Linear Programming. Transportation Problem

2009 ◽  
pp. 129-138
Author(s):  
Bernd Luderer ◽  
Volker Nollau ◽  
Klaus Vetters
Keyword(s):  
Linear Programming ◽  
Transportation Problem

scholarly journals Statistical Methods for Solving Transportation Problems

2019 ◽  
Vol 25 (2) ◽  
pp. 10-13
Author(s):  
Alina Baboş
Keyword(s):  
Linear Programming ◽  
Statistical Methods ◽  
Approximation Method ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Basic Feasible Solution ◽  
Statistical Tools ◽  
Numerical Examples ◽  
North West ◽  
Shipping Cost

Abstract Transportation problem is one of the models of Linear Programming problem. It deals with the situation in which a commodity from several sources is shipped to different destinations with the main objective to minimize the total shipping cost. There are three well-known methods namely, North West Corner Method Least Cost Method, Vogel’s Approximation Method to find the initial basic feasible solution of a transportation problem. In this paper, we present some statistical methods for finding the initial basic feasible solution. We use three statistical tools: arithmetic and harmonic mean and median. We present numerical examples, and we compare these results with other classical methods.

An Extended Programming Experience

1981 ◽  
Vol 13 (1) ◽  
pp. 19-27 ◽  
Author(s):  
B Harris
Keyword(s):  
Linear Programming ◽  
Transportation Problem ◽  
Dual Methods ◽  
Solution Methods ◽  
Research Problems ◽  
Computational Aspects ◽  
Standard Solution ◽  
Order Bounds

The paper summarizes a twenty-year experience with the computational aspects of the transportation problem of linear programming. The problem is completely described and standard solution methods are summarized. The order bounds for these computations are examined. Attention then turns to some sample research problems, including shortening the search for a move, solving a condensed problem, choosing a starting basis, and several recently developed dual methods. Brief reference is made to the difficulties which arise in publishing unorthodox approaches such as those discussed in the paper.

scholarly journals EVALUASI DESENTRALISASI, SENTRALISASI, DAN ZONING PELAKSANAAN AUDIT TERHADAP EFISIENSI BIAYA PERJALANAN DINAS AUDIT KEPABEANAN DAN CUKAI

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Ario Seno Nugroho ◽  
Muhamad Fachrudin
Keyword(s):  
Linear Programming ◽  
Organizational Structure ◽  
Cost Efficiency ◽  
Transportation Problem ◽  
Quantitative Data ◽  
Organization Structure ◽  
Transportation Cost ◽  
Simulation Method ◽  
Microsoft Excel ◽  
Compliance Audit

ABSTRACT:Organization structure is an important factor in determining organization’s achievement of its objectives. The Directorate of Audit on Customs and Excise’ objective is to conduct compliance audit on entities practicing import, export and excise matters. The directorate has been implemented three types of organization structure: centralization, decentralization, and zoning, where each type by nature having its advantages and drawbacks. This study simulates quantitative data by using descriptive quantitative approach to determine the most ideal organizational structure of the directorate in terms of cost efficiency. The simulation method being used is linear program adjusted by several constrains in transportation cost. The simulation is conducted by using solver program provided in Ms Excel. The results show that decentralization is the most efficient organization type in terms of cost efficiency, followed by zoning, and centralization.Keywords: centralization, decentralization, zoning, linear programming, transportation problem. ABSTRAK:Bentuk organisasi dapat menentukan keberhasilan organisasi dalam memenuhi tujuan. Direktorat Audit Kepabeanan dan Cukai (Dit AKC), memiliki tujuan untuk melakukan audit kepada perusahaan yang melakukan impor, ekspor, dan cukai. Terdapat tiga bentuk organisasi yang telah digunakan oleh Dit AKC, yaitu: sentralisasi, desentralisasi, dan zoning. Setiap bentuk organisasi memiliki kelebihan dan kekurangan. Penelitian ini menggunakan pendekatan deskriptif kuantitatif dalam bentuk simulasi dan bertujuan mencari bentuk organisasi yang ideal untuk Dit AKC dari sisi efisiensi biaya. Metode simulasi yang digunakan adalah program linier, masalah transportasi. Penelitian ini menggunakan solver di Microsoft Excel. Hasil dari penelitian ini menunjukkan bentuk organisasi desentralisasi memberikan hasil paling efisien. Zoning dan sentralisasi memberikan hasil terbaik kedua dan ketiga.Kata Kunci: sentralisasi, desentralisasi, zoning, program linier, masalah transportasi 

scholarly journals Value- and Ambiguity-Based Approach for Solving Intuitionistic Fuzzy Transportation Problem with Total Quantity Discounts and Incremental Quantity Discounts

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
C. Veeramani ◽  
M. Joseph Robinson ◽  
S. Vasanthi
Keyword(s):  
Linear Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Quantity Discounts ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Transportation Problem ◽  
The Cost ◽  
Incremental Quantity Discounts ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

The cost of goods per unit transported from the source to the destination is considered to be fixed regardless of the number of units transported. But, in reality, the cost is often not fixed. Quantity discount is often allowed for large shipments. Furthermore, the transportation cost and the price break quantities are not deterministic. In this study, we introduce the concept of Value- and Ambiguity-based approach for solving the intuitionistic fuzzy transportation problem with total quantity discounts and incremental quantity discounts. Here, the cost and quantity price breakpoints are represented by trapezoidal intuitionistic fuzzy numbers. The Values and Ambiguities are defined as the degree of acceptance and rejection for trapezoidal intuitionistic fuzzy numbers. The trapezoidal intuitionistic fuzzy transportation problem is converted to a parametric transportation problem based on their Value indices and Ambiguity indices. Then, for different Values of the parameter, the transformed problem is reduced to the linear programming problem. Then, the linear programming problem is solved by using the classical methods. The proposed method is demonstrated with a numerical example. In conclusion, the intuitionistic fuzzy transportation problem with total quantity discounts is compared with the intuitionistic fuzzy transportation problem with incremental quantity discounts.

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