Problem:
You have solved the EOQ problem under the assumption that shortages are not allowed. Based on your findings, you have set the optimal order size and cycle length for future orders.
Your boss now informs you that your calculations were based on incorrect information and assumptions. It turns out that shortages are allowed and that unmet demand can be backlogged. It also turns out that the shortage penalty (3) is exactly the same as the holding penalty (h). All other parameters were correct (K , D, h).
The bad news is that you can no longer change your order size (q*) or your ordering frequency (number of annual orders) as you have signed a binding contract with your supplier. The good news is that you can change the inventory level at which an order is triggered.
At which inventory level should you place an order if your goal is to minimize total costs? What is your maximum shortage? By what amount did your total costs decrease?
Note that both the ordering costs and the purchasing costs remain unchanged in light of the new information. The only change in total cost pertains to holding and shortage penalties.