Just-in-Time (JIT) production systems have initially appeared in the Japanese manufacturing environment due to the scarcity of their critical resources. The main aim in JIT production systems is to eliminate waste. To achieve this objective, setup times, lead times, in-process inventories, and defective production must all be minimized. In the design process of a JIT production system, several factors such as lot size, number of kanbans, unit load size, and buffer capacities must be taken into account. In this study, a mathematical model is developed for a single-item, single-line, multi-stage, and multi-period JIT production system. The original model is nonlinear in both objective function and constraints. To reduce the computational difficulties, the nonlinear model is then approximated by a linear model. Next, a simulation model is developed to incorporate the stochastic nature of the demand. A sensitivity analysis is performed on unit load size and on buffer capacity under different demand patterns to examine their effects on the behavior of the model. The results show that thofee unit load size values exceeding 10 percent of the maximum demand in the planning horizon have no effect on the model.