In a previous post I showed how to write and solve a unit loss function G(k). Here I show how to use it.
Here I solve some (s,Q) inventory models. These models have a variable Q: order quantity. It is sometimes argued to use the EOQ order quantity for this. EOQ stands for Economic Order Quantity. In the model I try to see how much difference it makes when we use this EOQ or just solve for Q in the (s,Q) models directly.
The results are:
---- 155 PARAMETER results
EOQ Qendog Qeoq
EOQ .Q 5200.000
We can see for two inventory models (Cost per Stockout Event – CSOE and Cost per Item Short – CIS) the differences in Q and s are significant. However the effect on total cost and relevant cost is more limited: things are pretty flat out there.
In practice formulas based on the first order conditions are used to solve these inventory models. However I think there is a case to be made to look at the original cost functions and optimize these directly. This relates more to the original problem and also we may be a little bit more flexible if we want to add a few more wrinkles. In some cases there are closed solutions, e.g. the well known EOQ formula is:
In the model below again we use the original cost function and minimize that for Q. Note that for other cases it may not be that easy to find closed solutions.