Gams Fundamentals Course

The GAMS (General Algebraic Modeling System) Fundamentals course is designed to introduce users to the basics of GAMS, a high-level modeling system for mathematical optimization problems. GAMS is widely used in various fields, including economics, finance, energy, and logistics, to solve complex optimization problems. In this course, students will learn the fundamental concepts and techniques of GAMS, including how to formulate and solve linear and nonlinear optimization problems.

Introduction to GAMS

GAMS is a powerful modeling system that allows users to formulate and solve large-scale optimization problems. It provides a high-level modeling language that is easy to learn and use, making it accessible to users with limited programming experience. GAMS has a wide range of applications, including optimization problems in economics, finance, energy, and logistics. The GAMS system consists of three main components: the GAMS modeling language, the GAMS compiler, and the GAMS solver.

The GAMS modeling language is used to formulate optimization problems, while the GAMS compiler translates the model into a format that can be solved by the GAMS solver. The GAMS solver is responsible for finding the optimal solution to the optimization problem. GAMS supports a wide range of solvers, including linear programming, nonlinear programming, and mixed-integer programming solvers.

GAMS Modeling Language

The GAMS modeling language is a high-level language that is used to formulate optimization problems. It provides a wide range of features, including variables, equations, and constraints, that can be used to model complex optimization problems. The GAMS modeling language is easy to learn and use, making it accessible to users with limited programming experience.

Some of the key features of the GAMS modeling language include:

• Variables: GAMS provides a wide range of variable types, including scalar, vector, and matrix variables.
• Equations: GAMS provides a wide range of equation types, including linear and nonlinear equations.
• Constraints: GAMS provides a wide range of constraint types, including linear and nonlinear constraints.

GAMS Solvers

GAMS provides a wide range of solvers that can be used to solve optimization problems. These solvers include linear programming, nonlinear programming, and mixed-integer programming solvers. Each solver has its own strengths and weaknesses, and the choice of solver will depend on the specific optimization problem being solved.

Some of the key solvers available in GAMS include:

• Cplex: A linear programming solver that is widely used in industry and academia.
• Conopt: A nonlinear programming solver that is widely used in industry and academia.
• Gurobi: A mixed-integer programming solver that is widely used in industry and academia.

GAMS Solver Options

GAMS provides a wide range of solver options that can be used to customize the solution process. These options include the ability to specify the solver, the optimization algorithm, and the convergence tolerance.

Some of the key solver options available in GAMS include:

• Solver: The solver to be used to solve the optimization problem.
• Optimization Algorithm: The optimization algorithm to be used to solve the optimization problem.
• Convergence Tolerance: The convergence tolerance to be used to determine when the optimization problem has been solved to a satisfactory level of accuracy.

Formulating Optimization Problems in GAMS

Formulating optimization problems in GAMS involves using the GAMS modeling language to define the variables, equations, and constraints that make up the optimization problem. This can be a complex process, especially for large-scale optimization problems.

Some of the key steps involved in formulating optimization problems in GAMS include:

• Defining the Variables: The variables are the unknowns in the optimization problem, and must be defined using the GAMS modeling language.
• Defining the Equations: The equations are the relationships between the variables, and must be defined using the GAMS modeling language.
• Defining the Constraints: The constraints are the limitations on the variables, and must be defined using the GAMS modeling language.

Example Optimization Problem

An example optimization problem is the transportation problem, which involves finding the optimal way to transport goods from a set of sources to a set of destinations. This problem can be formulated in GAMS using the following code:

Sets
    i   “sources” / 1*3 /
    j   “destinations” / 1*3 /
;

Variables
    x(i,j) “transportation quantities”
;

Equations
    obj   “objective function”
    supply(i) “supply constraints”
    demand(j) “demand constraints”
;

obj..      sum((i,j), x(i,j)) =e= 100;
supply(i).. sum(j, x(i,j)) =l= 50;
demand(j).. sum(i, x(i,j)) =g= 50;

Model transport / all / ;

Solve transport using lp minimizing obj;