preparing for the game
TRANSCRIPT
Preparing for the Game
The first 30 days of the game will be initialized this evening
Preparing for the Game
Download Data
We will do one together
GOING OVER THE MODELS IN CLASS
OBJECTIVE #1: SUPPORT THE LITTLEFIELD GAME
STRATEGIC OPERATING PLAN
LITTLEFIELD
SIMULATION EXERCISE
LITTLEFIELD
FORECASTING
INVENTORY WAITING LINES
DECISION TREES
GOING OVER THE MODELS IN CLASS
OBJECTIVE #2: POVIDE TRADITIONAL OVERVIEW
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
SPECIAL TOPICS:
POISSON PROCESS FORECASTING
SIMULATION EXERCISE
LITTLEFIELD
d
GOING OVER THE MODELS IN CLASS
OBJECTIVE #2: POVIDE TRADITIONAL OVERVIEW
USES: MIN RELEVANT COSTS
SPECIAL TOPIC:
DEMAND NOT CONSTANTINVENTORY
SIMULATION EXERCISE:
LITTLEFIELD
EXERCISE &
DERIVATION
GOING OVER THE MODELS IN CLASS
OBJECTIVE #2: POVIDE TRADITIONAL OVERVIEW
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
SPECIAL TOPIC:
SERVER UTILIZATIONWAITING
LINES
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
PANTRY SHOPPERS
GOING OVER THE MODELS IN CLASS
OBJECTIVE #2: POVIDE TRADITIONAL OVERVIEW
USES: SEQUENTIAL DECISION MAKING UNDER
UNCERTAINTY
SPECIAL TOPICS:
RISKPERIOD LENGTHS
DECISION
TREES
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
ARCTIC INC
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
SPECIAL TOPICS:
POISSON PROCESS
SIMULATION EXERCISE
LITTLEFIELD
d
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
DEFINITIONS OF FORECASTING
THREE LAWS OF FORECASTING
ELEMENTS OF A GOOD FORECAST
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
DEFINITION OF FORECASTING
A FORECAST IS A STATEMENT ABOUT THE FUTURE VALUE OF A VARIABLE OF INTEREST, e.g.:
DEMAND
LEARNING-CURVE EFFECTS (TASK COMPLETION TIMES)
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
DEFINITION OF FORECASTING
FORECASTING IS DRIVING ALONG CA 99 AT 70 MPH
YOUR WINDSHIELD AND SIDE WINDOWS PAINTED BLACK
ONLY INFORMATION FOR STEERING IN REARVIEW MIRROR
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
THREE LAWS OF FORECASTING
1. FORECASTS ARE ALWAYS WRONG
2. AGGREGATE FORECASTS ARE MORE ACCURATE THAN
FORECASTS FOR SINGLE PRODUCTS
3. THE LARGER THE FORECAST HORIZON THE LESS ACCURATE THE
FORECAST WILL BE
GIVEN THESE LAWS OF
FORECASTING, WHY DO WE
FORECAST?
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
WHY WE FORECAST
FORECASTS ARE ALWAYS WRONG – B-U-U-U-T …
FORECAST ERROR MEASURES ARE VERY USEFUL
THEY PROVIDE AN IDEA OF JUST HOW WRONG WE CAN BE ON
AVERAGE
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
WHY WE FORECAST
USE THE FORECAST and the ERROR MEASURES together to
CREATE a one-TAILED CONFIDENCE INTERVAL
USED TO SET SAFETY STOCK
OR ADDITIONAL SERVICE RESOURCES
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
HOW DO WE SET SAFETY STOCK?
TOPIC OF ROP
Preparing for the Game
I. Plotting dataa. Plot with charting tool
i. Select columns A and Bii. Click on the "Chart Wizard" Icon iii. Under "Chart Type" on the left select "XY
(Scatter)"iv. On the right select "Scatter with data points
connected by lines (third icon down on the left)
v. When you are done customizing your chart click finish
day number of jobs arriving each day1 42 13 44 25 26 77 38 19 5
10 311 512 413 114 315 616 417 318 419 620 421 522 723 924 625 326 727 128 929 630 8
Job Arrivals first 30 Days
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30
Preparing for the Game
II. Adding trend linesa. Add a trend line
i. right click your mouse anywhere on the curve
ii. select “Add a trend line”
iii. select the option that places a formula on the graph
iv. Forecast out 30 units
day number of jobs arriving each day1 42 13 44 25 26 77 38 19 5
10 311 512 413 114 315 616 417 318 419 620 421 522 723 924 625 326 727 128 929 630 8
Job Arrivals first 30 Daysy = 0.1377x + 2.2989
R2 = 0.2743
0
2
4
6
8
10
12
0 5 10 15 20 25 30 35 40 45 50 55 60
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
SPECIAL TOPICS:
POISSON PROCESS
SIMULATION EXERCISE
LITTLEFIELD
d
III. IMPORTANT NOTE ON DEMAND VARIANCE
a. THE JOB ARRIVALS FOLLOW A POISSON DISTRIBUTION
b. SPECIAL FEATURE OF THE POISSON DISTRIBUTION
i. MEAN = VARIANCE
ii. RECALL: VARIANCE = (STANDARD DEVIATION)2
c. AS DEMAND INCREASES WITH TIME (SEE TREND LINE)
i. SO DOES THE STANDARD DEVIATION OF DEMAND!
i. INCREASING DEMAND WILL AFFECT EOQ
ii. INCREASING VARIANCE WILL AFFECT ROP
PREPARING FOR THE GAME
d
FORECASTING
USES: FORECAST + ERROR TO
DETERMINE OPERATING REROURCE
NEEDS
SPECIAL TOPICS:
POISSON PROCESS
SIMULATION EXERCISE
LITTLEFIELD
d
PREPARING FOR THE GAME
III. FORECAST OPERATIONAL PLANNING
a. PLAN WHEN YOU WILL NEED TO FORECAST AGAIN i. SEE “LITTLEFIELD_GAME.PDF”
b. CONSIDER THE QUANTITY OF DATA NEEDED
i. IDEAL: 30 DAYS
ii. FUNCTIONAL?
INVENTORY MANAGEMENT
USES: MIN RELEVANT COSTS
SPECIAL TOPIC:
DEMAND NOT CONSTANT
SIMULATION EXERCISE:
LITTLEFIELD
EXERCISE &
DERIVATION
EOQ Model
ASSUMPTIONS of the EOQ MODEL
• Only one product is involved
• Annual demand requirements known
• Demand is even throughout the year
• Lead time does not vary
• Each order is received in a single delivery
• There are no quantity discounts
EOQ Model
OBJECTIVE: MIN RELEVANT COSTS
Q2
Annualcarryingcost
Annualorderingcost
Total cost = +
H DQ
STC = +
INVENTORY MANAGEMENT
USES: MIN RELEVANT COSTS
SPECIAL TOPIC:
DEMAND NOT CONSTANT
SIMULATION EXERCISE:
LITTLEFIELD
EXERCISE &
DERIVATION
INVENTORY MANAGEMENT
EXERCISE &
DERIVATION
D = Annual demandH = Annual holding cost - $/unit/yearS = Fixed order cost ExampleD = 50,000 unitsH = $1 /unit/yearS = $1,000Operate 50 weeks/year
Cost Minimization Goal
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
An
nu
al C
ost
(optimal order quantity)
TCQ
HD
QS
2
Deriving the EOQ
Using calculus
• take the derivative of the TC function
• set the derivative (slope) equal to zero
• solve for Q.
Q = 2DS
H =
2(Annual Demand)(Order or Setup Cost)
Annual Holding CostOPT
Deriving the EOQ
The total cost curve reaches its minimum
where
the carrying = ordering costs
Q = 2DS
H =
2(Annual Demand)(Order or Setup Cost)
Annual Holding CostOPT
INVENTORY MANAGEMENT
USES: MIN RELEVANT COSTS
SPECIAL TOPIC:
DEMAND NOT CONSTANT
SIMULATION EXERCISE:
LITTLEFIELD
EXERCISE &
DERIVATION
EOQ Model
The INVENTORY CYCLE
Quantityon hand
Q
Receive order
Placeorder
Receive order
Placeorder
Receive order
Lead time
Reorderpoint
Usage rate
Time
Profile of Inventory Level Over Time
When to Reorder with EOQ Ordering
• Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered
• Safety Stock - Stock that is held in excess of expected demand due to variable demand rate *.
• Service Level - Probability that demand will not exceed supply during lead time.
• *Applies to lead-time uncertainty as well – but not in the Littlefield exercise
Determinants of the Reorder Point
• The rate of demand
• The lead time Demand*
• Stockout risk (safety stock)
* and/or lead time variability – but not in the Littlefield Exercise
Safety Stock
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Quanti
ty
Safety stock
Safety stock reduces risk of stockout during lead time
Reorder Point
ROP
Risk ofa stockout
Service level
Probability ofno stockout
Expecteddemand Safety
stock0 z
Quantity
z-scale
The ROP based on a normalDistribution of lead time demand
So What’s the D _ _ _ _ _ d ROP Equation?
LetL = lead timed = demand rate (demand expressed in
days) = standard deviation of demandSL = required service levelz = standard normal variate
ROP = d x L + z x xSqrt(L)
So What’s the D _ _ _ _ _ d ROP Equation?
ExampleL = 19 daysd = 24 units/day = 4 units/daySL = 98%z = 2.05
ROP = d x L + z x xSqrt(L)ROP = (24)(19) + (2.05)(4)sqrt(19)ROP = 492 units (round up)
DEMAND NOT CONSTANT
Inventory Level of raw kits at Littlefield
(not an average)
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
0 100 200 300 400
INVENTORY MANAGEMENT
USES: MIN RELEVANT COSTS
SPECIAL TOPIC:
DEMAND NOT CONSTANT
SIMULATION EXERCISE:
LITTLEFIELD
EXERCISE &
DERIVATION
INVENTORY MANAGEMENT
SIMULATION EXERCISE:
LITTLEFIELD
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
SPECIAL TOPIC:
SERVER UTILIZATION
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
PANTRY SHOPPERS
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
SPECIAL TOPIC:
SERVER UTILIZATION
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
PANTRY SHOPPERS
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
SPECIAL TOPIC:
SERVER UTILIZATION
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
PANTRY SHOPPERS
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
Example of an M/M/1 queue[1]
[1] Picture source: Heizer and Render. Production and Operations Management.
WAITING LINES
12 17
The following information is typically given:Symbol Units Description Example
Customers per time unit Arrival rate of customers into the system 12 cars/hour Customers per time unit Server’s service rate 17 cars/hour
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
Assumptions of the M/M/1 queue
and follow aPoissonprocess
1 .The average service time for Dave's car wash is hour(s)/car
Population Source assumed infinitely large
Queue capacity infinite
Queue discipline FCFS
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
Assumptions of the M/M/1 queue
More
Customers are Patient
That is, they do not
Balk
Renege
Jockey
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
Operating Characteristics of the M/M/1 queue
Symbol Formula/ Units Description
. 0 1 ., 1 Server capacity utilization
nP 1 nnP The probability that n customers
are in the system
L L
customers Average number of customers in
the system
qL qL L Average number of customers in the Queue
W 1
W
time units Average amount of time that a customer spends in the system
qW qW W time units Average amount of time that a customer spends in the queue
1 This simply means0 1. Stated otherwise, is a number strictly greater than 0 and strictly less than 1.
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
Operating Characteristics of the M/M/1 queue
Symbol Description Example
Server capacity utilization 12 17 0.7059
nP The probability that n customers are in the system
22 1 0 7059 0 7059
0 2941 0.4983
=0.1466
. .
.
P
L Average number of customers in the system
12 122 4
17 12 5.L
qL Average number of customers in the Queue
0 7059 2 4 169. . .qL
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
Operating Characteristics of the M/M/1 queue
Symbol Description Example
W Average amount of time that a customer spends in the system
1 10 2 hour
17 12 50 2 60 12 minutes
.
.
W
W
qW Average amount of time that a customer spends in the queue
0 7059 12
8 47 minutes
.
.
q
q
W
W
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
SPECIAL TOPIC:
SERVER UTILIZATION
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
PANTRY SHOPPERS
WAITING LINES
SPECIAL TOPIC:
SERVER UTILIZATION
What is a “good” range of values for ?
We know that should be between 0 and 1
But we need to take a closer look
WAITING LINES
SPECIAL TOPIC:
SERVER UTILIZATION
A closer look at
Recall L
L L
customers Average number of customers in the system
Recall:
But What Happens as ?
Draw the D _ _ _ _ d Picture
(DTDP)
The Second Law of EMBA 223
What is the first Law of EMBA 223
But What Happens as
? L L
Value of L vs.
= 0.995L = 199
= 0.99L = 99
= 0.90L = 9.00 = 0.75
L = 3.00
= 0.50L = 1.00
= 0.20L = 0.25
= 0.10L = 0.11
0.00
30.00
60.00
90.00
120.00
150.00
180.00
210.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
L
How do we use that Information?
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
SPECIAL TOPIC:
SERVER UTILIZATION
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
PANTRY SHOPPERS
WAITING LINES
MINI CASE:
PANTRY SHOPPERS
Read the Mini Case
Open “Chapter 13.xlt”
Go to the “Single Channel” worksheet
MINI CASE:
PANTRY SHOPPERS
WAITING LINES
USES: CONTROL OPERATING CHARACTERISTICS
AVERAGE LINE LENGTH
AVERAGE WAITING TIME
SPECIAL TOPIC:
SERVER UTILIZATION
SIMULATION EXERCISE
LITTLEFIELD
MINI CASE:
PANTRY SHOPPERS
WAITING LINES
SIMULATION EXERCISE
LITTLEFIELD