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").本数据集配套于题为《基于DC分解的离散有序中位数问题模型》的学术论文。该论文提出了一套基于有序中位数函数DC分解（DC decomposition）的建模框架，并针对离散有序中位数问题（Discrete Ordered Median Problem）开发了全新的混合整数线性规划模型。该问题是涵盖中位数、中心以及中心平均（cent-dian）经典选址目标的统一模型。 本数据集包含了该论文计算实验中使用的全部基准测试实例（instances.zip）与对应求解结果文件（solutions.zip），二者均在论文中得到分析与讨论。该实例集分为三个子类别：中等规模随机实例、大规模随机实例，以及源自Beasley数据集的结构化实例。其中中等、大规模随机实例集各包含315个实例文件与15个成本矩阵文件，而Beasley结构化实例集则包含420个实例文件与20个成本矩阵文件。所有文件均采用JSON格式存储。 每个实例文件完整定义了问题配置，包括潜在选址点数量n、待开放设施数p、代表客户-设施分配成本的成本矩阵引用，以及长度为n的λ型标识符与对应的λ向量，该向量用于确定有序中位数目标函数中的权重。实例命名遵循格式n{n}_p{p}_{lamb_type}_{cost_matrix_index}（Beasley实例需添加前缀b_），可唯一编码参数设置与关联的成本矩阵。成本矩阵文件为n×n矩阵，命名格式为costs_n{n}_{cost_matrix_index}（Beasley实例同样需添加前缀b_）。每个成本矩阵可被不同p与λ类型组合的多个实例复用。 每个求解结果文件记录了测试实例、所用模型，以及通过Gurobi完成的优化流程结果。具体包含以下字段：实例名称（"InstanceName"）、模型名称（"ModelName"）、Gurobi优化状态码（"Status"；2表示最优解，9表示超时，17表示内存超限）、优化耗时（"Runtime"）、求得的目标值（"Objective"）、最优下界（"BestBound"）、主论文中定义的最优性间隙（"Gap"）、变量总数（"NbVars"）、二进制变量数（"NbBinaryVars"）、约束总数（"NbConstraints"）、探索的分支定界节点数（"BnBNodes"）、单纯形迭代次数（"SimplexIterations"）、求得可行解数量（"FoundSolutions"）、优化过程中分配的最大内存（单位为吉字节，"MaxMemGBUsed"）、添加的惰性约束数（"LazyCuts"），以及自定义回调函数耗时（"CallbackTime"）。