Multi-item, multi-period production systems are prevalent in traditional production and distribution settings. A dynamic lot size production scheduling model (DLSPM) for multi-Production/inventory item multi-period production system with parallel machines is proposed in this paper. A mathematical framework that extends the DLSPM to multi-Production/inventory item-multi-period production planning constrained by storage space was built. The criteria of DLSPM explore optimal production schedule with the constraints of inventory, backlogs, production and demand to minimize the total inventory costs over finite planning horizon. Demand analogous to a typical production environment considered includes dynamic deterministic and fuzzy demand. The model was tested with both deterministic and fuzzy demand spread over ten years, for five equal planning periods, with a two Production/inventory item and two parallel machine test bed. From the various demand types, several iterations (sub problems) were generated and optimality condition was then verified. To capture the imprecision that is often inherent in the estimated future demand, demand was specified by fuzzy numbers and modeled using the triangular membership function distribution. Centre of gravity defuzzification scheme was used within finite intervals to obtain defuzzified demand. Tora Operations Research software was used to run the model using a test problem. Computational results vindicate the robustness and flexibility of the approach based on the quality of the solutions obtained.