Operations Management Dominic Supermarket Questions

DescriptionBUS ADM 475
Chapter 10
Resource Planning
2
Operations Management: Processes and Supply Chains
Chapter 11
Resource Planning
Content
• 1 Enterprise resource planning ERP
• 2 Material requirements planning MRP
4
What is Resource Planning?
Resource Planning
A process that takes sales
and operations plans;
processes information in
the way of time
standards, routings, and
other information on how
services or products are
produced; and then plans
the input requirements.
5
Enterprise Resource Planning
• What an ERP system does
– Integrating the firm’s functional areas
– Used by many different types of organizations
• How ERP systems are designed
– Single comprehensive database
– Managers to monitor all of the company’s products at
all locations and at all times
– Information is automatically updated in the all
applications when transactions occur
– Streamlines the data flows throughout the organization
– Requires a careful analysis of major processes
– Significant changes in ERP systems – interoperability
6
Enterprise Resource Planning
Back-Office Processes
Human
Resources
•Benefits
•Payroll
Manufacturing
•Material requirements
planning
•Scheduling
Accounting and Finance
•Accounts payable
and receivable
•General ledgers
•Asset management
Front-Office Processes
Data Analysis
•Product costing
•Job costs
Sales and Marketing
•Sales orders
•Pricing system
ERP System
Supply-Chain
Management
•Forecasting
•Purchasing
•Distribution
Customer Service
•Field service
•Quality
7
Materials Requirements
Planning (MRP)
8
End Item, Subassemblies, and Components
9
Independent and Dependent Demand
Independent Demand
(end item)
Scissors
Bottom Blade Assembly
Straight Blade
Screw
Straight Plastic
Grip
Dependent Demand
(component parts)
Top Blade Assembly
Bent Blade
Bent Plastic
Grip
Independent demand is uncertain
often determined by market condition.
Dependent demand is certain.
10
Demand Patterns
2000 –
2000 –
Order
1000 on
day 3
1500 –
Rims
Bicycles
1500 –
Order
1000 on
day 8
1000 –
500 –
1000 –
500 –
Reorder point
0
|
1
|
|
|
|
5
|
Day
(a) Parent inventory
|
|
|
|
10
0
|
1
|
|
|
|
5
|
|
|
|
Day
(b) Component’s dependent
demand
|
10
11
Dependent vs. Independent Demand
• Independent demand: Demand for end items.
• Dependent demand: Demand for items that
are subassemblies or component parts to be
used in production of finished goods.
➢ Once the independent demand is known, the
dependent demand can be determined.
12
Example 1
• Determine the quantities of B, C, D, E, and F needed to
assemble ten X’s, if you have the following in inventory:
Component
B
C
D
E
On hand
4
10
8
60
13
Component On hand
B
4
C
10
D
8
E
60
Example 1 Solution
X X : 10
B : 2 10 = 20
C :110 = 10
− 4 B(2)
16
D : 316 = 48 D(3)
−8
40
E(4)
E : 4  40 = 160
− 60
100
E
E :116 = 16
C
− 10
0
E:0
F :0
E(2)
F(2)
Thus, given the amounts of on-hand
inventory, 10 Xs will require
•B: 16
C: 0
•D: 40
F: 0
•E: 116 (=16+100)
14
Materials Requirements Planning
•MRP
– A computerized information system developed
specifically to help manufacturers manage dependent
demand inventory and schedule replenishment orders
•MRP Explosion
–A process that converts the requirements of various
final products into a material requirements plan that
specifies the replenishment schedules of all the
subassemblies, components, and raw materials needed
to produce final products.
15
MRP Inputs
Authorized
master production
schedule
Inventory
transactions
Inventory
records
MRP
explosion
Material
requirements
plan
Other
sources
of demand
Bills of
materials
Engineering
and process
designs
16
Bill of Materials






Bill of Materials
– A record of all components of an item, the parentcomponent relationship and the usage quantities
derived from engineering and process designs.
End items
Intermediate items
Subassemblies
Purchased items
Part commonality (sometimes called
standardization of parts or modularity)
17
Bill of Materials
Back
legs
Front
legs
Back slats
Seat cushion
Leg supports
Seat-frame
boards
A
Ladder-back
chair
18
Bill of Materials
A
Ladder-back
chair
F (2)
Back legs
B (1)
Ladder-back
subassembly
C (1)
Seat
subassembly
D (2)
Front
legs
G (4)
Back slats
H (1)
Seat frame
I (1)
Seat cushion
J (4)
Seat-frame
boards
E (4)
Leg
supports
19
Master Production Schedule (MPS)
•Master Production Schedule:
–A part of the material requirements plan that details how
many end items will be produced within specified periods
of time
•In a Master Production Schedule:
–Sums of quantities must equal sales and operational plan
–Production must be allocated efficiently over time
–Capacity limitations and bottlenecks may be determined
20
Master Production Schedule (MPS)
Authorized
production
plan
Prospective master
production
schedule
Are resources
available?
Yes
Material
requirements
planning
Authorized master
production
schedule
No
21
Developing an MPS
Step 1: Calculate projected on-hand inventories
On-hand
Projected on-hand
MPS quantity
Projected
inventory
at
inventory at end =
+ due at start – requirements
end of last week
of this week
of this week
this week
where:
Projected requirements = max(Forecast, Customer orders booked)
38 chairs already
55 chairs
Projected on-hand
MPS quantity
promised for
Inventory at the = currently + (0 for week 1) –
delivery in week 1
in stock
end of week 1
= 17 chairs
22
Developing an MPS
Item: Ladder-back chair
Quantity on
Hand:
April
55
1
2
30
30
Customer
orders
(booked)
38
27
Projected onhand
inventory
17
–13
MPS quantity
0
0
Forecast
MPS start
Explanation:
Forecast is less than booked orders
in week 1; projected on-hand
inventory balance
= 55 + 0 – 38 = 17.
Explanation:
Forecast exceeds booked orders in week
2; projected on-hand inventory balance =
17 + 0 – 30 = –13. The shortage signals
a need to schedule an MPS quantity for
completion in week 2.
23
Developing an MPS
Step 2: Determine the timing and size of MPS quantities
• The goal is to maintain a nonnegative
projected on-hand inventory balance
• As shortages are detected, MPS quantities
should be scheduled to cover them. The
exact quantities depend on the shortage, lotsize policy, etc.
17 chairs in
Inventory = inventory at the + MPS quantity – Forecast of
of 150 chairs
30 chairs
end of week 1
= 137 chairs
24
Master Production Schedule (MPS)
Order Policy: 150 units
Lead Time: 1 week
Item: Ladder-back chair
Quantity
on Hand:
April
55
May
1
2
3
4
5
6
7
8
Forecast
30
30
30
35
35
35
35
Customer
orders booked
38
27
30
24
8
0
0
0
0
Projected onhand inventory
17
137 107
77
42
7
122 87
MPS quantity
0
150
0
0
MPS start
150
0 150
150
0
Explanation:
On-hand inventory balance = 17 + 150 – 30
= 137. The MPS quantity is needed to
avoid a shortage of 30 – 17 = 13 chairs in
week 2.
0
25
Inventory Record

A record that shows an item’s lot-size policy,
lead time, and various time-phased data.

The time-phased information contained in the
inventory record consists of:





Gross requirements
Schedule receipts
Projected on-hand inventory
Planned receipts
Planned order releases
26
Inventory Record
• Gross requirements: Total expected demand derived
from all parent production plans in a time period.
• Scheduled receipts: Open orders already scheduled to
arrive from vendors or elsewhere in the pipeline by the
beginning of a period.
• Planned receipts: The quantity to be planned, which is
expected to be received by the beginning of the period.
• Planned order releases: Planned amount to order in
each time period; planned receipts offset by lead time.
27
Inventory Record
•Projected on-hand inventory: Expected amount of
inventory that will be on hand at the end of each time
period after gross requirements have been satisfied:
Projected on-hand
inventory
at end of week t
=
Inventory on
hand at end of
week t–1
+
Scheduled
and planned
receipts in
week t

Gross
requirements
in week t
•Planning for the receipt of new orders will keep the
projected on-hand inventory from dropping below zero.
28
Inventory Record
Item: C
Description: Seat subassembly
Lot Size: 230 units
Lead Time: 2 weeks
Week
Gross
requirements
Scheduled
receipts
Projected
on-hand
inventory
37
1
2
3
4
5
6
7
8
150
0
0
120
0
150
120
0
230
0
0
0
0
0
0
0
117
117
117
227
227
77
187
187
Planned
receipts
Planned order
releases
230
230
Without a planned receipt in week 4, a
shortage of 3 units will occur: 117 + 0 + 0 –
120 = –3 units. Adding the planned receipt
brings the balance to 117 + 0 + 230 – 120
= 227 units.
230
230
The first planned receipt lasts until week 7,
when projected inventory would drop to 77 + 0 +
0 – 120 = –43 units. Adding the second
planned receipt brings the balance to 77 + 0 +
230 – 120 = 187 units.
29
MRP Processing Logic
• Based on the master production schedule to determine
the components schedules for successively lowerlevel items throughout the product structures.
• It calculates schedules for each of the time periods
(usually weekly) in the scheduling time horizon
➢ Gross requirements
➢ Scheduled receipts
➢ Projected on-hand inventory
➢ Planned receipts
➢ Planned order releases
30
Planning Factors
• Lead time
➢ An estimate of the time between placing and order
and receiving the item in inventory.
• Lot-sizing rules for planned receipts
➢ Fixed order quantity (FOQ) rule maintains the
same order quantity each time an order is issued
➢ Lot-for-lot (L4L) rule where the lot size covers
the gross requirements of a single period
➢ Periodic order quantity (POQ) not required
31
MRP Outputs
MRP explosion
Material requirements plan
Action notices
• Releasing new
orders
• Adjusting due dates
Priority reports
• Dispatch lists
• Supplier
schedules
Routings
and time
standards
Capacity reports
• Capacity requirements
planning
• Finite capacity scheduling
• Input-output control
Manufacturing resources plan
Performance reports
Cost and price
data
32
MRP Explosion
• Translates the MPS and other sources of demand
into the requirements needed for all of the
subassemblies, components, and raw materials
the firm needs to produce parent items.
• An item’s gross requirements are derived from
three sources:
✓ The MPS for immediate parents that are end
items
✓ The planned order releases for immediate parents
that are not end items
✓ Any other requirements not originating in the
MPS, such as the demand for replacement parts
33
Example 2
The MPS start quantities for product A
calls for the assembly department to begin
final assembly according to the following
schedule:
A
LT = 2
B (1)
•100 units in week 2; 200 units in week 4
•120 units in week 6; 180 units in week 7
LT = 1
C (2)
LT = 2
•60 units in week 8.
•Develop a material requirements plan for
the next 8 weeks for items B, C, and D.
D (1)
LT = 3
34
Example 2 (cont.)
INVENTORY RECORD DATA
Data Category
Item
C
B
D
Lot-sizing rule
L4L
L4L
Lead time
Scheduled receipts
Beginning (on-hand)
inventory
1 week
2 weeks
FOQ = 500
units
3 weeks
None
200 (week 1)
None
20
0
425
35
Example 2 Solution
Master Production Schedule
1
Item A MPS
Start
Item: B
2
3
100
4
5
200
6
7
8
120 180
60
Gross
requirements
2
10
Lot Size: L4L
Lead Time: 1 week
All times 1
1
9
3
100
4
Week
5
6
200
7
8
120
180
60
0
0
0
120
180
60
120 180
60
9
10
0
0
Scheduled
receipts
Projected
on-hand
inventory
20
20
Planned
receipts
Planned order
releases

0
0
80
80
0
200
200
0
36
Example 2 Solution
Master Production Schedule
1
Item A MPS
Start
Item: C
2
3
100
4
5
200
6
7
8
120
180
60
9
10
Lot Size: L4L
Lead Time: 2 wks
All times 2
Week
1
Gross
requirements
2
200
Scheduled
receipts
200
Projected
on-hand
inventory
200
0
0
Planned
receipts
Planned order
releases
3
4
400
0
0
400
400
5
6
7
8
9
10
0
0
240 360 120
0
0
0
0
240 360 120
240 360 120
37
Example 2 Solution
1
Item C
Planned order
releases
Item: D
2
3
400
4
5
6
7
8
9
10
240 360 120
Lot Size: FOQ =500 units
Lead Time: 3 weeks
All times 1
Week
1
Gross
requirements
2
3
400
4
240
5
6
7
8
9
10
360 120
Scheduled
receipts
Projected
on-hand
inventory
425
425
25
Planned
receipts
Planned order
releases
25
285 425 305 305 305 305 305
500 500
500
500
38
Recap
•Basic resource planning, ERP concepts
•Dependent and independent demands
•MRP inputs: BOM, MPS, inventory record
•MRP concepts: gross requirements, scheduled
receipts, projected on-hand inventory, planned
receipts, planned order release, L4L, FOQ
•Problem solving (examples 1 and 2)
Chapter 8
BUS ADM 475
Managing Economies of
Scale in a SC
2
Supply Chain Management: Strategy, Planning, and Operation
Chapter 11
Managing Economies of Scale in a
Supply Chain: Cycle Inventory
Content
• 1 EOQ Model
• 2 Order Aggregation
• 3 Trade Promotion
• 4 All Unit Quantity Discount
4
Learning Objectives
1. Balance the appropriate costs to choose the optimal
lot size and cycle inventory in a supply chain.
2. Understand the impact of trade promotions on lot
size and cycle inventory.
3. Understand the impact of quantity discounts on lot
size and cycle inventory.
4. Devise appropriate discounting schemes for a
supply chain.
5
Role of Cycle Inventory
in a Supply Chain
•Lot or batch size is the quantity that a stage of a
supply chain either produces or purchases at a
time
•Cycle inventory is the average inventory in a
supply chain due to either production or
purchases in lot sizes that are larger than those
demanded by the customer
Q: Quantity in a lot or batch size
D: Demand per unit time
6
Inventory Profile
Figure 1
7
Cycle Inventory
lot size Q
Cycle inventory =
=
2
2
average inventory
Average flow time =
average flow rate
Average flow time
cycle inventory Q
=
=
resulting from cycle
demand
2D
inventory
8
Role of Cycle Inventory
in a Supply Chain
• Lower cycle inventory has
➢ Shorter average flow time
➢ Lower working capital requirements
➢ Lower inventory holding costs
• Cycle inventory is held to
➢ Take advantage of economies of scale
➢ Reduce costs in the supply chain
9
Role of Cycle Inventory in a Supply Chain
•Average price paid per unit purchased is a key cost in the
lot-sizing decision
Material cost = C
•Fixed ordering cost includes all costs that do not vary with
the size of the order but are incurred each time an order is
placed
Fixed ordering cost = S
•Holding cost is the cost of carrying one unit in inventory
for a specified period of time
Holding cost = H = hC
10
Role of Cycle Inventory
in a Supply Chain
• Primary role of cycle inventory is to allow
different stages to purchase product in lot sizes
that minimize the sum of material, ordering, and
holding costs
• Ideally, cycle inventory decisions should consider
costs across the entire supply chain
• In practice, each stage generally makes its own
supply chain decisions, which increases total cycle
inventory and total costs in the supply chain
11
Role of Cycle Inventory
in a Supply Chain
• Economies of scale exploited in three
typical situations
1. A fixed cost is incurred each time an order is
placed or produced
2. The supplier offers price discounts based on the
quantity purchased per lot
3. The supplier offers short-term price discounts
or holds trade promotions
12
Estimating Cycle Inventory Related
Costs in Practice
• Inventory Holding Cost
➢ Cost of capital (major)
➢ Obsolescence cost
➢ Handling cost
➢ Occupancy cost
➢ Miscellaneous costs
Theft, security, damage, tax, insurance
13
Estimating Cycle Inventory Related
Costs in Practice
• Ordering Cost
➢ Buyer time
➢ Transportation costs
➢ Receiving costs
➢ Other costs
14
Economies of Scale to Exploit Fixed Costs
•Lot sizing for a single product (EOQ)
D = Annual demand of the product
S = Fixed cost incurred per order
C = Cost per unit
H = Holding cost per year as a fraction of product
cost = hC
•Basic assumptions
➢ Demand is steady at D units per unit time
➢ No shortages are allowed
➢ Replenishment lead time is fixed and known
15
Economies of Scale
to Exploit Fixed Costs
• Minimize total costs of
➢ Annual material cost
➢ Annual ordering cost
➢ Annual holding cost
16
Lot Sizing for a Single Product
Annual material cost = CD
D
Number of orders per year =
Q
æ Dö
Annual ordering cost = ç ÷ S
èQø
æQ ö
æQö
Annual holding cost = ç ÷ H = ç ÷ hC
è2ø
è2ø
æ Dö
æQ ö
Total annual cost, TC = CD + ç ÷ S + ç ÷ hC
èQø
è2ø
17
Lot Sizing for a Single Product
Figure 2
18
Lot Sizing for a Single Product
• The economic order quantity (EOQ)
2DS
Optimal lot size, Q* =
hC
• The optimal ordering frequency
D
n* =
=
Q*
DhC
2S
19
EOQ Example
Example 1 Demand for the Deskpro computer at Best Buy is
1,000 units per month. Best buy incurs a fixed order placement,
transportation, and receiving cost of $4,000 each time an order is
placed. Each computer costs Best Buy $500 and the retailer has a
holding cost of 20 percent. Evaluate the number of computers that
the store manager should order in each replenishment.
Annual demand, D = 1,000 x 12 = 12,000 units
S = $4,000, C = $500, h = 0.2
2 ´12,000 ´ 4,000
Optimal order size = Q* =
= 980
0.2 ´ 500
20
EOQ Example
Q * 980
Cycle inventory =
=
= 490
2
2
D 12, 000
Number of orders per year =
=
= 12.24
Q*
980
æQ *ö
D
Annual ordering and holding cost =
S +ç
÷ hC = 97,980
Q*
è 2 ø
Q*
490
Average flow time =
=
= 0.041 yr = 0.49 month
2 D 12, 000
21
EOQ Example
• If lot size reduced to Q = 200 units
D
 Q*
Annual inventory-related costs =
S +
 hC
Q*
 2 
12, 000
 200 
=
(4000) + 
 (0.2)(500) = 250, 000
200
 2 
• Compared with Q* =980 units,
Annual inventory-related costs = 97,980
22
Aggregating Multiple Products
in a Single Order
• Savings in transportation costs
➢ Reduces fixed cost for each product
➢ Lot size for each product can be reduced
➢ Cycle inventory is reduced
• Single delivery from multiple suppliers or
single truck delivering to multiple retailers
• Receiving and loading costs reduced
23
Lot Sizing with Multiple
Products or Customers
• Ordering, transportation, and receiving costs
grow with the variety of products or pickup
points
• Lot sizes and ordering policy that minimize
total cost
Di: Annual demand for product i
S: Order cost incurred each time an order is placed,
independent of the variety of products in the order
si: Additional order cost incurred if product i is included
in the order
24
Lot Sizing with Multiple
Products or Customers
• Three approaches
1. Each product manager orders his or her model
independently
2. The product managers jointly order every
product in each lot
3. Product managers order jointly but not every
order contains every product; that is, each lot
contains a selected subset of the products (not
required)
25
Multiple Products Ordered and Delivered
Independently
Example 3 Best Buy sells three models of computers,
Litepro, Medpro, and Heavypro. Their respective annual
demands are as follows:
DL = 12,000/yr, DM = 1,200/yr, DH = 120/yr
Furthermore, common fixed ordering cost per order is
S = $4,000
Product-specific fixed ordering cost per order:
sL = $1,000, sM = $1,000, sH = $1,000
Holding cost per year as a fraction of the product cost:
h = 0.2
Unit cost: CL = $500, CM = $500, CH = $500
26
Multiple Products Ordered and Delivered
Independently
Litepro
Medpro
Heavypro
Demand per year
12,000
1,200
120
Fixed cost/order
$5,000
$5,000
$5,000
Optimal order size
1,095
346
110
Cycle inventory
548
173
55
Annual holding cost
$54,772
$17,321
$5,477
Order frequency
11.0/year
3.5/year
1.1/year
Annual ordering cost
$54,772
$17,321
$5,477
Average flow time
2.4 weeks
7.5 weeks
23.7 weeks
Annual holding and
ordering cost
$109,544
$34,642
$10,954
• Total annual cost = $155,140
Table 1
27
Lots Ordered and Delivered Jointly
S* = S + sL + sM + sH
Annual order cost = S * n
DL hC L DM hCM DH hC H
Annual holding cost =
+
+
2n
2n
2n
DL hC L DM hCM DH hC H
Total annual cost =
+
+
+S*n
2n
2n
2n
n* =
DL hC L + DM hCM + DH hC H
In general, n* =
2S *
 D hC
k
i =1
i
2S *
i
28
Products Ordered and Delivered Jointly
S* = S + sA + sB + sC = $7,000 per order
12,000 ´100 +1,200 ´100 +120 ´100
n* =
= 9.75
2 ´ 7,000
Annual order cost = 9.75 x 7,000 = $68,250
Annual ordering and holding cost
= $61,512 + $6,151 + $615 + $68,250 = $136,528
• Recall when order them independently,
total annual cost is $155,140
29
Products Ordered and Delivered Jointly
Table 2
Order Jointly
Litepro
Medpro
Heavypro
Demand per year (D)
12,000
1,200
120
Order frequency (n∗)
9.75/year
9.75/year
9.75/year
1,230
123
12.3
615
61.5
6.15
Annual holding cost
$61,512
$6,151
$615
Average flow time
2.67 weeks
2.67 weeks
2.67 weeks
Order Independently
Litepro
Medpro
Heavypro
11.0/year
3.5/year
1.1/year
Optimal order size
1,095
346
110
Cycle inventory
548
173
55
Annual holding cost
$54,772
$17,321
$5,477
Average flow time
2.4 weeks
7.5 weeks
23.7 weeks
Optimal order size (D/n∗)
Cycle inventory
Order frequency
30
Short-Term Discounting:
Trade Promotions
• Trade promotions are price discounts for a
limited period of time
• Key goals
1. Induce retailers to use price discounts,
displays, or advertising to spur sales
2. Shift inventory from the manufacturer to the
retailer and the customer
3. Defend a brand against competition
31
Short-Term Discounting:
Trade Promotions
• Impact on the behavior of the retailer and
supply chain performance
• Retailer has two primary options
1. Pass through some or all of the promotion to
customers to spur sales
2. Pass through very little of the promotion to
customers but purchase in greater quantity
during the promotion period to exploit the
temporary reduction in price (forward buy)
32
Forward Buying Inventory Profile
Figure 5
33
Forward Buy
• Costs to be considered – material cost,
holding cost, and order cost
• Three assumptions
1. The discount is offered once, with no future
discounts
2. The retailer takes no action to influence
customer demand
3. Analyze a period over which the demand is an
integer multiple of Q*
34
Forward Buy
• Optimal order quantity
*
dD
CQ
d
d
Forward buy = Q – Q *
Q =
+
(C − d )h C − d
d : discount offered ($/unit),
D: annual Demand (units/year),
C : normal cost ($) per unit
h : holding cost per year as a fraction of product cost
Q* : current lot-size (units/order)
35
Impact of Trade Promotions
on Lot Sizes
Example 11 (in the textbook) Drug Online (DO) is a retailer that
sells Vitaherb, a popular vitamin diet supplement. Demand for
Vitaherb is 120,000 bottles per year. The manufacturer currently
charges $3 for each bottle, and DO incurs a holding cost of 20
percent. DO currently orders in lots of 6,324 bottles. The
manufacturer has offered a discount of $0.15 for all bottles
purchased by retailers over the coming month. How many bottles
of Vitaherb should DO order given the promotion?
*
dD
CQ
Answer: Q d =
+
(C − d )h C − d
0.15 120, 000 3  6,324
d
Q =
+
= 38, 235.79  38, 236
(3 − 0.15)  0.20 3 − 0.15
36
Impact of Trade Promotions
Discount 0.15/3 = 0.05
on Lot Sizes
Cycle Inventory:
▪ With trade promotions
19118/ 3162 =6.05
Cycle inventory at DO= Qd/2 = 38,236/2 = 19,118 bottles
Average flow time = Qd/(2D) = 38,236/(2*120,000)
= 0.159317 year = 1.9118 months
Forward buy = Qd – Q* = 38,236 – 6,324 = 31,912 bottles
• Without trade promotions
Cycle inventory at DO= Q*/2 = 6,324/2 = 3,162 bottles
Average flow time = Q*/(2D) = 6,324/(2*120,000)
= 0.02635 year = 0.3162 months
37
How Much of a Discount Should the
Retailer Pass Through?
Example 12 Assume that DO faces a demand curve for
Vitaherb of 300,000-60,000p. The normal price charged
by the manufacturer to the retailer is CR = $3 per bottle.
Ignoring all inventory-related costs, evaluate the optimal
response of DO to a discount of $0.15 per unit.
Profits for the retailer
ProfR = (300,000 – 60,000p)(p – CR )
• Optimal retail price
p = (300,000 + 60,000CR)/120,000
• Without promotion, optimal retail price and demand are
p = [300,000 + (60,000)(3)]/120,000 =4
DR = 300,000 – 60,000p = 60,000
38
Example 12 (continued)
• Optimal retail price
p = (300,000 + 60,000CR)/120,000
• With promotion, optimal retail price and demand are
p = [300,000 + (60,000)(3-0.15)]/120,000 = 3.925
DR = 300,000 – 60,000p = 300,000-(60,000)(3.925)=64,500
Manufacturer offers $0.15 discount to the retailer, but the
retailer only passes through 4-3.925=$0.075 discount to
the consumers. Demand increases about
7.5% = (64,500-60,000)/60,000
39
Trade Promotions
• Trade promotions generally hurt supply chain
➢ increase lot size and cycle inventory significantly
➢ do not increase customer demand significantly
• Good for products with high deal elasticity and high
holding costs, or due to competition
• Counter measures
➢ EDLP (every day low pricing)
➢ Discount applies to items sold to customers (sell-through) not
the quantity purchased by the retailer (sell-in)
➢ Scan based promotions
40
Economies of Scale to
Exploit Quantity Discounts
• Volume based discount – discount is based on total
quantity purchased over a given period (not required)
• Lot size-based discount – discounts based on
quantity ordered in a single lot
➢ All-unit quantity discounts
➢ Marginal unit quantity discount or multi-block tariffs (not
required)
41
Quantity Discounts
• Two basic questions
1. What is the optimal purchasing decision for a
buyer seeking to maximize profits? How does
this decision affect the supply chain in terms
of lot sizes, cycle inventories, and flow
times?
2. Under what conditions should a supplier offer
quantity discounts? What are appropriate
pricing schedules that a supplier seeking to
maximize profits should offer?
42
All-Unit Quantity Discounts
Figure 3
43
All-Unit Quantity Discounts
• Pricing schedule has specified quantity break points
q0, q1, …, qr, where q0 = 0
• If an order is placed that is at least as large as qi but
strictly smaller than qi+1, then each unit has an
average unit cost of Ci
• Unit cost generally decreases as the quantity
increases, i.e., C0 > C1 > … > Cr
• Objective is to decide on a lot size that will
minimize the sum of material, order, and holding
costs
44
All-Unit Quantity Discounts
Step 1: Evaluate the optimal lot size (EOQ) for each
price Ci, 0 ≤ i ≤ r (for qi  Q  qi +1)
as follows
2DS
Qi =
hCi
*
Q
Step 2: We next select the order quantity i for each
price Ci
1.
2.
3.
qi  Qi  qi +1 , then set Qi* = Qi
Qi  qi , then set Qi* = qi
Qi  qi +1 , then ignore this case.
45
All-Unit Quantity Discounts
Step 3: Calculate the total annual cost of
ordering Qi* units
æDö
æ Q* ö
Total annual cost, TCi = çç * ÷÷ S + çç i ÷÷ hCi + DCi
è Qi ø
è 2ø
*
Q
Step 4: Select i with the lowest total cost TC
i
46
All-Unit Quantity Discount Example
DO is an online retailer of prescription drugs and health supplements.
Demand for Vitamins is 10,000 bottles per month. DO incurs a fixed
ordering cost of $100 each time an order of vitamins is placed with the
manufacturer. DO incurs a holding cost of 20 percent. The
manufacturer uses the following all unit discount pricing schedule.
Evaluate the number of bottles that DO should order in each lot.
Order Quantity
Unit Price
0–4,999
$3.00
5,000–9,999
$2.96
10,000 or more
$2.92
q0 = 0, q1 = 5,000, q2 = 10,000; C0 = $3.00, C1 = $2.96, C2 = $2.92
D = 120,000/year, S = $100/lot, h = 0.2
47
All-Unit Quantity Discount Example
q0 = 0, q1 = 5,000, q2 = 10,000; C0 = $3.00, C1 = $2.96, C2 = $2.92
D = 120,000/year, S = $100/lot, h = 0.2
Step 1
Q0 =
2DS
2DS
2DS
= 6,324; Q1 =
= 6,367; Q2 =
= 6,410
hC0
hC1
hC2
Step 2
Ignore i = 0 because Q0 = 6,324 > q1 = 5,000
For i = 1, 2
Q1* = Q1 = 6,367; Q2* = q2 = 10,000
48
All-Unit Quantity Discount Example
Step 3
D
 Q1* 
TC1 =  *  S +   hC1 + DC1
 2 
 Q1 
 120, 000 
 6367 
=
 (100) + 
 (0.2)(2.96) + (120, 000)(2.96) = $358,969;
 6367 
 2 
 120, 000 
 10, 000 
TC2 = 
(100) + 
 (0.2)(2.92) + (120, 000)(2.92) = $354,520

 2 
 10, 000 
Step 4
Lowest total cost is for i = 2
*
Order Q2 = 10,000 bottles per lot at $2.92 per bottle
49
Impact of Quantity Discounts on the
Supply Chain
Recall that DO (retailer’s) information: D = 120,000 bottles/year,
SR = $100, hR = 0.2, CR = $3
Now consider the manufacturer’s cost: SM = $250, hM = 0.2, CM = $2
QR =
2 DS R
2 120, 000 100
=
= 6,324
hR CR
0.2  3
D
 QR 
Annual costs for DO =   S R +   hRCR = $3,795
 2 
 QR 
 D
Q 
Annual costs for manufacturer =   S M +  R  hM CM = $6, 009
 2 
 QR 
Annual supply chain cost
(manufacturer + DO)
= $6,009 + $3,795 = $9,804
50
Locally Optimal Lot Sizes
Annual cost for DO
and manufacturer
æ Dö
æQ ö
æ Dö
æQ ö
= ç ÷ S R + ç ÷ hRC R + ç ÷ S M + ç ÷ hM CM
èQø
è2ø
èQø
è2ø
The optimal Q for the
= Q* =
supply chain is
2 D( S R + S M )
= 9,165  6,324
hR CR + hM CM
 D 
 Q*
Annual costs for DO = 
S
+
 R 
 hR CR = $4, 059  $3, 795
 2 
 Q*
 D 
 Q*
Annual costs for manufacturer = 
S
+
 M 
 hM CM = $5,106  $6, 009
 2 
 Q*
Annual supply chain cost
(manufacturer + DO)
= $5,106 + $4,059 = $9,165< $9,804 51 Designing a Suitable Lot Size-Based Quantity Discount • Design a suitable quantity discount that gets DO to order in lots of 9,165 units when it aims to minimize only its own total costs • Manufacturer needs to offer an incentive of at least $264 = 4,059-3,795 per year to DO in terms of decreased material cost if DO orders in lots of 9,165 units • Appropriate quantity discount is $3 if DO orders in lots smaller than 9,165 units and $2.9978 = 3-264/120,000 for orders of 9,165 or more 52 Quantity Discount Takeaways • Lot size based discounts increase lot size and cycle inventory in the supply chain • Quantity discounts can increase the supply chain surplus for the following two main reasons 1. Improved coordination to increase total supply chain profits 2. Extraction of surplus through price discrimination 53 Recap • EOQ, lot size, cycle inventory, average flow time, etc. • Order Aggregation • Trade Promotion • All Unit Lot Size Based-Quantity Discount Purchase answer to see full attachment

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