9. 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 Page 61the 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 vary L1 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 this purpose, analyze the impact of increasing L1, and therefore decreasing L2, on total safety stock.

10. Suppose you are selecting a supplier. Would you prefer a supplier with a short but highly variable delivery lead time or a supplier with a longer but less variable lead time?

 11. Although we typically model inventory-related costs as either fixed or variable, in the real world the situation is more complex. Discuss some inventory-related costs that are fixed in the short term but may be considered variable if a longer time horizon is considered