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The purpose of this paper is to extend a methodology for solving multi‐objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers.

The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods.

The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal.

The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined.

The paper proposed a novel and well‐defined algorithm to solve the considered problem.

Train re-scheduling remains a longstanding challenge in railway operation. To design high-quality timetable in fuzzy environment, the purpose of this paper is to study train re-scheduling problem under the fuzzy environment, in which the fuzzy coefficients of the constraint resources have the fuzzy boundaries.

Based on the improved fuzzy linear programming, the train re-scheduling model is constructed. Aiming at dealing with the fuzzy characteristics of the constraint coefficients value range boundaries, the description method of this kind of objective function is proposed and the solving approach is presented. The model has more adaptability to model a common train re-scheduling problem, in which some resources of the constraints are uncertain and have the characteristics of fuzziness and the boundaries of the resources are fuzzy.

Two numerical examples are carried out and it shows that the model proposed in this paper can describe the train re-scheduling problem precisely, dealing with the fuzzy boundaries of the fuzzy coefficients of the constraint resources. And the algorithm present is suitable to solve the problem. The approach proposed in this paper can be a reference for developers of railway dispatching system.

It is the first time to study train re-scheduling problem under the fuzzy environment, in which the fuzzy coefficients of the constraint resources have the fuzzy boundaries.

The purpose of this paper is to discuss the animal diet problem in grey environment which is adapted to the real situations. In particular, a new approach to solve these problems is proposed.

With the objective to produce the least-cost diet, in the traditional model for optimizing the diet problem, the price of foods, the nutrients requirements and the necessity of foods requirement have been considered as grey interval numbers. Grey linear programming approach has been employed to solve the grey diet problem. Grey linear programming with flexibility in selection of the coefficients can be more effective for solving the diet problems. In this research, only the positioned method has been used. The grey diet model is solved by using GAMS software based on the positioned method.

The main contribution of this work is to introduce a new model in the practical case that is concerned with diet problem under a kind of uncertainty environment and furthermore, proposing a novel method to solve the formulated problem. In this way, using a grey model and applying all restrictions, the least cost for one kilogram of total mixed ration was 6,893-10,163 Rials, and at this level, cow’s nutrient requirement was met. Based on the numerical examination, which was done on the real case, the achieved results have showed that the uncertainty of foods requirement and nutrients requirements had slight effect on the animal budget diet.

This problem must be viewed from another perspective because of the uncertainty regarding the amount of nutrients per unit of foods and the diversity of animals’ daily needs to receive them. In particular, a new method to optimize the fully mixed diet of lactating cows in early lactation that are readily available in the northeast of Iran in uncertainty environment has been proposed.

A sustainable freight transportation system involves freight processes that are economically efficient, socially inclusive and environment friendly. For enhancing sustainability in the freight operations, mode selection is a crucial strategic decision. Therefore, the purpose of this paper is selecting the best mode, or a combination of modes based on various criteria to carry shipments from origin to destination.

This study has used an integrated grey relational analysis based intuitionistic fuzzy multi-criteria decision-making process (GRA–IFP) and fuzzy multi-objective linear programming model. Three scenarios have been developed for analyzing sensitivity of decision variables with the variations in parameters under relevant conditions. A real case of Indian third-party logistics service provider has been used to demonstrate the effectiveness of the model.

The most relevant criterion emerged out in this study for multi-mode selection problem is costs. It can be concluded from the study that multi-modal freight transportation has the potential to improve the sustainability of freight transportation by reducing the costs, damages, emissions, traffic congestion and by increasing the speed of delivering the shipment. The sensitivity analysis further shows that road is the economical mode, whereas sea and rail together are the greenest as well as socially responsible modes of transportation.

This study provides an integrated tool, which can be used by freight transporters to decide upon the sustainable modes of transportation for their various shipments.

Modelling of the multiproject cash flow decisions in a contracting firm facilitates optimal resource utilization, financial planning, profit forecasting and enables the inclusion of cash‐flow liquidity in forecasting. However, a great challenge for contracting firm to manage his multiproject cash flow when large and multiple construction projects are involved (manipulate large amount of resources, e.g. labour, plant, material, cost, etc.). In such cases, the complexity of the problem, hence the constraints involved, renders most existing regular optimization techniques computationally intractable within reasonable time frames. This limit inhibits the ability of contracting firms to complete construction projects at maximum efficiency through efficient utilization of resources among projects. Recently, artificial neural networks have demonstrated its strength in solving many optimization problems efficiently. In this regard a novel recurrent‐neural‐network model that integrates multi‐objective linear programming and neural network (MOLPNN) techniques has been developed. The model was applied to a relatively large contracting company running 10 projects concurrently in Hong Kong. The case study verified the feasibility and applicability of the MOLPNN to the defined problem. A comparison undertaken of two optimal schedules (i.e. risk‐avoiding scheme A and risk‐seeking scheme B) of cash flow based on the decision maker's preference is described in this paper.

Distribution network design involves a set of strategic decisions in supply chains because of their long-term impacts on the total logistics cost and environment. To incorporate a trade-off between financial and environmental aspects of these decisions, this paper aims to determine an optimal location, among candidate locations, of a new logistics center, its capacity, as well as optimal network flows for an existing distribution network, while concurrently minimizing the total logistics cost and gas emission. In addition, uncertainty in transportation and warehousing costs are considered.

The problem is formulated as a fuzzy multiobjective mathematical model. The effectiveness of this model is demonstrated using an industrial case study. The problem instance is a four-echelon distribution network with 22 products and a planning horizon of 20 periods. The model is solved by using the min–max and augmented ε-constraint methods with CPLEX as the solver. In addition to illustrating model’s applicability, the effect of choosing a new warehouse in the model is investigated through a scenario analysis.

For the applicability of the model, the results indicate that the augmented ε-constraint approach provides a set of Pareto solutions, which represents the ideal trade-off between the total logistics cost and gas emission. Through a case study problem instance, the augmented ε-constraint approach is recommended for similar network design problems. From a scenario analysis, when the operational cost of the new warehouse is within a specific fraction of the warehousing cost of third-party warehouses, the solution with the new warehouse outperforms that without the new warehouse with respective to financial and environmental objectives.

The proposed model is an effective decision support tool for management, who would like to assess the impact of network planning decisions on the performance of their supply chains with respect to both financial and environmental aspects under uncertainty.

An appropriate space allocation among different residence types gives higher profitability and liquidity for cash flow management in real estate projects for developers. Thereby, a balance between debt and equity should be kept for capital formation in developers where high level of cost, profit and risk exists. The purpose of this paper is to provide cash flow optimization under debt and equity financing while providing an appropriate space allocation of residence types via synchronous consideration of profitability and liquidity.

A novel optimization methodology that includes project financing, optimization and experimental design modules is proposed. The first module, project financing, considers the flexibility of utilizing one or both of debt financing and equity financing when making capital. The optimization module addresses space allocation among different residence types for a construction while maximizing profitability and liquidity using two mixed-integer linear programming models in a pre-emptive manner. The experimental design module assesses the effects of decisive parameters within the methodology via multivariate analysis of variance (MANOVA).

The proposed methodology is applied to a real-life residential project in Istanbul. The optimization module yielded 42.5% profitability via the first linear programming model and 2.2% trade-off between liquidity and profitability while minimizing the payback period by the second linear programming model. Meanwhile, MANOVA results showed that profit per square meter and sale rate trends are the most prominent factors considering their significant effects on net present value and payback period.

To the best knowledge of the author, related papers focused only on profitability under equity financing. Liquidity (as an objective) and equity financing (as a financing method) have not been handled. Hence, this paper not only performs profitability and liquidity-oriented cash flow optimization under debt and equity financing but also optimizes space allocation of residences for the first time.

Some essential issues about modeling of reverse logistics (RL) systems and product recovery networks include consideration of the qualities of the returned products, taking into account uncertainty and integrating the forward and reverse flows. The purpose of this paper is to develop the integrated RL model, which focuses on the control of inventory and production planning problems in a case of uncertainty in demand, quantities and qualities of returns.

The model involves a forward production route, three alternative recovery routes and a disposal route. Various levels of qualities are considered for returned products. A fuzzy mixed integer programming model (FMIP) is developed to provide a solution for the problems of production planning and inventory control. After maximizing the satisfaction degree, different solutions can have the same maximum. Moreover, policies that use all recovery routes and reduce the overall uncertainty have no chance to be chosen. To tackle these problems, a two-phase approach method is applied.

According to the results of the numerical example, using different and appropriate recovery options based on the quality of returns can significantly decrease the recovery costs. Similarly, it is shown that the two-phase approach can be an effective and efficient method to reach a satisfactory solution for such problems.

In this study, after maximizing the FMIP model, a two-phase approach ‒ as a novel optimization technique in this research ‒ is employed to achieve a desirable solution.

The purpose of this paper is to propose a comprehensive methodology and a problem-specific model for the configuration of the optimal strategic supplier portfolio in terms of traditional, performance-related objectives and sustainability targets.

To bridge the research gap, i.e., to align strategic supplier portfolio selection with corporate sustainability targets, a hybrid model of the analytic network process (ANP) and goal programming (GP) is developed. To validate the model, a case example is presented and managerial feedback is collected.

By enabling the integration of sustainability targets into strategic supplier portfolio configuration, the hybrid ANP-GP model contributes to research in the area of sustainable supply chain management. Results indicate that simplifying the model by omitting one or more details may lead to unfortunate actions.

The model has been applied using a case example in the automotive industry. To strengthen the findings, it should be examined under other terms as well.

Integrating economic, environmental, and social targets into strategic supplier portfolio configuration reduces supply risks and promotes the achievement of the sustainability goals of the purchasing company.

Strategic supplier selection counts among the decisions that have an impact on the environment and society for several years. Configuring economically rational, environmentally friendly, and socially responsible supplier bases supports worldwide efforts towards sustainable development.

Although sustainable supplier selection has gained importance in recent years, this is the first time that a comprehensive model for the determination of the optimal strategic supplier portfolio in terms of performance-related objectives and sustainability targets has been proposed.

Sustainable supplier selection is of vital importance in sustainability decision of supply chain under carbon neutrality. Multi-criteria decision-making approaches are widely used in sustainable supplier selection and generally classified the involved criteria into three sustainable development (SD) dimensions: Environmental, Social and Economic. During the assignment of appropriate weighted scores to the criteria, most of the methods considered mutually exclusive criteria. However, some criteria cover multidimensions since ambiguity vagueness makes them difficult to classify into one dimension exclusively. The purpose of this paper is to find proper approaches addressed to multidimensional overlapping criteria in the evaluation of suppliers’ sustainability performance.

This study proposes three approaches to resolve the multidimensional overlapping criteria issue by data envelopment analysis (DEA) methods. The first approach uses all dimensional criteria and “dimensional overlapping criteria” in a single DEA model. The second approach consists of two-stage DEA. The first stage is to find SD dimensional performances, which are used in the second stage. The third approach uses an aggregate weight-constrained DEA model with additional constraints. Such approaches are applied to an empirical case study with six dimensions.

Results indicate that the third approach is better than the first two approaches in balancing the development among all dimensions instead of focusing on the superiority dimension to obtain high performance.

Discussing overlapping criteria in the context of sustainable supplier evaluation and other multi-criteria evaluation have a noticeable impact on evaluation systems, but appropriate approaches for this issue are currently under-researched.