Abstract In this study, a multi‐objective formulation is proposed for designing a supply chain of perishable products including suppliers, plants, distributors, and customers under sustainable development. In addition to the studies of the literature, direct shipment between producers and customers and also alternative products possibility are allowed. In this problem, the objectives, such as facilities establishment costs, transportation costs, negative environmental impacts, and social impact (fixed and variable employment rates) are optimized simultaneously. As in real situations, most of the transportation activities of such supply chain are performed by hiring transportation devices, the open routing logic is applied to form the traveling path of each hired transportation device. Furthermore, the possibility of direct shipment from the plants to the customers is considered in order to increase profitability of the plants. Because of the NP‐hard nature of the supply chain design problems, some meta‐heuristic solution approaches of the literature are modified to multi‐objective form and applied to solve the problem. Several test problems from small to large sizes are generated randomly to evaluate the meta‐heuristic algorithms. As a result, among the proposed algorithms, the multi‐objective gray wolf optimizer (MGWO) performs better than others by considering four well‐known evaluation metrics. Finally, a case study from perishable products supply chain of Iran is solved and analyzed to show the applicability of the proposed problem.

Abstract Financial development means some improvements on providing the information about investment possibilities in a region or country. In this study, a new perspective of financial development is considered which is called the multi‐criteria global financial development‐ranking problem. In this problem, some countries from the Middle East are considered to be ranked according to the criteria of global financial development from the world bank database. Due to high number of criteria that may affect the quality of the obtained ranking negatively, a solution methodology in three stages is proposed. First, as a novelty, an improved version of the weighted principal component analysis (PCA) approach is proposed to select the most important criteria from the initial set of criteria and also determine their importance weights. This approach considers both linear and nonlinear relationships of the data instead of considering just linear relationships. Then using the reduced decision matrix and the obtained importance weight values, the technique for order of preference by similarity to ideal solution multi‐criteria decision approach is used to rank the countries of case study. The computational study is done based on the proposed improved weighted PCA approach and the obtained results are analyzed and compared by those of the classical approaches, for example, some versions of the classical weighted PCA approach.

The multi-floor facility layout problem (MFLP) is one of the most important and complex facility layout problems that has many applications in designing the facilities of manufacturing and service sectors. In this study, a hybrid version of the Dantzig-Wolfe decomposition algorithm is proposed to solve the MFLP for the first time. The proposed solution approach is performed in two steps. In the first step, a mathematical formulation is applied to assign the departments to the floors in a way that the departments with higher material flow between them be located on the same or closer floors. In the second step, the output of the first step is considered and the MFLP is decomposed into a master problem and some sub-problems to form the Dantzig-Wolfe decomposition algorithm and find the optimal layout of each floor separately. Then the integrated layout of multiple floors is formed easily. The proposed algorithm is evaluated using some sample problems from the literature and some newly generated test problems. The obtained results show the superiority of the proposed algorithm compared to the approaches of the literature.

Summary The system under investigation contains a single refinery, a unique distribution center, and a multiproduct pipeline. The basic aim is to plan the optimal sequence for pumping products to achieve financial benefit and satisfy the customers with on‐time delivery. In this study, some restrictions (such as batch sizing, discharging rate, forbidden sequences, and settling periods) are considered and the problem is formulated as a MILP model. Although the multiproduct pipeline scheduling problem has high time complexity, meta‐heuristic algorithms have been used rarely in the literature. Another contribution of this work is to develop several meta‐heuristic algorithms to solve the proposed MILP effectively. Therefore, as a novelty, some classical meta‐heuristics like population‐based simulated annealing and population‐based variable neighborhood search are hybridized by the gravitational search algorithm for obtaining better performance. Parameters of the algorithms are tuned by an optimization problem and then all algorithms are compared by numerical examples. The achieved results demonstrate the validity of the model and the efficient performance of the proposed algorithms against exact methods. These algorithms also lead to better solutions in much lower computational time. Among them, the hybrid algorithm obtained by combining the SA and GSA meta‐heuristics are superior to the other algorithms.

Abstract In the cases that the historical data of an uncertain event is not available, belief degree‐based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi‐objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree‐based uncertainty theory. This article is almost the first study on belief degree‐based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance‐constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi‐objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.

Abstract A novel optimization problem of carton box manufacturing industries is introduced in this paper. A mixed integer linear formulation with multiple objective functions is developed in order to determine the value of some criteria of carton raw sheets such as size, amount, and supplier under simultaneous minimization of multiple goals such as purchasing cost of raw sheets under discount policy, wastage remained from raw sheets, and quantity of surplus of carton boxes. In order to cope with the unstable market of this sector, some parameters of the proposed formulation such as demand value of the products and price given for raw sheets are assumed to be fuzzy numbers. To tackle such fuzzy multiobjective problem, first, the fuzzy problem is converted to a crisp form using the concepts of necessity‐based chance‐constrained modelling approach. Then a new hybrid form of the fuzzy programming approach is proposed to solve the obtained crisp multiobjective problem effectively. Computational experiments on a real case given by a carton box factory show the superior result of the proposed solution approach compared with the well‐known multiobjective solution methods taken from the literature.

A linear fractional transportation problem in uncertain environment is studied in this paper where the uncertain parameters of the problem are of belief degree—based uncertainty. For the first time, this type of uncertainty is considered for the linear fractional transportation problem. Belief degree—based uncertainty is useful for the cases that no historical information of an uncertain event is available. Zigzag type uncertainty distribution is used to show the belief degree—based uncertainty of the parameters of the problem. As solution methodology, the uncertain linear fractional transportation problem is converted to a crisp form using three approaches of expected value model, expected value and chance-constrained model, and chance-constrained model, separately. An extensive computational study on a real illustrative example shows the efficiency of the proposed formulation and the conversion approaches. The sensitivity analysis over the example illustrates the high dependency of the objective function value to the changes of the confidence level values of the chance constraints in the expected value and chance-constrained programming approach and the chance-constrained programming approach.

A well-known version of minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs is applied as in most of real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy cost of sending and passing a specified flow value in to and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh’s extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different α-cut values to construct the fuzzy cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of the minimal cost flow problem. The obtained results and the procedure applied to obtain them prove the superiority of the proposed approach comparing to the previous approaches of the literature.