Researching and solving a bicriteria supply management problem with the given volumes of batches

We consider the supply management problem in which a product is supplied by batches. For all providers, the volumes of these batches are known. The total preference of the supply assignments is maximized and the number of providers for the consumer with a maximum volume of demand is minimized. For other consumers, the upper bounds on a number of providers depend on their demand. The NP-hardness of finding a feasible solution to this problem is shown. A bicriteria model of integer linear programming (ILP) is constructed for the problem under consideration. We showed that the cardinality of a complete set of alternatives (CSA) is polynomial. To search for solutions of CSA, we construct and investigate experimentally the single-criterion model of ILP. A heuristic algorithm for finding solutions close to the Pareto optimal is proposed. It is based on fixing values of a part of integer variables and solving the smaller-dimension ILP problem. This algorithm is implemented using the CPLEX solver. The results of the computational experiment for the heuristic algorithm on random instances are presented.