Many problems in production planning and supply chain optimization can be modeled as Economic Lot Size problem (ELS). This paper first demonstrates forward and backward algorithms for the economic lot size problem with backlogging, and then applies the two algorithms to analyze the sensitivities of setup cost and demand. The result for setup cost sensitivity is the same as the one described in  for economic lot size problem without backlogging. These analyses are especially useful for online or real-time applications which are common in current E_commerce.
Yi, Feng; Kumar, Arun; and Ozdamar, Linet, "Sensitivity Analysis for Economic Lot Size Problem" (2003). ICEB 2003 Proceedings. 155.