After the COVID-19 pandemic, all organizations are involved in tackling the challenges of the disease, which continues after vaccination. it has affected various sectors of organizations including the supply chain, and has made coordination along the supply chain extremely difficult. The present study purpose to analyze the challenges of green supply chain in post- COVID-19 conditions. This study has an applied and developmental objective with a hybrid approach. This study was conducted in two stages and each stage had several consecutive steps. In the first stage, based on the results of thematic analysis, 21 challenges affecting the green supply chain in post- COVID-19 conditions were identified which were classified into 10 main challenges and 11 sub-challenges. In the second stage, the main challenges were analyzed based on hesitant fuzzy DEMATEL technique. Four challenges in an optimistic mode and five in a pessimistic mode were known as the causes. resulting in affecting all of the three levels in the supply chain and its disruption at the national and global level.

Sustainability encompasses the interaction between environmental, economic, and social systems at various levels. In transportation systems, vehicles rely on different fuels to meet energy demands. However, these fuels contribute to environmental pollution by releasing greenhouse gases. Considering this context, the present study investigates a sustainable fixed-charge multi-objective multi-driver multi-route multi-conveyance shortest path problem (FCMOMDMRMCSPP). The primary intent is to identify the most efficient route that minimizes cost, time, risk, carbon emissions, and distance while traveling between sources and destinations. Real-world scenarios often involve uncertainties, making it difficult to precisely define the parameters of FCMOMDMRMCSPP. Triangular fuzzy numbers are introduced in the proposed model to address this ambiguity. The possibilistic programming approach is employed to transform the fuzzy problem into a deterministic one. The resulting deterministic model is then solved using two multi-objective genetic algorithms (MOGAs): aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and NSGA-III. An aquatic fish haul system problem has been examined as an application within the framework of the proposed model. For α = 0 and 0.1, the AL-based NSGA-II and III generate 6, 11, and 4 solutions that satisfy the decision-maker’s (DM’s) ALs in cases I, II, and III of the AL and shape parameter combination, respectively. Similarly, for α = 0.5, these methods yield 5, 11, and 4 solutions, while for α = 0.9, they provide 6, 11, and 4 solutions for the same cases. A comparative analysis is conducted between the compromise solutions obtained from the proposed techniques and those derived from the hybrid genetic algorithm, NSGA-II and NSGA-III. A sensitivity analysis of the objective functions concerning the shape parameter and AL is also performed. Finally, the coverage performance measure is computed to assess the effectiveness of the proposed methods.

Abstract. An r-graph is an r-regular graph G on an even number of vertices where every odd set X ⊆V(G) is connected by at least r edges to its complement V(G) \ X. Every r-graph has a perfect matching and in a poorly matchable r-graph every pair of perfect matchings intersect, which implies that poorly matchable r-graphs are not r-edge-colourable. We prove, for each fixed r ≥ 3, that poorly matchable r-graph recognition is coNP-complete, an indication that, for each odd d ≥ 3, it may be a hard problem to recognise d-regular (d−1)-edge-connected non-d-edge-colourable graphs, referred to as d-snarks in this paper. We show how to construct, for every fixed odd d ≥ 5, an infinite family of d-snarks. These families provide a natural extension to the well-known Loupekine snarks. We also discuss how the hunting of the smallest d-snarks may help in strengthening and better understanding the major Overfull Conjecture on edge-colouring simple graphs.

In modern production–distribution supply chains, decentralization has increased significantly, due to increasing production network efficiency. This study investigates a production scheduling and vehicle routing problem in a make-to-order context under a decentralized decision-making structure. Specifically, two different decision makers hierarchically decide the production and distribution schedules to minimize their incurred costs and we formulate the problem as a bi-level mixed-integer optimization model as a static Stackelberg game between manufacturer and distributor. At the upper level, the manufacturer decides its best scheduling under a flexible job-shop manufacturing system, and at the lower level, the distributor decides its distribution scheduling (routing) which influences the upper-level decisions. The model derives the best production–distribution scheduling scheme, with the objective of minimizing the cost of the manufacturer (leader) at the lowest possible cost for the distributor (follower). As the lower level represents a mixed-integer programming problem, it is challenging to solve the resulting bi-level model. Therefore, we extend an efficient decomposition algorithm based on Duplication Method and Column Generation. Finally, to discuss the decentralization value, the results of the presented bi-level model are compared with those of the centralized approach.

This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.

Two major problems are encountered when using fuzzy SVM: (a) the number of local minima increases exponentially with the number of samples and (b) the quantity of required computer storage, required for a regular quadratic programming solver, increases by an exponential magnitude as the problem size expands. The Kernel-Adatron family of algorithms gaining attention lately which has allowed to handle very large classification and regression problems. However, these methods treat different types of samples (Noise, border, and core) with the same manner, which causes searches in unpromising areas and increases the number of iterations. In this work, we introduce a hybrid method to overcome these shortcoming, namely Optimal Recurrent Neural Network Density Based fuzzy Support Vector Machine (Opt-RNN-DBFSVM). This method consists of four steps: (a) characterization of different samples, (b) elimination of samples with a low probability of being a support vector, (c) construction of an appropriate recurrent neural network based on an original energy function, and (d) solution of the system of differential equations, managing the dynamics of the RNN, using the Euler–Cauchy method involving an optimal time step. Thanks to its recurrent architecture, the RNN remembers the regions explored during the search process. We demonstrated that RNN-FSVM converges to feasible support vectors and Opt-RNN-DBFSVM has a very low time complexity compared to RNN-FSVM with constant time step, and KAs-FSVM. Several experiments were performed on academic data sets. We used several classification performance measures to compare Opt-RNN-DBFSVM to different classification methods and the results obtained show the good performance of the proposed method.

To cope with global warming and achieve the goal of carbon emission reduction, various carbon policies have been implemented in many countries and regions. Some studies have indicated that with the popularity of low carbon, a small proportion of consumers show a green purchasing tendency. However, for firms, it is still difficult to predict the green purchase preferences of most consumers, and firms may face greater market demand uncertainty, which will bring profit risks. We assume that a firm’s decision is subject to its behavioral considerations, that is, its risk attitude. Considering the risk preferences of decision-makers and carbon emission policies, this paper addresses decision optimization in operations management. Our purpose is to analyze the optimal production decisions of risk-averse firms under carbon cap and carbon tax policies. Adopting the CVaR (conditional value-at-risk) criterion, we construct an optimization model with the constraints of carbon policies and obtain the analytic formula of optimal solutions. Then, we compare the optimal operational decisions for risk-averse firms and risk-neutral firms and further explore the impact of risk aversion on production and the parameters of carbon policy. Finally, some numerical studies are presented to analyze the carbon policies and risk aversion on firms’ operational decisions and give some managerial insights based on the analysis results.

Let G = (V(G), E(G)) be a graph. A function f : V(G) → ℙ({1, 2}) is a 2-rainbow dominating function if for every vertex v with f(v) = ∅, f(N(v)) = {1, 2}. An outer-independent 2-rainbow dominating function (OI2RD function) of G is a 2-rainbow dominating function f for which the set of all v 2208 V(G) with f(v) = ∅ is independent. The outer independent 2-rainbow domination number (OI2RD number) γoir2(G) is the minimum weight of an OI2RD function of G. In this paper, we first prove that n/2 is a lower bound on the OI2RD number of a connected claw-free graph of order n and characterize all such graphs for which the equality holds, solving an open problem given in an earlier paper. In addition, a study of this parameter for some graph products is carried out. In particular, we give a closed (resp. an exact) formula for the OI2RD number of rooted (resp. corona) product graphs and prove upper bounds on this parameter for the Cartesian product and direct product of two graphs.

Considering the importance of small and medium-sized industrial units for economic growth, social cohesion, regional and local development, this study presents a model for the merger so that they can make use of each other’s capacities and facilities to achieve higher efficiency levels. The involved criteria have been chosen using the SCOR model with the consideration of sustainability, resilience and agility criteria in each part of the supply chain network. PCA has been used to reduce the dimensionality and the efficiency of units has been determined by network DEA. Next, a mathematical model has been used to determine the best combination for merger. The model chosen for the finalization of the merger process is inverse network DEA, which tries to determine the final inputs of the merged units for a specific target. In addition to theoretical benefits, the results have practical applications. The results can give supply chain partners a common language for better communication and help them settle on standardized definitions. The model has been implemented using real-world data gathered from other articles, which pertain to 26 stone industries of Iran. The DEA model and the mathematical model have been solved through GAMS and the PCA approach through MATLAB.