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Mathematical Problems in Engineering
Volume 2017, Article ID 4391970, 9 pages
Research Article

Mathematical Model of Inventory Policy under Limited Storage Space for Continuous and Periodic Review Policies with Backlog and Lost Sales

1School of Manufacturing Systems and Mechanical Engineering, Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani 12121, Thailand
2Department of Agro-Industrial Technology, Faculty of Agro-Industry, Kasetsart University, Bangkok 10900, Thailand

Correspondence should be addressed to Jirachai Buddhakulsomsiri;

Received 31 May 2017; Accepted 25 October 2017; Published 10 December 2017

Academic Editor: Thomas Hanne

Copyright © 2017 Kanokwan Singha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper involves developing new mathematical expressions to find reorder point and order quantity for inventory management policies that explicitly consider storage space capacity. Both continuous and periodic reviews, as well as backlogged and lost demand during stockout, are considered. With storage space capacity, when on-hand inventory exceeds the capacity, the over-ordering cost of storage at an external warehouse is charged on a per-unit-period basis. The objective is to minimize the total cost, consisting of ordering, shortage, holding, and over-ordering costs. Demand and lead time are stochastic and discrete in nature. 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. Due to the complexity of the developed mathematical expressions, the problems are solved using an iterative method. The method is tested with problem instances that use real data from industry. Optimal solutions of the problem instance are determined by performing exhaustive search. The proposed method can effectively find optimal solutions for continuous review policies and near optimal solutions for periodic review policies. Fundamental insights about the inventory policies are reported from a comparison between continuous review and periodic review solutions, as well as a comparison between backlog and lost sales cases.