We consider an inventory routing problem where a common vendor is responsible for replenishing the inventories of several customers over a perpetual time horizon. The objective of the vendor is to minimize the total cost of transportation of a single product from a single depot to a set of customers with deterministic and stationary consumption rates over a planning horizon while avoiding stock-outs at the customer locations. We focus on constructing a repeatable (cyclic) delivery schedule for the product delivery. We propose a novel algorithm, called the Iterative Clustering-Based Constructive Heuristic Algorithm, to solve the problem in two stages: (i) clustering, and (ii) delivery schedule generation. To test the performance of the proposed algorithm in terms of solution quality and computational efficiency, we perform a computational study on both randomly generated instances and real-life instances provided by an industrial gases manufacturer. We also compare the performance of the proposed algorithm against an algorithm developed for general routing problems.