The paper is devoted to theoretic and numeric investigation of a nonlinear integral equation with an unknown function in the upper limit of integration. This equation appears in optimal replacement problems of engineering and production economics. Its solution is essential for finding the optimal policy of equipment replacement under technological advances. Solvability and qualitative dynamics of the solution are analyzed. Computational algorithm for solving the equation is constructed. A numeric example illustrates the obtained results. © 2008 Elsevier Inc. All rights reserved.