Initial feasible solution

Sugar mills in Brazil represent significant capital investments. To maintain appropriate returns on their investment, sugar companies seek to run the mills at capacity over the entire nine months of the sugarcane harvest season. Because the sugar content of cane degrades considerably once it is cut, maintaining inventories of cut cane is undesirable. Instead, mills want to coordinate the arrival of cut cane with production. In this paper, we present a model of the sugarcane harvest logistics problem in Brazil. We introduce a series of valid inequalities for the model, introduce heuristics for finding an initial feasible solution, and for lifting the lower bound. Computational results demonstrate the effectiveness of the inequalities and heuristics. In addition, we explore the value of allowing trucks to serve multiple rather than single locations and demonstrate the value of allowing the harvest speed to vary.

Solving the four index fully fuzzy transportation problem

Croatian Operational Research Review ◽

10.17535/crorr.2020.0016 ◽

2020 ◽

Vol 11 (2) ◽

pp. 199-215

Author(s):

Manal Hedid ◽

Rachid Zitouni

Keyword(s):

Numerical Analysis ◽

Comparative Study ◽

Transportation Problem ◽

Fuzzy Numbers ◽

Feasible Solution ◽

Second Phase ◽

Approximation Methods ◽

Fuzzy Transportation Problem ◽

Two Phases

In this paper, we will solve the four index fully fuzzy transportation problem (\textit{FFTP$_{4}$}) with some adapted classical methods. All problem's data will be presented as fuzzy numbers. In order to defuzificate these data, we will use the ranking function procedure. Our method to solve the \textit{FFTP$_{4}$} composed of two phases; in the first one, we will use an adaptation of well-known algorithms to find an initial feasible solution, which are the least cost, Russell's approximation and Vogel's approximation methods. In the second phase, we will test the optimality of the initial solution, if it is not optimal, we will improve it. A numerical analysis of the proposed methods is performed by solving different examples of different sizes; it is determined that they are stable, robust, and efficient. A proper comparative study between the adapted methods identifies the suitable method for solving \textit{FFTP$_{4}$}.

A Note on the Connection Between the Primal-Dual and the A* Algorithm

International Journal of Operations Research and Information Systems ◽

10.4018/joris.2010101305 ◽

2010 ◽

Vol 1 (1) ◽

pp. 73-85 ◽

Cited By ~ 4

Author(s):

Xugang Ye ◽

Shih-Ping Han ◽

Anhua Lin

Keyword(s):

Network Flow ◽

Feasible Solution ◽

Weighted Graph ◽

Dual Algorithm ◽

Heuristic Function ◽

Network Flow Problems ◽

A Algorithm ◽

Flow Problems ◽

Primal Dual ◽

The primal-dual algorithm for linear programming is very effective for solving network flow problems. For the method to work, an initial feasible solution to the dual is required. In this article, we show that, for the shortest path problem in a positively weighted graph equipped with a consistent heuristic function, the primal-dual algorithm will become the well-known A* algorithm if a special initial feasible solution to the dual is chosen. We also show how the improvements of the dual objective are related to the A* iterations.

Cutting Path Optimization Using Tabu Search

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.473.739 ◽

2011 ◽

Vol 473 ◽

pp. 739-748 ◽

Cited By ~ 14

Author(s):

Reginald Dewil ◽

Pieter Vansteenwegen ◽

Dirk Cattrysse

Keyword(s):

Tabu Search ◽

Software Package ◽

Feasible Solution ◽

Test Cases ◽

Finish Cutting ◽

Commercial Software Package ◽

Cutter Head ◽

Cutting Path ◽

The Given

This paper deals with generating paths for cutting irregular parts nested on a metal sheet. The objective is to minimize the total non-cutting time for the cutter head starting at a known location, cutting all the required elements and returning to the known location. In contrast to most literature on this topic, a part does not have to be cut at once. If this reduces the total non-cutting time, it is possible to cut a number of elements on a given part, then cut other parts and then return later to finish cutting the given part. The problem is modeled as a generalized traveling salesperson problem with special precedence constraints. An initial feasible solution is generated and improved by local moves embedded in a tabu search framework. The proposed algorithm shows promising results in comparison with a commercial software package on a limited set of test cases.

PENYELESAIAN MODEL TRANSPORTASI MENGGUNAKAN METODE ASM

JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON ◽

10.20527/epsilon.v14i1.2395 ◽

2020 ◽

Vol 14 (1) ◽

pp. 40

Author(s):

Nurul Iftitah ◽

Pardi Affandi ◽

Akhmad Yusuf

Keyword(s):

Transportation Problem ◽

Feasible Solution ◽

Direct Method ◽

Optimal Solution ◽

Transportation Model ◽

The Cost

(demand). the method that could be used for solving the transportation problem is to directly find the optimal solution. The direct method that used in this study id the ASM method for solving the balance transportation problem and revised ASM method for solving the unbalance transportation problem. This study aims to construct a transportation model using those methods and it solution. The method on this study is to identify the transportation model, construct the transportation model matrixes, construct an algorithm table using ASM method and to determine the optimal solution of the transportation problem. The obtained result from this study was the model ASM method could determine the optimum value without using initial feasible solution. On solving the unbalance transportation problem, there is an addition of dummy cell or column step. Then reducing the cost of cell and column and change the dummy cost with the biggest cost of reduced cell or column.

ANALISIS PERBANDINGAN PENGIRIMAN BARANG MENGGUNAKAN METODE VOGEL’S APPROXIMATION METHOD (VAM) DAN MODIFIED DISTRIBUTION (MODI)

JURTEKSI ◽

10.33330/jurteksi.v5i1.292 ◽

2019 ◽

Vol 5 (1) ◽

pp. 51-58

Author(s):

Oni Dewi Lestari ◽

Tika Christy

Keyword(s):

Approximation Method ◽

Feasible Solution ◽

Transportation Model ◽

Stepping Stone ◽

Operational Costs ◽

Working Principle ◽

Cost Plan

Abstract: The transportation model relates to determining the lowest cost plan for sending one item from a number of sources to a number of destinations. The working principle of the VAM method is to achieve an initial feasible solution. MODI Method (Modified Distribution) is a method of solving transportation cases developed from stepping stone method. The purpose of this research is to analyze the comparison of goods delivery using the VAM method and the MODI method. The results of the study indicate that operational costs are issued using the VAM method in January 2015, which is Rp. 34.100 and operational costs incurred using the VAM method in February 2015, namely Rp. 39.400. While the operational costs incurred using the MODI method in January 2015 are Rp. 33.800 and operational costs incurred using the MODI method in February 2015, which is Rp. 37.900. Keywords: vam method, modi method, transportation model Abstrak: Model transportasi berkaitan dengan penentuan rencana biaya terendah untuk mengirimkan satu barang dari sejumlah sumber ke sejumlah tujuan. Prinsip kerja metode VAM ialah untuk mencapai solusi fisibel awal. Metode MODI (Modified Distribution) merupakan metode penyelesaian kasus transportasi yang di kembangkan dari metode stepping stone. Tujuan penelitian ini, menganalisa perbandingan pengiriman barang menggunakan metode VAM dan metode MODI. Hasil penelitian menunjukkan bahwa biaya operasional yang dikeluarkan dengan menggunakan metode VAM pada bulan januari 2015 yaitu Rp. 34.100 dan biaya operasional yang dikeluarkan dengan menggunakan metode VAM pada bulan februari 2015 yaitu Rp. 39.400. Sedangkan biaya operasional yang dikeluarkan dengan menggunakan metode MODI pada bulan januari 2015 yaitu Rp. 33.800 dan biaya operasional yang dikeluarkan dengan menggunakan metode MODI pada bulan februari 2015 yaitu Rp. 37.900. Kata kunci: metode vam, metode modi, model transportasi

A combination of TDM and KSAM to determine initial feasible solution of transportation problems

Journal of Soft Computing Exploration ◽

10.52465/joscex.v2i1.16 ◽

2021 ◽

Vol 2 (1) ◽

Keyword(s):

Feasible Solution ◽

Transportation Problems ◽

A Comprehensive Method for Arriving at Initial Feasible Solution for Optimization Problems in Engineering with Illustrative Examples

Turkish Journal of Computer and Mathematics Education (TURCOMAT) ◽

10.17762/turcomat.v12i5.1785 ◽

2021 ◽

Vol 12 (5) ◽

pp. 1189-1205

Author(s):

Chandrasekhar Putcha, Et. al.

Keyword(s):

Feasible Solution ◽

Optimization Problems ◽

Computer Software ◽

Optimal Solution ◽

Simplex Algorithm ◽

The Other ◽

Basic Feasible Solution ◽

Adequate Number ◽

Comprehensive Method ◽

Two methods have been used extensively for arriving at initial basic feasible solution (IBF). One of them is Northwest corner rule and the other on is Russell method (Hillier & Lieberman, 2005.) Both methods have drawbacks. The IBF obtained is either far from optimal solution or does not have adequate number of entries to initiate transportation simplex algorithm. The Northwest Corner rule gives an initial feasible solution that is far from optimal while the IBF solution obtained using Russell method doesn’t give enough number of entries to start the transportation simplex algorithm. Hence, there is a need for developing a method for arriving at initial basic feasible solution with adequate number of entries needed to initiate transportation simplex algorithm, which can then be used to get an optimal solution. A computer software has been developed based on the new proposed method for this purpose. The proposed new method has been validated through four simple but illustrative examples.