DOI: 10.14457/tu.the.2017.328
title: An algorithm to determine (R, Q) parameters for independent products in a distribution network with limited storage space

description: This research presents an algorithm development to find optimal solution of inventory policy parameters: order quantity (Q) and reorder point (R) for a single product in a decentralized distribution center. The study explores the problem that explicitly considers when the storage space is limited. Product demand, lead time, and cost data are from a case study distribution center (DC) in Thailand. The DC manages hundreds of products, that are characterized in terms of their movement (fast, medium, slow) and levels of demand variation. These products are assumed to be managed independently, which makes the multiple product problem becomes many single product problems. The DC operates under an information decentralized system, i.e. sales data at the retailers are not shared with the case study DC. In other words, the DC uses replenishment orders from retail stores as their demands. The incoming lead time from the manufacturer is discrete and time varying. With the lack of real time inventory control system, the DC implement (R, Q) policy for each item. The challenge is to properly set the parameters of the inventory policy for each product to minimize the total inventory management cost, consisting of ordering cost, inventory holding cost, shortage cost (backordering cost), and over-ordering cost. The over-ordering cost is a cost component that incurs at an external rent warehouse. This cost is charged on a per-unit-per-time basis. It is caused by the DC placing a replenishment order that is too large such that the inventory on-hands at the beginning of a replenishment cycle exceeds the available storage space. In the first part of this study, the problem is considered while assuming that there are sufficiently available storage space. Five methods with different degrees of computational requirement are implemented to find the (R, Q) solution. The purpose is to identify an appropriate method to find an initial solution for the problem that later explicitly considers storage space. An empirical distribution is used to model the demand during varying lead time (DDLT) due to the lack-of-fits of widely used probability distributions to the DDLT data. With the use of empirical distribution, the demand during varying lead time is modeled using an empirical distribution so that the findings are not subject to assumptions of demand and lead time probability distributions. A computational experiment on the case study products is performed, where method performance is evaluated through simulation. Statistical analysis of the results is conducted to identify the most effective methods to determine the inventory policy parameters. The results indicates that an iterative method is effective and appropriate.Then, new mathematical expressions to (R, Q) solution under limited storage space capacity are developed. Due to the complexity of the developed mathematical expressions, the mathematical expressions are solved using an iterative method adopted from the previous test. The developed iterative method is tested with real product data from the case study DC. To verify that the method can find the optimal solutions, an exhaustive search that is highly time consuming is performed to find optimal solutions. Comparison of the results shows that the developed method can effectively find optimal solutions with much less computational time.