1. Random Demand: Fixed Order Quantity
Dr. Ron Lembke

2. Random Demand Don’t know how many we will sell
Sales will differ by period
Average always remains the same
Standard deviation remains constant
How would our policies change?
How would our order quantity change?
EOQ balances ordering vs holding, and is unchanged
How would our reorder point change?
That’s a good question

3. Constant Demand vs Random
Steady demand
Always buy Q
Reorder at R=dL
Sell dL during LT
Inv = Q after arrival
Random demand
Always buy Q
Reorder at R=dL + ?
Sell ? during LT
Inv = ? after arrival
Inv Q Q Q Q R R L L

4. Random Demand
Reorder when on-hand inventory is equal to the amount you expect to sell during LT, plus an extra amount of safety stock
Assume daily demand has a normal distribution
If we want to satisfy all of the demand 95% of the time, how many standard deviations above the mean should the inventory level be?
Just considers a probability of running out, not the number of units we’ll be short.

5. Random Demand Random demand Sometimes use SS Always buy Q
Reorder at R=dL + SS
Sometimes use SS
Sometimes don’t
On average use 0 SS
Inv R dL SS L L L L

6. St Dev Over Lead Time We can add up variances, not standard deviations
Standard deviation of demand over LT =

7. Demand over the Per Day R = Expected Demand over LT + Safety Stock
= Average demand per day
= Lead Time in days
= st deviation of demand over per day
z from normal table, e.g. z.95 = 1.65

8. Random Demand Fixed Order Quantity
Demand per day averages 40 with standard deviation 15, lead time is 5 days, service level of 90%
= 40
= 5 days
= 15
= 1.30

9. Fixed-Time Period Model
Place an order every, say, week.
Time period is fixed, order quantity will vary
Order enough so amount on hand plus on order gets up to a target amount
Q = S – Inv
Order “up to” policies

10. Fixed Order Period Order every T days Q = S – Inv
Order comes in L days after being placed
Amount on hand after arrival differs
Order today, next order comes T+L days later T L S
Inv
On hand
On hand
+ on order T L

11. Fixed-Time Period Model
S = Order-Up-To Level
S = 40*(7+2) * Sqrt(7+2)*10
S = 40* * 3 * 10
S = = 396
Cycle stock = 360
Safety Stock = 36
= 40
= 2 days
= 10
= 1.20
= 7 days
Service level = 88.5%

12. Service Level Criteria
Type I: specify probability that you do not run out during the lead time
Chance that 100% of customers go home happy
Type II: (Fill Rate) proportion of demands met from stock
100% chance that this many go home happy, on average

13. Two Types of Service
Cycle Demand Stock-Outs Sum 1,450 55
Type I:
8 of 10 periods
80% service
Type II:
1,395 / 1,450 =
96%

14. Summary Fixed Order Quantity – always order same Fixed Time Period
Random demand – reorder point needs to change
Standard Deviation over the LT is given
Standard Deviation per day is given
Fixed Time Period
Always order once a month, e.g.
Amount on hand plus on order will add up to S
Different service metrics: Type I, Type II