مدل سازی ریاضی

Railway tracks are among the most critical and costly components of any railroad. Optimal and timely maintenance allocation ensures system reliability and effective resource utilization. This article presents a mathematical model designed for condition-based preventive maintenance of railway tracks. The objective is to minimize total maintenance costs while maintaining system availability and reliability. The cost function considers maintenance and renewal expenses, track possession costs, and unplanned failure costs during the planning horizon. The network is divided into segments, with the standard deviation of the longitudinal level calculated as the track quality index. Prediction and recovery models are developed to assess variations in the track quality index over the planning period. Preventive operations, including inspections, tamping, and ballast replacement, are assigned to track segments based on the allowable index limits and other constraints. The expected number of random failures is estimated using the non-homogeneous Poisson process, and preventive operations aim to reduce the incidence of such failures.

Given the complexity and non-linearity of the mathematical model, a meta-heuristic method based on a genetic algorithm was developed in MATLAB software. Initial random solutions were generated using a heuristic method. As a case study, input parameters were collected and modeled for one kilometer of railway in the Arak region. The efficiency of the proposed genetic algorithm was then compared with the results obtained using GAMS software.

For the case study, the mathematical model was solved for various problem dimensions using both methods. When GAMS software was able to achieve the optimal solution, both methods produced identical results. When GAMS could only report a feasible solution, the genetic algorithm outperformed it. For higher dimensions where GAMS provided a solution, the genetic algorithm produced results with objective function values that were 40% better.

The planning of preventive maintenance operations for railway tracks during the project period is achieved through solving the proposed mathematical model. This allocation is based on the quality index of the tracks and considers the reducing effect of preventive operations on the expected number of random failures, ensuring the required minimum availability and reliability of the system. The variability of the model's input parameters allows for consideration of influencing heterogeneous factors based on the tracks, traffic, and environment, enabling adaptation to different conditions or the implementation of various strategies. Additionally, the proposed genetic algorithm can efficiently solve different dimensions of problem instances.

this research, with the aim of evaluating the green innovation ecosystem and the way of green science and technology policy of selected European countries in order to ensure that Europe is moving towards minimizing Carbon, holistic sustainable development, and the green, innovative and competitive economy are on the move. This research is trying to provide a set of useful input, mediator and output indicators to determine the model indicating the stages affecting the performance of the green innovation ecosystem of the selected countries by examining the background of similar research. By collecting the available data through data banks, and preparing the ground for mathematical modeling, the mathematical model was designed by combining methods of network data envelopment analysis and game theory with the help of Lingo software to combine relative efficiency in functional areas and create a Calculate the final weighted score to evaluate the performance of the green innovation ecosystem for EU member states. The results indicate that according to the designed conceptual model including four stages of knowledge creation and development, knowledge implementation, financial and economic transformations and environmental protection, with the change in the performance of countries in the stage of financial and economic transformations, efficiency The total number of countries increases significantly;

The intertwined supply chain refers to a network of interconnected supply chains that, through long-term collaboration, can deliver products and services to multiple customers, even in the face of various disruptions. In the case of the tiles and ceramics industry, it is essential to enhance resilience and integration across all chains to address issues such as capacity limitations at centers, which are often due to the unavailability of raw materials and production machinery caused by sanctions. These challenges have led to inadequate production management and increased costs. The aim of this research is to design a resilient three-level intertwined supply network capable of withstanding disruptions and uncertainty while simultaneously increasing profit and enhancing resilience.

This research employs a capacity development strategy and supplier separation to address disruptions at centers and uses fuzzy chance-constrained programming to tackle demand uncertainty. The model of this research is a multi-product, multi-period, mixed-integer linear programming model. To solve the bi-objective optimization (profit and risk), the augmented epsilon constraint method was used, resulting in a Pareto solution set. To validate the model, real data related to the intertwined supply network of tiles and ceramics (interconnected supply chains of tiles and ceramics, glaze, and alumina balls) were used, and the model was solved using GAMS software.

Based on the model output and the results of the decision variables, profit increased by three percent in the deterministic case compared to the uncertain case, while risk decreased by seven percent. The numerical results of the sensitivity analysis show that changing the epsilon parameter from zero to five-hundredths and from five-hundredths to one-tenth leads to a two to seven percent increase in profit. Additionally, the optimal capacity increase in the alumina ball production center is twenty percent, in the tile production center is ten percent, and in the glaze production center is thirty percent.

In the current global context, where the evolution of supply chains is moving towards intertwined supply networks, there are very few studies conducted on these networks. Given the nature of the intertwined supply network, the presented general model facilitates the transfer of raw materials or products through both intra-chain relationships (such as between suppliers and producers, and between producers and customers) and inter-chain relationships (such as between suppliers of one chain and those of another, between producers of one chain and those of another, between customers (production centers) of one chain and customers (final) of another, and the reverse relationship from producers of one chain to suppliers of another). The model simultaneously considers strategic decisions, including the selection of centers that require capacity increases, while optimizing operational decisions (such as production levels, inventory levels, and transportation levels) accordingly.

Today, due to the competitive environment of the market, cooperation in the form of supply chain networks is necessary for the survival of businesses, and for efficient and effective cooperation between members, there is a need for coherent management of the supply chain. To realize this, there is a need for continuous coordination between supply chain performance on the one hand and market expectations on the other hand. One of the methods of maintaining this coordination is the continuous redesign of the supply chain network over time. In the supply chain network redesign problem, the goal is to improve an existing supply chain, while in the supply chain network design problem, a new supply chain is created from scratch. in real conditions; Often, the problem of redesigning the supply chain is more widely used than the problem of designing the supply chain, while in the literature, the vast majority of researches are focused on designing a supply chain from scratch. One of the decisions of the redesign problem that has been hidden from the attention of researchers is the decision to change the use of supply chain facilities. in other words; Changing the facility layer in the supply chain is considered as a new decision.

The decision to change the use of facilities in the traditional supply chain problem is challenging, because it changes not only the network flows but also the network structure (topology). Changing the basic structure of the supply chain network is a non-linear problem. In this research, an innovative innovation has been used to face this challenge, by first changing the perspective of the supply chain network from a traditional layered network to a rotating network and then presenting Innovative mathematical modeling based on the innovative perspective of the rotating supply chain network.

Redesigning the supply chain network with the possibility of changing the usage of facilities due to changes in the network structure is a non-linear problem. In this research, by changing the perspective and creating innovative variables and constraints, a linear mixed integer multi-period programming model has been presented for the problem. Also, in this model, the transition mode of changing the usage of facilities from one layer to another layer is considered, and achieving this capability is one of the amazing results of using the innovative perspective of the rotating network of the supply chain. This model was solved using an example in GAMS software with the CPLEX method, and MATLAB software has been used to show the results of this model and an innovative view of the supply chain.

In the past, supply chain managers faced with the decision to change the usage of facilities in the supply chain network due to the limitations of the traditional layer view for mathematical modeling and optimal redesign of the network under their management. They have faced a challenge, which now the managers have the possibility to face it with the help of this innovative model and changing the perspective towards the supply chain network. As a management proposal, we can point out the need to use the principles of optimization and supply chain management as a new management approach and paradigm. At the strategic level of the supply chain, due to its wide nature and dimensions, the amount of costs is high and small improvements in it will lead to a significant competitive advantage increase for the supply chain under management. for this reason; Chain managers are advised to use the model presented in this article for chains in which it is possible to change the use of facilities, to improve the chain under their management.

Designing a multi-objective multiple allocation-routing problem in a humanitarian supply chain is important because it improves efficiency and productivity in the supply chain. By designing a multi-objective multiple assignment-routing problem, we can consider different objectives at the same time and seek to optimize them. As a result, designing a multiple multi-objective allocation-routing problem in a humanitarian supply chain can improve the overall performance of the company and lead to the economic and social growth of the region.

In this article, an integer mathematical model for the allocation of essential product to all destinations through multiple hub allocation-routing coverage is presented in a way that reduces the cost of allocation and the number of possible paths for allocation in a humanitarian supply chain. The proposed model is able to estimate well the binary optimal solutions of the problem that is route and vehicle allocation through the solution using the scattering search method. Based on the solution of the proposed model, the shortest possible route for allocating essential items to different considered cities is provided. Also, the lowest possible cost has been determined for allocating the route for relief. Finally, the allocation of each vehicle according to their type to each city has been specified. This allocation of vehicles to each of the cities has been done in such a way that each of the vehicles covers each of the cities at least once.

Based on the obtained results, the lowest routing allocation cost was gained using the suggested model. The results of the research show that the proposed model improves both the efficiency and effectiveness of humanitarian aid logistics, and its findings provide valuable guidance for improving decision-making regarding route allocation, the type of dispatch vehicle and cost in the field of humanitarian logistics, and for designing a suitable strategy for Dealing with disasters will be beneficial in the future.

Environmental pollution has become one of the most important human concerns. Today, the high volume of industrial waste created by military products, environmental pressures and lack of resources have promoted the manufacturing industries in this field to move towards the implementation of a closed loop supply chain. The main goal of this article is to design a mathematical model to empower the environmental capabilities of the closed loop supply chain. This research is an applied research in terms of purpose and a quantitative research in terms of data and information collection and analysis method. Therefore, a fuzzy mathematical programming model has been designed. The presented model is a 4-objective model, the first objective of which is to minimize emissions, the second objective is to minimize environmental waste, the third objective is to minimize cost, and the fourth objective is to minimize the risk of raw material supply. After designing the model, validation of the model has been done by solving it in small dimensions and then using four algorithms NSGAII, MOPSO, MOACO, MOSA to solve the model in medium and large dimensions and its results have been compared. Based on the results of sensitivity analysis of the model, the response of the model to different parameters has been investigated. The results show that the simultaneous consideration of environmental, economic and risk dimensions in the parameters leads to the improvement of the performance of the closed loop supply chain in terms of empowering the environmental capabilities and profitability.

The current research has considered the design of the four-level supply chain of perishable goods, including manufacturing factories, distribution centers, wholesalers, and retailers, in conditions of uncertainty in important parameters. The aim is to make strategic and tactical decisions, including the location, number, and size of distribution centers and wholesalers, stock levels in stocking centers, determining the flow of goods between facilities at different supply chain levels, and choosing the type of means of transporting goods between facilities. This is achieved through a three-objective mathematical model. The goals include minimizing the expected total cost in the supply chain, achieving the shortest travel time of goods in the chain, and at the same time minimizing the amount of deviation from customer demand. The presented model tries to pay attention to environmental uncertainty and consider different operational scenarios, as well as the possible approach in important parameters. This takes into account the product life cycle, the different rate of spoilage of the goods in different storage facilities, the different capacity of the facilities in different scenarios, and considering different methods of product transportation with different rates of product spoilage. All of this aims to cover the lack of previous research in the field of perishable goods supply chain design. Considering the multi-objective nature of the model and the need to create flexibility in decision-making for decision-makers, this research uses Normal Boundary Intersection (NBI), which allows decision-makers to choose the most optimal solution according to the importance of different goals. GAMS 24 software and MILP solver were used to solve the mathematical model.

Increasing operating profit is a challenge faced by pharmaceutical distribution companies. Most of the researches conducted in this field have a cost reduction approach. The online monitoring system is one of the effective methods that can be used for managers' decision-making and improving the performance of the pharmaceutical distribution chain with the approach of reducing costs and increasing revenues. To create this system, conceptual, mathematical and computer modeling is needed. The aim of this research is to develop a mathematical model of the online monitoring system to improve the pharmaceutical distribution system based on a conceptual model using a reinforcement learning approach. The mathematical model was derived based on the factor-based conceptual model and using the multi-factorial reinforcement learning approach. After extracting the mathematical model, the effectiveness of the model was validated by comparing the results obtained from the output of the mathematical model and the actual results in a pharmaceutical distribution company. The findings of the research showed that the developed mathematical model has the ability to continuously improve the goals, decisions and performance of the pharmaceutical distribution chain processes, according to the interactions and changes in the behavior of agents and the state of the environment.

In the city of Qom, there is no dual water supply network with a separate meter inside the citizens' homes. On the other hand, high quality water sources do not meet all the drinking and non-drinking needs of the consumption areas. Therefore, the water and sewage company should respond to the drinking and non-drinking needs of the citizens by optimally managing the distribution of various available water resources. In this paper, the problem has been investigated in the form of two optimization mathematical models.In the first model, the current water allocation to citizens has been modeled and optimally solved, in which water resources should be allocated to citizens at the lowest cost, provided that all the needs of citizens are covered. In the second model, it is suggested that by scheduling the allocation of water resources, citizens will have access to quality water for drinking at a certain pre-determined time, and other consumption needs of citizens will be met with low quality water during the rest hours of the day and night.In the proposed model, both the allocation of water resources for the drinking and non-drinking needs of the citizens under the condition of covering all the needs of the citizens and the allocation of water resources with the lowest cost for the needs of the citizens are included. Finally, the application of the proposed model is presented with numerical analysis.

The present study has presented an intelligent integrated model for simultaneously optimizing knowledge sharing and customer loyalty in social networks with a digital marketing approach. In this research, first, the components of knowledge sharing, customer loyalty, and digital marketing are identified from the research literature, and then the research data has been collected using standard questionnaires with 5 Likert spectra for all three variables and a questionnaire of AHP method from an Iranian IT-based company. Research processes include the AHP method (to calculate the weights of the loyalty criteria to use in the mathematical model), and a new two-objective mathematical model (to simultaneously optimization of knowledge sharing and customer loyalty). The results of the hybrid approach using data collected from a company active in the field of digital marketing in Tehran showed that the relationship between customer loyalty and knowledge sharing has a significant positive effect of 47.6%. The results of regression analysis also showed that there is a positive and significant relationship between knowledge sharing and customer loyalty under the digital marketing approach of 53.1%. AHP analysis showed that protest behavior and purchase intention are the most important components of customer loyalty. Coding and running the proposed two-objective mathematical model in GAMS Software provided a level of optimization in which the full knowledge shared with the maximum customer loyalty was achieved.
Extended Abstract

In today's complex and ambiguous environments, globalization, new changes in financing structures and changes in supply and demand conditions in the context of online business have caused organizations to pay special attention to knowledge management to maintain, grow and provide better services in their environment (Basherpour and et al, 2018). For this purpose, one of the most important tools for the continuous creation of knowledge is sharing it among all units and members of the organization with an emphasis on technology and social interaction, which plays an important role in the survival of the organization in the competitive environment (Ronan and et al, 2020). Especially in organizations that have online marketing, the production and dissemination of knowledge are of particular importance (Sadeghi & Soltani, 2018). On the other hand; Customers are a special aspect of the success of any organization. Therefore, organizations need to share knowledge with their customers (Dehdashti & Bashirpour, 2018). In this regard, one strategy is to conduct more empirical studies, define more precise variables and explore their interactive relationships in specialized subjects such as social networks (Arab ghomi & nili AhmadAbadi, 2015). Because today social networks play a vital role in sharing knowledge and the platform of these networks is a reality of today's human world, and it is possible to obtain a detailed map of action strategies in this field by means of scientific approaches (Ivala & Gachago, 2012). Now although social networks offer a new potential for people to share their knowledge with others, a model has not yet been presented that minimizes the cost of sharing knowledge and maximizes shared knowledge (in normal mode and under maximum customer loyalty) provide an optimization in costs and the amount of shared knowledge. Therefore, this research attempts to answer this question: "How to simultaneously optimize knowledge sharing and customer loyalty in social networks with a digital marketing approach?"
Theoretical framework
Topics related to knowledge sharing, digital marketing, social networks, and customer loyalty are topics that have been studied a lot. Table (1) shows a general summary of some of this research. 

In this research, an intelligent decision-making model is presented to simultaneously optimize knowledge sharing and customer loyalty in the context of social networks under the digital marketing approach. Hence; first, the indicators of knowledge sharing and customer loyalty are identified using research literature. Then, the research data is collected using standard questionnaires with a 5-point Likert scale for all three variables and a special questionnaire for the AHP method from an IT- oriented company. The research processes will include descriptive statistics analysis, regression test (estimating the relationship between variables as one-to-many) in SPSS software; and AHP analysis (determining the weight of loyalty sub-criteria) in Expert Choice software. Also, a double-objective mathematical model (maximization of shared knowledge in normal mode and with the presence of customer loyalty plus minimization of knowledge sharing costs) has been presented and coded; and solved in Games software to simultaneously optimize knowledge sharing and customer loyalty in social networks.
Discussion and

In this research, by using previous research, the components of knowledge sharing, customer loyalty, and digital marketing were first identified from the research literature. After identifying the sub-criteria of each criterion; by using standard questionnaires with a 5-point Likert scale, data related to three problem variables; and by using a questionnaire specific to the AHP method, the data required for this method were collected from an Iranian IT-oriented company. Research processes included: descriptive statistics analysis, regression test (estimation of the relationship between variables) in SPSS software, and AHP analysis (determining the weight of loyalty sub-criteria) in Expert Choice software. In addition; A double-objective mathematical model for the optimization of knowledge sharing and customer loyalty in social networks was presented for the first time and the model was coded and solved in Games software. The research findings are described in three categories:1) The results of the regression test showed that there is a positive and meaningful relationship of 47.6% between customer loyalty and knowledge sharing, and a 47.25% relationship between digital marketing and knowledge sharing. Also, the results of the regression analysis showed that there is a positive and significant relationship between knowledge sharing and customer loyalty under the digital marketing approach at the rate of 53.1%.
2) AHP findings showed that the most important loyalty criteria include: Verbal marketing, purchase intentions, price sensitivity, and protest behavior with weights of: 0.055, 0.238, 0.149, and 0.557, respectively.
3) The findings of coding and implementation of the proposed multi-objective mathematical model showed that if it is focused on the customer loyalty index along with knowledge sharing, a greater degree of simultaneous optimization is obtained between these two variables. It is possible to achieve better performance by maximizing the amount of knowledge sharing and customer loyalty under digital recovery approaches.

The current research was conducted to simultaneously optimize knowledge sharing and customer loyalty in social networks under the digital marketing approach. To achieve this goal, after studying the subject literature and extracting the required criteria and foundations, the research processes were carried out in three stages. The research findings confirmed that knowledge sharing has a positive and significant relationship with customer loyalty and digital marketing. More importantly, the sharing of knowledge and customer loyalty under the digital marketing approach has more than 50% direct, positive, and meaningful impact. Therefore, the optimization of knowledge sharing and customer loyalty at the same time can have a significant effect on improving performance and increasing the efficiency of a group with digital marketing. The management of this effect and how to optimize it together was presented by a multi-objective mathematical model and investigated in a case study in this research.

The purpose of this research was to provide a mathematical model for smart supply chains with Vendor Managed Inventory (VMI) through the Internet of Things (IoT) technology to overcome traditional supply chain challenges and solve problems such as uncertainty, high costs, and changes in customer demands. Creating an intelligent and agile supply chain is essential to tackle these challenges and problems. Generally, customers are still skeptical and doubtful of the smart supply chain, and this skepticism is more likely to arise in the financial context. To improve efficiency, all organizations and institutions need to adapt themselves to external and internal changes, maintain supply chain inventory, and be flexible with customer demands.

Previous studies discussed intelligent supply chains, IoT, and their combination and described the advantages and disadvantages of using these technologies. Despite much research in this field, no mathematical modeling has been done for a smart supply chain that incorporates technology and automation. Based on such needs and objectives, this study sought to design a two-objective mathematical model, with a four-level supply chain. In this model, there is a direct relationship from suppliers to manufacturers, from producers to retailers, and from retailers to customers. The supply chain was intelligently designed, and the chain levels used Wireless Sensor Network (WSN) technologies, Radio Frequency Identification (RFID), blockchain, and Internet sales.

The designed model in this research was validated by GAMS software. The researchers identified 10 problems of small and medium dimensions in the model. They presented the results in the form of objective function values ​​and solution time. The basic problem was solved using the -constraint method. The results obtained from solving the model and the Pareto diagram were presented in detail. The optimal implementation of the mentioned technologies, as well as the time and cost response to this implementation, proved the efficiency of the model.

The present study put forward a two-objective mathematical planning model. The first and second objectives of this model were to minimize the cost and decrease the time of the supply chain, respectively. By solving the basic problem, using the -constraint method, the values ​​of the objective functions and the Pareto diagram showed desired results. Solving the model in small and medium-sized dimensions using GAMS software, the values of the objective functions and the solution time were achieved. Also, the results proved the validity of the provided model suggesting that it can be used in larger dimensions. However, due to the lack of memory in GAMS software, for large dimensions, the suggested mathematical model for the smart supply chain needs to be checked using MATLAB software and meta-heuristic algorithms.

The main solution for companies to simultaneously achieve economic and environmental goals is to implement a closed loop supply chain. The main goal of this research is to design a mathematical model to empower the environmental capabilities and profitability of the closed loop supply chain in military industries. The presented model is a 4-objective model, the first objective of which is to minimize emissions, the second objective is to minimize environmental waste, the third objective is to minimize cost, and the fourth objective is to minimize the risk of raw material supply. After designing the model, validation of the model has been done by solving it in small dimensions and then using four algorithms NSGAII, MOPSO, MOACO, MOSA to solve the model in medium and large dimensions and its results have been compared. Based on the results, the parameters of the model have been adjusted and the response of the model to different parameters has been investigated. The results show that simultaneous consideration of environmental and economic dimensions in the parameters leads to the improvement of the performance of the closed loop supply chain in terms of empowering the environmental capabilities and profitability.

Project scheduling with certain data has a long history of research. Meanwhile, the use of uncertain parameters is limited to PERT technique and some innovative algorithms for calculating project completion time, which are not capable of considering all types of uncertainties. In this research, we developed some mathematical models to calculate the critical path and the activities’ float under normal conditions and time-cost trade-off.; In addition to validity check of the models, we developed an algorithm to generate extreme scenarios based on the interval values of the input parameters. The developed algorithm is able to generate the optimal interval for the values of the decision variables in the project schedule. Solving the scheduling problem of a real construction project involving more than 80 activities showed that if the input parameters of the problem were interval numbers, the values of the output decision variables of the models would often be interval numbers with a less degree of uncertainty. The spread of uncertainty and risks in the project is often linear. This means that with an optimal plan for the project schedule, most of the estimated errors and risks in the project would cause predictable behavior in uncertain decision variables especially, activities’ float.

Supply chain design has a significant impact on its efficiency and effectiveness. Thus, The purpose of this study is to design a four echelon supply chain including manufacturing, plants, distribution centers, wholesalers and retailers for perishable products. The problem is modeled as a multi-objective mathematical modeling for strategic and tactical levels of decision-making in terms of the number, size and  location of distribution centers and wholesalers, the product flow between different facilities, the inventory levels in distribution centers and also selecting the  transportation vehicles. The objectives of the model is minimizing total cost and total travel time of product in supply chain by considering product life time. Regardings  products life time, varying perishability rates in different storage facilities and also different perishability rates for transportation facilities, are incorporated in the model, to cover the research gap in designing perishable products supply chain. Given to the multi-objective nature of the model, this study applies Normal Boundary Intersection (NBI) method which has significant superiority compared over other approaches like goal programming. GAMS 24 and CPLEX solver were used for solving in a case study in iran dairy industry.

Designing health facilities has long been one of the most important issues for health planners. During the disaster, the health network, which includes a set of clinics and hospitals, are activated to help the injured people. The purpose of this study is to add temporary emergency treatment centers to the network, in order to prevent the influx and overcrowding at the two levels of clinics and hospitals during the disaster and to create a hierarchical structure to serve the casualties. In this paper, a mixed linear integer programming with integers is used. Gams optimization software was used to solve the model. The results showed that the hierarchical model reduced the crowding in hospitals and clinics during disaster compared to the simple model. In this model, while optimizing the cost of setting up emergency treatment centers, the time and distance traveled for casualties are minimized. Using the proposed model of the best places to establish emergency treatment centers among the selected candidate points and then the optimal allocation of injuries is determined hierarchically from city areas to temporary emergency treatment centers, and from there to clinics and ultimately to hospitals.

The use of intuition and intuitive decision-making as an effective management factor has attracted increasing attention in scientific circles and research at the global level. This research, stating the essential role of intuitive decision-making in today's complex world and using a quantity model based on uncertainty, attempts to provide an effective model for enhancing the effectiveness of intuitive decision-makers and identifying the best intuitive decision in proportion to an optimal model. To achieve this goal, first an intuitive decision-making model based on four of its constituent elements and then a non-linear programing model of intuitive decision-making based on Dempster-Shafer's theory that uses mathematical techniques are presented. In the next step, a practical real-life modeling that utilizes mathematical methods to solve the research problem has been put into effect. This model, in situations where the data are ambiguous and a logical basis is missing, can be a good solution for reducing the potential risks of intuitive decision-making. In fact, in this model, by aggregating the opinions of experts (organizational decision makers), a reference model is proposed that can be used as a basis for making intuitive decisions.

Despite the increasing importance of cash flow management in the financial supply chain, limited works have been conducted in this field. This research optimizes the flow of money in the medical supply chain from the viewpoint of a distribution company. In this context, the focal company receives the medical supplies from the upstream suppliers and sells them to the downstream retailers and makes payments to suppliers with earned money from retailers. The imbalance between the cash inflow and outflow causes the imposition of a penalty for late-payments and supply risk as a result of the poor reputation in the market. In this context, the question is which payment sequence will minimize the total monetary outflows and the risk of supply. To answer this question, a bi-objective 0-1 linear programming model was developed. Solving the model by genetic algorithm determined the best sequence of payments and minimized the cash outflow as well as the risk of violation of the due date for the invoices.

Neglecting the supply chain management of perishable goods could create a lot of costs for organizations and companies. Blood is a perishable product in the healthcare supply chain, the  shortage of which could prove quite problematic and disastrous. Any improvements in the blood supply chain management operations may increase service efficiency and decrease the cost of the healthcare system, saving the lives of lots of people. In this paper, a mixed-integer nonlinear programming model is proposed for comprehensive blood supply chain management, which includes gathering, processing and distributing blood and blood products by taking into account the demand lifetime and age. This model aims at decreasing supply chain costs and blood product deficiency. Robust optimization is utilized to take into account the inherent uncertainty and volatility of the demand and supply. The proposed model is first tested on a small-scale numerical example in GAMS software. Then a large-scale problem is solved using Whale and Imperialist Competition algorithms and the results are compared. In addition, a case study is presented to show the applicability of the proposed model.

Coalition formation is an important step towards developing the social welfare by improving the performance. This is pursued in two main research streams: (i) algorithmic approaches to achieve the optimal coalition structure and (ii) cooperative game theory to distribute the coalition payoff based on fairness and stability criteria. The aim of this paper is to integrate the strengths of the two approaches in order to achieve an optimal and stable coalition structure. The main innovation of the paper is using mathematical modeling to incorporates stability condition in a set partitioning problem through core solution concept to overcome decentralized procedures of coalition formation and payoff distribution. A numerical example is used to investigate the performance of overlapping and non-overlapping optimal coalition structure models. The results show that cooperation leads to improve social welfare. This improvement has an ascending trend with a decreasing slope and does not change after increasing the upper limit of players allowed to join the coalition to the certain extent. This is due to several reasons which prevent players to form grand coalition and suggests that, to form large coalitions, one should compare achieved gains with the managerial complexities and the increased costs of coordination and communication between players.

The purpose of the layout design is to find the most efficient arrangement of equipment, manpower in departments or units in order to maximize productivity in product production. Existing heuristic models do not consider the organizations need to locate units within certain departments, but in practice many organizations need to design a layout that limits the location of units in their respective departments. Particularly for organizations with an operational organizational structure, and often each of the units in each executive department should be located in their own office. The purpose of this article is that in an organization composed of several main departments and each department comprising several units, optimal placement is made in such a way that the limits of locating the units within the departments that are similar to the work process are met. Many layout design problems are not suited to solve mathematical problems because some of the facilities need to be put together. In this paper, constraints are added to design the facility layout in specific departments and a mathematical model is proposed for optimization. The benefits of introducing departmental constraints are: Compared to existing models, it provides more pragmatic logic for layout and facility design, and can help improve computational efficiency by reducing overlap constraints across facilities.