Multi-Period Inventory Problem

You sell a product for which monthly demand is Poisson with a mean of 400.  The units cost you $1,500 each, and you sell them for $2,800.  You can carry inventory from month to month, and estimate your inventory holding cost as $10 per unit left in inventory at the end of a month.

Every time you order, there is a fixed cost of $600, plus the $1,500 per unit cost of the products ordered.

You want to simulate a 24-month period, at the outset of which you have 700 units in stock.  For every unit in stock at the end of this period, you assess a “salvage” credit of $1,500.

You are considering ordering policies of the following form: if the ending inventory for a given month is less than or equal to some “threshold” value R, immediately order another Q units.  For simplicity, assume that these units become available immediately at the beginning of the next month.

Your boss asks you to evaluate the following possible combinations of R and Q.  Which one seems to yield the highest expected profit over the 24 month period?

Policy	R	Q
1	400	800
2	400	1000
3	400	1200
4	500	1000
5	500	1200
6	600	1000
7	600	1200

For each policy, you also wish to estimate the probability of having a “stockout” at some time during the 24 month period.  A “stockout” means that there is insufficient stock to meet customer demand.