1. A job execution management apparatus comprising: a receiving unit that receives an allocation request for allocating a plurality of partial jobs formed by segmenting a job to a plurality of data processing apparatuses; a storage unit that stores apparatus function information in which functions executable by the respective data processing apparatuses are defined; an allocation unit that allocates the respective plurality of partial jobs to the data processing apparatuses which are capable of executing the plurality of partial jobs by referring to the apparatus function information according to the allocation request; a setting unit that sets so that, when a partial job is allocated to one of the data processing apparatuses, information for specifying the data processing apparatus allocated to the partial job, start time information for specifying the time when the execution of the partial job is started and end time information for specifying the end time of the execution of the partial job are made correspondence with the partial job; an execution instruction unit that instructs the execution of a partial job to the corresponding data processing apparatus according to the setting of the setting unit; and a reallocation unit, after the instruction from the execution instruction unit, (i) that specifies partial jobs among the partial jobs which are instructed to be executed, the execution of the specified partial jobs being not finished until the times specified by the end time information corresponding to the partial jobs, and (ii) that reallocates at least one of the data processing apparatuses which is capable of executing the unfinished partial jobs, excluding the data processing apparatuses to which the unfinished partial jobs are allocated by the allocation unit, to each of the specified unfinished partial jobs by referring to the apparatus function information, wherein the execution instruction unit instructs the data processing apparatuses reallocated by the reallocation unit to execute the unfinished partial jobs.