In Example 12.7, we discussed the equivalence between the model with shortage costs and the model with a service level constraint. We also showed how to illustrate this equivalence with SolverTable. Extend the SolverTable in the Ordering Cameras 1.xlsx file, with the unit shortage cost as the single input varied from $1 to $15 in increments of $1. As outputs, keep track of the order quantity, the safety stock, the reorder point, the fraction of demand met with existing inventory, and the expected annual setup, holding, and shortage costs. Discuss whether these go in the direction you would expect. Also, discuss how these results relate the two models, one with shortage costs and the other with a service level constraint. (What is equivalent to what?)
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.