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When designing an optimization model for use in a mass casualty event response, it is common to encounter the heavy and considerable demand of injured patients and inadequate resources and personnel to provide patients with care. The purpose of this study is to create a model that is more practical in the real world. So the concept of “predicting the resource and personnel shortages” has been used in this research. Their model helps to predict the resource and personnel shortages during a mass casualty event. In this paper, to deal with the shortages, some temporary emergency operation centers near the hospitals have been created, and extra patients have been allocated to the operation center nearest to the hospitals with the purpose of improving the performance of the hospitals, reducing congestion in the hospitals and considering the welfare of the applicants.

The authors research will focus on where to locate health-care facilities and how to allocate the patients to multiple hospitals to take into view that in some cases of emergency situations, the patients may exceed the resource and personnel capacity of hospitals to provide conventional standards of care.

In view of the fact that the problem is high degree of complexity, two multi-objective meta-heuristic algorithms, including non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA), were proposed to solve the model where their performances were compared in terms of four multi-objective metrics including maximum spread index (MSI), spacing (S), number of Pareto solution (NPS) and CPU run-time values. For comparison purpose, paired t-test was used. The results of 15 numerical examples showed that there is no significant difference based on MSI, S and NPS metrics, and NRGA significantly works better than NSGA-II in terms of CPU time, and the technique for the order of preference by similarity to ideal solution results showed that NRGA is a better procedure than NSGA-II.

The planning horizon and time variable have not been considered in the model, for example, the length of patients’ hospitalization at hospitals.

Presenting an effective strategy to respond to a mass casualty event (natural and man-made) is the main goal of the authors’ research.

This paper strategy is used in all of the health-care centers, such as hospitals, clinics and emergency centers when dealing with disasters and encountering with the heavy and considerable demands of injured patients and inadequate resources and personnel to provide patients with care.

This paper attempts to shed light onto the formulation and the solution of a three-objective optimization model. The first part of the objective function attempts to maximize the covered population of injured patients, the second objective minimizes the distance between hospitals and temporary emergency operation centers and the third objective minimizes the distance between the warehouses and temporary centers.

This paper aims to develop a multi-objective problem for scheduling the operations of trucks entering and exiting cross-docks where the number of unloaded or loaded products by trucks is fuzzy logistic. The first objective function minimizes the maximum time to receive the products. The second objective function minimizes the emission cost of trucks. Finally, the third objective function minimizes the number of trucks assigned to the entrance and exit doors.

Two steps are implemented to validate and modify the proposed model. In the first step, two random numerical examples in small dimensions were solved by GAMS software with min-max objective function as well as genetic algorithms (GA) and particle swarm optimization. In the second step, due to the increasing dimensions of the problem and computational complexity, the problem in question is part of the NP-Hard problem, and therefore multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment.

Therefore, non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are used to solve 30 random problems in high dimensions. Then, the algorithms were ranked using the TOPSIS method for each problem according to the results obtained from the evaluation criteria. The analysis of the results confirms the applicability of the proposed model and solution methods.

This paper proposes mathematical model of truck scheduling for a real problem, including cross-docks that play an essential role in supply chains, as they could reduce order delivery time, inventory holding costs and shipping costs. To solve the proposed multi-objective mathematical model, as the problem is NP-hard, multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment. Therefore, NSGA-II and NRGA are used to solve 30 random problems in high dimensions.

The production-distribution (P-D) problems are two critical problems in many industries, in particular, in manufacturing systems and the supply chain management. In previous researches on P-D planning, the demands of the retailers and their inventory levels have less been controlled. This may lead into huge challenges for a P-D plan such as the bullwhip effects. Therefore, to remove this challenge, the purpose of this paper is to integrate a P-D planning and the vendor-managed inventory (VMI) as a strong strategy to manage the bullwhip effects in supply chains. The proposed P-D-VMI aims to minimize the total cost of the manufacturer, the total cost of the retailers, and the total distribution time simultaneously.

This paper presents a multi-objective non-linear model for a P-D planning in a three-level supply chain including several external suppliers at the first level, a single manufacturer at the second level, and multi-retailer at the third level. A non-dominated sorting genetic algorithm and a non-dominated ranking genetic algorithm are designed and tuned to solve the proposed problem. Then, their performances are statistically analyzed and ranked by the TOPSIS method.

The applicability of the proposed model and solution methodologies are demonstrated under several problems. A sensitivity analysis indicates the market scale and demand elasticity have a substantial impact on the total cost of the manufacturer in the proposed P-D-VMI.

Although the P-D planning is a popular approach, there has been little discussion about the P-D planning based on VMI so far. The novelty comes from developing a practical and new approach that integrates the P-D planning and VMI.

Today’s, supply chain production and distribution of products to improve the customer satisfaction in the shortest possible time by paying the minimum cost, has become the most important challenge in global market. On the other hand, minimizing the total cost of the transportation and distribution is one of the critical items for companies. To handle this challenge, this paper aims to present a multi-objective multi-facility model of green closed-loop supply chain (GCLSC) under uncertain environment. In this model, the proposed GCLSC considers three classes in case of the leading chain and three classes in terms of the recursive chain. The objectives are to maximize the total profit of the GCLSC, satisfaction of demand, the satisfactions of the customers and getting to the proper cost of the consumers, distribution centers and recursive centers.

Then, this model is designed by considering several products under several periods regarding the recovery possibility of products. Finally, to evaluate the proposed model, several numerical examples are randomly designed and then solved using non-dominated sorting genetic algorithm and non-dominated ranking genetic algorithm. Then, they are ranked by TOPSIS along with analytical hierarchy process so-called analytic hierarchy process-technique for order of preference by similarity to ideal solution (AHP-TOPSIS).

The results indicated that non-dominated ranked genetic algorithm (NRGA) algorithm outperforms non-dominated sorting genetic algorithm (NSGA-II) algorithm in terms of computation times. However, in other metrics, any significant difference was not seen. At the end, to rank the algorithms, a multi-criterion decision technique was used. The obtained results of this method indicated that NSGA-II had better performance than ones obtained by NRGA.

This study is motivated by the need of integrating the leading supply chain and retrogressive supply chain. In short, the highlights of the differences of this research with the mentioned studies are as follows: developing multi-objective multi-facility model of fuzzy GCLSC under uncertain environment and integrating the leading supply chain and retrogressive supply chain.

The purpose of this paper is to propose a new mixed-integer formulation for the time-dependent multi-skilled resource-constrained project scheduling problem (MSRCPSP/t) considering learning effect. The proposed model extends the basic form of the MSRCPSP by three concepts: workforces have different efficiencies, it is possible for workforces to improve their efficiencies by learning from more efficient workers and the availability of workforces and resource requests of activities are time-dependent. To spread dexterity from more efficient workforces to others, this study has integrated the concept of diffusion maximization in social networks into the proposed model. In this respect, the diffusion of dexterity is formulated based on the linear threshold model for a network of workforces who share common skills. The proposed model is bi-objective, aiming to minimize make-span and total costs of project, simultaneously.

The MSRCPSP is an non-deterministic polynomial-time hard (NP-hard) problem in the strong sense. Therefore, an improved version of the non-dominated sorting genetic algorithm II (IM-NSGA-II) is developed to optimize the make-span and total costs of project, concurrently. For the proposed algorithm, this paper has designed new genetic operators that help to spread dexterity among workforces. To validate the solutions obtained by the IM-NSGA-II, four other evolutionary algorithms – the classical NSGA-II, non-dominated ranked genetic algorithm, Pareto envelope-based selection algorithm II and strength Pareto evolutionary algorithm II – are used. All algorithms are calibrated via the Taguchi method.

Comprehensive numerical tests are conducted to evaluate the performance of the IM-NSGA-II in comparison with the other four methods in terms of convergence, diversity and computational time. The computational results reveal that the IM-NSGA-II outperforms the other methods in terms of most of the metrics. Besides, a sensitivity analysis is implemented to investigate the impact of learning on objective function values. The outputs show the significant impact of learning on objective function values.

The proposed model and algorithm can be used for scheduling activities of small- and large-size real-world projects.

Based on the previous studies reviewed in this paper, one of the research gaps is the MSRCPSP with time-dependent resource capacities and requests. Therefore, this paper proposes a multi-objective model for the MSRCPSP with time-dependent resource profiles. Besides, the evaluation of learning effect on efficiency of workforces has not been studied sufficiently in the literature. In this study, the effect of learning on efficiency of workforces has been considered. In the scarce number of proposed models with learning effect, the researchers have assumed that the efficiency of workforces increases as they spend more time on performing a skill. To the best of the authors’ knowledge, the effect of learning from more efficient co-workers has not been studied in the literature of the RCPSP. Therefore, in this research, the effect of learning from more efficient co-workers has been investigated. In addition, a modified version of the NSGA-II algorithm is developed to solve the model.

Pumped-storage hydroelectricity (PSH) is considered as an effective method to moderate the difference in demand and supply of electricity. This study aims to understanding of the high capacity of energy production, storage and permanent exploitation has been the prominent feature of pumped-storage hydroelectricity.

In this paper, the optimization of energy production and maintenance costs in one of the large Iranian PSH has been discussed. Hence, a mathematical model mixed integer nonlinear programming developed in this area. Minimizing the difference in supply and demand in the energy production network to multiple energies has been exploited to optimal attainment scheme. To evaluate the model, exact solution CPLEX and to solve the proposed programming model, the efficient metaheuristics are utilized by the tuned parameters achieved from the Taguchi approach. Further analysis of the parameters of the problem is conducted to verify the model behavior in various test problems.

The results of this paper have shown that the meta-heuristic algorithm has been done in a suitable time, despite the approximation of the optimal answer, and the consequences of research indicate that the model proposed in the studied power plant is applicable.

In pumped-storage hydroelectricity plants, one of the main challenges in energy production issues is the development of production, maintenance and repair scheduling concepts that improves plant efficiency. To evaluate the mathematical model presented, exact solution CPLEX and to solve the proposed bi-objective mixed-integer linear programming model, set of efficient metaheuristics are used. Therefore, according to the level of optimization performed in the case study, it has caused the improvement of planning by 7%–12% and effective optimization processes.

In real manufacturing systems, schedules are often disrupted with uncertainty factors such as random machine breakdown, random process time, random job arrivals or job cancellations. This paper aims to investigate robust scheduling for a two-stage assembly flow shop scheduling with random machine breakdowns and considers two objectives makespan and robustness simultaneously.

Owing to its structural and algorithmic complexity, the authors proposed imperialist competitive algorithm (ICA), genetic algorithm (GA) and hybridized with simulation techniques for handling these complexities. For better efficiency of the proposed algorithms, the authors used artificial neural network (ANN) to predict the parameters of the proposed algorithms in uncertain condition. Also Taguchi method is applied for analyzing the effect of the parameters of the problem on each other and quality of solutions.

Finally, experimental study and analysis of variance (ANOVA) is done to investigate the effect of different proposed measures on the performance of the obtained results. ANOVA's results indicate the job and weight of makespan factors have a significant impact on the robustness of the proposed meta-heuristics algorithms. Also, it is obvious that the most effective parameter on the robustness for GA and ICA is job.

Robustness is calculated by the expected value of the relative difference between the deterministic and actual makespan.

The purpose of this research is to address the complex multiobjective unrelated parallel machine scheduling problem with real-world constraints, including sequence-dependent setup times and periodic machine maintenance. The primary goal is to minimize total tardiness, earliness and total completion times simultaneously. This study aims to provide effective solution methods, including a Mixed-Integer Programming (MIP) model, an Epsilon-constraint method and the Nondominated Sorting Genetic Algorithm (NSGA-II), to offer valuable insights into solving large-sized instances of this challenging problem.

This study addresses a multiobjective unrelated parallel machine scheduling problem with sequence-dependent setup times and periodic machine maintenance activities. An MIP model is introduced to formulate the problem, and an Epsilon-constraint method is applied for a solution. To handle the NP-hard nature of the problem for larger instances, an NSGA-II is developed. The research involves the creation of 45 problem instances for computational experiments, which evaluate the performance of the algorithms in terms of proposed measures.

The research findings demonstrate the effectiveness of the proposed solution approaches for the multiobjective unrelated parallel machine scheduling problem. Computational experiments on 45 generated problem instances reveal that the NSGA-II algorithm outperforms the Epsilon-constraint method, particularly for larger instances. The algorithms successfully minimize total tardiness, earliness and total completion times, showcasing their practical applicability and efficiency in handling real-world scheduling scenarios.

This study contributes original value by addressing a complex multiobjective unrelated parallel machine scheduling problem with real-world constraints, including sequence-dependent setup times and periodic machine maintenance activities. The introduction of an MIP model, the application of the Epsilon-constraint method and the development of the NSGA-II algorithm offer innovative approaches to solving this NP-hard problem. The research provides valuable insights into efficient scheduling methods applicable in various industries, enhancing decision-making processes and operational efficiency.

The proposed IT2FMOVMI model intends to concurrently minimize total cost and warehouse space for the single vendor-retailer, multi-item and a consolidated vendor store. Regarding demand and order quantities with the deterministic and type-1 fuzzy numbers, we have also formulated the classic/crisp MOVMI model and type-1 fuzzy MOVMI (T1FMOVMI) model. The suggested solution technique can solve both crisp MOVMI and T1FMOVMI problems. By finding the optimal ordered quantities and backorder levels, the Pareto-fronts are constructed to form the solution sets for the three models.

A multi-objective vendor managed inventory (MOVMI) is the most recognized marketing and delivery technique for the service provider and the retail in the supply chain in Industry 4.0. Due to the evolving market conditions, the characteristics of the individual product, the delivery period and the manufacturing costs, the demand rate and order quantity of the MOVMI device are highly unpredictable. In such a scenario, a MOVMI system with a deterministic demand rate and order quantity cannot be designed to estimate the highly unforeseen cost of the problem. This paper introduces a novel interval type-2 fuzzy multi-objective vendor managed inventory (IT2FMOVMI) system, which uses interval type-2 fuzzy numbers (IT2FNs) to represent demand rate and order quantities. As the model is an NP-hard, the well-known meta-heuristic algorithm named NSGA-II (Non-dominated sorted genetic algorithm-II) with EKM (Enhanced Karnink-Mendel) algorithm based solution method has been established.

The experimental simulations for the five test problems that demonstrated distinct conditions are considered from the real-datasets of SAPCO company. Experimental study concludes that T1FMOVMI and crisp MOVMI schemes are outclassed by IT2FMOVMI model, offering more accurate Pareto-Fronts and efficiency measurement values.

Using fuzzy sets theory, a significant amount of work has been already done in past decades from various points of views to model the MOVMI. However, this is the very first attempt to introduce type-2 fuzzy modelling for the problem to address the realistic implementation of the imprecise parameters.

In this paper, a multi-objective multi-echelon supply-distribution model is proposed to optimize interactions of entities located within an Industrial Cluster (IC) including small- and medium-sized enterprises (SMEs), using a third-party logistics provider (3PL)-managed supply-demand hub in industrial cluster (SDHIC) as a specific public provider of warehousing and logistics services.

The three considered objectives are minimizing the total logistics costs, maximizing the rate of demand satisfaction and maximizing the quality of delivery. Because some parameters such as “demand of customers” are naturally fuzzy because of incompleteness and/or inaccessibility of the needed information, the triangular fuzzy number is applied for all fuzzy parameters to handle this difficulty. The proposed model is primarily changed into a correspondent supplementary crisp model. To solve such a model, a revised multi-choice goal programming (RMCGP) approach is then used with the purpose of finding a compromise solution.

Experimental results demonstrate that all enterprises involved in such a supply chain benefit with several advantages using SDHIC by consolidating shipments and merging the storage space of inventories. The applicability of the presented model is shown by conducting these experiments over an applied industrial case study.

The main contributions of this research are proposing a practical mathematical approach to the supply chain of ICs using a specific public warehouse managed by a 3PL, called SDHIC, bridging the existing gaps with respect to the already published researches in this area by applying real-world assumptions such as uncertainty; optimizing the interactions of involved entities in the supply chain of an IC, comprising suppliers, SMEs as manufacturers and customers; minimizing the total incurred logistics costs to such a system through optimum usage of lands, facilities, labors, etc. and boosting the satisfaction of customers through maximizing the service level criteria, illustrating the positive consequences of cooperation of 3PL with the SMEs/manufacturers in an IC, showing the applicability of the adopted approach by implementing it on an applied industrial instance.