Methods for obtaining estimates and bounds on computational effort in the Accelerated bound-and-scan algorithm are presented. The basic tools of analysis used are various results from the theory of partitions of numbers, and central-limit theorem, and geometric interpretations of the algorithm. The results of the analysis are used to provide partial answers to questions such as a What is the greatest amount of time the algorithm could require to solve a given problem. b What is the expected computation time. c How should the variables and constraints be ordered. d How does the computation time depend on the number of variables. and E How is the computation time affected by the quality of the starting solution.