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Cost and deterioration of transportation & availabilities and requirements for stages (1, 2 and 3) resp.
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This paper presents a solution algorithm to solve one class of bicriteria multistage transportation problem. This class represents bi-criteria multistage transportation problem without any restrictions on the intermediate stages. A way to find the non-dominated extreme points in the criteria space is developed. This method involves a parametric sea...
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In this article, the optimal loading of homogeneous marine cargo is considered. A mathematical formulation in terms of a mixed-integer linear program can be given. Still, the level of complexity turns out to be too high to perform full-scale computations. On the one hand, the reasons for this are the multitude of variables and constraints. On the o...
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... These approaches can be classified into three main categories. The first category comprises methods designed to identify all efficient solutions, including those based on linear programming ( [35], [10], [5], [19], [34], [11]) and dynamic programming ( [13], [12]). The second category includes methods that focus on finding a single efficient solution or compromise solution, such as goal programming ( [6], [25], [37], [27], [30]), interactive methods [32], lexicographic optimization ( [36], [28]), the minimize distance method ( [1], [22] ), and the decomposition approach ( [3], [4]). ...
... Assuming that m = n, ten instances of each triplet (m, n, r) are randomly generated, with m and n values in{10, 11,12,15,20,25,30}, the number of criteria r in {3,4,5}, the c k coefficients are in in [1,100] and the coefficients of a and d are in [1,30]. For the non-degenerate case, MOTP-Algorithm is compared to Isermann's method (refer [19]). ...
In today’s competitive market, practically all models are designed to address transportation problems involving multiple, often conflicting, objectives, such as minimizing transportation cost, minimizing transportation time, maximizing reliability, minimizing environmental impact, maximizing social equity, and minimizing product deterioration. In this respect, this paper proposes a method to optimize a multi-objective transportation problem (MOTP). We developed a branch-and-bound-based algorithm coupled with a classical transportation method to find the non-dominated points in the criteria space, in a finite number of steps. The algorithm utilizes reduced costs of all the criteria cost matrices to define the promising regions that may containnon-dominated points. This algorithm is strengthened by efficient bounds allowing us to prune a large number of nodes in the search tree and hence eliminate many dominated points. Efficient bounds further enhance the algorithm by pruning a large number of search tree nodes and eliminating dominated points. The suggested approach effectively addresses the non-degenerate case as well as the degenerate case, the latter of which, to our knowledge, has not been discussed in prior studies on MOTP. To handle degeneracy, we integrated the improved N-tree method into our approach. The effectiveness of our algorithm was assessed by comparing it to Isermann’s method for the non-degenerate case, where it was noticed that our approach gives better results. Additionally, computational experiments confirmed its efficiency in handling degenerate cases. Two numericalexamples are presented to illustrate the step-by-step application of the proposed method.
... The key idea behind dynamic programming is to solve each sub-problem only once and store the result, typically in a table. This avoids redundant calculations and significantly reduces the time complexity compared to solving the same sub-problems multiple times [40]. ...
The equipment replacement problem plays a crucial role in various engineering disciplines. It helps to determine the optimal economic lifespan of equipment. Optimizing the decision-making process for equipment replacement is essential for enhancing management effectiveness and supporting the achievement of business goals. Numerous models have been developed to identify the optimal replacement strategies. Some of these models are grounded in mathematical programming techniques such as linear programming, integer programming, goal programming, and dynamic programming. Additionally, some researchers have designed their heuristic models to determine the most suitable replacement policies. However, many of these heuristic models are limited by their focus on a single objective, often overlooking the complexity of multi-objective scenarios and uncertainties. A lot of the mathematical programming models concentrate on sensitivity analysis, parametric study, muti-objective and fuzzy parameters. In this paper, we present a comparative analysis of various replacement models, highlighting the strengths and weaknesses of both heuristic and mathematical programming models. The solution algorithm as well as an illustrative example using backward dynamic programming are included.
... So most real transportation problems are multistage problems. Ellaimony et al. [10] presented the bicriteria multistage transportation problem with the mathematical model for all types of the problem as the author classified it to four types which are BMTP1, BMTP2, BMTP3 and BMTP4. An introduction to dynamic programming is also presented. ...
... Koopman also worked on the optimum utilization of the transportation system and used a model of transportation, in activity analysis of production and allocation. It is known as the Hitchcock Koopman transportation problem [2]. More other papers were published on this topic with more features and methods of solution. ...
... From these methods, goal programming, the weighting method, multiple criteria decision-making procedures, the decomposition approach, the interactive method, the minimize distance method, and many other different methods. Some of these methods are illustrated and implemented in these research papers [2,7,8,9,10,11,12,13,14]. In this paper, the minimize distance method strategy is applied to find the efficient solutions of a real multi-objective transportation problem. ...
The classical transportation problem aims at finding the optimal distribution of a certain product from different sources to different destinations. The objective of this optimal distribution could be minimizing the total transportation cost, time, distance or any other related single objective. In real world applications there are more than one objective function to be studied while transporting products for companies. Therefore, the multi-objective techniques should be implemented on such problems. The minimize distance method is a proofed method to find the best compromise solution of multi-objective linear programming problems. In this paper we applied the minimize distance method on a real two objective transportation problem. Two LINGO codes are prepared to find the best compromise solution and more other efficient solutions to be ready for the decision maker to choose from. The model, the solution algorithm, the collected data and the output results are included in this paper as a case study.
... Dripping method has been used to find a set of efficient solution for bi-criteria TP (Pandian and Anuradha, 2011). Ellaimony et al. (2015) presented an algorithm for bi-criteria multistage TP using dynamic programming technique. Minimisation of transportation cost as linear programming model is discussed by Marques et al. (2007). ...
... Dripping method has been used to find a set of efficient solution for bi-criteria TP (Pandian and Anuradha, 2011). Ellaimony et al. (2015) presented an algorithm for bi-criteria multistage TP using dynamic programming technique. Minimisation of transportation cost as linear programming model is discussed by Marques et al. (2007). ...
... Brezina (2010) extended the classical transportation problem to a multi-stage transportation problem considering the capacity limit. Ellaimony (2015) presented an algorithm based on dynamic programming technique to solve a bi-criteria multi-stage transportation problem. Pandian and Natarajan (2011) proposed a zero point method to solve the two-stage transportation problem. ...
In the recent past, sustainability has become a major concern for transportation policies and planning in both developed and developing countries. This paper focuses on transportation sustainability for a three-stage fixed charge transportation problem. The major components of transportation sustainability considered include economical issues, social concerns, environmental concerns, and transportation system efficiency. Another important issue considered from a social point of view is the interrelationships between various customers of an end product, which has several benefits culminating in a healthier bottom line. The approach adopted in this paper consists of two phases, wherein the efficiency of vehicles is evaluated independently on all three parameters of sustainability using the data envelopment analysis technique in the first phase. The second phase consists of optimizing an integrated multi-objective optimization model that utilizes efficiency of the vehicles obtained from the first phase in a benefit criterion, considering the interrelationships among customers in terms of minimizing the independence values, and maximizing total profits along with many real-world constraints. Numerical illustration of a real-world case is included in order to demonstrate the utility of the proposed approach.