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 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.

The Gap Function: Evaluating Integer Programming Models over Multiple Right-Hand Sides

2021 ◽  
Author(s):  
Temitayo Ajayi ◽  
Christopher Thomas ◽  
Andrew J. Schaefer
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Optimization Problems ◽  
Programming Model ◽  
Programming Models ◽  
Linear Programming Relaxation ◽  
Gap Functions ◽  
Model Quality ◽  
Right Hand ◽  
The Right

For an integer programming model with fixed data, the linear programming relaxation gap is considered one of the most important measures of model quality. There is no consensus, however, on appropriate measures of model quality that account for data variation. In particular, when the right-hand side is not known exactly, one must assess a model based on its behavior over many right-hand sides. Gap functions are the linear programming relaxation gaps parametrized by the right-hand side. Despite drawing research interest in the early days of integer programming, the properties and applications of these functions have been little studied. In this paper, we construct measures of integer programming model quality over sets of right-hand sides based on the absolute and relative gap functions. In particular, we formulate optimization problems to compute the expectation and extrema of gap functions over finite discrete sets and bounded hyperrectangles. These optimization problems are linear programs (albeit of an exponentially large size) that contain at most one special ordered-set constraint. These measures for integer programming models, along with their associated formulations, provide a framework for determining a model’s quality over a range of right-hand sides.

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.

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>

Simulation and optimization of an experimental membrane wastewater treatment plant using computational intelligence methods

2011 ◽  
Vol 63 (10) ◽  
pp. 2255-2260 ◽  
Author(s):  
T. Ludwig ◽  
P. Kern ◽  
M. Bongards ◽  
C. Wolf
Keyword(s):  
Wastewater Treatment ◽  
Simulation Model ◽  
Computational Intelligence ◽  
Municipal Wastewater ◽  
Optimization Problems ◽  
Treatment Plant ◽  
Simulation Software ◽  
Simulation And Optimization ◽  
Highly Nonlinear ◽  
Computational Intelligence Methods

The optimization of relaxation and filtration times of submerged microfiltration flat modules in membrane bioreactors used for municipal wastewater treatment is essential for efficient plant operation. However, the optimization and control of such plants and their filtration processes is a challenging problem due to the underlying highly nonlinear and complex processes. This paper presents the use of genetic algorithms for this optimization problem in conjunction with a fully calibrated simulation model, as computational intelligence methods are perfectly suited to the nonconvex multi-objective nature of the optimization problems posed by these complex systems. The simulation model is developed and calibrated using membrane modules from the wastewater simulation software GPS-X based on the Activated Sludge Model No.1 (ASM1). Simulation results have been validated at a technical reference plant. They clearly show that filtration process costs for cleaning and energy can be reduced significantly by intelligent process optimization.

scholarly journals Aggregation of spatial units in linear programming models to explore land use options

1996 ◽  
Vol 44 (2) ◽  
pp. 145-162 ◽  
Author(s):  
R.J. Hijmans ◽  
M.K. Van Ittersum
Keyword(s):  
Land Use ◽  
Linear Programming ◽  
Programming Model ◽  
Programming Models ◽  
The European Union ◽  
Objective Functions ◽  
Land Use Allocation ◽  
Policy Level ◽  
Ecological Criteria ◽  
Use Studies

Consequences of aggregating spatial units in an interactive multiple-goal linear programming (IMGLP) model are analysed for a schematized and an existing IMGLP model (GOAL) exploring land use options for the European Union. A discrimination was made between effects on objective functions for the system as a whole, and effects on related optimum land use allocation within the system. In GOAL, effects on land use allocation are more important than effects on the value of objective functions. Several rules or factors were identified that determine the effect of aggregation, among which the degree in curvilinearity in input-output relations and the method of aggregation are important ones. However, because of complicated interacting effects, the aggregation error is difficult to predict. Therefore, in land use studies using IMGLP it is important to first optimize the linear programming model at the non-aggregated level and then aggregate to the appropriate policy level. If aggregation is inevitable because LP models become too big, aggregation according to agro-ecological criteria, i.e., aggregation of units with similar output-input ratios and constraints, results in the smallest errors.

LEXICOGRAPHIC METHOD FOR MATRIX GAMES WITH PAYOFFS OF TRIANGULAR FUZZY NUMBERS

2008 ◽  
Vol 16 (03) ◽  
pp. 371-389 ◽  
Author(s):  
DENG-FENG LI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Programming Models ◽  
Matrix Game ◽  
Triangular Fuzzy Numbers ◽  
Matrix Games ◽  
Lexicographic Method

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology.

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 A Mathematical Programming Model for Vegetable Rotations

1985 ◽  
Vol 17 (1) ◽  
pp. 169-176 ◽  
Author(s):  
Wesley N. Musser ◽  
Vickie J. Alexander ◽  
Bernard V. Tew ◽  
Doyle A. Smittle
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Crop Production ◽  
Programming Model ◽  
Crop Rotations ◽  
Programming Models ◽  
Vegetable Production ◽  
Model Design ◽  
Mathematical Programming Model ◽  
Large Numbers

AbstractRotations have historically been used to alleviate pest problems in crop production. This paper considers methods of modeling rotations in linear programming models for Southeastern vegetable production. In such models, entering each possible crop rotation as a separate activity can be burdensome because of the large numbers of possible rotational alternatives. Conventional methodology for double crop rotations reduces the number of activities but must be adapted to accommodate triple crop rotational requirements in vegetable production. This paper demonstrates these methods both for a simple example and an empirical problem with numerous rotation alternatives. While the methods presented in this paper may have computational disadvantages compared to entering each rotation as a separate activity, they do have advantages in model design and data management.

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