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Demand planning based on demand data in the supply chain includes the most significant steps in production planning. Therefore, the supply chain's correct demand forecasting may reduce this effect, known as the bullwhip effect or uncertainty concerning customer demand, thus reducing companies' and organizations' costs and surplus activities. Therefore, this article examined the statistical population characteristics to test the hypotheses through the path analysis drawn using descriptive statistics and FCM(fuzzy cognitive map)  method. Then, the model strength was investigated using structural equation modeling (SEM) in AMOS software, and structural equations were presented. This article selected the Aftab oil factory as a case study. The findings of this study emphasized that demand management performance is highly essential for industries. Companies can design the sector independently as a demand management sector for evaluating customer demands at different levels of the supply chain. According to the fit of the main model, CFI and NFI indices are equal to 0.99 and 0.97, respectively, which are close to the optimal fit threshold. RMSEA and SRMR indices are equal to 0.01 and 0.01, respectively, both showing a relatively good fit of the model.

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A look at the world production and consumption indicates that production systems resiliency and sustainability is highly regarded by businessmen and the general users for long surviving of human being race and ecological endurance. By conducting theoretical studies and reviewing the literature, and searching previous studies to identify the resilience factors important to manufacturing industries, a list of effective strategies was determined. The most important strategies of resilience considered in this study are: capacity management, multi sourcing, demand management, information sharing, additional inventory holding, contracting with backups, risk management and disaster recovery, dropping market feeding strategy, enlightenment of business flow complexity, and suppliers/facilities reinforcement. In this article, DEMATEL approach is used to demonstrate how production resilience factors can impacts on each other and what the interrelationships among these factors are. After that, a questionnaire was designed for pairwise comparisons of resilience strategies of capacity scaling, multi sourcing, contracts, inventory management, risk management, and production level. Then, a system dynamics approach is used to model the interrelations among the resilience factors by taking feedback loops into consideration managing to trace their impacts on production and inventory levels. A production system with its main processes of: production order rate, planned work, work in process (WIP), production rate, inventory level, desired shipment rate, backlogs, rejected rate, rework rate, required capacity, and capacity scaling are designed for this study. This model presents a production system with circular resilience’s strategies impacts on production scaling and hence their impacts on sustainability indicators of job creation, and salary (social pillar), profit and investment (economic pillar), and ecosystem destruction (environment pillar). System dynamics approach helped us in presenting the long trends of sustainability indicators as shown by a number of figures in the body of this article. Five scenarios are developed and the results were presented to the team of our experts presenting them by wi=0, wp=0 (case 1), wi=0, wp=0.5 (case 2), wi=1, wp=0 (case 3), wi=0, wp=1 (case 4), and wi=0.36, wp=0.47 (case 5). Experts’ opinions were gathered and then use TOPSIS approach for determining the best case the among cases discussed above. The results indicates that the data generated by Vensim computer software for five cases, case 5 with wi=0.36 and wp=0.47 is the best case among all cases.

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In cost efficiency models, the capability of producing observed outputs of a target decision making unit (DMU) is evaluated by its minimum cost. Traditional cost efficiency models are considered for situations where data set is known for each DMU, while, some of them are imprecise in practice. Several studies have carried out to evaluate cost efficiency using fuzzy data envelopment analysis (DEA) methods for dealing with the imprecise data that have drawbacks. The issue of presenting improve strategy is ignored for inefficient units, as well as the applied models are not easily implemented. This paper proposes a new extension to evaluate fuzzy cost efficiency using fuzzy extended multiplication and division operations. This method offers a fully fuzzy model with triangular fuzzy input-output data along with triangular fuzzy input prices. In the proposed extension, a new definition of fuzzy cost efficiency is suggested based on the extended operations. Finally, a numerical example is provided to show the applicability of the proposed models.
 

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In the evaluation of decision making units with classical models of data envelopment analysis, it is assumed that the factors are deterministic. In some decision-making problems, the amount of inputs or outputs of the units is not exactly known and it is a three-parameter interval in grey form. In this case, it is recommended to choose the factors from their center of gravity. In the classic models of data envelopment analysis, all factors are also considered desirable, but in real problems there are undesirable factors too which cannot be used to evaluate problems with undesirable inputs and undesirable outputs. In this paper, a model is presented for calculating the efficiency of decision making units in the presence of the center of gravity of undesirable three-parameter interval grey undesirable factors based on the combination of strong and weak disposability principles. To this end, the proposed method is discussed with a practical example.
 

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The purpose of this article is to investigate the modes of vehicles based on the type and number of urban travel facilities for passengers. As you know, to divide transportation models based on  goal programming, is to divide all transportation modes for urban station routes by type and region.The main objective of this is to present the best mode (vehicle) of transportation based on travel modeling in transportation areas of urban trips for multi-objective transportation goal programming. In this case, the type of transportation solution is determined in the desired area on the way to the stations, according to which the pollution reduction, travel time reduction, cost reduction, availability, maximum safety and comfort of the means of transportation are reduced, increased or liminated.
 

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Supply chains often have different technologies. Additionally, organizations with multiple stages can evaluate their operational efficiency by analyzing scale elasticity, which helps determine if they are functioning optimally or if there is room for improvement. This evaluation allows for the identification of potential inefficiencies and opportunities for enhancement. Consequently, this research introduces a two-stage DEA-based approach with undesirable outputs to examine the scale elasticity of supply chains within meta and group frontiers. The measurement of group and meta performance of general systems and stages is conducted for this purpose. Moreover, the study addresses the scale elasticity of supply chains with undesirable outputs by considering the heterogeneity of technologies. To achieve this, the study focuses on the right and left scale elasticity of efficient general systems and each stage. A real-world application from the soft drink industry is provided to illustrate the proposed model. The results show the applicability of the introduced methodology.
 

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In this article, the modeling and solution of a cryptocurrency capital portfolio optimization problem has been discussed. The presented model, which is based on Markowitz's mean-variance method, aims to maximize the non-deterministic internal return and minimize the cryptocurrency investment risk. A combined PSO and SCA algorithm was used to optimize this two-objective model. The results of the investigation of 40 investment portfolios in a probable state showed that with the increase in the internal rate of return, the investment risk increases. So in the optimistic state, there is the highest internal rate of return and in the pessimistic state, there is the lowest investment risk. Investigations of the investment portfolio in the probable state also showed that more than 80% of the investment was made to optimize the objective functions in 5 cryptocurrencies BTC, ETH, USTD, ADA, and XRP. So in the secondary analysis, it was observed that in the case of investing in the top 5 cryptocurrencies, the average internal rate of return increased by 9.92%, and the average investment risk decreased by 0.1%.
 

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Enhancing the efficacy and productivity of transportation system has been on the most common issues in recent decades, noteworthy to the industrial managers and expert so that the products are delivered to the clients at right time and the least costs. Therefore, there are two important issues; one is to create hub as the as intermediaries for streaming from multiple origins to multiple destinations and also responding to the tours of every hub at the proper time. The other is a route where the vehicles should pay at time window of each destination node. On the other hand, these problems may cause cost differences between hub and interruption of their balance. Accordingly, this paper presents a model dealing with cost balancing among the vehicles as well as reducing the total cost of the system. Given the multi-objective and NP-Hard nature of the issue, a multi-objective imperialist competitive algorithm (MOICA) is suggested to provide Pareto solutions. The provided solutions are at small, average and large scales are compared with the solutions provided by Non-Dominated Sorting Genetic Algorithm (NSGA-II) algorithm. Then, its performance is determined using the index for evaluating the algorithm performance efficacy to solve the problem at large dimensions.
 

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Regression is a statistical technique used in finance, investment, and several other domains to assess the magnitude and precision of the association between a dependent variable (often represented as Y) and a set of other factors (referred to as independent variables). This work introduces a linear programming approach for constructing regression models for Neutrosophic data. To achieve this objective, we use the least absolute deviation approach to transform the regression issue into a linear programming problem. Ultimately, the efficacy of the suggested approach in resolving such problems has been shown via the presentation of a concrete illustration.
 

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The traditional inverse data envelopment analysis (IDEA) models assess specific performance metrics in relation to changes in others, without taking into consideration the existence of random and undesirable outputs. This study presents a novel inverse DEA model with random and undesirable outputs, enabling the estimation of some random performance measures for changes of other random measures. The proposed chance-constrained inverse DEA model integrates both managerial and natural disposability constraints. By using the introduced approach, the estimation of natural disposable random inputs is presented for changes in random desirable outputs. Also, undesirable outputs are assessed for the perturbation of managerial disposable random inputs while the stochastic efficiency is maintained. The models are solved as  linear problems, with a numerical example provided to illustrate their application. The findings indicate that this approach is effective for evaluating efficiency and performance metrics in scenarios involving random and undesirable outputs.
 

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Traditional maximal p-hub covering problems focus on scenarios where network flow is constrained by resource limitations. However, many existing models rely on static parameters, overlooking the inherent randomness present in real-world logistics. This oversight can result in suboptimal network designs that are vulnerable to congestion and rising costs as demand varies. To address this issue, we propose a novel mathematical model for the capacitated single allocation maximal p-hub covering problem that takes into account stochastic variations in origin-destination flows. Although solving this model poses computational challenges, we utilize a Lagrangian relaxation algorithm to enhance efficiency. Computational experiments using the CAB dataset highlight the effectiveness of our approach in achieving optimal solutions while reducing computation time. This framework offers valuable insights for designing robust hub-and-spoke networks in the face of demand uncertainty.
 

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One of the ways to evaluate the performance of decision-making units (DMUs) such as banks and commercial companies is to use the concepts of economic efficiency in data envelopment analysis (DEA). In the process of evaluating the performance of the DMUs, it is important to apply the superior information of the decision maker (DM). In this paper, we obtain cost and revenue efficiency measurement models to evaluate DMUs based on the DM's opinion. In this regard, we use the method of production trade-offs in DEA. Using the production trade-off method, we apply the importance of inputs and outputs to the efficiency measurement process based on the opinion of the DM. We assumed that the cost (price) of each input (output) is different for different DMUs. We present the efficiency scores ​​and efficient targets corresponding to the DMUs. We present an application of the presented models in the banking sector and present the results of the paper.
 

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Facility location and routing problems have attracted significant research attention since the 1960s due to their practical relevance and complexity. Efficiently establishing production facilities, optimizing vehicle routes, and implementing effective inventory systems are essential for improving organizational performance. In this study, we propose an integrated location-routing model for the pharmaceutical supply chain, designed to satisfy all retailer demands through an appropriate inventory policy, ensuring no demand is unmet. The proposed mixed-integer mathematical model considers a four-tier supply chain, including manufacturers, distributors, wholesalers, and retailers, with the objective of establishing cost-effective warehouses while fulfilling all demand requirements. Demand uncertainty is addressed using a scenario-based probabilistic approach. The model is solved using GAMS for a small-scale case study. For larger-scale instances, where exact solutions are computationally challenging, a meta-heuristic approach—specifically, a genetic algorithm—is employed to efficiently obtain near-optimal solutions.
 

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The explosive growth of global e-commerce and the increasing complexity of last-mile logistics have made the strategic placement of smart lockers a critical concern in modern urban logistics systems. Conventional methods, which rely solely on Multi-Criteria Decision Making (MCDM) methods for obtaining solutions, suffer from several limitations when implemented in uncertain, significant, and multi-objective scenarios. This paper proposes a stochastic multi-objective optimisation model for the BWM, prioritising decision criteria, which is solved by combining a hybrid metaheuristic solution methodology. The proposed model optimizes both total cost and sustainability performance from economic, environmental, and social perspectives, as well as robustness to demand uncertainty. An empirical study using Babol City, Iran, is presented to test and demonstrate the proposed framework. Candidate locker location and demand areas were examined based on expert-elicited criteria weights, with the preparation of a multi-objective mixed-integer programming model. In order to alleviate the computation burden, a combined structure of NSGA-II and LNS (referred to as NSGA-II+LNS) was proposed, which outperforms classical evolutionary algorithms in terms of convergence into the Pareto frontier. Factual results indicate that factoring in economic affordability, accessibility, and environmental impact is key to optimal locker capacity design. Robust solutions under demand fluctuation can save up to 18% more on service reliability, providing strong deterministic answers. This article makes the following theoretical and practical contributions: (i) a novel sustainable-oriented, deterministic model for smart locker location is proposed; (ii) advanced metaheuristics are integrated with MCDM in urban logistics, whereas fewer studies have focused on integrating them; and (iii) policy implications are suggested not only to policymakers but also to logistics operators who want robust last-mile delivery strategies..
 

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Extant quantitative models in Resource Allocation and Operational Systems often rely on statistical optimization or behavioral frameworks, frequently failing to model and quantify the deterministic structural conflicts that arise when operational and informational constraints are ignored. This paper addresses a critical analytical gap in Industrial Information Integration: the necessity of a deterministic modeling framework to quantify the systemic risks inherent in resource scarcity and misallocation. We introduce a novel analytical framework, derived from the Generalized Pigeonhole Principle (GPP), to quantify the inevitable consequences of resource imbalance within complex organizational systems. The framework develops a three-tiered conceptual model: (1) the Base Principle (quantifying the inevitable Structural Non-Allocation Rate, (N-M)), (2) the Generalized Principle (modeling Inevitable Operational Congestion, λ_min), and (3) the Weighted Principle (quantifying Qualitative Mismatch, f). We demonstrate the model's predictive and explanatory power through scenario-based analytical simulations, providing a foundational validation for its applicability across workforce planning and capacity development contexts. The analysis yields testable propositions linking these mathematical inevitabilities directly to systemic consequences (e.g., structural attrition/turnover, intragroup operational conflict). This research provides a new, parsimonious analytical language for Operational Systems Modeling, fundamentally shifting the focus from optimizing individual performance to managing unavoidable structural pressures. The model serves as a robust quantitative decision-support tool for strategic workforce planning and lays the essential groundwork for future dynamic modeling of operational capacity and resource demand.

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Existing merger approaches in data envelopment analysis integrate decision-making units in a single stage‎, ‎but in practice‎, ‎merging units may not be possible or affordable at once‎. ‎We propose a finite multi-stage framework for the gradual merger of decision-making units that incorporates practical constraints‎. ‎The model determines input and output contributions of the merged units at each stage and constructs a strictly increasing efficiency sequence that converges to a Pareto-efficient state‎. ‎Each new unit is optimized using both input ‎and output orientation while preserving a uniform return to scale type across stages‎. ‎The framework is validated through a multi-stage merger application on a subset of Iranian banks.
 

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Measuring capacity utilization is an important aspect among processes in order to determine overcapacity or undercapacity. Furthermore, in many situations, the convexity and homogeneity properties are not satisfied. Accordingly, in this paper, meta-frontier free disposal hull (FDH) frameworks are proposed to estimate output-oriented and input-oriented capacity utilization (CU) rates of firms under nonconvexity property and heterogeneity of technology. Also, the introduced technique is applied to assess capacity utilization of some Iranian hospitals. The findings show the presented approach is beneficial to measure capacity utilization rates of systems in the presence of nonconvexity and heterogeneity.
 

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Cooperative game theory is an important tool for analyzing cooperation and benefit allocation among coalition members, but classical models usually do not consider the existence of a minimum capacity required for cooperation to be activated. In this study, “threshold coalition games” are introduced, in which the formation of an effective coalition requires crossing a certain threshold of collective capacity. Also, a coalition activation index and a new rule called “threshold allocation value” are presented to determine the players’ shares, and their properties, including efficiency, symmetry, and uniqueness, are proven. Finally, a numerical example shows that the proposed model can model threshold-based cooperation structures coherently and provides a suitable framework for future research in cooperative game theory.
 

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The optimal planning of hybrid renewable energy systems has become increasingly important due to rising energy demand, environmental concerns, and the need for reliable electricity supply in remote and isolated regions. This study presents a comprehensive mixed-integer linear programming (MILP) framework for the optimal design of a hybrid solar–wind–battery–fuel cell–diesel microgrid. The proposed model simultaneously determines the optimal type, size, and operation of system components over the project lifetime while minimizing the equivalent annual cost. Unlike many existing optimization approaches, the framework integrates economic, environmental, and reliability considerations into a unified objective function by incorporating carbon emission penalties, load curtailment penalties, and renewable energy incentive policies. Furthermore, replacement costs and component lifetime degradation are reformulated into linear constraints, enabling the problem to be solved efficiently using exact optimization techniques. Hourly meteorological and load data are employed to accurately capture seasonal and daily variations in renewable energy generation and electricity demand. The optimization model is implemented in GAMS and solved using the CPLEX solver. Different system configurations and regulatory scenarios are evaluated to investigate the influence of diesel generators, battery storage, hydrogen technologies, and government support policies on system performance. The results demonstrate that an appropriately designed hybrid microgrid can substantially improve renewable energy penetration while maintaining system reliability and reducing the overall lifecycle cost. Moreover, regulatory incentive mechanisms significantly increase the economic viability of renewable energy resources and decrease dependence on fossil-fuel-based generation. The proposed MILP framework provides an effective decision-support tool for policymakers, system planners, and investors involved in the development of sustainable hybrid microgrids.
 

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Industrial Tourism (IT) can lead to economic prosperity, job creation, capital attraction, and greater interaction between industry and society. On the other hand, the Industrial Tourism Supply Chain (ITSC) comprises activities and stakeholders, including transportation, industrial units, accommodation centers, and facilitators, whose coordinated performance directly affects the quality of tourists' experience and the efficiency of this industry. Therefore, the present study examines ITSC considering sustainability aspects to address gaps in the field. Moreover, the important issue of destination attractiveness is considered in the proposed model. The proposed model is solved using the Revised Multiple-Choice Goal Program (RMCGP) method. To evaluate the proposed model, a case study in Mazandaran province, Iran, is considered, and a sensitivity analysis is conducted on some key parameters. The output results show that the activity in this industry and the provision of services are economically justified.