Consider the following supply chain Let L1 be the lead time

Consider the following supply chain

Let L₁ be the lead time from the factory to the cross-dock and L₂ be the lead time from the cross-dock to each retailer. Let L= L₁ + L₂ and assume L is fixed.

a) Let L₁=0, L₂=L, that is, the cross-dock is very close to the factory. Compute the total amount of safety stock in the system if the daily demand at each retailer follows a normal distribution with average and standard deviation of D and S, respectively.

b) Let L₁=L, L₂=0, that is, the cross-dock is very close to the retailers. Compute the total amount of safety stock in the system if the daily demand at each retailer follows a normal distribution with average and standard deviation of D and S, respectively.

c) Now determine the most beneficial place to locate the cross dock by varying L₁ (that also varies L₂ = L- L₁). Again, daily demand follows a normal distribution with average and standard deviation of D and S, respectively.

Solution

Safety stock = Standard deviation x Average normal distribution

Observe that the longer L1, the more time the system has before allocation of inventory to the retailers need to be made by the cross-dock facility. Thus, the longer L1 the more the system can take advantage of the risk pooling concept. Hence, the total amount of inventory is smaller when the cross dock facility is closer to the retail outlet.