scholarly journals Modified Dynamically-updated Weighted Opportunity Cost Based Algorithm for Unbalanced Transportation Problem

2021 ◽  
Vol 12 (2) ◽  
pp. 119-131
Author(s):  
ARM Jalal Uddin Jamali ◽  
Ringku Rani Mondal
Keyword(s):  
Opportunity Cost ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Transportation Cost ◽  
Engineering Science ◽  
Weight Factor ◽  
Total Cost ◽  
Transportation Problems ◽  
Control Of Flow ◽  
Effectiveness And Efficiency

Recently, Weighted Opportunity Cost (WOC) based algorithms are developed for solving balanced Transportation Problems (TPs). The exceptionality of the WOC based approaches is to introduce supply and demand as weight factor to cost entries for the control of flow of allocations. But in the unbalanced TP, there exist a pitfall whenever balancing the TP with zero dummy transportation cost as done in existing classical approaches, so that the total cost is unaffected due to dummy transportations. A modified dynamically-updated weighted opportunity cost-based algorithm embedded on Least Cost Method (LCM) is proposed which is suitable for both balanced and unbalanced TPs. Numerical instances have been carried out to demonstrate the effectiveness and efficiency of the proposed method. It is observed that, the proposed modified dynamically-updated weighted opportunity cost-based algorithm sometimes outperforms for the LCM as well as the existing weighted opportunity cost-based algorithm in unbalanced TPs. Journal of Engineering Science 12(2), 2021, 119-131

scholarly journals Sequentially Updated Weighted Cost Opportunity Based Algorithm in Transportation Problem

2019 ◽  
Vol 38 ◽  
pp. 47-55
Author(s):  
ARM Jalal Uddin Jamali ◽  
Pushpa Akhtar
Keyword(s):  
Opportunity Cost ◽  
Feasible Solution ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Basic Feasible Solution ◽  
New Approach ◽  
Cost Matrix ◽  
Transportation Problems ◽  
The Cost ◽  
First Time

Transportation models are of multidisciplinary fields of interest. In classical transportation approaches, the flow of allocation is controlled by the cost entries and/or manipulation of cost entries – so called Distribution Indicator (DI) or Total Opportunity Cost (TOC). But these DI or TOC tables are formulated by the manipulation of cost entries only. None of them considers demand and/or supply entry to formulate the DI/ TOC table. Recently authors have developed weighted opportunity cost (WOC) matrix where this weighted opportunity cost matrix is formulated by the manipulation of supply and demand entries along with cost entries as well. In this WOC matrix, the supply and demand entries act as weight factors. Moreover by incorporating this WOC matrix in Least Cost Matrix, authors have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems. But in that approach, WOC matrix was invariant in every step of allocation procedures. That is, after the first time formulation of the weighted opportunity cost matrix, the WOC matrix was invariant throughout all allocation procedures. On the other hand in VAM method, the flow of allocation is controlled by the DI table and this table is updated after each allocation step. Motivated by this idea, we have reformed the WOC matrix as Sequentially Updated Weighted Opportunity Cost (SUWOC) matrix. The significance difference of these two matrices is that, WOC matrix is invariant through all over the allocation procedures whereas SUWOC   matrix is updated in each step of allocation procedures. Note that here update (/invariant) means changed (/unchanged) the weighted opportunity cost of the cells. Finally by incorporating this SUWOC matrix in Least Cost Matrix, we have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems.  Some experiments have been carried out to justify the validity and the effectiveness of the proposed SUWOC-LCM approach. Experimental results reveal that the SUWOC-LCM approach outperforms to find out IBFS. Moreover sometime this approach is able to find out optimal solution too. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 47-55

scholarly journals An Improved Vogel's Approximation Method for the Transportation Problem

2011 ◽  
Vol 16 (2) ◽  
pp. 370-381 ◽  
Author(s):  
Serdar Korukoğlu ◽  
Serkan Ballı
Keyword(s):  
Approximation Method ◽  
Operations Research ◽  
Opportunity Cost ◽  
Transportation Problem ◽  
Large Scale ◽  
Efficient Solutions ◽  
Important Task ◽  
Computational Experiments ◽  
Optimal Solutions ◽  
Transportation Problems

Determining efficient solutions for large scale transportation problems is an important task in operations research. In this study, Vogel’s Approximation Method (VAM) which is one of well-known transportation methods in the literature was investigated to obtain more efficient initial solutions. A variant of VAM was proposed by using total opportunity cost and regarding alternative allocation costs. Computational experiments were carried out to evaluate VAM and improved version of VAM (IVAM). It was seen that IVAM conspicuously obtains more efficient initial solutions for large scale transportation problems. Performance of IVAM over VAM was discussed in terms of iteration numbers and CPU times required to reach the optimal solutions.

scholarly journals One Point Conventional Model to Optimize Trapezoidal Fuzzy Transportation Problem

2019 ◽  
Vol 4 (5) ◽  
pp. 1251-1263 ◽  
Author(s):  
Dinesh C. S. Bisht ◽  
Pankaj Kumar Srivastava
Keyword(s):  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Conventional Model ◽  
Transportation Problems ◽  
Fuzzy Transportation Problem

This article puts forward a new one point approach to optimize trapezoidal fuzzy transportation problem. It proposes the method having point wise breakup of the trapezoidal number in such a way, that fuzzy transportation problem is converted into four crisp transportation problems. The method is equipped with minimum of supply and demand approach. In the end, the solutions are combined to construct the optimal solution. Modified distribution is applied on each crisp problem to develop optimal solution. The scheme presented is compared with competitive methods available in literature and it is found to be in good coordination with these. The scheme is equally good to be applied on unbalanced problems. Two numerical problems are considered to test the performance of the proposed approach.

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

2020 ◽  
Vol 5 (1) ◽  
pp. 456
Author(s):  
Tolulope Latunde ◽  
Joseph Oluwaseun Richard ◽  
Opeyemi Odunayo Esan ◽  
Damilola Deborah Dare
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Transportation Cost ◽  
North West ◽  
Life Problems ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Road Freight Transportation ◽  
The Cost ◽  
Cost Of Transportation

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

scholarly journals An Attempt To Exemplify The Economic Principles In Real Property Valuation

2015 ◽  
Vol 23 (3) ◽  
pp. 5-13 ◽  
Author(s):  
Ewa Kucharska-Stasiak ◽  
Sabina Źróbek
Keyword(s):  
Economic Theory ◽  
Opportunity Cost ◽  
Supply And Demand ◽  
Real Property ◽  
Basic Principles ◽  
Research Results ◽  
Property Valuation ◽  
Important Principle ◽  
Income Approach ◽  
Traditional Approaches

Abstract The economic theory argues that the value of assets, including the value of real property, is influenced by many factors which determine the behavior of operators engaged in market transactions. The knowledge of basic principles and assumptions which underpin the development of value is essential to understanding the methods and procedures of valuation. The thesis, upon which the authors of this article based their theoretical and practical considerations, is formulated as follows: “The knowledge of economic principles of valuation improves the accuracy of valuation and allows for more appropriate interpretation of its results”. Therefore, these factors should be taken into account by appraisers estimating the value of property. Over a dozen so-called key principles of valuation have been formulated in literature. Among them are the principles of anticipation, change, substitution, supply and demand, competition, balance, highest and best use, conformity, and externalities. It is assumed that the most important principle in the valuation of property is the principle of anticipation. Some of the principles are relevant to all the traditional approaches to determining value, while others apply only to selected approaches e.g., the principle of opportunity cost, which is mainly used in valuations using the income approach. The thesis is supported by research results and an analysis of practical examples.

scholarly journals Transportation with volume discount: a case study of a logistic operator in Ghana

2014 ◽  
Vol 8 (2) ◽  
pp. 7-37
Author(s):  
Abdul-Salam Sibidoo Mubashiru
Keyword(s):  
Integer Programming ◽  
Production Scheduling ◽  
Transportation Problem ◽  
Transportation Network ◽  
Supply And Demand ◽  
Network Models ◽  
Cost Effective ◽  
Capital Budgeting ◽  
Integer Programming Problems ◽  
Optimality Algorithm

Network models and integer programming are well known variety of decision making problems. A very useful and widespread area of application is the management and efficient use of scarce resources to increase productivity. These applications include operational problems such as the distributions of goods, production scheduling and machine sequencing, and planning problems such as capital budgeting facility allocation, portfolio selection, and design problems such as telecommunication and transportation network design. The transportation problem, which is one of network integer programming problems is a problem that deals with distributing any commodity from any group of 'sources' to any group of destinations or 'sinks' in the most cost effective way with a given 'supply' and 'demand' constraints. Depending on the nature of the cost function, the transportation problem can be categorized into linear and nonlinear transportation problem. We applied Karush-Kuhn-Tucker (KKT) optimality algorithm to solve our problem of transportation with volume discount for a logistic operator in Ghana.

Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

2013 ◽  
pp. 328-347 ◽  
Author(s):  
Amit Kumar ◽  
Amarpreet Kaur
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Programming Formulation ◽  
Transportation Problems ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Formulation ◽  
Fuzzy Transportation Problem

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

Solving Solid Transportation Problems With Multi-Choice Cost and Stochastic Supply and Demand

2018 ◽  
pp. 137-170 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Deshabrata Roy Mahapatra
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
New Approach ◽  
Non Linear Programming ◽  
The Cost

In this chapter, the authors propose a new approach to analyze the Solid Transportation Problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming, which is incorporated in three constraints, namely sources, destinations, and capacities constraints, followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into a solid transportation problem, and this new problem is called Multi-Choice Stochastic Solid Transportation Problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique that will select an appropriate choice from a set of multi-choice, which optimize the objective function. The stochastic constraints of STP converts into deterministic constraints by stochastic programming approach. Finally, the authors construct a non-linear programming problem for MCSSTP, and by solving it, they derive an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

Sign in / Sign up

Export Citation Format

Share Document