Deterministic Inventory Models

  • Dinesh Shenoy
  • Roberto Rosas


In this chapter, we discuss mathematical models to manage inventory of a single item whose demand is known and is constant. We start our discussion with the most fundamental of inventory models – the Economic Order Quantity (EOQ) model – which assumes that the demand for the item is constant, the order is filled instantaneously, and there are no shortages. We derive an expression for the total annual inventory cost (TIC) comprising the ordering cost, carrying cost, and the cost of procurement, and determine the optimal order quantity that minimizes the TIC. We also discuss computation of the reorder level when lead time is assumed to be constant and known. Later in this chapter, we discuss extensions of the EOQ model to other situations where supply is not instantaneous (i.e., supply is gradual), and another where planned shortages are allowed. Toward the end of this chapter, we also discuss a periodic review model under certainty.


Economic order quantity Total inventory cost Replenishment policy Gradual replenishment Planned shortages 


  1. Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J., & Ohlmann, J. W. (2016). An introduction to management science: Quantitative approaches to decision making (14th ed.). Boston: Cengage Learning.Google Scholar
  2. Gaither, N. (1987). Production and operations management – A problem-solving and decision-making approach (3rd ed.). Chicago: The Dryden Press.Google Scholar
  3. Hillier, F. S., & Lieberman, G. J. (2001). Introduction to operations research (7th ed.). New York: McGraw-Hill.Google Scholar
  4. Jacobs, F. R., & Chase, R. B. (2011). Operations and supply chain management (13th ed.). New York: McGraw-Hill Irwin.Google Scholar
  5. Monks, J. (1987). Operations management – theory and problems. Singapore: McGraw-Hill International Edition.Google Scholar
  6. Muckstadt, J. A., & Sapra, A. (2010). Principles of inventory management: When you are down to four, springer series in operations research and financial engineering. Ithaca: Springer Science.Google Scholar
  7. Nahmias, S. (2005). Production and operations analysis (5th ed.). Boston: McGraw-Hill International Edition.Google Scholar
  8. Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory management and production planning and scheduling (3rd ed.). New York: Wiley.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Dinesh Shenoy
    • 1
  • Roberto Rosas
    • 1
  1. 1.Tecnológico de MonterreyCampus LeónMexico

Personalised recommendations