Formulas - University of Colorado Boulder



Chapter 10: Notation

Single product

|Cycle inventory = |Q/2 |

|Average flow time = |(average inventory)/(average demand) |

|Holding cost H = |hC |

|Annual material cost = |CD |

|Annual order cost = |(D/Q)S |

|Annual holding cost = |(Q/2)H |

|Optimal lot size Q* = |SQRT((2DS)/H) |

|Optimal order frequency n* = |D/Q* = SQRT((DH)/2S) |

|Order cost given a desired lot size S = |(H(Q2))/2D |

Multiple products

|Combined fixed order cost S* = |S + ∑for each product i si |

|Annual order cost = |nS* |

|Annual holding cost = |∑for each product i (DiHi)/(2n) |

|Optimal order frequency n* = |SQRT((∑for each product i (DiHi))/(2S*)) |

Chapter 11: Formulas

|Expected lead time demand DL = |LD |

|Standard dev. of lead time demand (L = |SQRT(L)(D |

|(when lead time is constant) | |

|Standard dev. of lead time demand (L = |SQRT(L((D2) + D2(sL2)) |

|(when lead time is uncertain) | |

|Cycle service level CSL = |F(ROP, DL, (L) |

|Reorder point ROP = |F-1(CSL, DL, (L) |

|Safety inventory ss = |ROP – DL also Fs-1(CSL)(L |

|Fill rate fr = |1 – ESC/Q |

Chapter 12: Formulas

|Cost of overstocking Co = |c – s |

|Cost of understocking Cu = |p – c |

|Optimal cycle service level CSL* = |(p – c)/(p – s) also Cu/(Cu + Co) |

|Optimal order size O* = |F-1(CSL*, (, () |

Chapter 14: Formulas

|Optimal cycle service level CSL* = |(p – c)/(p – b) |

|(under buyback contract) | |

|Optimal cycle service level CSL* = |((1 – ()p – c)/((1 – ()p – s) |

|(under revenue sharing contract) | |

Chapter 15: Formulas

|Optimal price for each segment i pi = |Ai/(2Bi) + c/2 |

|Capacity for higher price segment CH = |F-1(1 – (pL/pH), DH, (H) |

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