partition is more preferable than taking memory away from a production partition embodiments of the invention are configured for a user to specify priorities for logical partitions based on the user specified priority the hypervisor will then obtain memory from the lower priority partitions in order trying to leave enough memory to satisfy the partition 39 s minimum memory requirements embodiments of the invention are configured for a user to specify coefficients to the partitions to indicate to the hypervisor the relative amount of memory to take from each partition in order to satisfy the hypervisor 39 s memory requirements embodiments of the invention are configured for a user to specify multiple u201c tiers u201d so that partitions in the lowest tier may have all of their memory removed before partitions in the higher tiers are touched embodiments of the invention may be configured to determine the amount of hypervisor memory that is required that is unique to a partition and penalize the partitions in line with their relative use of hypervisor memory for example hpt hardware page tables are allocated in the hypervisor for each partition the size of the hpt will vary depending on the partition 39 s maximum memory size therefore if a system has two partitions and logical partition 1 lpar 1 is using x mb megabytes of memory for hpt space and lpar 2 is using 2 u00d7 mb of memory.