A firm uses the order$-$up$-$to model to manage its inventory. The firm is planning changes that will reduce lead time to receive replenishments because the firm anticipates that the coefficient of variation of demand will increase even though mean demand per period remains the same. Assume that the target in$-$stock probability is kept at a constant level. What can be said about the likely change in the firm's on$-$order and on$-$hand inventories, respectively?

a$.$ On$-$order inventory: Will surely decrease; On$-$hand inventory: Will surely increase

b$.$ More information is needed to determine the impact of these changes.

c$.$ On$-$order inventory: Will surely decrease; On$-$hand inventory: Will surely decrease

d$.$ On$-$order inventory: Will surely increase; On$-$hand inventory: Will surely increase

e$.$ On$-$order inventory: Remains the same; On$-$hand inventory: Will surely increase

f$.$ On$-$order inventory: Remains the same; On$-$hand inventory: Remains the same

g$.$ On$-$order inventory: Will surely increase; On$-$hand inventory: Will surely decrease

h$.$ On$-$order inventory: Will surely decrease; On$-$hand inventory: Remains the same