Xenon Drives

1
Xenon Drives

• What are the main issues in this case?

2
Xenon Drives

• Xenon has 4 warehouses which experience a demand
  that is not steady from one week to the next.
  Weekly demand is in fact normally distributed
  with a mean of 5,000 and a standard deviation of
  1,500. Lead-time is two weeks. Fixed order costs
  are 20,000/order and it costs 50 to hold one
  drive in inventory during one year.
• Given the current ordering and transfer costs,
  what is the EOQ?
• What is the average inventory at each warehouse?
• Xenon would like this probability to be no higher
  than 5 for customer satisfaction. How much
  safety stock is needed to satisfy this service
  level?

3
Analysis of each of Xenons 4 warehouses

• d 5,000 drives/ week s 1,500 drives/ week
• H
• S LT 2 weeks
• Desired service level F(z) 95.
• Optimal order quantity
• Annual ordering cost per warehouse
• s lead time demand
• Safety stock
• Reorder point
• Average inventory
• Annual holding cost per warehouse

4
Analysis of each of Xenons 4 warehouses

• d 5,000 drives/ week s drives/ week
• H 50 / drive, year
• S 20,000 / order LT 2 weeks
• Desired service level F(z)
• Optimal order quantity
• Annual ordering cost per warehouse
• s lead time demand
• Safety stock
• Reorder point
• Average inventory
• Annual holding cost per warehouse

5
Analysis of 4 warehouses at Xenon

• d 5,000 drives/ week,260000/year s
  drives/ week
• H 50 / drive, year
• S 20,000 / order LT 2 weeks
• Desired service level F(z) .
• Optimal order quantity 14422 units
• Annual ordering cost per warehouse 360,555.
• s lead time demand units
• Safety stock
• Reorder point rL ss 10000
• Average inventory 7211
  Annual holding cost per warehouse 360,555 K
• Annual SS holding cost
• Total cost for the 4 warehouses 2.884 M

6
Capacity Pooling

• I cant see why it requires any more inventory to
  keep a months supply on hand in one warehouse
  than in four branches.

7
Analysis of a single joint warehouse

• d 20,000 drives/ week 1.04M/yr sone
  drives/ week
• H 50 / drive, year sall drives/ week
• S 20,000 / order LT 2 weeks
• Desired service level F(z)
• Optimal order quantity 28844 units
• Annual ordering cost 721K
• s lead time demand units
• Safety stock
• Reorder point rL 40000
• Average inventory 14422
• Annual cycle holding cost 721K
• Annual SS cost K
• Annual total inventory cost 1.442 M

8
Recommendations?
9
Recommendations on

• Warehouse Rent- 5000
• Set up cost- 15000 fulltime, 5000 part time
• Item cost- 200 production, 50 overhead
• Ground Transportation- -10 fee, 3 week LT
• Payment Terms- current, quarterly
• Coordination across four regions

10
Analysis of a single joint warehousewith
appropriate charges

• d 20,000 drives/ week ,1.04M/yr sone
  drives/ week
• H 40 / drive, year sall drives/ week
• S 5,000 / order LT 2 weeks
• Desired service level F(z)
• Optimal order quantity 16124.5 units
• Annual ordering cost 322K
• Annual cycle holding cost 322K
• Annual SS cost K
• Annual total inventory cost 0.664 M
• Labor Charge 540 K
• RD opportunity losses 30 k
• With labor and RD charges 1.495 M
• Current Cost for Central Warehouse 1.79 M

11
Having the wrong charges costs at least 300K in
inefficient management of inventory.

• Annual total inv. Cost (correct charges) 0.92
  M
• Labor Charge 540 K
• RD opportunity losses 30 k
• With labor and RD charges 1.495 M
• Current Cost for Central Warehouse 1.79 M
• Savings 0.3 M

12
Analysis of 4 warehouses at Xenon with
appropriate charges

• d 5,000 drives/ week,.26M/yr s drives/
  week
• H 40 / drive, year
• S 5,000 / order LT 2 weeks
• Desired service level F(z)
• Optimal order quantity 8062
• Annual ordering cost per warehouse 161.2 K
• Annual cycle holding cost per warehouse 161.2 K
• Annual SS cost
• Total cost for the 4 warehouses 1.289 M
• Labor Charge 1.8 M
• RD opportunity losses 60 K
• With labor and RD charges 2.99 M
• Current Cost for Central Warehouse 3.58 M
• Savings 0.6 M

13
WHAT HAPPENS IF REGIONS GET TOGETHER AND SHARE
ORDERING COST
14
Analysis of 4 warehouses at Xenon with
appropriate charges

• d 5,000 drives/ week,.26M/yr s drives/
  week
• H 40 / drive, year
• S 1250/ order LT 2 weeks
• Desired service level F(z)
• Optimal order quantity 4031
• Annual ordering cost per warehouse 80.6 K
• Annual cycle holding cost per warehouse 80.6 K
• Annual SS cost
• Total cost for the 4 warehouses .6449 M
• Labor Charge M
• RD opportunity losses K
• With labor and RD charges M
• Current Cost for Central Warehouse M
• Savings 0 M

15
Does Xenon match the EOQ assumptions?

• No interference ?
• Orders from the different warehouses could
  interfere and cause changes in lead time.
• Constant demand?
• Continuous holding costs?
• Price is constant?
• Order cost is constant?
• Lead time is constant?

16
Learning Objectives Q

• TC of holding and setup increases with the square
  root of D. So if we double D we increase our
  costs by square root of D.

17
Demand uncertainty and forecasting

• Forecasts depend on
• historical data
• market intelligence
• Forecasts are usually (always?) wrong.
• A good forecast has at least 2 numbers (includes
  a measure of forecast error, e.g., standard
  deviation).
• The longer the forecast horizon, the less
  accurate the forecast.

18
Service Level

• Service Level
• Probability of not running out in an order cycle.
• For Xenon, we want a 95 chance of not stocking
  out.
• How much safety stock is needed to satisfy this
  service level?

19
Safety Stocks
Inventory on hand
Q
order
order
order
ROP
safety stock reduces stockout
Lead time
safety stock
Lead time
Time t
L
20
Reorder Point and Service Level
desired service level
1.0-(desired service level)
Mean Demand over Leadtime
Reorder Point (ROP)
Reorder Point Mean Demand over Leadtime
Safety Stock
21
Handling demand uncertainty with safety stocks

• LT Supply lead time,
• rN(d, s r) Demand per unit time is normally
  distributed with mean d and standard
  deviation sr,
• Service level P(no stock out in an order
  cycle)
• P(demand during lead time lt ROP)
• F(z) use tables to find z
• Safety stock ss
• Reorder point ROP LT x d ss

22
The standard normal distribution F(z)

• Transform X N(m,s) to z N(0,1)
• z (X - m) / s.
• F(z) Prob( N(0,1) lt z)
• Transform back, knowing z
• X m zs.

23
Learning Objectives safety stocks

• Safety stock increases with an increase in
• demand variability or forecast error,
• delivery lead time for the same level of service,
• delivery lead time variability for the same level
  of service.

24
Pooling

• Costs grow as the square root of demand.
• EOQ
• Safety stock
• Coordination costs may grow as well.

25
Additional Topics - safety stock

• Sometimes one prefers to set the number of
  stockouts per period rather than the probability
  of stocking out. This is called the fill rate
  and works by a similar system.
• P 1-E(z)slt/Q
• E(Z) estimated from table.

26
Other Supply Chain Issues

• Strategy and safety stock.
• Retailer has a stockout cost of 50 for a unit.
• Supplier has a stockout cost of 100 for a unit.
• Left to themselves, will the retailer hold the
  optimal amount of SS?
• What solution do you propose?

27
Stockout versus SS costs
28
Safety Stock Levels Depend on Incentives
29
Additional Topics EOQ for production and usage
Inventory on hand
order
order
ROP
Q is ordered each time
Lead time
Lead time
Time t
30
Additional Topics Periodic Review Model with
Service Level

• Order Quantity d(TLT) - I
• d demand
• LT lead time
• T review interval
• I inventory on hand

31
Reorder Point for Periodic Review
q d(TLT) - I
Inventory on hand
order
order
Inventory(I)
Inventory(I)
Lead time
Lead time
period
Time t
32
Safety Stock for Periodic Review
Inventory on hand
order
order
Inventory(I)
Inventory(I)
Lead time
Lead time
period
Time t
Vulnerable period TLT
33
Perishable Goods - the newsboy problem

• You are ordering newspapers and you want to know
  how many you should order. If unsold they have no
  value. The unit cost is Cu. If you fail to meet
  all the demand you miss the CM from the unmet
  sales.
• F(Q) Cu/(CM Cu)
• Pick Z so that you have a F(Q) chance to meet
  all of the demand.
• Q sz mean demand

34
Forecasting demand