Bi-objective Mathematical Model Research Articles

A bed allocation model for pandemic situation considering general demand: A case study of Iran.

Pandemics place a new type of demand from patients affected by the pandemic, imposing significant strain on hospital departments, particularly the intensive care unit. A crucial challenge during pandemics is the imbalance in addressing the needs of both pandemic patients and general patients. Often, the community's focus shifts toward the pandemic patients, causing an imbalance that can result in severe issues. Simultaneously considering both demands, pandemic-related and general healthcare needs, has been largely overlooked. In this article, we propose a bi-objective mathematical model for locating temporary hospitals and allocating patients to existing and temporary hospitals, considering both demand types during pandemics. Hospital departments, such as emergency beds, serve both demand types, but due to infection risks, accommodating a pandemic patient and a general patient in the same department is not feasible. The first objective function is to minimize the bed shortages considering both types of demands, whereas the second objective is cost minimization, which includes the fixed and variable costs of temporary facilities, the penalty cost of changing the allocation of existing facilities (between general and pandemic demand), the cost of adding expandable beds to existing facilities, and the service cost for different services and beds. To show the applicability of the model, a real case study has been conducted on the COVID-19 pandemic in the city of Qom, Iran. Comparing the model results with real data reveals that using the proposed model can increase demand coverage by 16%.

Decision support for allocating farmed fish to customer orders using a bi-objective optimization model

Aquaculture is an important industry in certain coastal areas. Focusing on farming of salmon and trout, an operational planning problem arises with the goal of allocating supply of fish to demand expressed through customer orders. This paper provides a conceptual model of such a planning problem, defines a corresponding bi-objective mathematical programming model. The problem is novel with respect to the structure of the transportation of fish, and the rules for satisfying customer orders with respect to fish size, quality, certification, and health status. Computational experiments are conducted to gain further insights into the use of the provided model to provide support for planners involved in the operational decision making. Results indicate that the bi-objective optimization model can be useful in situations where supply is insufficient to cover all the demand within a given planning horizon.

Developing an integrated blood supply chain network in disaster conditions considering multi-purpose capabilities

PurposeThis study aims to minimize the cost and time of blood delivery in the whole blood supply chain network (BSCN) in disaster conditions. In other words, integrating all strategic, tactical and operational decisions of three levels of blood collection, processing and distribution leads to satisfying the demand at the right time.Design/methodology/approachThis paper proposes an integrated BSCN in disaster conditions to consider four categories of facilities, including temporary blood collection centers, field hospitals, main blood processing centers and medical centers, to optimize demand response time appropriately. The proposed model applies the location of all permanent and emergency facilities in three levels: blood collection, processing and distribution. Other essential decisions, including multipurpose facilities, emergency transportation, inventory and allocation, were also used in the model. The LP metric method is applied to solve the proposed bi-objective mathematical model for the BSCN.FindingsThe findings show that this model clarifies its efficiency in the total cost and blood delivery time reduction, which results in a low carbon transmission of the blood supply chain.Originality/valueThe researchers proposed an integrated BSCN in disaster conditions to minimize the cost and time of blood delivery. They considered multipurpose capabilities for facilities (e.g. field hospitals are responsible for the three purposes of blood collection, processing and distribution), and so locating permanent and emergency facilities at three levels of blood collection, processing and distribution, support facilities, emergency transportation and traffic on the route with pollution were used to present a new model.

A bi-objective model for location, dispatch and relocation of ambulances with a revision of dispatch policies

PurposeUntimely responses to emergency situations in urban areas contribute to a rising mortality rate and impact society's primary capital. The efficient dispatch and relocation of ambulances pose operational and momentary challenges, necessitating an optimal policy based on the system's real-time status. While previous studies have addressed these concerns, limited attention has been given to the optimal allocation of technicians to respond to emergency situation and minimize overall system costs.Design/methodology/approachIn this paper, a bi-objective mathematical model is proposed to maximize system coverage and enable flexible movement across bases for location, dispatch and relocation of ambulances. Ambulances relocation involves two key decisions: (1) allocating ambulances to bases after completing services and (2) deciding to change the current ambulance location among existing bases to potentially improve response times to future emergencies. The model also considers the varying capabilities of technicians for proper allocation in emergency situations.FindingsThe Augmented Epsilon-Constrained (AEC) method is employed to solve the proposed model for small-sized problem. Due to the NP-Hardness of the model, the NSGA-II and MOPSO metaheuristic algorithms are utilized to obtain efficient solutions for large-sized problems. The findings demonstrate the superiority of the MOPSO algorithm.Practical implicationsThis study can be useful for emergency medical centers and healthcare companies in providing more effective responses to emergency situations by sending technicians and ambulances.Originality/valueIn this study, a two-objective mathematical model is developed for ambulance location and dispatch and solved by using the AEC method as well as the NSGA-II and MOPSO metaheuristic algorithms. The mathematical model encompasses three primary types of decision-making: (1) Allocating ambulances to bases after completing their service, (2) deciding to relocate the current ambulance among existing bases to potentially enhance response times to future emergencies and (3) considering the diverse abilities of technicians for accurate allocation to emergency situations.

A bi-objective optimization mathematical model integrated with bulk arrival Markovian queueing system and machine learning in publishing industries

ABSTRACT In the publishing industry, it is vital to comprehend customers’ needs and take their pleasure into account. Thus, publishing houses (PHs) must effectively address the necessity to increase profitability as well as minimize the waiting time of the printing requests in the queue. Although some researchers have studied publishing industries’ management, there is still a lack of research modeling PHs as a practical queueing system that reflects their performance precisely. Moreover, most models have not considered the machine learning technique for predicting the circulation of books integrated with a queueing model and mathematical programming. Furthermore, no study has modeled the PH as a M[X]/M/1 queueing system to practically improve the system. To fill these gaps, this paper develops a novel bi-objective mathematical model with a bulk arrival queueing system and a machine learning technique to minimize the total cost and maximize the resource utilization rate. Also, different machine learning classifier algorithms are implemented to estimate the circulation for each publishing product. Owing to the model’s bi-objective character, an enhanced LP-metrics method is presented. We have also examined a real-world case study to validate our approach and demonstrate its applicability to real-world issues. A 25% increase in profitability served as proof of the model’s effectiveness.

Integrated System Design for Post-Disaster Management: Multi-Facility, Multi-Period, and Bi-Objective Optimization Approach

Disaster management requires efficient allocation of essential facilities with consideration of various objectives. During the response and recovery phase of disaster management (RRDM), various types of missions occur in multiple periods, and each of them needs different support from facilities. In this study, a bi-objective mathematical model was derived to support multi-period RRDM by optimal allocation of required facilities such as drone stations, shelters, emergency medical facilities, and warehouses according to the mission life cycle. Connectivity between facilities was considered to ensure inter-facility complementarity. For efficient derivation of Pareto solutions, a modified epsilon-constraint algorithm for bi-objective optimization was developed. The algorithm was tested with a realistic disaster simulation scenario using HAZUS 4.0 as a demonstration of the benefits of the proposed approach. With the simulation experiments, the proposed approach was expected to provide efficient operational plans and guidelines to decision makers for the bi-objective optimization problem in RRDM systems. In addition, the consideration of inter-facility connectivity can play an important role in the RRDM, especially for robustness and readiness.

Design and optimization of a pharmaceutical supply chain network under COVID-19 pandemic disruption

Efficient management of pharmaceutical supply chains during the COVID-19 pandemic is critical to mitigate material and human losses. This paper addresses the design of a pharmaceutical supply chain network under pandemic disruption, introducing a novel bi-objective mathematical model. Traditional supply chain management strategies often fall short in the face of sudden disruptions, necessitating the development of resilient systems. Our model seeks to minimise economic costs and shortages as primary objectives, addressing the specific challenge of sudden surges in demand for pharmaceuticals. To enhance resilience, we propose solutions including the establishment of temporary distribution points and the creation of backup inventory. We employ a scenario-based, discrete, and linear modelling approach, solving the model using goal-planning methods and validating its efficacy through numerical examples. Additionally, we conduct a case study in the metropolitan area of Mashhad, further demonstrating the applicability and effectiveness of our approach. This research contributes to the advancement of resilient supply chain design in the pharmaceutical sector, offering insights that can inform improved management practices and bolster resilience in pharmaceutical supply chains.

A Fuzzy-probabilistic Bi-objective Mathematical Model for Integrated Order Allocation, Production Planning, and Inventory Management

A Fuzzy-probabilistic Bi-objective Mathematical Model for Integrated Order Allocation, Production Planning, and Inventory Management

A fuzzy-probabilistic bi-objective mathematical model for integrated order allocation, production planning, and inventory management

A fuzzy-probabilistic bi-objective mathematical model for integrated order allocation, production planning, and inventory management

A Fuzzy Bi-objective Mathematical Model for Perishable Medical Goods Supply Chain Network Considering Crisis Situations: An Empirical Study.

In case of crisis, the salvation of injuries depends on the timely provision of medical goods, relief supplies, and equipment. The aim of this study is to present a mathematical model for the supply chain network of perishable medical goods in crisis situation considering the uncertain environment. In this paper, a three-level supply chain including suppliers, intermediate warehouses, and final customers is developed for perishable medical items. The uncertainty of customer demand for service and the spent time in the intermediate warehouses are considered using the exponential distribution functions. Also, it is assumed that the life-cycle of perishable medical goods follow the Weibull distribution function. The model attempts to minimize the total costs of the supply chain and total presence time of perishable items in the whole chain. The LP-Metric method is employed for solving small-sized problems. Due to the NP-Hardness of the problem, the modified Multi-objective Particle Swarm Optimization (MOPSO) and Non-dominated Sorting Genetic Algorithm (NSGA-II) are utilized as 2 well-known and efficient meta-heuristic algorithms for solving large-sized problems. The findings indicate that the meta-heuristic algorithms are efficient in achieving close to the optimal solution for large-size problems in a reasonable time. Also, the results demonstrate that NSGA-II outperforms MOPSO in terms of the high quality solution. Finally, the applicability of the model to real-world problems is demonstrated using a real case study. This paper can assist the planners and decision-makers of perishable drugs supply chain networks in crisis conditions with on-time supplying and distributing the required emergency items.

Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model

Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and the maintenance workshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon. We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.

A Multi-Stage Approach for External Trucks and Yard Cranes Scheduling with CO2 Emissions Considerations in Container Terminals

Background: In container terminals, optimizing the scheduling of external trucks and yard cranes is crucial as it directly impacts the truck turnaround time, which is one of the most critical performance measures. Furthermore, proper scheduling of external trucks contributes to reducing CO2 emissions. Methods: This paper proposes a new approach based on a mixed integer programming model to schedule external trucks and yard cranes with the objective of minimizing CO2 emissions and reducing truck turnaround time, the gap between trucking companies’ preferred arrival time and appointed time, and the energy consumption of yard cranes. The proposed approach combines data analysis and operations research techniques. Specifically, it employs a K-means clustering algorithm to reduce the number of necessary truck trips for container handling. Additionally, a two-stage mathematical model is applied. The first stage employs a bi-objective mathematical model to plan the arrival of external trucks at the terminal gates. The second stage involves a mathematical model that schedules yard cranes’ movements between different yard blocks. Results: The results show that implementing this methodology in a hypothetical case study may lead to a substantial daily reduction of approximately 31% in CO2 emissions. Additionally, the results provide valuable insights into the trade-off between satisfying the trucking companies’ preferred arrival time and the total turnaround time. Conclusions: The integration of data clustering with mathematical modeling demonstrates a notable reduction in emissions, underscoring the viability of this strategy in promoting sustainability in port-related activities.

Sustainable agritourism supply chain considering water consumption: a bi-objective mathematical model

Sustainable agritourism supply chain considering water consumption: a bi-objective mathematical model

A hybrid meta-heuristic approach to design a Bi-objective cosmetic tourism supply chain: A case study

In recent decades, medical tourism especially cosmetic tourism has increased in many countries. In this study, a bi-objective mathematical model is designed for the cosmetic tourism supply chain for the first time. In the first objective function, the profit margin in the supply chain is maximized. In contrast, the distance between the medical and accommodation centers is minimized in the second objective function. The general revised multi-choice goal programming (GRMCGP) method is an exact method for optimizing the problem. To solve the problem, model is run by Lingo software. Then, a new hybrid genetic algorithm named genetic algorithm-general revised multi-choice goal programming (GA-GRMCGP), to solve large-scale instances, is utilized. Moreover, a case study is considered to validate the proposed mathematical model. Furthermore, sensitivity analyses are carried out to evaluate the effectiveness of the research. Finally, the results of the exact and meta-heuristic algorithms are compared and discussed.

A flexible framework to coordinate debris clearance and relief distribution operations: A robust machine learning approach

This study aims to offer an integrated, flexible action plan to bridge two vital operations in the response phase of disaster management, namely debris clearance and relief items distribution. On this subject, a broad range of associated decisions, including location-allocation, inventory, scheduling, and routing, are reflected in a multi-period environment. Also, so as to provide a pliable decision chain, two substantial kinds of flexibility are considered, including network design and due dates. So, a new bi-objective mathematical model is proposed, where the first objective minimizes the total cost, and the second one minimizes the total operation time. Since travel time information accuracy has an undeniable influence on system performance, a new two-phase data-driven methodology, including a hybrid machine learning model and the distributionally robust optimization with φ- divergence, is offered to estimate reliable travel time and tackle its uncertainty. Additionally, the application and validation of the recommended model and solution methodology are investigated in a real case study. What is more, in order to explain the superiority of the proposed solution approach concerning robustness solution, various simulation experiments are executed. Ultimately, several numerical experiments are implemented, and captured results manifest that the proposed framework can enhance the system’s performance. The obtained results reveal that considering the flexibility in network design and delivery date reduces the total costs and operation time by 7 and 6 percent.

A multi-agency coordination resource allocation and routing decision-making problem: A coordinated truck-and-drone DSS for improved wildfire detection coverage

This study proposes a novel coordinated truck-drone system as a decision support system to improve fire suppression operations. The problem in this study is formulated as a bi-objective mathematical model to minimize total monitoring cost and time, considering trucks as mobile drone depots and that drones can fly at various altitudes and access hard-to-reach areas. In addition, time and cost parameters in the mathematical model are deemed uncertain, rendering the model more realistic. Accelerated Benders' decomposition (ABD) is utilized to solve the model rapidly. Furthermore, a column-and-constraint generation (CCG) algorithm is employed, which is an effective method for solving scenario-based models under uncertainty. Two criteria are subsequently used to evaluate and compare proposed robust optimization approaches (risk averse and min-max relative regret). The results indicate that the proposed system can assist firefighters in determining the optimal number of drones and trucks to patrol and the time and cost required to visit all areas. Moreover, the findings demonstrate that the min-max relative regret approach can outperform other methods during the hot season when the risk of wildfire is elevated. In contrast, when the fire risk is lower during the cold season, time and cost can be effectively managed, and a risk-averse strategy can be implemented. Finally, the proposed solution framework can facilitate optimal strategic organizational decision planning.

Bi-objective energy-efficient scheduling in a seru production system considering reconfiguration of serus

Owing to movable workstations, light equipment and multi-skilled workers, serus can be constructed, modified and dismantled rapidly. Such an advantage enables serus to be reconfigured in response to frequent changes in product types. As different configurations lead to different processing time and energy consumption, an important issue is how to arrange a best configuration of seru with the tasks assigned to it. To this end, we focus on solving the task dispatching, product sequencing and seru reconfiguration problems simultaneously considering economic and environmental performance. A bi-objective mathematical model with objectives of minimizing the total earliness and tardiness and the total carbon dioxide emission is formulated. The problem is proved to be strongly NP-hard, and a non-dominated sorting genetic algorithm-II (NSGA-II) is developed. The algorithm is tested by a medium-size numerical example and ninety sets of large-size problems. Based on the computational results, the impact of configuration flexibility and the relation between processing time and energy consumption on the value of objective functions is analyzed.

Sustainable open pit fleet management system: integrating economic and environmental objectives into truck allocation

ABSTRACT Fleet management systems in open pit mines make two important semi-dynamic and dynamic decisions to maximize utilization of available equipment: the decision of allocation and the decision of dispatching the trucks to the shovels. In this paper, we propose a bi-objective mathematical model that incorporates the minimization of carbon emission into the allocation optimization model. We also consider different inputs that might impact upon truck allocation decisions such as the fleet size, truck velocity, truck age groups, etc. The presented mathematical model is examined using two different case studies from an iron mine and a copper mine containing a different number of shovels, dumps, and trucks. The results reveal that the developed model enhances the production performance while controlling emissions. It is indicated that the average truck velocity and, the age of trucks are among the critical factors, which can highly affect the amount of carbon emissions.

Improvement of demand fulfillment in Advanced Planning System through decentralized decision support system

In a tight supply situation, industries such as the semiconductor sector face challenges in allocating supply to customers through complex hierarchical supply chain planning systems, which involve the use of Advanced Planning Systems (APS) and human planners in updating allocation plans. This article focuses on designing, developing, and testing a prototype Decision Support System (DSS) based on a mathematical model to assist human planners and improve demand fulfillment systems in APS when demand exceeds supply. By incorporating digitalization and supporting human interventions in planning, our approach enhances these systems.The bi-objective mathematical model aims to maximize customer service levels while maintaining a maximum amount of stock available for unforeseen planning situations. We developed the proposed mathematical model into a web application decision support tool, called the Regional Customer Allocation Support Tool (ReCAST). The ReCAST prototype was applied to a semiconductor case study, demonstrating its effectiveness in supporting decision-making processes by planners in a real-world context.

Two-echelon multi-depot multi-period location-routing problem with pickup and delivery

Efficient logistics network designs can contribute to operational cost savings and efficiency improvements. In this study, a two-echelon multi-depot multi-period location-routing problem with pickup and delivery (2E-MDMPLRPPD) is proposed, seeking to construct a logistics network with high efficiency by optimizing periodic location decisions and routing schemes. On the basis of the changing time windows of customers and facilities, the proposed 2E-MDMPLRPPD explores their potential periodicity and divides the whole planning horizon into multiple periods for conducting location decisions and arranging customer services. Vehicle-sharing strategies, which encourage vehicles to be shared by facilities across multiple periods, have also been integrated into the 2E-MDMPLRPPD optimization to improve resource utilization and sustainability. The 2E-MDMPLRPPD is formulated as a bi-objective mathematical model, with the minimization of the total operational cost and number of vehicles as the two objective functions. To solve the optimization model, this study develops a hybrid multi-objective particle swarm optimization (HMOPSO) algorithm and introduces a three-dimensional (3D) k-means clustering to assist the proposed hybrid algorithm. The 3D k-means is the key to providing initial feasible candidate location strategies and simplifying the logistics network, reducing the complexity and difficulty for the following further optimization by HMOPSO. The proposed HMOPSO, integrating the Clarke–Wright saving algorithm and variable neighborhood search (VNS) into the standard MOPSO, shows good performance in solving the proposed 2E-MDMPLRPPD optimization, which is demonstrated through an algorithm comparison with MOPSO, multi-objective VNS and non-dominated sorting genetic algorithm-II. Finally, the proposed model and algorithm are applied to a real-world case study of 2E-MDMPLRPPD in Chengdu, China. A two-period location-routing strategy can achieve the best optimization results, and based on the period division and periodic location strategy, the operating cost and required vehicles can save $15,394 and 25, respectively. A series of comparative analyses in different period divisions and location selection scenarios are implemented, and the practical significance in cost-saving and efficiency improvements is verified. Thus, this study can provide insights for logistics enterprises and facilitate sustainable and efficient urban logistics operations.