Review of Normal random variable .y follows normal distribution with mean value being u and standard deviation being o; .z follows standard normal distribution with u=0 and o =1. The R.V.y and z have the relationship:y =u+z Given and x: Prob(y<=)Prob(< Given probability B:Prob(y <z)=B,we can find the quantile x: Prob(z <b)=B,z=u+bo SEIEE AU406 16
+ - SEIEE AU406 Review of Normal Random Variable 16
Evaluating Safety Inventory given a Replenishment policy In the following part,we assume continuous review policy is used The continuous review policy consists of a lot size ordered when the inventory on hand declines to the ROP(Reorder point). Assume that weekly demand is normally distributed,with mean D and standard deviation op. Assume replenishment lead time of L weeks. Expected demand during lead time D'L Safety inventory,ss ROP -DL SEIEE AU406 17
+ - SEIEE AU406 Evaluating Safety Inventory given a Replenishment policy In the following part, we assume continuous review policy is used The continuous review policy consists of a lot size Q ordered when the inventory on hand declines to the ROP(Reorder point). Assume that weekly demand is normally distributed, with mean D and standard deviation 𝜎𝐷. Assume replenishment lead time of L weeks. 17
Example 1:Evaluating Safety Inventory Given an Inventory Policy Assume that weekly demand for phones at B&M Office Supplies is normally distributed,with a mean of 2,500 and a standard deviation of 500. The manufacturer takes two weeks to fill an order placed by the B&M manager.The store manager currently orders 10,000 phones when the inventory on hand drops to 6,000. Evaluate the safety inventory and the average inventory carried by B&M.Also evaluate the average time a phone spends at B&M. SEIEE AU406 18
+ - SEIEE AU406 Example 1:Evaluating Safety Inventory Given an Inventory Policy Assume that weekly demand for phones at B&M Office Supplies is normally distributed, with a mean of 2,500 and a standard deviation of 500. The manufacturer takes two weeks to fill an order placed by the B&M manager. The store manager currently orders 10,000 phones when the inventory on hand drops to 6,000. Evaluate the safety inventory and the average inventory carried by B&M. Also evaluate the average time a phone spends at B&M. 18
Evaluating Cycle Service Level Given a Replenishment Policy Given a replenishment policy,our goal is to evaluate CSL, the probability of not stocking out in a replenishment cycle. CSL Prob(demand during lead time of L weeks ROP) We know that demand during lead time is normally distributed,with a mean of D,and a standard deviation of oL CSL F(ROP,DL,GL)=NORMDIST(ROP,DL GL,1) SEIEE AU406 19
+ - SEIEE AU406 Evaluating Cycle Service Level Given a Replenishment Policy Given a replenishment policy, our goal is to evaluate CSL, the probability of not stocking out in a replenishment cycle. 19 We know that demand during lead time is normally distributed, with a mean of 𝐷𝐿 and a standard deviation of 𝜎𝐿
Example 2:Evaluating Cycle Service Level Given a Replenishment Policy Weekly demand for phones at B&M is normally distributed,with a mean of 2,500 and a standard deviation of 500. The replenishment lead time is two weeks.Assume that the demand is independent from one week to the next. Evaluate the CSL resulting from a policy of ordering 10,000 phones when there are 6,000 phones in inventory. How about the case when the demands of consecutive day are correlated? SEIEE AU406 20
+ - SEIEE AU406 Example 2: Evaluating Cycle Service Level Given a Replenishment Policy Weekly demand for phones at B&M is normally distributed, with a mean of 2,500 and a standard deviation of 500. The replenishment lead time is two weeks. Assume that the demand is independent from one week to the next. Evaluate the CSL resulting from a policy of ordering 10,000 phones when there are 6,000 phones in inventory. How about the case when the demands of consecutive day are correlated? 20