Satisficing Solutions to Infeasible Set Partitions

A mathematical model to identify satisficing solutions to infeasible set partitions is introduced. The set-partitioning model has been of interest to the location analyst, since it is the basis of a number of spatial problems. This model incorporates the concept of natural slack in a way that permits the decisionmaker to approximate a spatial partition from one of two satisficing directions. One direction identifies the solution which guarantees full demand coverage while minimizing partition overlap. The other identifies the solution which maintains strict partition integrity while minimizing total demand not included in a partition. The first approach yields a set-covering solution and the second yields a set-packing solution. Consequently, the relationships among set covering, set packing, and set partitioning are demonstrated for infeasible spatial partitions. Additionally, a sample problem is presented to illustrate these relationships and the potential of the formulation for use in multiobjective locational analysis is discussed.