## How can optimization solvers produce better decisions?

Optimization solvers help improve decision-making around planning, allocating and scheduling scarce resources. They embed powerful algorithms that can solve mathematical programming models, constraint programming and constraint-based scheduling models.

Solvers like IBM CPLEX® Optimizer can find answers for linear programming, mixed integer programming, quadratic programming and quadratically constrained programming problems.

For detailed scheduling problems, IBM offers solvers designed for constraint-based scheduling models. For combinatorial problems such as a configuration or packing issue, you can build constraint programming models to solve them. And you can try the solvers at no charge.

## Types of optimization solvers

#### Linear programming solvers

These mathematical solvers are for decisions where the objective function and constraints have linear relationships and all decision variables can take continuous values in the result.

#### Mixed integer programming solvers

When decisions involve discrete choices, integer programming solvers can be used. The decision variables can take integer values only and some decision variables can take continuous values in the result. For decisions with continuous and discrete choices, use mixed integer programming solvers.

Quadratic programming solvers are used when the objective function has quadratic terms. The quadratic terms can be convex or non-convex. When the decision variables can be either continuous or integer, mixed integer quadratic programming solvers (MIQP) are used.

Solvers like CPLEX can solve problems with convex quadratic constraints as well. These problems can also be formulated as second-order cone programs (SOCPs), including formulations with rotated cones. When the decision variables can be either continuous or integer, mixed integer quadratic constrained programming solvers are used.

#### Constraint programming solvers

Find optimal solutions for combinatorial problems with integer decision variables as well as detailed sequencing and scheduling problems. The constraints can be linear or non-linear. The decision variables in sequencing and scheduling are about resources represented as cumul function and activities represented as interval variables.

## Resources

#### Constraint programming

Solve detailed scheduling problems and combinatorial optimization problems.

#### Prescriptive analytics

Leverage optimization software that can deliver prescriptive capabilities to recommend a best-action plan for complex decisions.

#### Decision Optimization product family

Solve planning and scheduling problems, using modeling tools and solvers to make better business decisions.