1. An information processing system comprising: a plurality of information processing apparatuses; and a management device that manages placement of a job that is processed by one of the information processing apparatuses to the one of the information processing apparatuses, wherein the management device includes an information acquiring unit that acquires information related to each of a plurality of jobs that are submitted in a predetermined time period, a weight calculating unit that calculates the degree of influence due to a frequency of appearance or an occupied time period for each of shapes of the jobs, by multiplying a product of a percentage of a number of the jobs and a predetermined coefficient by an occupancy of an execution time period of each of shapes of the jobs, the predetermined coefficient being statistically calculated on the basis of a result obtained by submitting a specific job to the information processing system and executing the specific job, and the weight calculating unit calculates the frequency of submission for each of shapes of the jobs in the predetermined time period, a shape determining unit that determines, as pre-placement target shapes, shapes of a predetermined number of jobs in the order the degree of influence is high, a pre placement table computing unit that determines, on the basis of the pre-placement target shapes and the degree of influence, pre placement of the jobs that is a way of placing the jobs to one of the information processing apparatuses, and a job placement unit that allocates a job, when the shape of a submitted job matches one of the pre-placement target shapes, the submitted job to the one of the information processing apparatuses in accordance with the pre placement.