Industrial management
Sara Bagherzadeh Rahmani; Javad Rezaeian; Ahmad Ebrahimi
Abstract
In today’s project-based organizations, where multiple projects are executed concurrently within work teams, human resources play a crucial role in the success or failure of these organizations. Consequently, human resources are recognized as one of the most essential resources for these organizations, ...
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In today’s project-based organizations, where multiple projects are executed concurrently within work teams, human resources play a crucial role in the success or failure of these organizations. Consequently, human resources are recognized as one of the most essential resources for these organizations, and their optimization can significantly increase productivity while reducing organizational time and costs. This underscores the importance of effective human resource management and highlights the need for special attention to this area. Therefore, this study presents a mixed-integer nonlinear programming model for the multi-objective project scheduling problem with resource constraints, multi-skilled personnel allocation and the assignment of projects to work teams. The mathematical model of this research includes the multiple objectives of simultaneous minimization of the total costs of setting up work teams and the use of human resources and the total flow time of projects. To make the model more realistic, the effect of learning is also considered. Subsequently, a diverse set of test problems at varying scales was designed. Then, the Multi-Objective Artificial Immune System (MOAIS) algorithm and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) were utilized to solve the problems. The results demonstrate the superior performance of the NSGA-II algorithm compared to the MOAIS algorithm.
Introduction
Human resource management is one of the fundamental pillars of organizational success and, alongside financial and technological resources, plays a crucial role in process optimization and achieving strategic objectives. Optimal workforce allocation and effective project scheduling enhance productivity, reduce costs, and ensure the efficient utilization of resources. Teamwork and knowledge sharing facilitate learning and skill development, which, in complex projects with limited resources, lead to shorter project completion times and improved organizational efficiency.
Accordingly, this study addresses the project scheduling problem by considering human resource constraints, multi-skilled work teams, setup times, varying project start times, and work-team dependent learning effect. The primary objective is to simultaneously minimize the total costs of setting up work teams and the use of human resources, as well as the total project flow time. To achieve this, a Mixed-Integer Linear Programming (MILP) model is developed.
Given that the problem is NP-hard, employing metaheuristic algorithms is essential for obtaining near-optimal solutions within a reasonable computational time. This research utilizes two metaheuristic algorithms, NSGA-II and MOAIS.
The findings of this study provide valuable insights for project managers and decision-makers, aiding in optimized project scheduling, efficient workforce allocation, and enhanced organizational productivity.
Research Background
In this section, we mention only a few of the most relevant studies to the current one. Su et al. (2021) explored team formation in project scheduling and presented a simple mathematical model for task scheduling in single-skilled workgroups with restricted access to resources, aiming to minimize makespan (Cmax). In their model, workers were assigned to fixed groups, and tasks were allocated based on processing time and workforce availability. They proposed a hybrid genetic algorithm with a bin-packing strategy to solve the problem.
Mozhdehi et al. (2024) developed a mixed-integer mathematical model for multi-project scheduling with limited resources and multi-skilled workforce. They considered workforce agility, which improves either through collaborative teamwork and knowledge-sharing with more skilled colleagues or by dedicating more time to skill development. Their results indicated that incorporating workforce agility into project scheduling models significantly reduces project completion time.
Methods
In this study, a Mixed-Integer Linear Programming (MILP) model was developed to address the multi-project scheduling problem with multi-skilled work teams. The model integrates human resource constraints, setup times, and work-team dependent learning effect, ensuring a practical and efficient scheduling framework.
For solving the model, the single-objective version was first handled using the Branch and Bound algorithm in Lingo software. Then, for the multi-objective version, two metaheuristic algorithms, NSGA-II and MOAIS, were implemented to generate high-quality trade-off solutions.
To assess and compare the performance of these algorithms, a set of test problems of different scales (small, medium, and large) was designed and solved. The Taguchi Experimental Design Method was employed to fine-tune the key algorithm parameters, optimizing efficiency and accuracy.
Evaluating the performance of multi-objective metaheuristic algorithms is more complex than that of single-objective optimization due to the presence of non-dominated solutions that cannot be strictly ranked. In this study, the following key metrics were used to assess solution quality and diversity:
Number of Pareto Solutions (NPS)
Mean Ideal Distance (MID)
Diversity Metric (DM)
Spread of Non-dominated Solutions (SNS)
Discussion and Results
Results of sensitivity analysis reveals that increasing the learning rate of work teams significantly reduces project completion time. This finding underscores the importance of incorporating learning effects in multi-skilled workforce scheduling models. With a higher learning rate, teams execute tasks more efficiently and in less time, directly contributing to organizational productivity improvements.
Furthermore, computational results indicate that in small to medium-sized problems, there is no significant performance difference between NSGA-II and MOAIS. However, in large-scale problems, NSGA-II outperforms MOAIS. This superiority is attributed to NSGA-II’s population evolution mechanism, which enables a broader exploration of the solution space and prevents premature convergence to local optima. In contrast, MOAIS, due to its elitist nature, primarily focuses on replicating high-quality solutions, avoiding exploration in other regions of the search space. This increases the likelihood of getting trapped in local optima, thereby reducing search diversity. Furthermore, performance comparison results indicate that NSGA-II demonstrates superior Pareto front coverage and convergence to optimal solutions compared to MOAIS.
Conclusion
This study investigated the project scheduling problem considering human resource constraints, multi-skilled work teams, setup times, varying project start times, and work-team dependent learning effects. The primary objective was the simultaneous minimization of the total costs of setting up work teams and the use of human resources and the total flowtime of projects. To achieve this, a Mixed-Integer Linear Programming (MILP) model was developed, and its performance was evaluated through sensitivity analyses and numerical experiments. The results demonstrated that the proposed model performed effectively under various constraints and exhibited high accuracy and efficiency.
Given the NP-hard nature and multi-objective characteristics of the problem, two metaheuristic algorithms, NSGA-II and MOAIS, were implemented to solve it. The algorithm parameters were fine-tuned using the Taguchi Experimental Design Method, and their performance was compared across different problem sizes. Computational results indicated that while both algorithms performed similarly in small to medium-sized problems, NSGA-II outperformed MOAIS in large-scale instances. Further analysis revealed that MOAIS, due to its elitist-based nature, primarily focuses on replicating high-quality solutions, often avoiding broader exploration within the solution space. This characteristic increases the likelihood of getting trapped in local optima, reducing solution diversity. In contrast, NSGA-II, through its non-dominated sorting mechanism, allows lower-fitness solutions to participate in the evolution process, leading to broader solution space exploration and preventing premature convergence.
For future research, it is recommended to extend the model by incorporating additional operational assumptions, such as activity failure probabilities, simultaneous consideration of learning and forgetting effects, rework processes, and uncertainty of certain parameters in the problem. Furthermore, exploring more advanced heuristic and hybrid metaheuristic algorithms is suggested to enhance the efficiency of the solution approach.
uncertainty
Hossein Firouzi; Javad Rezaeian; Mohammad Mehdi Movahedi; Alireza Rashidi Komijan
Abstract
This paper presents a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic, incorporating dimensions of sustainability. The objectives of the model are as follows: 1) Minimizing the costs associated with building facilities ...
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This paper presents a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic, incorporating dimensions of sustainability. The objectives of the model are as follows: 1) Minimizing the costs associated with building facilities and waste treatment centers, vehicle fuel costs, and environmental costs due to pollutant emissions; 2) Maximizing the energy generated from the waste combustion process; 3) Minimizing the risk of virus transmission resulting from inadequate waste management; and 4) Maximizing the number of job opportunities in the established centers. It is important to note that existing uncertainties are addressed through the application of fuzzy set theory. Given the multi-objective nature of the model, two multi-objective algorithms, namely the Pareto archive-based Krill Herd Algorithm and Non-dominated Sorting Genetic Algorithm II (NSGA-II), are employed to solve the defined problem. The results indicate that the proposed Krill Herd Algorithm converges to a solution with higher quality and dispersion compared to NSGA-II. Additionally, through a comparison of the spacing index and running time of the two algorithms, it is observed that NSGA-II explores the solution space with higher uniformity and solves the model in less time.IntroductionHospital waste encompasses a broad spectrum of both hazardous and non-hazardous materials. The management of hospital waste involves the development of a suitable supply chain network for handling waste generated in the healthcare sector. Improper disposal or mishandling of contaminated waste not only contributes to environmental pollution but also poses a risk of transferring viral pathogens to healthcare and recycling personnel. Research has shown that inadequate disposal of medical waste can lead to the transmission of up to 30% of hepatitis B, 1-3% of hepatitis C, and 0.3% of HIV infections from patients to healthcare workers. This paper aims to design a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic while considering the dimensions of sustainability.Literatur ReviewIn recent years, various studies have delved into the complexities of medical and hospital waste management, proposing mathematical models to address this intricate issue. The current study is built upon the work of Valizadeh et al. (2021). In their paper, a hybrid mathematical modeling approach was introduced, featuring a Bi-level programming model specifically tailored for infectious waste management during the COVID-19 pandemic. The outcomes revealed that, at the higher level of the model, governmental decisions aiming to minimize total costs associated with infectious waste management were crucial. This involved the conversion of collected infectious waste into energy, with the generated revenue being reinvested back into the system. The findings indicated that, through energy production from waste during the COVID-19 pandemic, approximately 34% of the total costs related to waste collection and transportation could be offset. The uniqueness of this study lies in its consideration of three sustainability dimensions: risk, vehicle routing, energy production, employment, and emission of polluting gases. Consequently, the novelty of this research, when compared to previous studies and the article by Valizadeh et al. (2021), is evident in several aspects. It introduces an integrated multi-objective positioning-routing model for the supply chain of waste management under pandemic conditions, taking into account sustainability dimensions, notably the economic aspect, and employs meta-heuristic algorithms for model resolution.MethdologyTo ensure the proper management of hospital waste, the waste is categorized into two groups: infectious and non-infectious waste. It is assumed that waste in hospitals and health centers is segregated and placed in infectious and non-infectious waste bins. The collected waste undergoes further processing: infectious waste is transported to incineration centers, where it is burned and converted into electrical energy, while non-infectious waste is sent to waste recycling centers, where it is reprocessed and returned to the production cycle in the industry. A multi-objective mathematical model is presented to integrate location-routing decisions in the supply chain of hospital waste management, with the following modeling assumptions:Waste segregation at the source helps prevent all waste from becoming viral, reducing the spread of viruses through waste.The risk of spreading viruses is assumed to be relatively equal for each type of waste.Two types of vehicles are considered for transporting waste: the first type carries non-infectious waste, while the second type carries infectious waste.The number of cars, waste collectors, and the capacity of waste incinerators are considered constant in this study.The mathematical model is multi-objective, with the objectives being to optimize the three dimensions of sustainability (economic, social, and environmental).The economic goal is to minimize system costs, including the cost of site location, recycling, collection, segregation of non-infectious waste, and incineration.The environmental goal is to minimize the emission of pollutants in the transportation and processing system in various facilities, as well as to maximize the production of electrical energy.The social goal is to minimize the risk of virus transmission and maximize the employment rate.Results and DiscussionThis research presents a multi-objective mathematical model for the reverse supply chain of hospital waste management during the COVID-19 pandemic in Iran and solves it. The pandemic period is considered a time of maximum utilization of health centers and waste disposal. In this context, a three-objective mathematical model was initially introduced. To solve the model, the krill herd optimization algorithm was employed. The performance of the krill herd optimization algorithm was scientifically and practically evaluated by comparing it with the well-known NSGA-II algorithm. After designing the model, both the multi-objective krill herd algorithm based on Pareto Archive and the NSGA-II algorithm were utilized to solve the model. The results of solving the model demonstrated that the proposed krill herd algorithm, designed in combination with VNS, effectively solved the model and determined the optimal solution within a boundary. Comparing the results of this algorithm with those obtained by the renowned NSGA-II algorithm revealed that the krill herd algorithm produced solutions of much higher quality.ConclusionThe comparison of the Index of dispersion between the two algorithms indicates that the krill herd optimization algorithm explores more points in the solution space, leading to a lower probability of getting stuck in local optima compared to the NSGA-II algorithm. On the other hand, the index of uniformity for the NSGA-II algorithm is lower than that of the krill herd algorithm (lower values are better), suggesting that the multi-objective genetic algorithm explores the solution space more uniformly. Considering the execution time of the two algorithms, it was observed that the NSGA-II algorithm solved the model in less time. Additionally, the increasing trend of execution time in both algorithms confirms the NP-HARD nature of the hospital waste management problem. According to the output of the MATLAB software, considering the presented model, the results affirm the capability to optimally select hospital waste recycling centers.
Somayeh Kavianpour; Gavad Rezaeian
Abstract
Appropriate scheduling of shifts for nurses, is a critical issue in hospital management. This study improves the scheduling of shifts for nurses in health services organizations to provide lower cost and also to reduce the computational complexity and finally to realize the outcome of these actions on ...
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Appropriate scheduling of shifts for nurses, is a critical issue in hospital management. This study improves the scheduling of shifts for nurses in health services organizations to provide lower cost and also to reduce the computational complexity and finally to realize the outcome of these actions on job satisfaction and quality of received services. A linear mathematical model is proposed and since this problem is NP-hard, Genetic Algorithm is provided for solving the problem and finally Implemented in Imam Khomeini hospital of Noor city as a real sample. Computational results and performance of the proposed algorithm in terms of solution quality and computational time were analyzed. Accreditation standards for hospitals as well as the Productivity laws are used in the proposed model. Production of timetables by the proposed model, resulting in improved satisfaction levels of nurses and their job performance.
