Aggregate production planning (APP) that is an important concept of supply chain management (SCM), is one of the tools to determine production rates, inventory levels, and workforce requirements for fulfilling customer demands in a multi-period setting. Traditional APP models employ a single objective function to optimize monetary issues only. In this paper, we present a multi-objective APP model to analyze economic, social, environmental, and cultural pillars inclusively; moreover, each pillar includes several sub-pillars in the model. The resulting model includes an accurate representation of the problem with binary and continuous variables under sustainability considerations. We illustrate the effectiveness of the model in an appliance manufacturer and solve the problem using an exact solution method for multi-objective mixed-integer linear programs (MOMILP). We find a large number of the non-dominated (ND) points in the objective function space and analyze their trade-offs systematically. We show how this framework supports multiple criteria decision-making process in the APP problems in the presence of sustainability considerations. Our approach provides a comprehensive analysis of the ND points of sustainable APP (SAPP) problems, and hence, the trade-offs of objective functions are insightful to the decision makers.