Optimization with GAMS: Operations Research Bootcamp A-Z

Explore fundamental concepts of optimization, including objective functions, constraints, linear and nonlinear models, continuous and integer variables, convex versus non-convex problems.

Discover why GAMS, the general algebraic modelling system, translates real-world optimization problems into code and access solvers like IPT, Grau, and B or C flags.

Learn to download and install the Gams modeling system with the free demo license, and complete setup by entering the license after choosing Gams id or studio.

Learn to set up the GAMS IDE, verify licenses, access solvers for linear and mixed-integer problems, manage windows, save models, and locate the GAMS directory.

Explore the basics of linear programming: maximize or minimize a linear objective function under linear constraints with real variables, preparing you to tackle your first LP problem.

Formulate linear programming problem by defining X1 deluxe and X2 regular, maximizing 4X1+3X2 with 2X1+X2 ≤ 60 hours and X1+X2 ≤ 40 square yards of leather, with X1,X2 ≥ 0.

Learn to build a basic GAMS linear programming model by defining variables x1 and x2, setting the objective, formulating equations and constraints, and solving with an LP solver.

Develop a linear programming model to maximize revenue from desks, tables, and chairs using lumber, finishing, and carpentry constraints. Learn to define sets and data ranges for scalable decision variables.

Develop a GAMS linear programming model from sets and parameters to variables, constraints, and a maximized objective, using desks, tables, and chairs data to compute optimal production and costs.

Formulate and solve a transportation linear program to minimize electricity transmission costs from three power plants to four cities, subject to supply and demand constraints, using a sets-based formulation.

Model a two-plant, four-city linear program in GAMS using sets, parameters, variables, and equations from a PIRG data table to obtain an optimal solution.

Review integer programming, including a linear objective function and constraints, and clarify relationships among integer programming, mixed integer programming, and mixed integer linear programming, with notes on branch inbound methods.

Formulate the problem as an integer programming model to maximize weekly profit, using sets and parameters, labor and material constraints, and a big-M binary for fixed machinery costs.

In GAMS, this lecture builds an integer programming model for a production planning problem, defining sets, parameters, variables, and constraints, solved to optimal plan: 25 pants and a 75 profit.

formulate an integer linear programming model to minimize production and salary costs on two production lines, meeting weekly demands for three seed types with up to 30 workers per line.

Explore model development in GAMS by building a mixed-integer program with sets, parameters, data tables, and integer and binary variables, solving to optimal production planning.

Formulate an integer programming model for a five-city traveling salesman problem using a distance matrix, binary decision variables, and a big M auxiliary variable to prevent subtours, minimizing total distance.

minimize distance in a milp challenge using gams by building sets, aliasing i and j, and defining a c i j table with x i j binaries to obtain route.

Explore non-linear programming by optimizing a non-linear objective under non-linear constraints with continuous real variables, and recognize that at least one nonlinear equation characterizes this programming.

formulate a nonlinear programming model to maximize the walkway area between the outer terrace and a central 10 by 18 space, with equal-width walkway and a 250-meter handrail limit.

Model and solve a nonlinear programming problem in GAMS by defining the objective function and constraints, then maximize the walkway using an NLP solver like IPO (demo license).

Formulate a nonlinear programming model to minimize the box perimeter while placing three circles of radii 6, 12, and 16 inside the box without overlap, using coordinates and box constraints.

Learn how to build a GAMS model from scratch by defining variables and an objective, adding linear and nonlinear constraints, and solving with different solvers to compare results.

Formulate a nonlinear programming problem to locate a single warehouse in the plane that minimizes total weighted distance to four customers, using the distance formula and shipments, in gams.

Code a multi-challenge location allocation model in GAMS to place a warehouse by minimizing total distance to customers, using sets, parameters, variables, and constraints.

Introduce mixed integer nonlinear programming. It contrasts with linear programming by using both integer and real variables with linear or nonlinear objectives and constraints.

Formulates a mixed integer non-linear program to maximize profit from oil extraction over two years, with x1 and x2, price 30 - x1 and 35 - x2, under resource constraints.

Develop a GAMS model to maximize profit from oil extraction by defining integer variables, an objective function, and two constraints, and explore mixed integer nonlinear programming with different solvers.

Formulate a mixed integer nonlinear program to minimize the coil spring volume under constant load, selecting wire type and number of springs while meeting stress, length, and deflection constraints.

Develop a GAMS coil compression model by reading Excel data into sets and parameters, then minimize coil volume via a structured objective with wire and coil diameter constraints.

Explore a minlp challenge to design a least-cost centrifugal pump configuration across three levels, lines, and pumps, using discrete binaries and continuous flow fractions under pressure and power constraints.

code and solve a MINLP pump configuration problem in gams, reading data from an excel file, defining sets, parameters, variables, bounds, and constraints, and exporting results to excel.

Explore multi-objective optimization using sequential linear goal programming to balance profit, efficiency, and emissions in a power generation example, including deviation variables and constraint handling.

Learn to code a three-objective optimization in GAMS using sequential linear goal programming, defining sets and variables, three objectives (f1, f2, f3), and staged constraints with priority-driven stages.

Master flow control in optimization models using if, loop, while, and for statements. See dollar-sign forms and if-else structures, index-based loops, and constraint-friendly formulations.

Review the full optimization workflow from understanding the problem to modeling, solving with Gams, and evaluating results. Learn data input, external reporting, multi‑objective handling, and conditional statements, with recommended readings.