In our discussion to this point, we have focused on situations with demand uncertainty in the form of a forecast error. In many practical situations, supply uncertainty also plays a significant role. The impact of supply uncertainty is well illustrated by the impact of the grounding of MSC Napoli on the south coast of Britain in January 2007. The container ship was carrying more than 1,000 tons of nickel, a key ingredient of stainless steel. Given that 1,000 tons was almost 20 percent of the 5,052 tons of nickel then stored in warehouses globally, this delay in bringing nickel to market resulted in significant shortages and raised the price of nickel by about 20 percent in the first 3.5 weeks of January 2007. Supply uncertainty arises because of many factors, including production delays, transportation delays, and quality problems. Supply chains must account for supply uncertainty when planning safety inventories.
In this section, we incorporate supply uncertainty by assuming that lead time is uncertain and identify the impact of lead time uncertainty on safety inventories. Assume that the customer demand per period for tablets at Amazon and the replenishment lead time from the supplier are normally distributed. We are provided the following inputs:
D: Average demand per period
σD: Standard deviation of demand per period
L: Average lead time for replenishment
sL: Standard deviation of lead time
We consider the safety inventory requirements given that Amazon follows a continuous review policy to manage tablet inventory. Amazon experiences a stockout of product if demand during the lead time exceeds the ROP—that is, the quantity on hand when Amazon places a replenishment order. Thus, we need to identify the distribution of customer demand during the lead time. Given that both lead time and periodic demand are uncertain, demand during the lead time is normally distributed with a mean of DL and a standard deviation sL, where
Given the distribution of demand during the lead time in Equation 12.11 and a desired CSL, Amazon can obtain the required safety inventory using Equation 12.5. If product availability is specified as a fill rate, Amazon can obtain the required safety inventory using the procedure outlined in Example 12-5. In Example 12-7, we illustrate the impact of lead time uncertainty on the required level of safety inventory at Amazon (see worksheet Example 12-7).
EXAMPLE 12-7 Impact of Lead Time Uncertainty on Safety Inventory
Daily demand for tablets at Amazon is normally distributed, with a mean of 2,500 and a standard deviation of 500. The tablet supplier takes an average of L = 7 days to replenish inventory at Amazon. Amazon is targeting a CSL of 90 percent (providing a fill rate close to 100 percent) for its tablet inventory. Evaluate the safety inventory of tablets that Amazon must carry if the standard deviation of the lead time is seven days. Amazon is working with the supplier to reduce the standard deviation to zero. Evaluate the reduction in safety inventory that Amazon can expect as a result of this initiative.
In this case, we have
Average demand per period, D = 2,500
Standard deviation of demand per period, sD = 500
Average lead time for replenishment, L = 7 days
Standard deviation of lead time, sL = 7 days
We first evaluate the distribution of demand during the lead time. Using Equation 12.11, we have Mean demand during lead time,
The required safety inventory is obtained using Equations 12.5 and 12.27, as follows:
ss = NORMSINV(CSL) X sL = NORMSINV (0.90) X 17,550 = 22,491 tablets
If the standard deviation of lead time is seven days, Amazon must carry a safety inventory of 22,491 tablets. This is equivalent to about nine days of demand for tablets.
In Table 12-2, we provide the required safety inventory as Amazon works with the supplier to reduce the standard deviation of lead time (sL) from six down to zero. From Table 12-2, observe that the reduction in lead time uncertainty allows Amazon to reduce its safety inventory of tablets by a significant amount. As the standard deviation of lead time declines from seven days to zero, the amount of safety inventory declines from about nine days of demand to less than a day of demand.
The preceding example emphasizes the impact of lead time variability on safety inventory requirements (and thus material flow time) and the large potential benefits from reducing lead time variability or improving on-time deliveries. Often, safety inventory calculations in practice do not include any measure of supply uncertainty, resulting in levels that may be lower than required. This hurts product availability.
In practice, variability of supply lead time is caused by practices at both the supplier and the party receiving the order. Suppliers sometimes have poor planning tools that do not allow them to schedule production in a way that can be executed. Today, most supply chain planning software suites have good production planning tools that allow suppliers to promise lead times that can be met. This helps reduce lead time variability. The lack of visibility for a supplier into future customer plans is also a significant factor that increases supply chain uncertainty. W.W. Grainger was able to get its suppliers to reduce both lead time and lead time variability by sharing its future plans with them. This allowed suppliers to schedule Grainger orders into production without waiting for the orders to actually arrive. The quantity produced was finalized closer to actual production. In other instances, the behavior of the party placing the order often increases lead time variability. In one instance, a distributor placed orders to all suppliers on the same day of the week. As a result, all deliveries arrived on the same day of the week. The surge in deliveries made it impossible for all of them to be recorded into inventory on the day they arrived. This led to a perception that supply lead times were long and variable. Just by leveling out the orders over the week, the lead time and the lead time variability were significantly reduced, allowing the distributor to reduce its safety inventory.
Next, we discuss how aggregation can help reduce the amount of safety inventory in the supply chain.
Source: Chopra Sunil, Meindl Peter (2014), Supply Chain Management: Strategy, Planning, and Operation, Pearson; 6th edition.