Formulas - Leeds School of Business
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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