Interpretation of Different Approaches to Sensitivity Analysis in Cash Flow Problem

Abstract

Cash is the driving power of all business and cash-flow statement is one of the major issues of institutions, especially in crisis. Optimal cash-flow plan of a company could be one of the most important indicators of that business's financial health and can be considered as its financial analysts' ability and skill. Linear optimization (LO) is one of the mathematical tools in modeling the cash-flow problem and its rich literature helps analysts to device the optimal one when the situation satisfies the requirements of the LO model. However, the situation is always due to variation and the optimal solution arisen from the LO model have to be analyzed according to measurable variation of input data. Sensitivity analysis and parametric programming is the tool to this analysis. Using the Simplex method to find a basic optimal solution and having multiple optimal solutions is one of the reasons that different solvers lead to different optimal solutions. In these situations, sensitivity analysis may produce confusing results. Moreover, there are different points of views to sensitivity analysis such as optimal basis invariancy, optimal partition invariancy, support set invariancy to name some examples. Here, we briefly review different approaches to sensitivity analysis in LO and a short term cash-flow problem of a dummy institution is modeled as an LO problem. It is shown that the problem has multiple optimal solutions which are degenerate, the situation that usually occurs in practice and causes of ambiguous and unclear results. The confusing results in analyzing the sensitivity of these solutions are highlighted in this example. Then, a strictly complementary optimal solution is provided and its useful interpretation in sensitivity analysis is mentioned in a nutshell. In the sequel, the concept of the results arising in different points of views to sensitivity analysis is analyzed. Keywords: Cashflow Problem; Linear Optimization; Sensitivity Analysis. 2010 Mathematics Subject Classification: 62P05