3.7.15. 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 effectively used. Usually an equivalence class corresponds to one 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).