This paper presents quadratic programming models of memory conflict in multiprocessor systems where main memory consists of a set of memory modules common to all processors. Two jobs (programs) are said to be in conflict, or subject to memory conflict, whenever at a given time portions of them must be executed in the same memory module by different processors. We are interested in minimizing the total conflict by the proper assignment of jobs to main memory. Two allocation models are considered: one in which the jobs-to-memory assignment is to be made independent of any particular processors-to-jobs schedule, that is, expected memory conflict is to be minimized over the space of all schedules; and the second in which a definite processor schedule is assumed to be available. For both models, algorithms are formulated for the assignment of jobs to memory.