A Single Machine Capacitated Production Planning Problem Under Uncertainty: A Grey Linear Programming Approach

The production planning is an important problem in most of manufacturing systems in practice. Unlike many researches existing in literature, this problem encounters with great uncertainties in parameters and input data. In this paper, a single machine capacitated production planning problem is considered and a linear programming formulation is presented. The production costs are assumed to be uncertain parameters. To handle the uncertainties in the model, the grey systems theory is employed and the concept of grey numbers is incorporated into an optimization framework. In such systems, the uncertain parameters with unknown distributions can be handled by grey numbers. The grey linear programming (GLP) is a development of the classical linear programming which allows uncertainty to be effectively communicated into the optimization process. Finally, the uncertain problem is transformed into a GLP, and is solved by two linear deterministic sub-models.