In an EOQ inventory model, how can you minimize inventory cost given a Holding Cost (H) and an Ordering Cost (S) that depend solely on the order quantity? For example, if the ordering cost of a product is 30% of the product price, how can I calculate the order quantity that minimizes the total inventory cost?
The total inventory cost is given by this formula: Total Annual $\operatorname{cost}=\left(\frac{D}{Q}\right) S+\left(\frac{Q}{2}\right) H$ The problem arises because, given that S (Ordering Cost) is dependent on quantity Q, the variables cancels themselves and I cant find a way to choose Q to minimize the total cost.
The problem is that you are dealing with a discontinued function. You'll need a heuristical approach for that. Hint: try to visualize the total cost function and see where 'the breaking points' are at. The breaking points are the quantities where S changes. Find out the total costs for these quantities (use the appropriate value of S) and if for example, there are 2 breaking points, you need to calculate the EOQ and its total cost for every S-value which is 3 (with 3 I mean the amount of EOQ's you have to calculate, not the S-value).