Transcript Manufacturing Planning and Control

Manufacturing
Planning and Control
MPC 6th Edition
Chapter 11
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
Order Point Inventory
Control Methods
Order point methods are used to determine
appropriate order quantities and timing for
individual independent-demand product
items that are characterized by random
customer demand.
Performed well, these inventory management
functions can provide appropriate levels of
customer service without excess levels of
inventory and/or cost.
11-2
Agenda–Order Point
Inventory Control Methods
Definition
Basic Concepts
Management Issues
Inventory Costs
Economic Order Quantity (EOQ)
Order Timing
Multi-Item Management
Principles
11-3
Basic Concepts

Inventory supports both independent- and
dependent-demand items

Independent-demand inventories–primarily
influenced by factors outside of company
decisions (e.g. random variation)
• Demand forecasts estimate the average usage rate
and pattern of variation

Dependent-demand inventories–influenced
mainly by internal factors within the firm’s
control
11-4
Transit stock-goods
moving from one
location to another
Cycle stock-inventory
created when order
quantities exceed
immediate
requirements
Inventory
Functions
Safety stock-inventory
that provides
protection from
uncertainty in demand
or supply
Anticipation stockgoods held to satisfy
peak demand or
unusual order patterns
(e.g. promotions)
11-5
Inventory Management
Issues

Routine inventory decisions–how much to
order and when to order

Inventory control decision rules can simplify
these decisions
11-6
Parameters:

Q Order a fixed quantity Q.

S : Order up to a fiexed expected opening
inventory quantity S

R : Place an order when the inventrory
drops to R level.

T : Place order every (T) period
11-7
Inventory Management
Issues

Determining Inventory System Performance
Inventory turnover (annual sales divided by
average inventory investment)
 Fill rate (percentage of units available when
requested by customers)


Allows comparison of different systems and
evaluation of system changes
11-8
Inventory Management
Issues
Implementing Changes in Managing
Inventory–making the appropriate changes at
the right time is critical
 More formalized change management system
is required as the scope of the business
increases

11-9
Inventory-Related Costs
Inventory Cost Sources
Order preparationcosts incurred each
time an order is
placed (clerical,
receiving, shipping,
etc.)
Shortage and
customer service
Inventory carrying
costs-costs incurred
costs-cost of holding
when demand
items in stock (cost of
exceeds supply
capital, loss, damage,
(expediting, customer
taxes, etc.)
dissatisfaction, lost
sales)
Incremental costs–does the cost represent an actual expenditure or lost
profit? Does the cost actually vary with the decision being made?
11-10
Economic Order Quantity
(EOQ) Model

Describes the relationship between cost of
ordering, cost of carrying inventory, and the
order quantity
A
Q
TAC  ( )C P  ( )C H
Q
2
Total Costs
Ordering Costs
Inventory
Holding Costs
11-11
Determining the EOQ–
Graphical Method
A = 1,250
Cp = 6.25
CH = 25
TAC=(1,250/Q)6.25+(Q/2)25
TAC curve shows clear minimum
value at Q=25
11-12
Determining the EOQ–
Deriving the EOQ Formula
Derivative of TAC
with respect to Q
Set derivative
equal to zero and
solve for Q
Economic time between orders (TBO)
TBO 
EOQ
D
11-13
TV Retailer example:

_________
EOQ = √2*Cp*A/CH
If A = 1250 units/year
Cp = 6.25 $/order (or setting up)
CH = 25 $/unit/year
______________
EOQ = √2*6.25*1250/25 = 25
When we buy tv’s we should buy them in lots of
25.
11-14
Number of Orders NO = Demand/EOQ =
1250/25 = 50 orders/year (once a week)
 Time between orders TBO (weeks)
TBO = EOQ/Acerage weekly demand
Decision Rule: Q,T. Buy 25 every weak
 Total Annual Cost TAC = (A/Q)* Cp +
(Q/2)*CH=1250/25*6.25+25/2*25=625

11-15
Example




A major equipment producer sells 4000 units of its
$90/unit product per year. Ordering costs are $30
and holding costs are 8% of the product unit value
per year. Each items requires 5 square meters for
storage (product cannot be piled on top of each
other) and there is currently space in the
warehouse. The space available is of size 20 by
40 meters to store the items.
a) What lot size should he use?
b) What is the total annual cost?
c) Does he need additional space? How much, if
any?
11-16
Example (Cont.)
________________
 a) Q* = √2*4000*30/(.08*90) = 182.6
 b) TSC = 4000/182.6*30 +
182.6/2*(.08*90) = 652.6 + 652.6

c) Area = 182.6*5 = 912.9
Area = 20*40 = 800
 Additional area needed = 112.9 m2

11-17
Example
a)
b)
For a manufacturing operation, parts are
needed at a rate of 180 parts per day.
Set up costs is $150 and the carrying
cost is $0.25 per unit per year. The firm
operates 250 days per year.
What is the economic lot size?
What is the total stocking cost?
11-18
Example (cont.)
a)
b)
__________________
Q* = √2*150/0.25 = 7348.5
TAC = 7348.5/2*.25 +
250*180/7348.5*150 = 918.6 + 918.6
= 1837.1
11-19
Order Timing Decisions

Q,R rule
When stock reaches predetermined inventory
level (R), a fixed quantity (Q) is ordered
 Order point is influenced by demand rate,
replenishment lead time, uncertainty of
demand rate and replenishment lead time,
and acceptable level of customer service
 Safety stock is the difference between
average demand during lead time and the
reorder point

11-20
Safety Stock in a Q,R
system
Order
quantity (Q)
Inventory level
Reorder point
Safety stock
R
S
Time
Lead time
11-21
Determining the Safety
Stock in a Q,R system

Stockout probability–specify an acceptable
risk of stocking out during any given
replenishment cycle


Carry stock sufficient to satisfy expected
demand with this probability
Customer service level–define an acceptable
level of customer service (percent of demand
met from inventory)
SL  100 (100/ Q)
d max
 P(d )(d  R)
d  R 1
11-22
Stockout Probability
With a lead time
of one day, 95%
of cycles will
experience
demand for 7 or
fewer units
Safety stock of 7
units will provide 5%
chance of stockout
during a one day
lead time
Sum of demand
probability is
0.05 (5%)
11-23
Customer Service Level
A reorder point
of 5 units has a
35% chance of
stockout, with
an average of
0.56 units short
each cycle
Sum = 0.35
11-24
Discrete Distribution ex:
Problem :
Demand during lead time discrete distribution:
Probability
Deman
0.05
20
0.15
21
0.2
22
0.3
23
0.1
24
0.15
25
0.05
26
What is the probability of demand to be less than 22?
.2 = % 20
What is the probability of demand to exceed 22?
.3 + .1 + .15 + .05 = .6 =% 60
What is the expected demand during lead time?
(.05)20 + (.15)21 + (.2)22 + (.3)23 + (.1)24 + (.15)25 + (.05)26 = 22.9 units
11-25
Olasılık
Talep
0.05
20
0.15
21
0.2
22
0.3
23
0.1
24
0.15
25
0.05
26
If we take our reorder point as 22, what is our expected units short (the
demand that cant be filled)?
If demand is 20, 21, or 22, we don’t have any units short
We have shortage, only if demand is 23, 24 or 25
Expected units short= (.3)23 + .1(24) + .15(25) + .05(26) = 1.15
If the order quantity is 23, what would be our customer service level ?
1 – 1.15/23 = .95 = 95 %
11-26
Safety Stock with
Continuous Distributions
Reorder point
Probability of
at least one
stockout
during cycle
Expected
number of
stockouts per
cycle
11-27
Probability of Stocking Out
R = davg + S
(average deman during lead time davg
+ Safety Stock S)
S = Z σd
R = davg + Zσd
Z, standart deviation multiple corresponding to
relevant stockout probablility according to normal
distribution
(Example% 5 Stockout = 95% SL  Z=1,645).
σd ... Standard deviation in demand, during lead time
11-28
Probability of Stocking Out
Probability of demand
between 3.5 and 6.5 units
is 0.6827. Probability of
stockout when safety
stock is 1 unit is 0.3173
(1 – 0.6827)
Safety stock = Zσd
Reorder point = mean demand during replenishment lead time + Zσd
Z = appropriate value from standard normal table
σd = standard deviation of demand during replenishment lead time
11-29
Example
Q = 5;
σd = 1.5;
Stockout Probability = % 5 -> SL = 95%
R = d + Z σd = 5 + 1.645*1.5 = 5 + 2.5
= 7.5
Result: Reorder Point =8 ;
Order Quantity Q=5
Safety Stock= 3
11-30
Customer Service Criterion
Calculate E(Z) using
the desired service
level (SL) and
reorder quantity (Q)
Find the calculated
E(Z) in the chart to
determine the Z
value
Safety stock = Zσd
11-31
Customer Service Criterion
Annual stockout quantity=
Stockout probability* annual demand
(1 – SL) * D
This value is equal to stockout quantity per
order (σd E(Z)) * number of orders per year
(1 – SL) * D = σd E(Z) [D/Q]
(1-SL) = σd E(Z)/Q
E(Z) = Q(1- SL)/σd
11-32
Example
Q = 5; σd = 1.5
SL = 95%
E(Z) = Q(1 - .05)/σd = 5*.05/1.5
= .167
From the normal distribution table  Z = 0.6
R = d + Zσd = 5 + 0.6*1.5 = 5 + 0.9 = 5.9
Order Q=5, once inventory drops to 5.9 (6)
11-33
Example:
D = Annual demand 1000
LT=15 days
Q = 200
Service Level = 95 % (.95)
Annual number of days= 250 σd=50 units
Average daily demand=1000/250 = 4 /day
R = d + Z σd = 4*15 + Z(50)
E(Z)=(1-.95)200/50 = 0.2 from tables
Z = 0.49
R = 4(15) + 0.49*50 = 84.5
11-34
Example (Cont.)
Policy:
When inventory level gets to 85 or less then order
200.
What is the expected number of units short per
order?
E(Z) σd = 0.2 * 50 = 10
How many orders per year?
(1000/200)= 5
Total number of units short?
10*5 = 50 (Service level is 95%; 950/1000)
11-35
Time Period Correction
Factor

Variations in demand and lead time complicate
the calculations
When standard deviation of
demand is measured over a
different time period than
the lead time, correction is
required
When both demand and
lead time vary, additional
adjustments are required
2
d D m
 d  L  D  L2
Safety Stock  Z D m
D  averagedem and per period
m
lead tim e
dem and period
2
D
L  averagelead tim e in periods
11-36
Forecast Error Distribution
Safety stock can be based on forecast error
rather than historical demand variation
 Standard deviation = 1.25 MAD


MAD – mean absolution deviation
11-37
Multi-Item Management
Management attention should be focused on
the most important items
 ABC analysis segments the inventoried items
according to annual cost volume usage
(unit cost x annual usage)
 A items are the most important



This small percentage of items usually makes
up a majority of annual cost volume usage
B and C items are progressively less critical
11-38
ABC Analysis

3 classes


Basic classification parameter is annual cost


A class, B class, C class
$ volume = Annual demand x Unit cost
Result of ABC analysis
A class material is important
 Accurate Ccunting of A class material is more
important
 Forecasts regarding class A materials are of
more signaficance

11-39
ABC Analizi
Dollar Usage
Category # of items % of items % of $ use
A
15
11
84%
B
25
15
15
C
88
74
1
Total
128
100
100
11-40
ABC Analysis - Criticality
Criticality
Category # of items % of items % of $ use
I
5
4
40%
II
48
39
56
III
75
57
4
Total
128
100
100
11-41
ABC Analysis – Two sided
view
Dollar Usage
A
B
C
Total
Criticality
I
II III Total
2
12 1
15
1
19 5
25
2
17 69 88
5
48 75 128
11-42
ABC Analysis – Combined
Combined
#
Category of items
AA
14
BB
16
CC
98
Total
128
%
%
of items of $ use
11
78%
13
12
76
10
100
100
11-43
Inventory management policies
according to multi-criteria ABC analysis
AA
BB
CC
Counting
Frequency
monthly
Every six
months
yearly
Order quantity
Low
quatity
EOQ
Large quantity
High for
critical items
Low or none
Every 6
months
yearly
Safety stock
High for
critical
items
Reclassification Every 6
months
11-44
Principles
The difference between dependent and
independent demand must serve as the first
basis for determining appropriate inventory
management procedures.
 Organizational criteria must be clearly
established before we set safety stock levels and
measure performance.
 A sound basic independent demand system must
be in place before attempting to implement
advanced techniques.

11-45
Principles
Savings in inventory-related costs can be
achieved by a joint determination of the order
point and order quantity parameters.
 All criteria should be taken into account in
classifying inventory items for management
priorities.
 The functions of inventory are useful principles
to apply in determining whether or not inventory
reductions can be made.

11-46
Quiz – Chapter 11






Order point methods are generally used for _____________
demand items.
Cycle stock is are a result of manufacturing lot sizes?
(True/False)
Stock produced for upcoming promotional events would be
considered _______________ stock.
The two main decisions when managing independent
demand items are _______________ and ______________.
A measurement that relates inventory levels to product sales
volume is ___________ _____________.
The three types of costs associated with holding inventory
are ____________, ______________, and ____________.
11-47