Extending the solid step fixed-charge transportation problem to consider two-stage networks and multi-item shipments

This paper develops a new mathematical model for a capacitated solid step fixed-charge transportation problem. The problem is formulated as a two-stage transportation network and considers the option of shipping multiple items from the plants to the distribution centers (DC) and afterwards from DCs to customers. In order to tackle such an NP-hard problem, we propose two meta-heuristic algorithms; namely, Simulated Annealing (SA) and Imperialist Competitive Algorithm (ICA). Contrary to the previous studies, new neighborhood strategies maintaining the feasibility of the problem are developed. Additionally, the Taguchi method is used to tune the parameters of the algorithms. In order to validate and evaluate the performances of the model and algorithms, the results of the proposed SA and ICA are compared. The computational results show that the proposed algorithms provide relatively good solutions in a reasonable amount of time. Furthermore, the related comparison reveals that the ICA generates superior solutions compared to the ones obtained by the SA algorithm

On Solving Fixed Charge Transportation Problems Having Interval Valued Parameters

In this article, we propose a new method for solving the interval fixed charge transportation problem (IFCTP), wherein the parameters (associated cost, fixed cost, supply, and demand) are represented by interval numbers. First, an equivalent bi-objective fixed charge transportation problem (FCTP) is derived from the given IFCTP, and then the equivalent crisp problem is solved using a fuzzy programming technique. To demonstrate the solution procedure, two existing numerical examples (Safi and Razmjoo {\cite{bakp1}}) are coded and solved in LINGO 19.0. We establish the effectiveness of our proposed method through a comparison of the results achieved with those of two pre-existing methods

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

An Allocation-Routing Optimization Model for Integrated Solid Waste Management

Integrated smart waste management (ISWM) is an innovative and technologically advanced approach to managing and collecting waste. It is based on the Internet of Things (IoT) technology, a network of interconnected devices that communicate and exchange data. The data collected from IoT devices helps municipalities to optimize their waste management operations. They can use the information to schedule waste collections more efficiently and plan their routes accordingly. In this study, we consider an ISWM framework for the collection, recycling, and recovery steps to improve the performance of the waste system. Since ISWM typically involves the collaboration of various stakeholders and is affected by different sources of uncertainty, a novel multi-objective model is proposed to maximize the probabilistic profit of the network while minimizing the total travel time and transportation costs. In the proposed model, the chance-constrained programming approach is applied to deal with the profit uncertainty gained from waste recycling and recovery activities. Furthermore, some of the most proficient multi-objective meta-heuristic algorithms are applied to address the complexity of the problem. For optimal adjustment of parameter values, the Taguchi parameter design method is utilized to improve the performance of the proposed optimization algorithm. Finally, the most reliable algorithm is determined based on the Best Worst Method (BWM)

Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem

During past few decades, fuzzy decision is an important attention in the areas of science, engineering, economic system, business, etc. To solve day-to-day problem, researchers use fuzzy data in transportation problem for presenting the uncontrollable factors; and most of multi-objective transportation problems are solved using goal programming. However, when the problem contains interval-valued data, then the obtained solution was provided by goal programming may not satisfy by all decision-makers. In such condition, we consider a fixed-charge solid transportation problem in multi-objective environment where all the data are intuitionistic fuzzy numbers with membership and non-membership function. The intuitionistic fuzzy transportation problem transforms into interval-valued problem using (α, β)-cut, and thereafter, it reduces into a deterministic problem using accuracy function. Also the optimum value of alternative corresponds to the optimum value of accuracy function. A numerical example is included to illustrate the usefulness of our proposed model. Finally, conclusions and future works with the study are described.Portuguese Foundation for Science and Technology ("FCT-Fundacao para a Ciencia e a Tecnologia"), through the CIDMA-Center for Research and Development in Mathematics and Applications UID/MAT/ 04106/2019Spanish Ministry of Economy and Competitiveness, FEDER funds from the European Union TIN2014-55024-P TIN2017-86647-

Time Variant Multi-Objective Interval-Valued Transportation Problem in Sustainable Development

Sustainable development is treated as the achievement of continued economic development without detriment to environmental and natural resources. Now-a-days, in a competitive market scenario, most of us are willing to pay less and to gain more in quickly without considering negative externalities for the environment and quality of life for future generations. Recalling this fact, this paper explores the study of time variant multi-objective transportation problem (MOTP) with consideration of minimizing pollution. Time of transportation is of utmost importance in reality; based on this consideration, we formulate a MOTP, where we optimize transportation time as well as the cost function. The parameters of MOTP are interval-valued, so this form of MOTP is termed as a multi-objective interval transportation problem (MOITP). A procedure is taken into consideration for converting MOITP into deterministic form and then for solving it. Goal programming is applied to solve the converted transportation problem. A case study is conducted to justify the methodology by utilizing the environmental impact. At last, conclusions and future research directions are included regarding our study.The research of Jose Luis Verdegay is supported in part by the project, financed with FEDER funds, TIN2017-86647-P from the Spanish Govern