Instance and solution data for 'Models for the Discrete Ordered Median Problem based on DC decomposition'

This dataset accompanies the manuscript 'Models for the Discrete Ordered Median Problem based on DC decomposition'. The paper presents a modeling framework built on the known DC decomposition of ordered median functions and develops new mixed-integer linear programming formulations for the Discrete Ordered Median Problem, a unified model encompassing classical location objectives such as the median, center, and cent-dian.

The dataset includes the complete set of benchmark instances (instances.zip) used in the computational study together with the corresponding solution files (solutions.zip) analyzed in the manuscript. The instance collection is divided into three subcategories: medium-scale random instances, large-scale random instances, and structured instances derived from a dataset by Beasley. The medium- and large-scale random sets each contain 315 instance files and 15 cost matrix files, while the structured Beasley set contains 420 instance files and 20 cost matrix files. All files are provided in JSON format.

Each instance file specifies a complete problem configuration, including the number of potential locations n, the number of facilities p to be opened, a reference to a cost matrix representing client-facility allocation costs, and a λ-type identifier with the corresponding λ-vector of length n, which determines the weights in the ordered median objective function. Instance names follow the convention n{n}_p{p}_{lamb_type}_{cost_matrix_index} (with a "b_" prefix for Beasley instances), uniquely encoding the parameter settings and associated cost matrix. The cost matrix files contain n × n matrices and follow the naming scheme costs_n{n}_{cost_matrix_index} (again with a "b_" prefix for Beasley instances). Each cost matrix is used by multiple instances with different combinations of p and λ-types.

Each solution file records the tested instance and model, as well as the outcome of the optimization process performed with Gurobi. In particular, it includes the instance name ("InstanceName"), model name ("ModelName"), Gurobi optimization status code ("Status"; 2 - OPTIMAL, 9 - TIME_LIMIT, 17 - MEM_LIMIT), time spent optimizing ("Runtime"), best objective value found ("Objective"), best lower bound ("BestBound"), optimality gap as defined in the main manuscript ("Gap"), number of variables ("NbVars"), number of binary variables ("NbBinaryVars"), number of constraints ("NbConstraints"), number of branch-and-bound nodes explored ("BnBNodes"), number of simplex iterations ("SimplexIterations"), number feasible solutions found ("FoundSolutions"), maximum memory in gigabytes allocated during optimization ("MaxMemGBUsed"), number of lazy constraints added ("LazyCuts"), and time spent in custom callback functions ("CallbackTime").