Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2653–2663 | Cite as

A Generalized Economic Order Quantity Inventory Model with Shortage: Case Study of a Poultry Farmer

  • Amir Hossein Nobil
  • Amir Hosein Afshar Sedigh
  • Leopoldo Eduardo Cárdenas-BarrónEmail author
Research Article - Systems Engineering


We consider an EOQ inventory model for growing items, wherein the value and size of items increase during time, some instances of these items are livestock, fish, and poultry. The main difference between this inventory system and older ones is weight increment of products during stocking without buying more. This paper studies an inventory system of poultries that new-born items are fed to reach the ideal weight for consumers. In this study, based on the consumers’ preference of fresh foods over frozen items, we assume that shortage is permitted and consumers wait for fresh items when company pays some additional penalties, i.e., the shortage is fully backordered. On the other hand, for each cycle, the producer must prepare the place in terms of hygiene conditions; thus, a setup time per cycle is considered. The aim of this study is to obtain optimum system solution, such that total costs, including setup, purchasing, holding, feeding, and shortage, are minimized. To do so, we employ mathematical measures to approximate growing rates and model the system as a non-linear programming. To solve the obtained optimization model, we employ hessian matrix to obtain optimal solution for this inventory system. The proposed EOQ inventory model helps poultry industries in Iran to optimize their system considering costs and permissible shortage, and it can be employed in other countries. Finally, we provide a numerical example and its sensitivity analysis, plus some potential future directions.


Inventory management Economic order quantity Growing items Non-linear programming Permissible shortage Poultry 


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Faculty of Industrial and Mechanical Engineering, Qazvin BranchIslamic Azad UniversityQazvinIran
  2. 2.Department of Information ScienceUniversity of OtagoDunedinNew Zealand
  3. 3.School of Engineering and SciencesTecnológico de MonterreyMonterreyMexico

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