In many manufacturing problems, multi-objective optimizations are representative models, as objectives are considered a conflict with one another. In real-life applications, optimizing a specific solution concerning one objective may end up in unacceptable results concerning the other objectives. Many Manufacturing companies operate under uncertainties and this affects the system performance. Stochastic product demand is one of the challenges faced by manufacturing companies and often affects the manufacturing system’s performance and decision-making. Making the proper decisions regarding manufacturing lot-sizing problems is critical for any manufacturer because it makes the firm compete within the market. In this paper, Markov chains in conjunction with stochastic goal programming were used to develop an optimization model for the manufacturing lot size. The over-achievement or under-achievement of the manufacturing lot size was determined by defining the goal constraints, deviation variables, priorities, and objective function. The different states of demand for the product with stochastic demand were represented by states of a Markov chain. Using the applied mathematics solver in MATLAB TM, the optimization model was then solved, determining the quantity of product to be manufactured in a given quarter of the year as demand changes from one state to another.