Chapter 7: Managing Flow Variability
What are the key drivers of inventory when customer demands are unpredictable? Should
they invest in a better forecasting system? What should be the right inventory level?
What service level is appropriate to offer? Should they continue to serve their customers
using a decentralized network or build a central distribution facility to serve all
Matching inflows (supply) and outflows (demands) is a critical aspect of any business
7.1 Demand Forecasts and Forecast Errors
Demand varies over time.
Forecasting: a process of predicting future demand
Forecasting Methods: can be subjective or objective
• Subjective based on judgment and experience and include customer surveys and
• Objective: based on data analysis
Intuitively, we know that aggregation reduces variability, or reduces the amount of
variability relative to aggregate mean demand.
Less safety inventory is needed in the aggregate.
*Reducing variability and safety inventory by pooling and centralizing stock.
Stockouts occur whenever demand exceeds supply.
Ex. Order lamps at a 20,000 ROP. Demand is 2,000 per day. If demand is equally likely
to be above or below 20,000, then there is a 50% probability that keeping an inventory of
20,000 units will result in a stockout.
Stockouts imply that customer demands will go unsatisfied. This can lead to lost
customers and lost revenue and loss of customer goodwill, which may lead to future loss
To avoid stockouts, just in case actual demand exceeds the forecast, customers keep a
safety inventory, inventory in excess of the average or in excess of forecast demand, or
7.2.1 Service level measures
Consider economic tradeoffs between the cost of stockouts and the cost of carrying
excess inventory. Some are intangible, so you look at customer service and quality. The process manager often decides to provide a certain level of customer service and then
determines the amount of safety inventory needed to meet that objective.
cycle service level: the probability that there will be no stockout within a time
fill rate: the fraction of total demand satisfied from inventory on hand
Fill rate= 1 Expected Stockout/ Expected Demand
* not commonly used
Effective inventory policies can be devised to achieve a desired level of either measure of
7.2.2 Continuous Review, Reorder Point System
Review inventory either continuously (real time) or periodically (weekly/monthly)
How much should I order?
depends on the tradeoff between fixed cost of placing orders and the variable
holding cost of carrying the inventory that results from larger order quantities.
Reorder point policy: Having initially ordered a fixed quantity, the process manager
monitors inventory level continuously and then reorders (a quantity perhaps equal to
EOQ) once available inventory position falls to a prespecified reorder point.
Leadtime Demand (LTD): total flowunit requirement during replenishment time
The reorder point inventory is used to meet flowunit requirements until the new order is
received L periods later.
The risk of stockout occurs during this period of replenishment lead time.
Uncertainty in leadtime may be due to a supplier’s unreliability in delivering ontime
When the leadtime demand exceeds the reorder point, a stockout occurs.
ROP=LTD, reorder point is set at the average leadtime demand
If we carry just enough inventory to satisfy forecast demand during leadtime (with a
mean LTD), then actual leadtime demand is symmetric around its mean. This means that
if we carry just enough inventory to satisfy forecast demand during leadtime, then actual
leadtime demand will exceed forecast demand in 50% of our order cycles. We will suffer
stockouts and service level will be 50%
Safety Inventory= ROP LTD
ROP= Avg. LTD + Safety stock = LTD + Safety Inventory
If the actual leadtime demand is larger than its average value of LTD, th