<p> Excel formulas for van Ryzin’s inventory paper by Nils Rudi</p><p>When one deals with large number of SKU’s (end products), it is not very convenient to look up in the table of the Van-Ryzin note each time to go from L(z) to z (or from z to L(z). To ease the HP assignment (as well as supply you with better tools if you want to apply this methodology at your work) I have made Excel Macros/formulas to do these calculations directly. </p><p>To make sure that it works, try a few numbers and compare to the table in the Van-Ryzin note. If you can’t make it work, please contact me. (Note that these formulations are based on the US version of Excel, I think that the European version use “;” instead of “,” to separate fields in functions and “,” instead of “.” for decimal numbers.) </p><p>There are two alternatives. The easiest is to use the Excel Macros that I have programmed in the enclosed spreadsheet. You can develop your application in this spreadsheet to use these Macros. The other way is to use the formulas directly in your Excel spreadsheet.</p><p>MACROS</p><p>I have programmed two Macros: zFromL(L) that finds the z that corresponds to a given L, and LFromz(z) that finds the L that corresponds to a given z. Examples of use: Writing: =ZFromL(1) in an Excel cell gives –0.9, and writing =LFromz(2) in an Excel cell gives 0.00849.</p><p>FORMULAS</p><p>Let B be the L(z) value (or the pointer to the cell containing this value), and let A be the number of decimals precision you would like for the calculation of z (i.e. setting A equal to 2 gives two decimal numbers, e.g. having B (i.e. L(z)) equal to 0.342 and A equal to 2 gives a z value of 0.12.</p><p>The formula for going from L to z is:</p><p>=ROUND((-5.39256+5.621105*SQRT(LN(25/B^2))- 3.88368*SQRT(LN(25/B^2))^2+1.08973*SQRT(LN(25/B^2))^3)/(1- 0.72496*SQRT(LN(25/B^2)) +0.507327*SQRT(LN(25/B^2))^2+0.066914*SQRT(LN(25/B^2))^3- 0.00329*SQRT(LN(25/B^2))^4),A)</p><p>For c being the number of decimals and having z, the formula for going from z to L is: =ROUND(NORMDIST(z,0,1,FALSE)-z*NORMDIST(z,0,1,TRUE)-z,c)</p>