On logarithmic fixed-charge transportation problem

The fixed-charge transportation problem is an extension of the classical transportation problem in which a fixed cost, sometimes called a setup cost, is incurred for every origin. In this paper, an algorithm is presented to find the optimum time-cost trade-off pair in a fixed-charge bi-criterion transportation problem giving the same priority to both time and cost. The algorithm identifies efficient time-cost trade-off pairs and thereby arrives at the conclusion that among the trade-off pairs, the optimum trade-off pair has the minimum D1-distance from the ideal point. A numerical example is given to illustrate the developed algorithm

This work extends the theory of the fixed charge transportation problem (FCTP), currently based mostly on a forty-year-old publication by Hirsch and Danzig. This paper presents novel properties that need to be considered by those using existing, or those developing new methods for optimizing FCTP. It also defines the problem in an easier way, making it understandable to a wider spectrum of readers. While the analysis is limited to FCTP only, elements of it can easily be extended to the general fixed charge problem. Finally a novel, snap method for finding global minima for FCTPs with large fixed charge coefficients is introduced.

Logistics, supply chain management, and resource allocation are just a few of the many real-world contexts in which the Multi-Objective Linear Transportation Problem presents itself as a formidable optimization issue. In this paper, we seek to solve a multi-objective, linear and non-linear transportation problem by suggesting the most efficient solution possible. The unique Maximum divide and minimum allotment (MDMA) approach was proposed to find a workable answer to a particular transportation issue. It also calculates the solution to the problem using a number of different transportation methods and compares the result to MDMA methods. It is determined that the MDMA approach offers a practical algorithm and solution for the designated transportation problem.

The primary focus of this article is dedicated to a thorough investigation of the Fixed Load Transportation Problem (FCTP) and the proposition of an exceedingly efficient resolution method, with a specific emphasis on the achievement of optimal transportation plans within practical time constraints. The FCTP, recognized for its intricate nature, falls into the NP-complete category, notorious for its exponential growth in solution time as the problem's size escalates. Within the realm of combinatorial optimization, metaheuristic techniques like the Dragonfly algorithm and genetic algorithms have garnered substantial acclaim due to their remarkable capacity to deliver high-quality solutions to the challenging FCTP. These techniques demonstrate substantial potential in accelerating the resolution of this formidable problem. The central goal revolves around the exploration of groundbreaking solutions for the Fixed Load Transportation Problem, all while concurrently minimizing the time investment required to attain these optimal solutions. This undertaking necessitates the adept utilization of the Dragonfly algorithm, an algorithm inspired by natural processes, known for its adaptability and robustness in solving complex problems. The FCTP, functioning as an optimization problem, grapples with the multifaceted task of formulating distribution plans for products originating from multiple sources and destined for various endpoints. The overarching aspiration is to minimize overall transportation costs, a challenge that mandates meticulous considerations, including product availability at source locations and demand projections at destination points. The proposed methodology introduces an innovative approach tailored explicitly for addressing the Fixed Charge Transport Problem (FCTP) by harnessing the inherent capabilities of the Dragonfly algorithm. This adaptation of the algorithm's underlying processes is precisely engineered to handle large-scale FCTP instances, with the ultimate objective of unveiling solutions that have hitherto remained elusive. The numerical results stemming from our rigorous experiments unequivocally underscore the remarkable prowess of the Dragonfly algorithm in discovering novel and exceptionally efficient solutions. This demonstration unequivocally reaffirms its effectiveness in overcoming the inherent challenges posed by substantial FCTP instances. In summary, the research represents a significant leap forward in the domain of FCTP solution methodologies by seamlessly integrating the formidable capabilities of the Dragonfly algorithm into the problem-solving process. The insights and solutions presented in this article hold immense promise for significantly enhancing the efficiency and effectiveness of FCTP resolution, ultimately benefiting a broad spectrum of industries and logistics systems, and promising advancements in the optimization of transportation processes

In this paper, a transportation problem with an objective function as the sum of a linear and linear fractional function is considered. We present an algorithm to solve the above transportation problem. In addition, we consider two special cases of the problem, where the transportation flow is either restricted or enhanced. The first case deals with when one wishes to keep reserve stocks at the sources for emergencies, thereby restricting the total flow to a known specified level. The second case deals with when extra demand in the market compels some of the factories to increase their production, thereby enhancing the total flow to meet the customer demands fully. For the above special cases, we formulate a related linear plus linear fractional transportation problem. We present a numerical example to illustrate the proposed algorithm for the different cases. We show that the solution obtained is a local minimum occurring at an extreme point of the convex set of feasible solutions.

Objectives: To instigate and rationalize utilization of carbon from mobile capture technology in a fuzzy rough multi-objective fixed charge profit maximization transportation problem with truck slot and product blending constraints. Methods: Two trapezoidal fuzzy rough multi-objective profit maximization mathematical models based on carbon taxation policy and mobile carbon capture and utilization technology are formulated for multi-objective fixed-charge transportation problem with product blending and truck slot constraints. The fuzzy rough models are metamorphosed into deterministic problems using their expected values and further untangled using Global Criterion Method in LINGO (19.0). Numerical examples and their outcomes are ventilated to inspect the proposed models and their advantages. Findings: The solutions obtained by solving the two trapezoidal fuzzy rough multi-objective profit maximization sustainability models ensure mobile carbon capture and utilization technology as the most promising sustainability technique than carbon taxation policy. Utilization of onboard captured carbon elevate the profit by 82.64 dollars in spite of its additional expense on mobile capture and is found to be a progressive game changer in global climate emergency management than the usual taxing scheme. Novelty: Mathematical model for fuzzy rough blending and truck slot constrained multi-objective profit maximization fixed-charge transportation problem with mobile carbon capture and utilization technology is not yet investigated in literature. Mathematics Subject Classification (2020): 90B06, 90C08 Keywords: Fuzzy rough, Multi-objective, Fixed-charge, Product blending constraint, Truck slot constraint, Profit maximization, Mobile carbon capture and utilization

A heuristic algorithm for shipping more for less in distribution-related problems is proposed. Usually these problems are formulated as transportation problems. Many distribution problems, however, can only be modelled as fixed-charge transportation problems. The more-for-less paradox occurs when it is possible to ship more total goods for less (or equal) total cost while shipping the same amount or more from each origin and to each destination and keeping all the shipping costs non-negative. The existing literature has demonstrated the practicality of identifying cases where the paradoxical situation exists. Though vital to decision making, these topics are usually not covered in business classes because of the rigour required to solve these problems optimally. The proposed algorithm builds on the optimal solution of a transportation problem. As such, it is easy to understand and apply, and can serve as an effective tool for managers and students alike for extending the solution to search for more-for-less opportunities in distribution problems. We present numerical examples to illustrate applications of the proposed method.

The fixed charge transportation problem is an extension of the traditional transportation problem in which two kinds of costs, say direct cost and fixed charge, are taken into consideration. The direct cost is the cost associated with each source-destination pair, and the fixed charge occurs when the transportation activity takes place in the corresponding source-destination pair. In this paper, the fuzzy fixed charge transportation problem is modeled as chance-constrained programming by using the possibility measure and credibility measure firstly. Then a heuristic genetic algorithm is designed.

Recently, research on logistics caught more and more attention. One of the important issues on logistics system is to find optimal delivery routes with the least cost for products delivery. Numerous models have been developed for that reason. However, due to the diversity and complexity of practical problem, the existing models are usually not very satisfying to find the solution efficiently and convinently.In this paper, we treat a real-world logistics case with a company named ABC Co. ltd., in Kitakyusyu Japan. Firstly, based on the natures of this conveyance routing problem, as an extension of transportation problem (TP) and fixed charge transportation problem (fcTP) we formulate the problem as a minimum cost flow (MCF) model. Due to the complexity of fcTP, we proposed a priority-based genetic algorithm (pGA) approach to find the most acceptable solution to this problem. In this pGA approach, a two-stage path decoding method is adopted to develop delivery paths from a chromosome. We also apply the pGA approach to this problem, and compare our results with the current logistics network situation, and calculate the improvement of logistics cost to help the management to make decisions. Finally, in order to check the effectiveness of the proposed method, the results acquired are compared with those come from the two methods/ software, such as LINDO and CPLEX.

Solving fixed charge transportation problem with interval parameters

In classical fractional transportation programming problem, we want to optimize the objective function in the form of one or several ratios subject to some linear constraints. If in multi-objective transportation problem, objective function is in ration of two linear function under some linear restrictions, then the problem is called multi-objective linear fractional transportation problem (MOLFTP). In this paper we propose a new method to solve multi-objective linear fractional transportation problem which is extension of Nomani et al. (Int J Manag Sci Eng Manag (2016) [9]). Two numerical problems are presented to validate the proposed algorithm.

In this paper, an effective ant lion optimisation (ALO) algorithm is proposed for two stage supply chain network associated with fixed charge transportation problem (FCTP) which is strongly NP-hard. In a FCTP, fixed cost is incurred for every route, along with the variable cost that is proportional to the amount shipped. In some circumstances, the variable cost is associated with quadratic variables in which the cost function will be nonlinear. The aim of this paper is to determine the least cost transportation plan that minimises the total variable and fixed costs while satisfying the supply and demand requirements of each plant and customer. The performance of the proposed ALO is compared in terms of total cost with other algorithms addressed in the literature such as genetic algorithm, simulated annealing and ant colony optimisation. The computational results reveal that the proposed ALO provides better solutions.

This paper is about improving the performance of genetic algorithm (GA) to solve the fixed-charge transportation problem (FCTP). Several approaches have been developed, based on adaptation and improvement of genetic operators. We propose a new genetic algorithm adopting an immigration strategy to maintain the diversity in the population and then overcome the stagnation of the values of the objective function. Thereby, we applied two types of immigration, random immigration and memory-based immigration. The numerical results obtained with several standard instances of the FCTP problem demonstrate the effectiveness of these strategies in improving the performance of the GA. Especilly, for the second strategy.

The single-sink, fixed-charge transportation problem has a variety of applications, including supplier selection, product distribution/fleet selection, and process selection. In this paper we present a dynamic programming algorithm for solving this important problem that is very easy to implement and that improves considerably in terms of computational attractiveness on the best methods in the literature.

Optimization of the transportation expense of a firm with contractual supplies