Consider a generalization of the inventory model of Examples 12.2 and 12.3 in which there...

Consider a generalization of the inventory model of Examples 12.2 and 12.3 in which there are two new factors. The first of these is the inventory-evaluation interval m, which is the number of months between successive evaluations of the inventory level to determine whether an order will be placed. In the original model m = 1, but consideration is being given to changing m to 2, that is, evaluating only at the beginning of every other month. The second new factor arose since the supplier has introduced an “express” delivery option. Originally, if Z items were ordered, the ordering cost was 32 + 3Z and the delivery lag was uniformly distributed between 0.5 and 1 month. With express delivery, the supplier will cut the delivery time in half (distributed uniformly between 0.25 and 0.5 month) but will charge 48 + 4Z instead. The delivery priority P is thus either “normal” or “express” and is a qualitative factor. In this generalized model, then, there are k = 4 factors whose levels are given in the following coding chart:

Make n = 10 replications of the 2⁴ factorial design and construct 95 percent confidence intervals for the expected main and interaction effects. Does changing the inventory-evaluation interval, m, have much impact on average cost? (Hint: Look at the two-way interactions.) Is it worth using the express-delivery option?

Example 12.2

TABLE 12.4 Design matrix and simulation results for the 2² factorial design on s and d for the inventory model

TABLE 12.5 Sample means and variances of the responses for the inventory model

TABLE 12.6 96.667 percent confidence intervals for the expected effects, inventory model

Example 12.3