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

Published: 23 April 2026| Version 1 | DOI: 10.17632/chjvbjvfjk.1
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Description

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").

Files

Steps to reproduce

The considered values of n in the random instance sets are 20, 30, 50 (medium-scale instances) and 100, 150, 200 (large-scale instances). For the Beasley instances, n takes values 50, 100, 150, and 200. Given an instance size n, the parameter p is set to floor(n/4), floor(n/3), or floor(n/2). The λ-vectors can be generated with the generate_lamb.py script by providing the corresponding λ-type string. For the medium- and large-scale random instances, the n × n cost matrices c contain randomly generated entries in the interval [100, 1000], rounded to two decimal places. The structured cost matrices were derived from the Beasley dataset, as described in the manuscript. In both the random and structured instance sets, five cost matrices are considered for each value of n. An instance is fully defined by the combination of n, p, λ, and c. To obtain the solution information, each generated instance must be solved with the formulations from the manuscript, using the same Gurobi version (12.0.3) and settings reported there. The experiments were run on AMD EPYC 9454 processors on the bwUniCluster system.

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Categories

Combinatorial Optimization, Facility Location

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