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This paper considers a real case problem of supply chain network design inspired from a wheat distribution network in Iran. It generates a network with capacity acquisition and fleet management. The problem first is formulated as a mixed integer linear programming model. Then, a logic-based Benders decomposition algorithm is appropriately developed as the solution methodology. In the presented algorithm, the problem is decomposed into two models of master and subproblem. The master problem is improved by means of the preprocessing and valid inequalities. Moreover, three Benders cuts, one optimality and two feasibility cuts, are developed for the algorithm. The general and relative performance of the model and algorithm is experimentally evaluated. The wheat distribution system of Iran is considered here as the case study of this research. The model is developed based on Iran’s wheat distribution system. All the results show that the algorithm significantly outperforms the mathematical model of the case study. For example, the algorithm solves 95% of the tested instances to optimality, yet the model solves 29%.

This paper aims at designing a sustainable and resilient tire closed-loop supply chain network based on a real case study in Iran. To immune the network against disruptions, a new resiliency approach is proposed by extending efficient demand coverage plans. The developed model includes four objectives. The first objective minimizes the total costs of the network along with maximizing the coverage of customers’ demand. As a new concept, the second objective maximizes the operational reliability of facilities to extend a consistent and responsive tire supply chain. Also, to design a sustainable network, the third objective function minimizes CO2 emissions in the strategic and tactical planning horizons. Moreover, the fourth objective maximizes the social responsibility of the network via introducing new social factors. A new mixed fuzzy possibilistic flexible programming method is also proposed to handle constraints’ violations and parameters’ uncertainty. Outputs confirm the accurate performance of the extended model and ensure its applicability in the real-world case study.

Nowadays, due to growing development and competitiveness in global markets of products, companies are forced to make significant efforts for supply procurement, production, and goods distribution in order to survive in the market and be able to respond to their customers’ needs as quickly and cost-efficiently as possible. In this regard, supply chain management is considered a crucial indicator. This study presents a multiobjective, multifacility, closed-loop supply chain under uncertain environments considering green supply chain aspects. The model is designed with multiple products, periods, plants, customer markets, collection centers, recycle centers, distribution centers, return facilities, product recovery facilities, and suppliers. After modeling the study, the model is solved by the Nondominated Sorting Genetic Algorithms (NSGA-II) in order to rank the optimum solutions. The efficiency of the research model is indicated by the results and depicted graphs in the present study. Results show that the exact value of the triple objective functions is calculated. Also, the problem is solved in small, medium, and large dimensions. Then, the accuracy of the proposed model compared to the metaheuristic method is shown. Finally, by performing sensitivity analysis, we showed that target functions are less sensitive to reducing the capacity of centers.

This paper introduces a multi-period, multi-product green inventory routing problem with transshipment option, where capacitated vehicles distribute products from multiple suppliers to one customer to meet the given demand of products. The demand associated with the customer is assumed to be time-varying and deterministic. Greenhouse gas emissions from transport activities in a supply chain are a main reason for global warming. One of the main types of greenhouse gas is CO 2 from vehicles and its impact on the environment. Inventory and routing decisions can help in the reduction of CO 2 emissions if these emissions are taken into account by researchers. Also, as one of the main topics of this paper, the transshipment option is considered in the proposed model. The model is a mixed-integer programming (MIP) which has been solved and validated by General Algebraic Modeling System (GAMS). Finally, small and large-scale test problems are randomly generated and solved by the simulated annealing algorithm (SA). The computational results for different test problems showed that the proposed SA performs well and converges fast to reasonable solutions compared with GAMS. According to the results, it is determined that the transshipment option reduces CO 2 emissions and costs by shortening the distance traveled.

Stochastic Fractal Search (SFS) is a novel and powerful metaheuristic algorithm. This paper presents a Multi-Objective Stochastic Fractal Search (MOSFS) for the first time, to solve complex multi-objective optimization problems. The presented algorithm uses an external archive to collect efficient Pareto optimal solutions during the optimization process. Using dominance rules, leader selection and grid mechanisms, MOSFS precisely approximates the true Pareto optimal front. The MOSFS is implemented on nine multi-objective benchmark functions (CEC 2009 ) with multimodal, convex, discrete and non-convex optimal Pareto fronts. Performance of the proposed algorithm is compared to well-known algorithms. In addition, different performance measures are considered to evaluate the convergence and coverage abilities of the algorithms including Inverted Generational Distance, Maximum Spread and Spacing. Furthermore, statistical analyses are utilized to determine the superior algorithm. The results revealed that the MOSFS performs significantly better than other algorithms in both convergence and coverage and it is able to approximate true Pareto front precisely. In the end, MOSFS is implemented to solve a real-world engineering design problem called welded beam design problem and efficiency of the algorithm is compared to recently developed algorithms. The results of simulations and the Wilcoxon rank-sum test showed that the MOSFS is able to provide the most promising Pareto front for the problem considering various performance metrics at a 95% confidence level.

To benefit from globalization, the single-facility scheduling problem is extended to a distributed multi-facility level. This paper tackles both the mathematical modeling and solution techniques for the problem of distributed job shop scheduling. The problem is first mathematically formulated by a mixed integer linear programming model. This model supersedes the best available model in the literature in terms of both size and computational complexities. Moreover, novel simulated annealing algorithms are developed. These algorithms propose an advanced move operators matching the special encoding scheme used. The developed near-optimal search method has been enhanced by combining it with a local search method and adding advanced features to it such as the introduced restart phase. Also, we have hybridized the developed metaheuristic further with a greedy algorithm. Using the Taguchi method, the algorithm is finely tuned. Numerical experiments are conducted to evaluate the performance of the algorithms against an available genetic and a greedy algorithm. The results show that the proposed algorithm outperforms both algorithms.

In some industries as foundries, it is not technically feasible to interrupt a processor between jobs. This restriction gives rise to a scheduling problem called no-idle scheduling. This paper deals with scheduling of no-idle open shops to minimize maximum completion time of jobs, called makespan. The problem is first mathematically formulated by three different mixed integer linear programming models. Since open shop scheduling problems are NP-hard, only small instances can be solved to optimality using these models. Thus, to solve large instances, two meta-heuristics based on simulated annealing and genetic algorithms are developed. A complete numerical experiment is conducted and the developed models and algorithms are compared. The results show that genetic algorithm outperforms simulated annealing.

In field of scheduling, the majority of papers have assumed that setup times are negligible or independent of job sequence and can be added to processing times. While in some industries like textile, chemical, and automobile manufacturing, setup time is an important factor and must not be ignored. Despite its importance from both practical and academic aspects, multi-objective no-wait flexible flow line scheduling problems with sequence-dependent setup times have been given less attention. This paper considers this problem where the objective is to minimize both makespan and total tardiness. The problem is first mathematically formulated the problem as a mixed integer linear programming model. A novel bi-objective imperialist competitive algorithm is developed. This algorithm employs three advance mechanisms of imperialist behavior, imperialist completion, and independence. The algorithm is carefully evaluated for its performance against two well-known multi-objective algorithms. The results show that the proposed algorithm outperforms the other algorithms.

This paper studies a multi-objective production–distribution system. The objectives are to minimize total costs and maximize the reliability of transportations system. Each transportation system is assumed to be of unique reliability. In the real world, some parameters may be of vagueness; therefore, some tools such as fuzzy logic is applied to tackle with. The problem is formulated using a mixed integer programming model. Commercial software can optimally solve small sized instances. We propose two novel HEURISTICS called ranking genetic algorithm (RGA) and concessive variable neighborhood search (CVNS) in order to solve the large sized instances. RGA utilizes various crossover operators and compares their performances so that better crossover operators are used during the solution process. CVNS applies several neighborhood search structures with a novel learning procedure. The heuristics can recognize which neighborhood structure performs well and applies those more than the others. The results indicated that RGA is of higher performance.

This paper studies the pricing strategies in centralized and decentralized dual-channel supply chains. It first discusses that production cost and demand disruptions are highly correlated, and they influence the pricing and production decisions. Therefore, both disruptions should be considered simultaneously. A game-theoretical method is proposed to drive optimal wholesale and retail price for manufacture and retailer under these disruptions. Then, it is shown that the optimal prices are affected by sharing demand for the direct channel in both centralized and decentralized problems. Moreover, this paper models the dual-channel supply chains with production cost and demand disruptions in two structures, disruptions increasing/decreasing the demand. The models are then solved using the KKT conditions. Finally, a numerical example is presented to show total profit of supply chain for each structure.