Consider a supply chain consisting of a single manufacturing facility, a cross dock, and two retail outlets. Items are shipped from the manufacturing facility to the cross-dock facility and from there to the retail outlets. Let L1 be the lead time from the factory to the cross-dock facility and L2 be the lead time from the cross dock facility to each retail outlet. Let L = L1 + L2. In the analysis below, we fix L and varyL1 and L2.

a. Compare the amount of safety stock in two systems, one in which lead time from the cross-dock facility to a retail outlet is zero (i.e., L1 = L and L2 = 0) and a second system in which the lead time from the factory to the cross-dock facility is equal to zero (i.e., L1 = 0 and L2 = L).

b. To reduce safety stock, should the cross-dock facility be closer to the factory or the retail outlets? For thispurpose, analyze the impact of increasing L1, and therefore decreasing L2, on total safety stock.