Inventory Management Concepts - Georgetown...
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Inventory Management Concepts Reorder Points Safety Stock Service Levels Stratification Ken Homa
Transcript of Inventory Management Concepts - Georgetown...
Inventory Management Concepts Reorder Points Safety Stock Service Levels Stratification
Ken Homa
Tracking inventory levels over time …
Time
Inventory Level
Assume a standard order quantity …
Time
Inventory Level
Order Quantity
Decision: When to place next order?
Place order
Time
Inventory Level
Order Quantity
Depends how long from order to receipt …
Receive order
Time
Inventory Level
Order Quantity
Place order
… called Lead Time
Lead Time
Receive order
Time
Inventory Level
Order Quantity
Place order
Question: How much inventory is required to meet demand over the lead time?
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
If demand is perfectly predictable,simply place the order when inventory is sufficient to meet demand over the lead time
Inventory = L.T. Demand when order is
placed
When order is received inventory balance = 0 (i.e. the LT demand was perfectly predicted)
Demand is perfectly predictable, and, in this case, constant … so inventory declines ‘straight line’
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Reorder Point (ROP) … The inventory balance when an order is triggered
Inventory = L.T. Demand when order is
placed
ROP
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
For simplicity, assume that the order received is for a standard size equal to an optimal order quantity (e.g. EOQ).
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
Standard sized order received
Over time, inventory ‘cycles’ from the order quantity (just after receipt) to zero (just before order is received)
Maximum
Minimum
Note: Inventory is ‘withdrawn’ as sales (demand) materialize
Time
Inventory Level
Order Quantity
Note: If sales rate is not constant, time interval between orders may vary and the withdrawal pattern may not be linear. But, min/max is the same.
Average inventory = (Max. – Min.) / 2 = Order Quantity / 2
Maximum
Minimum
Average
Time
Inventory Level
Order Quantity
OQ /2
Note: Assumes that no additional layers of inventory are carried (e.g. ‘safety stock’)
Cycle Stock
Some TakeAways …
• Lead time = elapsed time between placing and receiving an order
• ROP = inventory balance when order is triggered
• If demand is perfectly predictable, ROP is the inventory level sufficient to meet demand over the lead time
• Inventory maximum = order quantity* minimum = zero average = order qty / 2*
* If safety stock = zero
X
But since demand is rarely constant or perfectly predictable, the ROP question is more complex.
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
???
X
If demand over the lead time is precisely equal to average demand (the expected value) then an ROP = avg. LT demand works fine.
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
But if demand is slower (less) than expected, there will be inventory on hand when the order is received
Implication: all demand is met, but inventory is higher than needed
Inventory at time of receipt
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
If demand is faster (more) than expected, there will be inventory stockouts before the order is received Implication: less inventory than needed so some demand not met
Stockout Point
Unfilled demand
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Over time, demand over the lead time will vary in a range around the expected (average) demand rate
Frequency
Frequency Distribution
Demand Over Lead Time
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Sometimes demand will be much less than expected …
Frequency
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Sometimes demand will a little less than expected …
Frequency
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Sometimes demand will be exactly as expected …
Frequency
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Sometimes demand will be more than expected …
Frequency
Receive order
Time
Inventory Level
Order Quantity
Place order
X
The distribution around the expected demand is (thankfully) often normal
Expected Demand
Frequency
Receive order
Time
Inventory Level
Order Quantity
Place order
X
Putting the distribution in context …
Expected Demand
Frequency
Receive order
Time
Inventory Level
Order Quantity
Place order
X
Sometimes there are stockouts … keyed to the statistical distribution
Stockouts
ROP = Expected Demand
Average
Time
Inventory Level
Order Quantity
X
To reduce the number of stockouts, add a layer of ‘safety stock’ and raise the reorder point …
Safety Stock
Average
Stockouts
ROP = Safety Stock + Expected LT Demand
Time
Inventory Level
Order Quantity
Note: stockouts have been reduced, but not totally eliminated
X
The probability of a stockout can be estimated statistically … service level is the ‘flip side’ of a stockout
Service Level
P(Stockout) Frequency
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
Safety Stock (SS)
X
Safety stock absorbs some of the stockout risk
P(Stockout)
SS
Frequency
Service Level
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Safety Stock (SS)
Reorder Point (ROP)
Reorder Point goes up by the amount of Safety Stock Average Inventory = (Order Qty / 2) + Safety Stock
SS ROP
P(Stockout) Frequency
Service Level
Expected LT Demand Average Inventory
OQ / 2 + SS
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
X
Safety Stock (SS)
Putting it all together …
SS ROP
P(Stockout) Frequency
Service Level
Expected LT Demand Average Inventory
OQ / 2 + SS
Reorder Point (ROP)
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
ROP = E(LTD) + SS
X
Safety Stock (SS)
Inventory Management
SS ROP
P(Stockout) Frequency
Service Level
Expected LT Demand Average Inventory
OQ / 2 + SS
Reorder Point (ROP)
Receive order
Time
Inventory Level
Order Quantity
Place order
Lead Time
ROP = E(LTD) + SS
Inventory to Achieve Service Level
0.800
1.300
1.800
2.300
2.800
3.300
80.0% 85.0% 90.0% 95.0% 100.0%
Service Level
Safe
ty F
acto
r
Amount of safety stock depends on standard error and service level objective … which gets translated via a service level factor that is analogous to normal distribution z-factors.
XSS
P(Stockout) Frequency
Service Level
ROP
ROP = E(LTD) + SS = E(LTD) + (k x SE) E(LTD) = Expected LT Demand SS = Safety Stock k = Service level factor SE = Std Error of LT Demand
Statistical note: If the best forecast is the historical average then the standard deviation of the historical series is used. But, to be precise, the standard error of the forecast is the appropriate measure. Safety stock protects against predictability errors, not variability per se. High variability that is perfectly predicted requires no safety stock.
Inventory to Achieve Service Level
0.800
1.300
1.800
2.300
2.800
3.300
80.0% 85.0% 90.0% 95.0% 100.0%
Service Level
Safe
ty F
acto
r
Amount of safety stock depends on standard error and service level objective … which gets translated via a service level factor that is analogous to normal distribution z-factors.
XSS
P(Stockout) Frequency
Service Level
ROP
ROP = E(LTD) + SS = E(LTD) + (k x SE) E(LTD) = Expected LT Demand SS = Safety Stock k = Service level factor SE = Std Error of LT Demand
WARNING ! Increasingly higher service levels require disproportionately more safety stock !
To reduce inventory, reduce safety stock …
• Shorten lead times …Less Lead Time Demand …More predictable (shorter-term forecast)
• Reduce forecasting error …Better mechanics …Aggregation benefits
• Change service level policy … Prudent stockout goals … Differentiated service levels
The ‘C’ Items Challenge Disproportionately high standard errors
Sales Typical% Items % Sales per Item* Std.Error
A 20% 80% 40 5-10%
B 30% 15% 5 25-50%
C 50% 5% 1 50-200%
* Indexed to C = 1 unit per item
The ‘C’ Items Challenge Disproportionately high standard errors => disproportionately high safety stock
Safety Stock Typical A-B-C
20%
50%
100%
29%
Safety Stk.% Sales
The ‘C’ Items Challenge Disproportionate inventory is often tied up in items generating a small percentage of sales
Inventory StrataTypical A-B-C
20%
80%
56%
30%
15%
26%
50%
5%
18%
Items Sales Safety Stk.
20%
44%
Meeting the ‘C’ Items Challenge …
• Prune the items from the line … Contingent on strategic need,
e.g. filling out the product line
• Protect at lower service levels … Lower services levels require
disproportionately less safety stock
• Differentiate service levels by strata … Example: achieve an overall SL = 95%
by protecting A items at 98% and Cs at 90%
• Make C items to order … If low volume, may be less time critical
i.e. customers may be willing to wait
Inventory TakeAways … • 1.If demand is perfectly predictable, reorder when the inventory
level is just sufficient to meet demand over the lead time
• 2.If demand is not perfectly predictable, safety stock is required to protect against stockouts
• 3.Safety stocks depend on forecast accuracy (the flip side of standard error) and service level policy.
• 4.Higher service levels require disproportionately more safety stock … the safety factor function is exponential, not linear
• 5.Pareto is alive and well … typically 20% items => 80% sales
• 6.Low volume ‘C’ items have high forecast errors, and require disproportionately high safety stocks
• 7.To cut inventory: forecast better, change service level policy (e.g. differentiate targets by strata), drop problem items
Inventory Management Concepts Reorder Points Safety Stock Service Levels Stratification
Ken Homa
