scholarly journals Comparative Study of Ranking Methods for Fuzzy Transportation

2019 ◽  
pp. 1592-1602
Author(s):  
Sami Kadhem kareem Al thabhawi
Keyword(s):  
Linear Programming ◽  
Comparative Study ◽  
Programming Model ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Basic Solution ◽  
Ranking Methods ◽  
Fuzzy Variables ◽  
Accurate Comparison ◽  
Total Transportation Cost

There are several methods that are used to solve the traditional transportation problems whose units of supply, demand quantities, and cost transportation are known exactly. These methods obtain basic solution, and develop it to the best solution through a series of consecutive calculations to obtain the optimal solution.The steps are more complex with fuzzy variables, so this paper presents the disadvantages of solutions of the traditional ways with existence of variables in the fuzzy form.This paper also presents a comparison between the results that emerged after using different conversion ranking formulas to convert from fuzzy form to crisp form on the same numerical example with a full fuzzy form. The problem has been then converted into a linear programming model, and the BIG-M method to be later used to find the optimal solution that represents the number of units transferred from processing or supply centers to a number of demand centers based on the known cost of transportation.Achieving the goal of the problem is by finding the lowest total transportation cost,while the comparison is based on that value. The results are presented in acomprehensive table that organizes data and results in a way that facilitates quickand accurate comparison. An amendment to one of the order formats was suggested,because it has different results compared to other formulas. One of the rankingequations is modified, because it has different results compared to other methods..

scholarly journals A Synchronous Optimization Model for Multiship Shuttle Tanker Fleet Design and Scheduling Considering Hard Time Window Constraint

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhenfeng Jiang ◽  
Dongxu Chen ◽  
Zhongzhen Yang
Keyword(s):  
Time Window ◽  
Programming Model ◽  
Transportation Cost ◽  
Exact Algorithm ◽  
Mixed Integer ◽  
Routing Problem ◽  
Hard Time ◽  
Proposed Model ◽  
Total Transportation Cost ◽  
Time Window Constraints

A Synchronous Optimization for Multiship Shuttle Tanker Fleet Design and Scheduling is solved in the context of development of floating production storage and offloading device (FPSO). In this paper, the shuttle tanker fleet scheduling problem is considered as a vehicle routing problem with hard time window constraints. A mixed integer programming model aiming at minimizing total transportation cost is proposed to model this problem. To solve this model, we propose an exact algorithm based on the column generation and perform numerical experiments. The experiment results show that the proposed model and algorithm can effectively solve the problem.

scholarly journals Applying Simulation Modelling in Quantifying Optimization Results

2021 ◽  
Vol 15 (4) ◽  
pp. 518-523
Author(s):  
Ratko Stanković ◽  
Diana Božić
Keyword(s):  
Linear Programming ◽  
Simulation Model ◽  
Input Data ◽  
Optimization Problems ◽  
Programming Model ◽  
Optimal Solution ◽  
Simulation Modelling ◽  
Simulation Software ◽  
Programming Models ◽  
Freight Forwarding

Improvements achieved by applying linear programming models in solving optimization problems in logistics cannot always be expressed by physically measurable values (dimensions), but in non-dimensional values. Therefore, it may be difficult to present the actual benefits of the improvements to the stake holders of the system being optimized. In this article, a possibility of applying simulation modelling in quantifying results of optimizing cross dock terminal gates allocation is outlined. Optimal solution is obtained on the linear programming model by using MS Excel spreadsheet optimizer, while the results are quantified on the simulation model, by using Rockwell Automation simulation software. Input data are collected from a freight forwarding company in Zagreb, specialized in groupage transport (Less Than Truckload - LTL).

scholarly journals A fuzzy multi-objective linear programming with interval-typed triangular fuzzy numbers

2019 ◽  
Vol 17 (1) ◽  
pp. 607-626 ◽  
Author(s):  
Chunquan Li
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Objective Functions ◽  
Triangular Fuzzy Numbers ◽  
Matlab Toolbox ◽  
Multi Objective ◽  
Cut Set ◽  
The Stability

Abstract A multi-objective linear programming problem (ITF-MOLP) is presented in this paper, in which coefficients of both the objective functions and constraints are interval-typed triangular fuzzy numbers. An algorithm of the ITF-MOLP is provided by introducing the cut set of interval-typed triangular fuzzy numbers and the dominance possibility criterion. In particular, for a given level, the ITF-MOLP is converted to the maximization of the sum of membership degrees of each objective in ITF-MOLP, whose membership degrees are established based on the deviation from optimal solutions of individual objectives, and the constraints are transformed to normal inequalities by utilizing the dominance possibility criterion when compared with two interval-typed triangular fuzzy numbers. Then the equivalent linear programming model is obtained which could be solved by Matlab toolbox. Finally several examples are provided to illuminate the proposed method by comparing with the existing methods and sensitive analysis demonstrates the stability of the optimal solution.

scholarly journals Multiobjective Scheduling of Remote-Area Employees with Minimum Cost of Transportation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Hesham K. Alfares
Keyword(s):  
Programming Model ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Transportation Cost ◽  
Solution Procedure ◽  
Primary Objective ◽  
Remote Work ◽  
Optimal Procedures ◽  
Oil Company ◽  
Cost Of Transportation

An integer programming model and optimal solution procedure are presented for assigning employees to the (10, 14) days-off schedule. This schedule is used by a large oil company to schedule employees in remote work locations. The primary objective is to minimize the total number of employees. Since employees are flown to their remote work sites, the company also aims to minimize transportation cost. Therefore, secondary objectives include (1) minimizing the number of active days-off work patterns, (2) consistently using the same set of active days-off patterns, (3) assigning work schedules fairly among employees, and (4) avoiding the use of specialized optimization solvers. A rotation schedule is used in which two scheduling rules are enforced: a minimum proportion of weekend days off needs to be given and a maximum limit on the number of successive workdays cannot be exceeded. Utilizing the problem structure, simple optimal procedures are developed to solve this unique complex scheduling problem.

Research on Optimization of "Deoxidation Alloying" of Molten Steel Based on Linear Programming

2020 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Anna Li ◽  
Dongqing Xu
Keyword(s):  
Linear Programming ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Molten Steel ◽  
Programming Model ◽  
Linear Regression Analysis ◽  
Optimal Solution ◽  
Principal Component ◽  
Multiple Linear Regression Analysis ◽  
Main Factors

<p>Aiming at the optimization of the supporting solution for molten steel "deoxidation alloying", the cost of "deoxidation alloying" is minimized from an economic perspective. Using Excel, Eviews and spss software programming, through factor analysis, clustering dimension reduction, principal component analysis Multiple linear regression analysis and linear programming optimization analysis, the author found out the main factors that affected the yield of alloy elements. This paper establishes a multiple linear regression mathematical model that affects the main factors of alloy elements and yield. According to the reference alloy price, the linear programming model is adopted to find the optimal solution of alloy ingredients.</p>

scholarly journals A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Farhad Ghassemi Tari
Keyword(s):  
Dynamic Programming ◽  
Programming Model ◽  
Transportation Network ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Solution Algorithm ◽  
Transportation Costs ◽  
Programming Algorithm ◽  
Fixed Cost

The problem of allocating different types of vehicles for transporting a set of products from a manufacturer to its depots/cross docks, in an existing transportation network, to minimize the total transportation costs, is considered. The distribution network involves a heterogeneous fleet of vehicles, with a variable transportation cost and a fixed cost in which a discount mechanism is applied on the fixed part of the transportation costs. It is assumed that the number of available vehicles is limited for some types. A mathematical programming model in the form of the discrete nonlinear optimization model is proposed. A hybrid dynamic programming algorithm is developed for finding the optimal solution. To increase the computational efficiency of the solution algorithm, several concepts and routines, such as the imbedded state routine, surrogate constraint concept, and bounding schemes, are incorporated in the dynamic programming algorithm. A real world case problem is selected and solved by the proposed solution algorithm, and the optimal solution is obtained.

The Improvement of Optimality Test over Possible Reaction Set in Bilevel Linear Optimization with Ambiguous Objective Function of the Follower

2015 ◽  
Vol 19 (5) ◽  
pp. 645-654 ◽  
Author(s):  
Puchit Sariddichainunta ◽  
◽  
Masahiro Inuiguchi
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Linear Optimization ◽  
Convex Polytope ◽  
Optimal Solution ◽  
Global Optimality ◽  
Basic Solution ◽  
Bilevel Linear Programming ◽  
Coefficient Vector ◽  
Optimality Test

Verifying a rational response is the most crucial step in searching for an optimal solution in bilevel linear programming. Such verification is even difficult in a model with ambiguous objective function of the follower who reacts rationally to a leader’s decision. In our model, we assume that the ambiguous coefficient vector of follower lies in a convex polytope and we formulate bilevel linear programming with the ambiguous objective function of the follower as a special three-level programming problem. We use thek-th best method that sequentially enumerates a solution and examine whether it is the best of all possible reactions. The optimality test process over possible reactions in lower-level problems usually encounters degenerate bases that become obstacles to verifying the optimality of an enumerated solution efficiently. To accelerate optimality verification, we propose search strategies and the evaluation of basic possible reactions adjacent to a degenerate basic solution. We introduce these methods in both local and global optimality testing, confirming the effectiveness of our proposed methods in numerical experiments.

A Linear Programming Model for Multiple-use Planning

1975 ◽  
Vol 5 (3) ◽  
pp. 485-491 ◽  
Author(s):  
William A. Leuschner ◽  
John R. Porter ◽  
Marion R. Reynolds ◽  
Harold E. Burkhart
Keyword(s):  
Linear Programming ◽  
Programming Model ◽  
Geographical Location ◽  
Optimal Solution ◽  
Linear Programming Model ◽  
Sensitivity Analyses ◽  
Multiple Use ◽  
Planning Unit ◽  
Wide Range ◽  
Choice Variable

Multiple-use planning is useful in matching forest production possibilities and social desires. A linear programming model for multiple-use planning is presented. Planning is approached as a set of production objectives which have a set of management activities to help achieve them and a set of constraints which limit the management activities. Timber yield is the objective function and other multiple-use objectives are stated as constraints. Production can be increased by certain management activities, but these activities are limited by budget, cutting, and other technical constraints. Size of the area cut is the choice variable and the solution is tied to 21.6-acre (8.74-ha) grid cells thereby identifying the geographical location of management and production activities. The model was tested on a planning unit and sensitivity analyses were performed on the initial optimal solution. These indicated that on this planning unit, there is a wide range of production alternatives which will not affect other multiple-use production possibilities and that production is sensitive to budget changes.

scholarly journals Use of Linear Programming Model to Determine the Optimum Cropping Pattern for an Irrigation Scheme in Masvingo, Zimbabwe

2013 ◽  
Vol 1 (4) ◽  
pp. 450-452
Author(s):  
Majeke F ◽  
Mubvuma S M T ◽  
J. Chirima, K. Makaza ◽  
T. Hungwe R. Gwazan ◽  
Nyoni ◽  
...  
Keyword(s):  
Linear Programming ◽  
Optimization Problems ◽  
Programming Model ◽  
Optimal Solution ◽  
Linear Programming Model ◽  
No Production ◽  
Cropping Pattern ◽  
Irrigation Scheme ◽  
Irrigation Planning ◽  
Optimal Cropping

Agricultural systems are often faced by challenges such as crop selection and irrigation planning which can be formulated as optimization problems. Decisions have to be made on the proper set of crops to be cultivated and a proper irrigation scheme. The objectives of such decisions are to maximize net profit or to minimize water waste. In this study, a linear programming model was developed that helped to determine the optimal cropping pattern for an irrigation scheme in Masvingo, Zimbabwe. Crops which considered were wheat, sugar beans for winter and cotton and maize for summer for the 2012/13 agricultural season. The linear programming model was solved by using Microsoft Excel (2007). The model recommended no production of wheat and cotton. Sugar beans and maize gained acreage by 50 percent and 88 percent respectively. On the whole, the optimal cropped acreage did not change as compared to the existing cropping plan. As a result of the optimal solution, a farmer‘s income could be increased by $1,668.60. The optimal income increased from existing level of $1,919.40 to $3,588.00 showing an improvement of 87 percent. The results show that LP models solutions are worthy implementing.

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