Lead time, supply

Consider a distribution supply chain consisting of a set of n downstream retailers linked to a common source warehouse. There is a common inventory pool at the warehouse shared by all downstream locations. Suppose the supplier lead time is Z. If every retailer faced a demand with a mean of /x and a variance of cr, then the common pool of inventory at the warehouse would be nLjx) + Zstandard normal value whose cumulative probability is the service level offered to retailers, and Z is the supply lead time. 

Safety stock costs If the demand time, the transit time, or both are uncertain, it may be necessary to carry inventory as a buffer against demand uncertainty. As discussed earlier, the extent of this inventory buffer depends on the magnitude of the demand uncertainty during the supply lead time and the planned in-stock service level. If the planned in-stock probability is expressed as service and the demand over lead time has a standard deviation of ct i, then the safety stock level is expressed as (Note that we assume that... 

If demand is normally distributed with mean and standard deviation op and the lead time is normally distributed with mean fli and standard deviation cr, then the demand during the supply lead time is distributed with a mean f L f d... 

Consider a supply chain with two spare-parts demand stations that face a daily demand for a part that follows a normal distribution with a mean (fx) of 50 and a standard deviation (cr) of 25. Assume that the parts stations face a replenishment cost (K) of 125, a holding cost (h) of 0.2/day/part, a backorder cost (h) of 5/day/part. Also, suppose each station faces a supply lead time (Z) of 3 days to be replenished by the... 

Penalty Cost Penalty cost occurs when lead time is greater than the maximum value of supply lead time, i.e. (LT > LT )... 

Supply lead time measures the average lime between when an order is placed and when the product arrives. Long lead times reduce responsiveness and add to the inventory the supply chain must carry. 

Supply lead time Order communication, supplier production scheduling, production time, customs, transportation, receiving Lead time increase results in poorer forecasts and higher inventories... 

Weekly demand for cleaner at each store is normally distributed, with a mean of 1,000 and a standard deviation of 100. Demand experienced by each store is independent, and supply lead time for both motors and cleaner is four weeks. W. W. Grainger has a holding cost of 25 percent. For each of the two products, evaluate the reduction in safety inventories that will result if they are removed from retail stores and carried only in a centralized DC. Assume a desired CSL of 0.95. 

In our discussion so far, we have assumed that each stage of the supply chain has a well-defined demand and supply distribution that it uses to set its safety inventory levels. In practice, this is not true for multiechelon supply chains. Consider a simple multiechelon supply chain with a supplier feeding a retailer that sells to the final customer. The retailer needs to know demand as well as supply uncertainty to set safety inventory levels. Supply uncertainty, however, is influenced by the level of safety inventory the supplier chooses to carry. If a retailer order arrives when the supplier has enough inventory, the supply lead time is short. In contrast, if the retailer order arrives when the supplier is out of stock, the replenishment lead time for the retailer increases. Thus, if the supplier increases its level of safety inventory, the retailer can reduce the safety inventory it holds. This implies that the level of safety inventory at aU stages in a multiechelon supply chain should be related. 

Return to the Sam s Club store in Exercise 6. Assume that the supply lead time from HP is normally distributed, with a mean of 2 weeks and a standard deviation of 1.5 weeks. How much safety inventory should Sam s Club carry if it wants to provide a CSL of 95 percent How does the required safety inventory change as the standard deviation of lead time is reduced from 1.5 weeks to zero in intervals of 0.5 weeks ... 

Supply lead time is more than 15 weeks. As a resnlt, a single order must be placed at the beginning of the season to cover the entire season s demand. 

Supply lead time is reduced to six weeks. As a result, two orders are placed for the season, one to be delivered at the beginning of the season and the other to be placed at the end of week 1 and delivered at the beginning of week 8. 

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