In the extensive literature dealing with the machining economics problem, the optimization of the multistage production system is rarely discussed, and when so it is considered mostly in terms of the Failure Replacement Strategy. However, when analysing this problem, the possibility of using the Opportunistic or Integrated Replacement Strategies also arises. In this work, we minimize the expected cost per unit under three different tool replacement strategies: Failure Replacement, Opportunistic Replacement and Integrated Replacement. For the first strategy, we show that the optimal solution is obtained using a one-dimensional search algorithm. For each of the other two strategies, we develop approximate models that are studied using simulations. These models appear to be very efficient.