Question: Consider a version of the EOQ model where ordering is restricted to power of 2 intervals. That is, the order interval T (length of an ordering cycle) is restricted to be either 1, 2, 4, 8, ... . In other words, T = 2ⁱ for some positive integer i. The decision of the inventory manager is then to identify the optimal i.

a) Reformulate the EOQ model so that the decision is now the length of the order interval T and T is restricted to be of the form 2ⁱ.

b) Show that the optimal value of i corresponds to the smallest integer i that satisfies sqrt(A / Dh) = 2ⁱ.

c) Show that the above inequality is equivalent to T* / sqrt(2) = 2ⁱ , where T* is the optimal order interval under the standard EOQ model.

d) Show that the optimal value of i also corresponds to the largest integer i that satisfies sqrt(2)T* = 2ⁱ.

e) Show that total cost is the same under T* / sqrt(2) and sqrt(2)T*.

f) Use the above fact to show that using the optimal power of two ordering interval increases cost (relative to the true ordering interval) by at most 6%.