-type attribute control chart for truncated life tests using the Type II Generalized Half-Logistic Distribution (GHLD), addressing the limitations of traditional binomial-based charts in detecting shifts for skewed or heavy-tailed lifetime data. The proposed chart incorporates truncated lifetime information, with control limits derived from the GHLD cumulative distribution function and its performance is evaluated through Average Run Length (ARL) analysis under both in-control and out-of-control conditions. Comparative analysis with a Weibull-based chart demonstrates faster detection of process shifts and improved efficiency. Validation using real industrial lifetime data confirms its robustness and practical applicability. Overall, the study introduces a reliable, sensitive, and efficient tool for industrial quality control, highlighting the effectiveness of integrating the TGHLD into attribute control chart methodology for truncated life testing.
The primary goal of this research is to establish the connection between 2-tuple linguistic (2TL) term sets and group-theoretic algebraic structures within the fuzzy linguistic contexts. We investigate the properties of group isomorphism and homomorphism between the linguistic 2-tuples and the numerical set [-n, n] , where n is a positive integer. To deepen the algebraic foundation, the notions of factor groups, normal subgroups, cosets, and linguistic kernels are introduced. Additionally, we define new operational laws for the 2TL term set to ensure computational consistency within the original linguistic domain. Finally, we prove an analogue of the fundamental theorem of classical group homomorphism for a 2TL group. Based on the listed linguistic group isomorphic properties and new operational laws, this paper further explores a constructive study of the matrix game theory (GT) by introducing the concept of linguistic matrix norms. This framework provides a novel methodology for addressing two-player zero-sum linguistic matrix games (ZSLMG) with 2TL information. Our approach enables the evaluation of approximate linguistic game values without the need to solve traditional linguistic linear mathematical equations. To further enhance the analytical capabilities of our approach, we define the 1' -norm and ∞ ' -norm of the given linguistic payoff matrix. Furthermore, we derive new results to determine the linguistic game value and the mixed strategy set, thereby effectively bypassing the complexities inherent in the existing linguistic linear programming (LLP) method. A real-world example is provided to validate the developed approach and demonstrate its overall utility and efficacy. We also compare our proposed method with other existing methods for uncertain matrix games. Nevertheless, we assert that the proposed framework offers a robust, empirical viewpoint on the theory of the imprecise matrix game.
Digital Supply Chain Twinning (DSCT) is a modern technology capable of establishing a new level of supply chain agility and strategic decision-making by developing movable virtual representations of physical supply networks. This study examines the adoption of DSCT in India’s foundry micro, small, and medium enterprises (MSMEs) through an entrepreneurial lens. Grounded in the Resource-Based View (RBV) and Dynamic Capabilities Theory (DCT), we identify and structurally model 17 key factors influencing DSCT implementation. Using Interpretive Structural Modeling (ISM) supported by expert insights, we develop a hierarchy of drivers, enablers, and outcomes of DSCT adoption, supplemented by MICMAC analysis to classify variables by their driving and dependence power. Entrepreneurial leadership emerges as a pivotal driver enabling firms to sense opportunities and seize them by reconfiguring resources for digital transformation. Technological readiness and related capabilities are validated as critical resources for supply chain efficiency. The ISM digraph reveals how foundational factors (e.g. entrepreneurial leadership, external support) cascade through intermediate enablers (e.g. tech readiness, cost of adoption, external market pressure) to influence operational outcomes like agility, flexibility, and competitiveness. Findings indicate that while foundry entrepreneurs recognise the potential of DSCT, its full value has not yet been realised in practice. Key strategic enablers including collaborative partnerships, real-time data utilisation, and proactiveness in innovation are necessary to overcome resource constraints and successfully implement DSCT. The study contributes to theory by integrating entrepreneurship with digital supply chain transformation and demonstrates how MSMEs can leverage DSCT for competitive advantage. Practical implications are offered for entrepreneurs, industry clusters, and policymakers to foster the necessary capabilities, infrastructure, and support mechanisms.
The paper conducts a stochastic analysis and comparative evaluation of two distinct redundant systems: (i) a component-redundant system and (ii) a unit-redundant system. In the proposed study, the primary unit comprises two non-identical components in a series arrangement, meaning both must function for the unit to operate. A redundant unit of the main unit, also consisting of two components, is considered. For component redundancy, every component within the primary unit is connected in parallel to its corresponding components of the redundant unit. Conversely, in unit redundancy, the entire redundant unit is parallel to the primary unit. The failure times of all components are regarded as exponential. Each system is subject to repair with an arbitrary repair rate, applied only when it experiences complete failure. The supplementary variable technique (SVT) is employed to evaluate various system effectiveness for both types of systems. Classical and Bayesian estimation techniques are applied to determine the unknown parameters of MTSF and steady-state availability in a particular case. Computational analysis and graphical comparisons indicate that the component-redundant system performs better than the unit-redundant system over a wide range of parameter values, exhibiting higher reliability, MTSF, availability, and profit due to more effective utilization of redundancy. Estimation results further show that its MTSF and steady-state availability closely match the true values, confirming its superior performance.
The Minimum Spanning Tree with Inner-node Costs (MSTIC) is an important variant of the classic spanning tree problem that incorporates both edge weights and costs for non-leaf nodes into the objective function. This problem is particularly relevant to real-world applications, such as network design and wireless sensor networks, where routers or hubs incur significantly higher installation costs compared to cables. The problem has been proven NP-hard and has primarily been addressed through approximation algorithms. In this paper, we propose two exact algorithms: an edge-based approach inspired by Kruskal’s algorithm and a node-based approach inspired by Prim’s algorithm. Two new theoretical results on edge stability and optimal leaf connection are established to improve pruning efficiency. Computational experiments on 210 synthetic benchmark instances with up to 100 nodes indicate that our algorithms can find optimal solutions in a short time for instances up to 40 nodes. The Prim-based algorithm achieves better performance than the Kruskal-based algorithm in terms of both solution quality and pruning efficiency. These algorithms are well-suited for decision-support systems that require exact optimal solutions in small- to medium-scale infrastructure planning.
This paper formulates a constrained optimization problem to derive sampling weights for non-representative data, addressing a critical issue in various research domains, including market, economic, and social research. While data often require reweighting (balancing) to ensure representativeness, even advanced methods like raking exhibit limitations when constraints extend beyond marginal frequencies. Unlike raking, which is limited to linear constraints (marginals), the proposed method flexibly handles nonlinear constraints (e.g., variances) and arbitrary loss functions. Additionally, the resulting weights can deviate significantly from 1, leading to excessive distortions of the original data. This paper demonstrates that deriving weights can be formulated as a constrained nonlinear optimization problem to minimize distortions. This minimal distortion weighting problem, accommodating both equality and inequality constraints, can be efficiently solved using Sequential Quadratic Programming (SQP). This approach offers a flexible solution for weighting non-representative survey data, supporting various constraint specifications. The effectiveness of this method is demonstrated through a numerical example involving nine linear and nonlinear constraints, as well as lower and upper bounds on weights. These findings highlight the potential of constrained nonlinear optimization, particularly SQP, as a flexible and powerful tool for addressing complex survey weighting challenges.
The relationship between the property’s qualities and their perception of value impacts the effectiveness of real estate valuation models. Choosing the appropriate parameters (such as neighborhood, landscape view, property area) for property valuation is up to the subjectivity of the decision maker; therefore, it is difficult to apply an accurate method that justifies selecting these attributes. This research aims to propose an approach for ordering parameters in real estate valuations for residential buildings in large cities. Fuzzy TOPSIS and Fuzzy SPOTIS methods were applied for ranking, according to the criteria the property attractiveness for the client and associated property liquidity. The analysis used two scenarios: the first scenario focused on low-standard and the second on high-standard properties. The two multicriteria methods showed similar ranking efficiency in the scenarios. Fuzzy SPOTIS is a recently developed multiple criteria decision support method and stands out for usability because of its absence of order reversal and simpler axiomatics compared to Fuzzy TOPSIS. The sensitivity analysis showed that modelling with Fuzzy SPOTIS is more susceptible to changes in criterion weights, especially at extreme values, compared to Fuzzy TOPSIS. The paper highlights how fuzzy methods can assist decision-makers in determining the best parameters for real estate and construction valuation, incorporating specialist insights.
This paper examines a bulk service queue in which customers arrive according to a renewal process and single server operates under a random serving capacity rule. The service time of a batch is governed by an exponential distribution and is dependent on the size of the batch being served. We observe the system at arrival points, which form a Markov chain, and thus obtain an explicit expression of the system content distribution at pre-arrival epoch in terms of the single root of the associated characteristic equation. Further, we develop a relationship between the system content distributions at pre-arrival and arbitrary epochs using the supplementary variable technique. We present some numerical results as well in order to illustrate the computational procedure. An additional contribution of this study is a comprehensive cost analysis aimed to optimize the overall system cost. The findings provide useful insights for designing random batch-size-dependent service systems.
In this study, we explore an integrated inventory system involving a single manufacturer and multiple retailers, focusing on carbon emission reduction under a stochastic fuzzy environment. Over time, the production system tends to enter an out-of-control state, leading to the production of defective items. To mitigate the defective rate and setup costs, we consider two types of continuous investment functions. The lead time demand is treated as a stochastic fuzzy variable, and shortages are partially backordered at the retailer’s end. We introduce a novel concept for calculating the expected value of strictly monotonic L–R fuzzy numbers using inverse credibility distributions to address shortages when both randomness and fuzziness are present simultaneously. The model aims to determine optimal values for several parameters, including the number of shipments, production rate, shipment quantity, reorder level, setup cost investment, and the probability of the out-of-control state, with the goal of minimizing the objective function. Due to the highly nonlinear nature of the model, it is difficult to achieve the analytical solutions. To overcome this, we employ a range of hybrid meta-heuristic algorithms. Numerical examples are used to illustrate the model, and a comparative analysis is performed to evaluate its effectiveness.
This study presents an inventory model designed for new technological products, such as laptops and smartphones, which have a very specific obsolescence life. The model is based on a linear demand function that incorporates parameters related to price, time, and advertisement. It permits partial backlogged shortages at specific intervals within a deterministic demand framework for the cycle length T. The objective of the study is to identify the optimal price, replenishment timing, and advertising investment, along with their constraints, as derived from the proposed assumptions for linear demand. The proposed study indicates that retailers may earn a profit of 114.54 per cycle when investing in advertising, whereas they earn only86.05 per cycle without advertising. Hence, the study demonstrates that advertising enables them to earn an additional 28.49 per cycle. To this end, the theoretical results, optimal conditions, numerical examples, and Hessian matrix analysis are utilized to illustrate how the proposed demand function can maximize profit per unit through the inventory model.
Micro, small, and medium enterprises (MSMEs) in the food processing sector frequently encounter challenges in managing raw material inventories due to manual stock control practices, which often lead to stockouts, overstocking, and increased operational costs. This condition is experienced by the banana crackers MSME, where inventory decisions are still based on estimation without systematic control. This study aims to design and implement an automated inventory control system by integrating the min–max method and the economic order quantity (EOQ) model to improve inventory efficiency and reduce total inventory costs. The research adopts a quantitative case study approach, using historical demand data, ordering costs, holding costs, and supplier lead time as input parameters. The EOQ model is utilized to determine the optimal order quantity, while the min–max method is applied to establish minimum and maximum inventory levels. These methods are integrated into an automated system that continuously monitors stock levels and generates reorder decisions automatically when inventory reaches the minimum threshold. The empirical results demonstrate that the integrated automated system significantly optimizes inventory performance compared to legacy manual practices. Total monthly inventory costs dropped by 31.25
This paper introduces the Mixed (p, q)-Rung Orthopair Fuzzy Set, a generalization of intuitionistic fuzzy framework designed to provide a more flexible and expressive representation of uncertainty. A comparative analysis is performed between the proposed intuitionistic fuzzy set and several notable extensions, including q-Rung orthopair fuzzy sets, Fermatean fuzzy sets, generalized fuzzy sets, and (m, n) -Rung orthopair fuzzy sets, with strong emphasis on their ability to represent hesitancy information. The basic algebraic operations of the Mixed (p, q)-Rung Orthopair Fuzzy Set are discussed. To facilitate uncertainty inherent decision-making, a new score function is derived, enabling robust ranking and prioritizing available alternatives within the proposed intuitionistic fuzzy framework. The effectiveness of the newly introduced score function is examined against established score functions for other intuitionistic fuzzy extensions, discussing its consistency and capability of discriminating uncertain information. In addition, a novel transportation optimization algorithm is constructed on the basis of new score function to address the application of the Mixed (p, q)-Rung Orthopair fuzzy score function in supply–demand transportation problem. A detailed interpretative example is elaborated to illustrate the utility and computational effectiveness of the proposed method. The results exhibits that the new fuzzy framework offers a more generalized, comprehensive, and practical mathematical tool for capturing uncertainty and solving transportation problems in complex decision-making environments. At length, the paper concludes with a summary of key findings of this work and highlighting the possible directions for future research.
This study develops a sustainable electronic waste (e-waste) supply chain model that incorporates emissions from five key sources–reverse logistics, setup, assessment, remodeling, and holding-under the hybrid carbon policy, which is the combination of carbon tax and cap-and-trade policies. The model considers price-dependent demand and integrates green investment decisions to reduce emissions across all sources. However, existing studies do not simultaneously consider multiple emission sources along with integrated carbon tax and cap-and-trade mechanisms within e-waste supply chains. A nonlinear optimization framework is formulated and solved using analytical optimality conditions and a structured solution procedure to determine the optimal selling price, remodeling time, and allocation of green investments for maximizing average profit. A numerical example involving multiple e-waste items is analyzed under three regulatory scenarios: (i) combined carbon tax and cap-and-trade, (ii) carbon tax only, and (iii) cap-and-trade only. The results indicate that the integrated regulatory approach leads to lower emissions than individual policy scenarios, while also identifying the most profitable item under different regulatory conditions. Sensitivity analysis further reveals that average profit is more responsive to changes in parameters than average emission, highlighting the significant impact on economic performance. From a practical perspective, the model serves as a decision-support framework for e-waste firms to optimize pricing, allocate green investments, and ensure regulatory compliance. The findings show that integrating economic and environmental decisions enhances profitability while reducing emissions, supporting sustainable supply chain operations.
Market segmentation can be subdivided into the subprocesses of segmentation, target market selection, and product positioning. Decisions on ventures into new market segments require to identify such new segments; the targeting process should be assisted by an assessment of the financial consequences. In particular, the development of new segments may also affect the profitability of the activities in already existing segments. Therefore, this paper presents an approach to value such investments in two steps, considering that market segmentation implies dealing with market imperfections, in particular with interdependencies between the different segments, investment, marketing and production. Hence, by optimising the development of the current segments and calculating the highest affordable price for an expansion into a new segment, both steps of the presented approach provide important information for marketing planning and controlling as well. This will be underlined by deriving formulas for determining the highest affordable price as a sum of (corrected) net present values. In real-world environments this maximum payable price is likely to be lower than according to approaches discussed in literature. Generalising the concept of net present values also for the given imperfect markets, these (corrected) net present values allow the decision maker to analyse the effects of changes in important market conditions and relevant parameters and to interpret them in monetary terms. Further information may be obtained through sensitivity analyses.
Graph Neural Networks (GNNs) have achieved remarkable success in modeling relational data, but they often assume deterministic relationships in graph structures. Real-world graphs, however, frequently exhibit uncertainty in node and edge attributes due to incomplete or noisy data. This paper proposes a novel Fuzzy Graph Attention Network (FuzzyGAT), which integrates fuzzy logic into the attention mechanism to represent uncertainty in graph-structured data. By modeling attention weights as fuzzy sets, FuzzyGAT enhances the robustness of GNNs in handling ambiguous relationships. We provide a detailed theoretical framework, including mathematical proofs of convergence and expressiveness, and demonstrate the model’s effectiveness through synthetic and benchmark datasets experiments. Our approach is designed to be distinct from existing methods by prioritizing uncertainty quantification in the attention mechanism. The code for FuzzyGAT developed by author for this work available at https://github.com/anujsharma25/FuzzyGAT .
This study presents a new mathematical framework, Pythagorean fuzzy soft planar graphs (PyFSPGs), which combines Pythagorean fuzzy multi-soft sets with planar graph theory to model complex networks under uncertainty. Existing intuitionistic fuzzy planar graph models are limited by the linear condition η + λ≤ 1 , restricting their capacity to represent higher-order uncertainty in spatial optimization. By adopting the quadratic Pythagorean condition η ^2 + λ ^2 ≤ 1 , the proposed framework offers greater flexibility and precision. The study establishes structural properties, defines a Pythagorean fuzzy soft planarity index, proves theoretical bounds on crossings between strong edges, and develops an algorithm for planarity assessment and crossing minimization. To demonstrate practical feasibility, the framework is applied to a real-world route planning problem for autonomous robots in a metropolitan transportation network. To minimize path-crossing risks in intelligent navigation, the model produces planarity values of PL(s_1) = (0.546, 0.516) , PL(s_2) = (0.531, 0.517) and PL(s_3) = (0.535, 0.538) across varying operational parameters. Comparative analysis shows that the PyFSPG model improves uncertainty representation and increases safety and efficiency in autonomous system operations. This provides a robust decision-support tool for logistics and smart manufacturing infrastructure.
In the era of Industry 4.0, the formulation of sustainable supply chain systems is important for enhancing both efficiency and competitiveness. This paper introduces a manufacturer-retailer sustainable supply chain model that incorporates smart production strategies for deteriorating items alongside investments in automation technology, facilitated by radio frequency identification (RFID) technology. So, using RFID an environmental and social partnership between the maker and seller, the manufacturer is more efficient and responsive. The model addresses key challenges related to product deterioration, inventory control, and real-time information exchange between manufacturers and retailers. By integrating autonomy and automation with a human element through radio frequency identification technology, the system enables intelligent inspection, thereby reducing waste and operational costs. The human involvement is implicitly represented through the autonomation investment function, which reflects investments in intelligent inspection, monitoring, and human-assisted quality control mechanisms. The smart production allows manufacturers to dynamically adjust production rates in response to demand fluctuations and deterioration rates. Analytical and numerical results indicate that radio frequency identification technology-based autonomation enhances decision-making, reduces total system costs, and improves responsiveness throughout the supply chain. This framework offers valuable insights for managers seeking sustainable, technology-driven inventory solutions in contexts involving deteriorating items. The model is numerically validated using the software Mathematica, and robustness analysis is conducted to examine the impact of various parameters on optimal results. This study is important; increasing environmental regulations and production waste in the rubber industry require sustainable and smart supply chain solutions. The purpose of this study is to develop a manufacturer–retailer sustainable supply chain model for deteriorating items using RFID-enabled autonomation technology. The proposed model is solved analytically using Hessian matrix conditions and validated through numerical and sensitivity analyses. By conducting this study, we developed a model cost reduction, and waste reduction, RFID benefits. This study demonstrates that RFID-enabled autonomation significantly improves sustainability and operational efficiency.
In the paper industry, the washing system is an essential component that removes contamination from pulp before proceeding to the next processing stages. This washing system consists of three subsystems namely screen unit, cleaner unit and decker unit, which are connected in series configuration. The purpose of the present study is to optimize the availability of washing system and identify the most critical component of washing system. For this purpose, reliability measures like reliability, availability, maintainability, and dependability analysis are conducted for each component of the washing system. Further, to evaluate the effectiveness of the system a stochastic model is then developed using the Markov birth–death process with the help of Chapman-Kolmogorov differential equations. The failure and repair rates are assumed to be constant and statistically independent. For maximizing the availability of the system this study used a comparison between two nature inspired algorithms such as Genetic Algorithm and Particle Swarm Optimization. The result of this study indicates that the Decker subsystem achieved the highest availability i.e. 0.993008988 with the reliability e^-0.14t and lowest mean time between failure. That shows Decker performs better among all subsystems. Further, it reveals that Genetic algorithm surpasses the particle swarm optimization algorithm by achieving the highest availability of the overall system of 0.9940 at a population size of 1500 after 250 iterations. The results of the study will be helpful for system designers and engineers to improve the availability of systems in paper industry as well as various sectors.
The dairy supply chain is highly vulnerable to disruption because of its time and temperature sensitive characteristics, which can lead to rapid product deterioration and significant economic loss. This study develops a stochastic optimization framework to support strategic resilience investment in perishable supply chains. The model introduces two principal innovations. First, it incorporates an integrated resilience-budgeting mechanism in which a finite resilience budget is allocated across absorptive, adaptive, and restorative capacities as first-stage decision variables. Second, the model treats recovery time as an endogenous decision-dependent variable determined by disruption severity and the share of budget assigned to restorative capacity, rather than as an exogenous constant The resulting formulation is expressed as a mixed-integer nonlinear program and subsequently linearized into a mixed-integer linear model to ensure tractability. Uncertainty in demand, supply, and disruption processes is incorporated through Monte Carlo simulation combined with scenario reduction. The model is applied to a dairy supply chain case, where maintaining service levels and minimizing recovery duration are critical. Sensitivity analysis shows that under constrained budgets, restorative capacity provides the highest marginal value and is prioritized, while increasing the total resilience budget allows for greater investment in adaptive and absorptive capacities without compromising service levels. Scenario-based results further indicate that budget allocation decisions should be guided by historical recovery and maintenance costs to effectively reduce recovery time. The study offers actionable decision support by linking historical disruption information to optimal future resilience investment. A primary limitation is the simplified functional relationship specified between budget allocation and recovery outcomes, which highlights the need for future empirical calibration. Overall, the research advances integrated and proactive resilience modeling for perishable supply chains by embedding recovery dynamics directly within a stochastic optimization framework.
