Двоетапна транспортна задача та її AMPL-реалізація
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Date
2018
Authors
Стецюк, Петро
Ляшко, Володимир
Мазютинець, Габріела
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Abstract
Наведено формулювання двоетапної транспортної задачі закритого типу та обґрунтовано
умови, за яких система лінійних обмежень задачі є несумісною. Ці умови використано під час розробки AMPL-коду для розв’язання задачі за допомогою сучасного програмного забезпечення для
задач лінійного програмування. Наведено демонстраційний приклад із результатами розрахунку за
допомогою програми gurobi NEOS-сервера.
The paper discusses the two-stage transportation problem of the closed type and investigates its properties. The problem is connected with finding an optimal plan for transportation of products from suppliers to consumers, using intermediate points. The formulation of the two-stage transportation problem is presented in the form of a linear programming problem, and the conditions under which the system of linear constraints is incompatible are substantiated. These conditions are connected with checking that the total quantity of products from suppliers does not equal the total quantity of products that consumers need. It is convenient for using an AMPL check operator to determine when the two-stage transportation problem has no solution. The AMPL code for solving the two-stage transportation problem with the help of up-to-date software for linear programming problems is offered. To describe the AMPL model, the code uses a check operator which stops the process of solving the two-stage transportation problem if the linear constraint system is incompatible. Otherwise an optimal plan for the transportation of products is printed, which can be found with the help of any program for solving the linear programming problem. A demonstration example with the results of the calculations using the gurobi program from the NEOS server is presented. The demonstration example involves the supply of products from three suppliers to five consumers, using only two intermediate points. The AMPL code to describe the input data of the demonstration example is given, and the output files of the program gurobi for two cases are presented: (1) when the check operator allows not to interrupt the process of solving the problem; (2) when the check operator reports the incompatibility of the system of linear equations. An optimal plan for transportation of products found by the program gurobi for the demonstration example is graphically illustrated. The developed AMPL code can be used in the study of academic disciplines for graduates of the specialities “Computer Science” and “Software Engineering” and students of economic departments. Its modifications for the two-stage transportation problem can be used by students of higher educational institutions to develop their own software projects related to the theory and methods of optimization.
The paper discusses the two-stage transportation problem of the closed type and investigates its properties. The problem is connected with finding an optimal plan for transportation of products from suppliers to consumers, using intermediate points. The formulation of the two-stage transportation problem is presented in the form of a linear programming problem, and the conditions under which the system of linear constraints is incompatible are substantiated. These conditions are connected with checking that the total quantity of products from suppliers does not equal the total quantity of products that consumers need. It is convenient for using an AMPL check operator to determine when the two-stage transportation problem has no solution. The AMPL code for solving the two-stage transportation problem with the help of up-to-date software for linear programming problems is offered. To describe the AMPL model, the code uses a check operator which stops the process of solving the two-stage transportation problem if the linear constraint system is incompatible. Otherwise an optimal plan for the transportation of products is printed, which can be found with the help of any program for solving the linear programming problem. A demonstration example with the results of the calculations using the gurobi program from the NEOS server is presented. The demonstration example involves the supply of products from three suppliers to five consumers, using only two intermediate points. The AMPL code to describe the input data of the demonstration example is given, and the output files of the program gurobi for two cases are presented: (1) when the check operator allows not to interrupt the process of solving the problem; (2) when the check operator reports the incompatibility of the system of linear equations. An optimal plan for transportation of products found by the program gurobi for the demonstration example is graphically illustrated. The developed AMPL code can be used in the study of academic disciplines for graduates of the specialities “Computer Science” and “Software Engineering” and students of economic departments. Its modifications for the two-stage transportation problem can be used by students of higher educational institutions to develop their own software projects related to the theory and methods of optimization.
Description
Keywords
двоетапна транспортна задача, задача лінійного програмування, мова моделювання AMPL, NEOS-сервер, стаття, two-stage transportation problem, linear programming problem, AMPL, NEOS server, gurobi
Citation
Стецюк П. І. Двоетапна транспортна задача та її AMPL-реалізація / Стецюк П. І., Ляшко В. І., Мазютинець Г. В. // Наукові записки НаУКМА. Комп'ютерні науки. - 2018. - Т. 1. - С. 14-20.