A light robust model for aggregate production planning with consideration of environmental impacts of machines

In the present study, a multi-period multi-product aggregate production planning model is developed under uncertainty, considering some important aspects of real-world production systems. In order to apply environmental concerns and control the pollution arising from machines, environmental improvement planning is included as a periodic decision variable. Also, the pollution caused by the production is restricted to an allowable level. A light robust optimization approach is employed in which demands and processing times of operations are uncertain parameters. An illustrative example is presented to demonstrate the model validity and some test problems are designed to analyze the impact of uncertainty on the objective function. Several sensitivity analyses are carried out to provide useful managerial insights.