The effect of discretizing the planning period on the optimal cost of capacity expansion systems

The optimal expansion schedule for building and expanding of water and wastewater treatment facilities is often determined by modelling the capacity expansion system concerned using a dynamic programming model. The model derived is commonly solved by discretizing the planning period into numerous intervals and solved via the discrete dynamic programming technique. The optimum cost obtained will somewhat be affected by the pattern of discretization. This article presents the results of a detailed sensitivity analysis on the effect of discretizing the planning period on the optimal cost derived from the discretized model. Three cases are considered in this study, namely, certain demand with infinite shortage cost, certain demand with finite shortage cost, and uncertain demand. The results of this study indicate that numerical error resulting from discretizing the planning period can be minimized if an appropriate discretization pattern is chosen.