We consider a single-echelon inventory system facing stochastic demand controlled by the standard (r,nQ,T) batch ordering policy. While an exact algorithm for optimizing all three policy variables exists, excessive computational requirements hinder industrial applications, particularly in multi-product environments. Aiming at reducing computation time, we revisit the exact total average cost function. After establishing a new analytical property, we show that the exact ordering cost can be very accurately approximated by two convex functions. Using these, the original problem is decomposed in two separate sub-problems easier to solve. For each sub-problem we establish properties linking each solution with the classical EOQ, which lead to a fast heuristic search algorithm for the policy variables evaluation. Numerical comparisons with both the exact algorithm and two popular meta-heuristics demonstrate the excellent performance of the heuristic in terms of solution quality and run-time.