We load and solve a 2x2 linear program

This example shows how to solve LP and MIP models.

This example shows how to read and write from and to MPS and LP files. Both formats are standard formats and can be input into most optimization solvers. While the MPS file preserves the order of the columns of a matrix, the LP format is more human-readable and suitable for debug purposes.

Learn about setting controls of Xpress

Query Attributes of Xpress

Add a new row and an indicator constraint

This example shows how to collect data about solution process using callbacks.

Formulate a quadratic optimization problem in Xpress

We formulate and solve Sudoku puzzles as binary optimization problems.

Incremental modelling of different Sudoku variants of increasing difficulty

In this example, we show how to use the FICO Xpress R-interface to model and solve the famous Travelling Salesperson Problem (TSP). The TSP is the classic combinatorial optimization problem to find the shortest so-called tour through a complete graph.

This example is a classical maximum flow problem. There are 2 reservoirs, 3 cities and 5 pumping stations. The three cities are supplied from the two reservoirs. All the 10 nodes are connected by a network of pipes, and we want to determine the maximum flow in this network to see whether the demands can be satisfied entirely.

In this example, 16 boxes are required to be loaded into 3 railway wagons each with capacity of 100 quintals. This example is similar to the bin packing problem, but instead of minimizing the number of bins used, here we would like to minimize the heaviest wagon load. This example also shows how to add a user solution found by a simple greedy heuristic.

A private telephone company exploits a network (shown below) among five cities and the edge labels represent the capacities of the link in terms of circuits. The capacity of an edge is consumed in increments of a bidirectional circuit and we do not consider any directed flows. Faced with demands for circuits, the company wants to know whether it is possible to satisfy the demands entirely. If it is not possible, the company wants to transmit as much as possible.

A company produces 6 types of glasses and wishes to plan its production for the next 12 weeks. We want to decide the quantities of each product to produce in each week to minimize total cost of production and storage.

This example simulates the situation where we are buying a required number of items and we get discounts incrementally, and we want to minimize the total cost. This is a problem suitable to be modeled with SOS2 since we can express the cost as a piecewise linear function of the number of items bought. For SOS2 formulation, please refer to the file 'approx.R'. In this file we model the incremental price breaks using binary variables.

This example concerns the optimal composition of investment portfolios according to maximum total return. We modify the problem several times by changing variable types or right hand sides.

In this example, we find an optimal schedule of jobs to different machines with different durations. The schedule must preserve the order in which the jobs need to be processed if only a single job can be run on a machine non-preemptively, i.e., without interrupting the job and picking it up later. The goal is to minimize the completion time of all jobs.

A crew consists of two pilots. Pilots are assigned to crews based on their language and aircraft skills. Two such matching problems are solved. The first is to determine whether there exists a perfect matching, i.e., one that assigns all pilots to some crew. The second problem is to find a perfect matching that maximizes a total crew score.

A timetabling problem for college courses under various constraints.

An introductory examples that shows how to model a production problem with 2 products and 2 resource constraints

We would like to find a minimum cost plan for moving rental cars between agencies to satisfy all the requirements.

We model a piecewise linear function with an SOS2 constraint

In this example, we model an infeasible linear programming problem. For analyzing the infeasibility, we use IIS detection of the Xpress Optimizer.

We solve a simple 2x2 LP problem to optimality, which serves as a showcase for basis handling methods and sensitivity analysis.

We showcase how to use the tuning capabilities with a default or custom tuner method.

This example tries to construct a production plan which meets four different goals in order of priority.