The EOQ Model: A Differential Cyclic System for Calculating Economic Order Quantity

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Rabha Ibrahim
Samir Hadid


The EOQ model determines the quantity that minimizes the total sum of all cost functions. We suggest a common structure for economic order quantity type non-linear differential models with costs functions with respect to time in a cyclic period. For this model, we analyze the related optimization problem and develop a relaxed method for determining a bounded interval containing the optimal cycle length. Also for a special class of transportation functions, we study these consequences and introduce algorithms to calculate the optimal size and the corresponding optimal order stage.

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  1. R. W. Grubbstrom, Modelling production opportunities an historical overview, Int. J. Product. Econ. 41 (1995), 1-14.
  2. A Caplin, J. Leahy, John, Economic Theory and the World of Practice: A Celebration of the (S, s) Model, J. Econ. Persp. 24 (1)(2010), 183-201.
  3. B. Malakooti, Operations and Production Systems with Multiple Objectives (2013). John Wiley & Sons.
  4. M.Holmbom, A. Segerstedt, Economic Order Quantities in production: From Harris to Economic Lot Scheduling Problems, Int. J. Product. Econ. 155 (2014) , 82-90.
  5. A. G. Lagodimos, et al., The discrete-time EOQ model: Solution and implications, Eur. J. Oper. Res. 266 (2018) ,112-121.
  6. R. W. Ibrahim, Maximize minimum utility function of fractional cloud computing system based on search algorithm utilizing the Mittag-Leffler sum, Int. J. Anal. Appl. 16(1) (2018), 125-136.
  7. R. W. Harris, How Many Parts to Make at Once, Operat. Res. 38 (6)(1990), 947.
  8. G. Mahata, P Mahata, Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain, Math. Comput. Model. 53 (2011), 1621-1636.
  9. S.G. Ferreira, The existence and uniqueness of the minimum norm solution to certain linear and nonlinear problems, Signal Proc. 55 (1996), 137-139.