Math 326, April 21 -
Inventory Control
Suppose you have a business selling desks. Assume customers buy at a steady
rate throughout the year, and you know you will sell 1000 desks each year. How
often should you order desks from the distributor to replenish your stock?
On the one hand, you want might want to keep inventory small, since excess
stock must be stored in a warehouse. You need to pay for that warehouse space at
a rate of $50 per desk per year, so
if you order more often you will need less storage space.
On the other hand, the distributor adds on a delivery charge, $600
charged every time you order.
So how many times should you place orders each year, so that order costs
and inventory costs are balanced to minimize your total costs?
Additional Questions
- Rebuild the model so that Order Size is the independent variable,
ranging from 1 to 1000. Note Orders per Year will no longer be an
integer, but this is okay, you will just order every time you run low
on stock.
- Many distributors provide a discount on the wholesale price of items
if you place larger orders. Add in an item cost column. Item cost will be
$20/item if order sizes are less than 200, $15/item if order sizes are greater or
equal to 200 but less than 500, and $10/item if on orders 500 or more.
Find the optimal order size under the conditions.
- In addition to the variable wholesale item cost, suppose you are not
able to rent only the warehouse space you need. Instead
you need to rent the whole warehouse for the whole year. You have 3 options: smaller
warehouse (400 capacity) at $5000/year, a bigger warehouse (600 capacity) at $6000/year
or both warehouses. Find the optimal order size under these conditions.