It is readily observed that the habitat of many biological species often undergoes some periodic changes because of the such effects as seasoning variations. On the other side, lots of ecological studies show that the vital parameters of an individual are closely connected with its body size, such as mass, length, surface area, volume, etc. Motivated by these considerations, we in this paper investigate an exploitation problem of renewable biological resources incorporating the individual's size-structure and periodical changes into the population model. Firstly we propose an integro-partial system to describe the population dynamics, in which the mortality, fertility, growth rate and harvesting effort are time-periodic functions and the boundary condition (i.e. renewal equation) is of global feedback form. Then we treat the well-posedness problem of the state system. By means of characteristics an integral equation is established for the population fertility, which is put into an abstract framework in a suitable space of functions. Roughly speaking, the model will be well posed if the reproducing number is less than one. Secondly we prove the existence of optimal policies via a maximizing sequence and a use of Mazur's theorem in convex analysis. Following that is a careful derivation of necessary optimality conditions, which is finished by tangent-normal cones and adjoint system techniques, and provide an exact description for the optimal strategies. Excluding the singular cases enable us to assert that optimal controllers are unique and take the form of bang-bang, but we cannot expect an explicit formula for them due to complexities. Finally, we present an algorithm to compute the optimal group and test it with an example.