In the first (R,Q) model in Example 12.7, the one with a shortage cost, we let both Q and the multiple k be changing cells. However, we stated that the optimal Q depends mainly on the fixed ordering cost, the holding cost, and the expected annual demand. This implies that a good approximation to the optimal Q is the EOQ from Equation (12.4), replacing D with the expected annual demand and s + ic with the given unit holding cost. Check how good this approximation is by using this EOQ formula to obtain Q and then using Solver with a single changing cell-the multiple k-to optimize the expected total annual cost. How close are the results to those in Example 12.7?
Example 12.7
ORDERING CAMERAS WITH UNCERTAIN DEMAND AT MACHEY'S
I n Example 12.1, we considered Machey's department store, which sells, on average, 1200 cameras per year. The store pays a setup cost of $125 per order, and the holding cost is $8 per camera per year. It takes one week for an order to arrive after it is placed. In that example, the optimal order quantity Q was found to be 194 cameras. Now we assume that the annual demand is normally distributed with mean 1200 and standard deviation 70. Machey's wants to know when to order and how many cameras to order at each ordering opportunity.
Objective To find the (R,Q) policy that minimizes the company's expected annual cost.
Example 12.1
ORDERING CAMERAS AT MACHEY'S
Machey's Department Store sells 1200 cameras per year, and the demand pattern throughout the year is very steady. The store orders its cameras from a regional warehouse, and it usually takes one week for the cameras to arrive after an order has been placed. Each time an order is placed, an ordering cost of $125 is incurred. The store pays $100 for each camera and sells them for $130 apiece. There is no physical storage cost, but the store's annual cost of capital is estimated at 8% per year-that is, it can earn 8% on any excess cash it invests. The store wants to determine how often it should order cameras, when it should place orders, and how many cameras it should order in each order.
Objective To determine when to order and how much to order so that the store never runs out of cameras and profit is maximized.
