Consider a group of n items that are each being independently controlled using an (R, S)

type of system (periodic-review, order-up-to-level). Let Ri be the prespecified value (in months) of R for item i. Suppose that we wish to allocate a total given SS in dollars (call it W ) among the n items to minimize the dollars of expected backorders per unit time summed across all n items.

a. Develop the decision rule for selecting ki, the safety factor for item i. Assume that forecast errors are normally distributed.

b. Illustrate for the following two-item case (r = 0.2 $/$/year; W = $1,180; and L =

1 month):

vi Ai Demand Di Ri σRi σLi σR+i+Li Item i ($/Units) ($) (Units/Year) (Months) (Units) (Units) (Units)

1 1 2.00 3,000 1.0 200 200 300 2 2 5.00 15,000 0.5 500 300 700