The numerical assessment of path planning for an autonomous robotic vacuum cleaner using an ant colony optimization method

Abstract

Wu and Ouyang (Production Planning & Control, Vol. 14 (2003), No. 6, pp.555–561) derived the integrated vendor-buyer system with shortages using algebraic method to determine the optimal replenishment policy. In this note, we will off er both basic inequalities, arithmetic-geometric mean inequality (AGM) and Cauchy-Bunyakovsky-Schwarz inequality (CBS), to derive both the optimal buyer's lot size and backorder level under the integrated total cost per unit time of the vendor and buyer minimized. Without the method of completing perfect square, the proposed methods derive the global minimum of the integrated total cost per unit time of the vendor and buyer more easily than the algebraic approach used by Wu and Ouyang (2003).