3.7.16. Assignment

A constraint related to assignment problems (i.e., 𝚔_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝), or a constraint putting a restriction on all items that are assigned to the same equivalence class or on all equivalence classes that are actually used. Usually an equivalence class corresponds to a single value (see, e.g., the 𝚋𝚊𝚕𝚊𝚗𝚌𝚎, 𝚋𝚒𝚗_𝚙𝚊𝚌𝚔𝚒𝚗𝚐, 𝚐𝚕𝚘𝚋𝚊𝚕_𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢, and 𝚜𝚞𝚖_𝚘𝚏_𝚠𝚎𝚒𝚐𝚑𝚝𝚜_𝚘𝚏_𝚍𝚒𝚜𝚝𝚒𝚗𝚌𝚝_𝚟𝚊𝚕𝚞𝚎𝚜 constraints), to an interval of consecutive values (see, e.g., the 𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕, 𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕_𝚊𝚗𝚍_𝚌𝚘𝚞𝚗𝚝, and 𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕_𝚊𝚗𝚍_𝚜𝚞𝚖 constraints) or to all values that are congruent modulo a given number (see, e.g., the 𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚖𝚘𝚍𝚞𝚕𝚘 constraint). The restriction on all items that are assigned to the same equivalence class can for instance be a constraint on the number of items (see, e.g., the 𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚊𝚝𝚕𝚎𝚊𝚜𝚝, 𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚊𝚝𝚖𝚘𝚜𝚝, 𝚐𝚕𝚘𝚋𝚊𝚕_𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢, and 𝚐𝚕𝚘𝚋𝚊𝚕_𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚕𝚘𝚠_𝚞𝚙 constraints) or a constraint on the sum of a specific attribute (see, e.g., the 𝚋𝚒𝚗_𝚙𝚊𝚌𝚔𝚒𝚗𝚐, and 𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕_𝚊𝚗𝚍_𝚜𝚞𝚖 constraints).