Studies in the literature on flexible job-shop scheduling problems (FJSP) generally assume that one worker is assigned to each machine and that processing times are constant. However, in some industries, multiple workers with cooperation can process complex operations faster than one worker. If the possibility of completing jobs in a shorter time with worker cooperation is not taken into account, the opportunity to create more effective schedules may not be taken advantage of. Therefore, it is essential to consider the flexibility of collaboration between employees. However, to increase labor efficiency in businesses, jobs are also expected to be done with the minimum number of workers possible. This study considers the FJSP with both machine and number of workers dependent processing times. The objectives are minimizing the total tardiness and the total number of workers. A bi-objective mathematical model and an NSGA-II algorithm for large-sized problems have been proposed. The performance of the proposed solution approaches is demonstrated by using randomly generated test problems. For each problem, the most successful Pareto solution among the obtained solutions by the mathematical model and the NSGA-II algorithm was determined using the TOPSIS method. Furthermore, the effect of the total number of workers on the total tardiness is examined. The performance of proposed solution approaches, and when the worker number increases, the total tardiness of jobs can be reduced by an average of 75.88%, have been shown through comprehensive experimental studies.

Optimizing the trade-off between crucial decisions has been a prominent issue to help decision-makers for synchronizing the production scheduling and distribution planning in supply chain management. In this article, a bi-objective integrated scheduling problem of production and distribution is addressed in a production environment with identical parallel machines. Besides, two objective functions are considered as measures for customer satisfaction and reduction of the manufacturer’s costs. The first objective is considered aiming at minimizing the total weighted tardiness and total operation time. The second objective is considered aiming at minimizing the total cost of the company’s reputational damage due to the number of tardy orders, total earliness penalty, and total batch delivery costs. First, a mathematical programming model is developed for the problem. Then, two well-known meta-heuristic algorithms are designed to spot near-optimal solutions since the problem is strongly NP-hard. A multi-objective particle swarm optimization (MOPSO) is designed using a mutation function, followed by a non-dominated sorting genetic algorithm (NSGA-II) with a one-point crossover operator and a heuristic mutation operator. The experiments on MOPSO and NSGA-II are carried out on small, medium, and large scale problems. Moreover, the performance of the two algorithms is compared according to some comparing criteria. The computational results reveal that the NSGA-II performs highly better than the MOPSO algorithm in small scale problems. In the case of medium and large scale problems, the efficiency of the MOPSO algorithm was significantly improved. Nevertheless, the NSGA-II performs robustly in the most important criteria.

During the past few years, transportation of agricultural products is increasingly becoming a crucial problem in supply chain logistics. In this paper, we present a new mathematical formulation and two solution approaches for an intermodal transportation problem. The proposed bi-objective model is applied to the transportation of agricultural products from Morocco to Europe to minimise both the transportation cost either in the form of uni-modal or intermodal, as well as the maximal overtime to delivery products. The first solution approach is based on a non-dominated sorting genetic algorithm improved by a local search heuristic and the second one is the GRASP algorithm (Greedy Randomised Adaptive Search Procedure) with iterated local search heuristics. They are tested on theoretical and real case benchmark instances and compared with the standard NSGA-II. Results are analysed and the efficiency of algorithms is discussed using some performance metrics.

This study proposes a simheuristic that hybridizes NSGA-II with Monte Carlo simulation to address a stochastic flexible flow shop problem featuring stochastic machine breakdowns. In real-world scenarios, machine breakdowns frequently occur, resulting in negative impacts such as time loss, late deliveries, decreased productivity, and order accumulation. Therefore, this study considers the times between failures and times to repair as stochastic parameters. Multiple objectives are concurrently addressed, including expected makespan, expected tardy jobs, and the standard deviation of tardy jobs. A mathematical model was formulated for the deterministic version of the problem and separately solved for the minimization of tardy jobs and the minimization of makespan in small instances. Subsequently, the proposed simheuristic was executed for both small and large instances. The results demonstrate that the NSGA-II simheuristic enhances outcomes across all objective functions compared to the simulation of optimal solutions provided by the mathematical models in small instances, yielding average GAPs of -16.64%, -21.87%, and -53.33% for expected tardy jobs, expected makespan, and standard deviation of tardy jobs, respectively. Furthermore, the simheuristic outperforms the simulation of solutions given by seven dispatching rules, showcasing average improvements of 48.01%, 48.18%, and 95.63% for the same objectives, respectively.

In recent years, one of the goals of any company is to increase overall production and process reliability. Hereupon supply chain reliability has been gaining growing attention and provides a technical framework for quantifying supply chain risks and uncertainties. In this paper, supply chain reliability was investigated in a two-stage stochastic programming model to design reliable closed-loop green four-echelon forward/backward supply chain networks. The purpose of this model was to maximize the total reliability of the supply chain based on the structural reliability theory. Our proposed model also minimized the cost of the supply chain by definition of recycling centres and the cost of penalizing unauthorized carbon emission and damages. The model optimized the locations of factories, warehouses, and recycling centres considering stochastic modes for demands and carbon price, as well as the flow between different sectors and the optimal orders. As the proposed model was a mixed-integer nonlinear problem, both e-constraint method and the metaheuristic algorithm (NSGA-II) were used in different scales and the sensitivity analysis was performed for critical parameters.

This paper presents a model to solve the multi-objective location-routing problem with capacitated vehicles. The main purposes of the model are to find the optimal number and location of depots, the optimal number of vehicles, and the best allocation of customers to distribution centers and to the vehicles. In addition, the model seeks to optimize vehicle routes and sequence to serve the customers. The proposed model considers vehicles’ traveled distances, service time and waiting time while guaranteeing that the sum of these parameters is lower than a predetermined value. Two objective functions are investigated. First objective function minimizes the total cost of the system and the second one minimizes the gap between the vehicles’ traveled distances. To solve the problem, a Multi-Objective Imperialist Competitive Algorithm (MOICA) is developed. The efficiency of the MOICA is demonstrated via comparing with a famous meta-heuristics, named Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). Based on response surface methodology, for each algorithm, several crossover and mutation strategies are adjusted. The results, in terms of two well-known comparison metrics, indicate that the proposed MOICA outperforms NSGA-II especially in large sized problems.

The life of many people across the world can face various dangers with incurrence of incidents and unpredictable diseases. Incidents often require quick relief as they directly affect human lives. The process of planning, management and monitoring the flow of relief sources to injured and sick individuals is called relief logistics. When best relief services are provided through available sources, relief logistics appear. In this article, a multi-objective model for relief resources distribution facilities under an uncertain condition is investigated in two ways of demand satisfaction by considering the relief resources accessibility and demand satisfaction in a fuzzy logic. In the presented model, the concepts of cost, chance of demand satisfaction, elevation of response capability of system, discount levels for relief commodities, late satisfaction of demand, hub for accumulation of late and returned orders and special route for time significance in distribution of relief commodities are considered. For the first problem, the chance of relief resources accessibility and for the second problem, demands were investigated using fuzzy logic. Considering the conducted analysis, the demand amount is taken more in the second problem than the first one, which has led to an increase in the cost of the second problem. On one hand, the chance of demand satisfaction with no late orders is higher than the second problem. Satisfaction of demand occurs more in the second problem as well. Thus, these problems should be utilized in a way that suits the space of this problem. To solve the problem and to do the sensitivity analysis, we present a NSGA-II algorithm to deal with multi-objectiveness of the problem. A ε-Constraint method is also proposed to evaluate the performance of the proposed algorithm.

In decision making when multiple criteria are determined, the best choice depends on having complete information and proper decision-making technique. The permutation method is one of the popular techniques used in the context of multiple criteria decision making (MCDM). In this paper, a method is presented where there is more than one vector of weights for the criteria and there are uncertainties associated with criteria weights or there are multiple decision makers. We first take different weight vectors to create a multi-objective problem and then we solve them simultaneously to achieve appropriate Pareto solutions of the permutation method. Therefore, MOPSO and NSGA-II algorithms are utilized to find non-dominated solutions. Some examples in different sizes are considered to compare the efficiency of the proposed methods. Results show that by increasing the number of options and considering the computational time, the proposed methods perform better compared with the exact method. Moreover, NSGA-II is more efficient than MOPSO for the considered problem.

Selection of an appropriate supplier along with planning a good inventory system has become an area of open research for the past few years. In this paper, we present a multi objective decision making supplier and inventory management model where two objectives including the quality and offering price of supplier are minimized, simultaneously. The proposed model is formulated as mixed integer programming and it is converted into an ordinary single objective function using Lp-Norm. In order to find efficient solution, we use NSGA-II as meta-heuristic technique and the performance of the proposed model is examined using some instances. The preliminary results indicate that both Lp-Norm and NSGA-II methods can be used to handle problems in various sizes.