The manufacturer of construction materials, which is the subject of this study, plans production and produces the materials based on the required delivery date after it receives an order from a construction company (customer). However, the progress of a construction project may be delayed due to bad weather, shortage of personnel, etc., and the construction company may request the manufacturer to postpone the delivery date of the order. The manufacturer of construction materials has no choice but to accept this request, which causes the material manufacturers to store the inventory of finished products from the day production finished to the postponed delivery date, resulting in an increase in storage costs. In order to solve this problem, this study examines the introduction of a Pull production system that is different from the current production system (Push production system). In this study, the author analytically calculated a mathematical formula (decision formula) to determine which type of production system is capable of reducing inventory more easily and numerically verified it. In addition, the relationship between the factors that affect the choice of production system (postponed delivery term, demand distribution, production lead time, production cycle time, and safety coefficient) was clarified using the proposed formula in this study. Furthermore, the author compared his formula with the results of numerical simulations conducted in existing studies. Using the formula proposed in this study, it is possible to easily calculate which production system is capable of reducing the expected value of inventory simply applying a spreadsheet software commonly used in business practice. © 2022 Japan Industrial Management Association. All rights reserved.