International Operations
Management
MGMT 6367
Lecture 04
Instructor: Yan Qin
Fall 2013
Outline – Supply Chain Management
 Push, Pull, and Push-Pull systems
 Distribution Strategies
 Design for Supply Chain efficiency
 Supply Chain Contracts
 Buy Back contracts
 Quantity Discount s
 More Supply Chain contracts
 Cycle inventory
Push-based Supply Chain
 In a push-based supply chain, production and distribution
decisions are based on demand forecasts.
 Products are pushed from upstream to downstream.
Pull-Based Supply Chain
 In a pull-based supply chain, production and distribution
are demand driven so that they are coordinated with true
customer demand rather than forecast demand.
Push Vs. Pull
Area
Push system
Pull system
Response time to
changes in demand
Slow, may lead to lost sales
Quick, demand driven
when there is upturn and
inventory obsolescence when
demand drops
Product customization Difficult
Relatively easy
DemandVariability to
upstream members
High
Low
Inventory level
High
Low (no inventory in a
pure pull system)
Economies of scale
Yes
Often difficult due to
small batches
Implementation
Easy, just build inventory
Difficult
Push-Pull Supply Chain
 In a push-pull system, some stages of the supply chain,
usually the initial stages, such as supplier and manufacturer,
are operated in a push-based manner while the remaining
stages employ a pull-based strategy.
Distribution Strategies
 Three common outbound distribution strategies:
 Direct shipment: Products are shipped directly from
supplier to the retail stores.
 Warehousing: Classical strategy in which warehouses keep
stock and fulfill orders from the retailer.
 Cross-docking: Products are distributed continuously from
suppliers through warehouses to customers. But the
warehouse rarely keep the products for more than 10 to 15
hours.
Direct Shipment
 Direct shipment is common for large retailers, which
requires fully loaded trucks.
Advantages
Disadvantages
Avoid of the expense of operating
a distribution center
Higher transportation costs if
shipments are small and the
supplier serves a number of
retailers
Reduced lead time
Cross-docking
 In cross-docking, the warehouse is used as an inventory
coordination point rather than as an inventory storage
point.
 The implementation of cross-docking requires:
 A significant start-up investment;
 Retailers and suppliers must be linked with advanced
information systems, such as at Wal-Mart.
 A fast and responsive transportation system.
 Effective only for large distribution systems in which a large
number of vehicles are delivering and picking up at any one
time.
Design product for Supply Chain efficiency
 Product design used to be an independent function isolated
from manufacturing and logistics.
 Design for manufacturability (DFM) movement:
 The link between product design and manufacturing was
established out of the need to know why products fail and
how to minimize the failure.
 It was recognized that product reliability is closely linked
with product design.
 DFM is also called concurrent engineering
Design product for Supply Chain efficiency
 Design for Logistics (DFL)
 Innovative product designs appear that take logistics
considerations into account.
 Two significant ways that logistics considerations enter into
product design phase:
 Product design for efficient transportation and shipment
 Delayed differentiation to take advantage of benefits such as
economies of scale.
Allocation of Supply Chain Profits
 With respect to the allocation of supply chain profit, firms
should care about two things:
 The size of a firm’s piece of the “pie”, where the pie refers to
the supply chain’s total profit;
 The size of the total “pie”.
Buy-back Contracts
 Buy-back contracts introduce new costs into the supply
chain since the original buyer will need to ship the leftover
inventory back to the original supplier.
 Buy-back contracts may also generate new revenue as the
supplier may be able to resell the leftover to another buyer,
possible at another location.
 What can be some other possible reasons for a supplier to
accept returns from a buyer?
More Supply Chain Contracts
 Three common-type of quantity discount supplier pricing:
 Linear Quantity Discount
This quantity discount scheme assumes that a supplier offers a
price that decreases in the quantity ordered by a retailer.
Let t be some constant discount rate and 𝑣𝑓 be the base price.
Unit price for order quantity Q:
𝑣 𝐿𝐷 𝑄 = 𝑣𝑓 − 𝑡 × 𝑄
Linear Quantity Discount
All-unit Quantity Discount
 All-unit Quantity Discount
The unit price offered by a supplier declines on a step function
basis. Define 𝑣𝑖 as a set of alternative unit prices such that
𝑣1 > 𝑣2 > ⋯ > 𝑣𝑛
And let 𝑞𝑖 be a set of quantities, called break points, such that
𝑞1 < 𝑞2 < ⋯ 𝑞𝑛
Set 𝑞0 = 0.
Then the all-unit quantity discount can be expressed as
𝑣𝑖 𝑓𝑜𝑟 𝑞𝑖−1 < 𝑄 ≤ 𝑞𝑖 ,
𝑓𝑜𝑟 𝑖 = 1,2,3 …
All-Unit Quantity Discount
Unit cost
Incremental Quantity Discount
 Incremental Quantity Discount
Under incremental quantity discounts, discounts are only applied
to additional units beyond the breakpoints. The unit cost/price
𝑣𝑖 for the quantity interval (𝑞𝑖−1 , 𝑞𝑖 ] decreases as 𝑖 increases.
The average unit cost/price can be calculated as follows:
𝑣1 𝑓𝑜𝑟 0 < 𝑄 ≤ 𝑞1 ,
𝑣1 𝑞1 +𝑣2 (𝑄−𝑞1 )
𝑄
for 𝑞1 < 𝑄 ≤ 𝑞2
𝑣1 𝑞1 +𝑣2 𝑞2 −𝑞1 +𝑣3 (𝑄−𝑞2 )
𝑄
for 𝑞1 < 𝑄 ≤ 𝑞2
The unit discounted price is just the total purchase cost divided by
the order quantity.
Example
 Suppose a trash bag company charges based on an
incremental scheme. Specifically, it charges 30 cents per
bag for the first 500 bags, 29 cents for all units beyond.
 Then for orders of no more than 500 bags, what is the
average cost?
 For orders of less than 1001 bags but more than 500, what
is the average cost?
Incremental Quantity Discount
Example: Quantity Discount
 Suppose a store has been given an all-unit quantity discount
schedule for a product. The normal cost for the product is $5. For
orders between 1001 and 2000 units, the unit cost drops to $4.8;
for orders of 2001 or more units, the unit cost is only $4.75. The
store expect the sales for that product in the next month to be
2500. How much does it pay?
 Now how much does the store pay if it is offered an incremental
quantity discount scheme with the same quantity break points
as stated above. The price is $5 for orders no greater than 1000.
For the next additional 1000 units, the unit price becomes $4.8.
For any additional units above 2000, the price drops to $4.75.
What is the purchasing cost?
Comments:
 Note that the average cost/price per unit with an all-unit
schedule will be less than the average cost per unit with the
corresponding incremental schedule.
 Notice the irrationality of the all-unit schedule? In the
example, 1,000 units would cost $5,000, whereas 1,001
units would only cost $4,804.8. This is an incentive for a
buyer to purchase more.
More Supply Chain Contracts
 Options Contracts
 With an options contract, a buyer pays a price to purchase
options and another price to exercise the purchased options.
 Revenue Sharing
 With revenue sharing, a buyer pays a wholesale price to the
supplier but then also pays a portion of the revenue earned.
More Supply Chain Contracts
 Quantity Flexibility Contracts
 Suppose a buyer and a supplier agree upon a 25% Quantity
Flexibility Contract.
 Price Protection
 With price protection, a supplier compensates the buyer on
remaining inventory for any price reduction.
Green Supply Chain

A fully developed green supply chain considers
sustainability for every participant at every step, from
product design to production, transportation, storage,
consumption, to eventual disposal or recycling.

The objective is to reduce waste, mitigate legal and
environmental risks, minimize or eliminate adverse health
impacts, improve the reputations of companies and their
products, and enable compliance with increasingly
stringent regulations and societal expectations.
Next: Cycle Inventory

We will next discuss
1. How to choose the optimal lot size and cycle
inventory to minimize the related costs in a supply
chain using the Economic Order Quantity model;
and
2. Quantify the impact of quantity discounts on lot size
and cycle inventory.
Cycle Inventory

A 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.
Let’s start with the simplest situation…
 Suppose (1) there is no uncertainty in demand and (2)
order lead time is zero.
 For effective inventory control in this overly simplified
situation, Ford W. Harris introduced the Economic Lot
Size model, or Economic Order Quantity (EOQ) model,
in 1915.
 The EOQ model illustrates the tradeoff between the setup
cost and inventory holding cost.
EOQ Model
 Three types of costs are considered in the EOQ model:
 Purchasing cost per unit, that is, selling price, denoted as C
 Setup cost, which is the fixed cost incurred by order
placement, denoted as K (aka, ordering cost)
 Inventory holding cost per unit per year, denoted as h
 The objective is to minimize the sum of the three types of
costs on an annual basis.
EOQ Model
 Let D denote the annual demand and Q denote the order
quantity. Then the total annual cost can be expressed as
𝐷
𝑄
𝑇𝐶 = 𝐷 × 𝐶 + 𝐾 × + ℎ ×
𝑄
2
Economic Order Quantity
 Using a little calculus, the order quantity that minimizes
the total annual cost is
𝑄∗
=
2𝐾𝐷
ℎ
Cycle Inventory under EOQ model

When demand is steady, cycle inventory and lot size are
related as follows:
Cycle inventory =

𝐿𝑜𝑡 𝑠𝑖𝑧𝑒
2
=
𝑄
2
𝑄∗
model,
2
Therefore, under the EOQ
is the optimal cycle
inventory level that minimizes the total cost.
Example: EOQ & Cycle Inventory
 Consider a hardware supply warehouse that is contractually
obligated to deliver 52,000 units of a fastener to a local
manufacturer in a year. Each time the warehouse places an
order from its suppliers, an ordering and transportation fee of
$20 is charged. The warehouse pays $1 per each fastener.
Annual inventory holding cost is 25% of the unit inventory
value, or $0.25 per year.
 The warehouse manager would like to know how much to
order each time when the inventory gets to zero.
 And what is the resulted cycle inventory level?
Impact of quantity discounts

We now consider pricing schedules that encourage buyers
to purchase in large lots.

The buyer’s objective is to select lot sizes to minimize the
total annual material, order, and holding costs when given
a quantity discount.
Find the optimal lot sizing response

To find the optimal lot size under an all-unit quantity
discount, we need to evaluate the optimal lot size for each
price and pick the one that minimizes the overall cost.

Step 1: Evaluate the optimal lot size for each price, 𝑣𝑖 , as
follows.
𝑄𝑖 =
2𝐷𝑆
ℎ𝑣𝑖
Find the optimal lot sizing response

Step 2: We next select the order quantity 𝑄𝑖 * for each
price 𝑣𝑖 . There are three possible cases for 𝑄𝑖 :
1. 𝑞𝑖−1 ≤ 𝑄𝑖 ≤ 𝑞𝑖
2. 𝑄𝑖 < 𝑞𝑖−1
3. 𝑄𝑖 > 𝑞𝑖
Case 3 can be ignore, since it is for 𝑄𝑖+1 .
In Case 1, we set 𝑄𝑖∗ = 𝑄𝑖 ;
In Case 2, we set 𝑄𝑖∗ =𝑞𝑖−1 to take advantage of the quantity
discount.
Find the optimal lot sizing response

Step 3: For each 𝑄𝑖∗ , calculate the resulted total annual
cost as follows:
Total cost, 𝑇𝐶𝑖 =

𝐷
𝑄𝑖∗
𝐾+
𝑄𝑖∗
2
ℎ𝑣𝑖 + 𝐷𝐶
Step 4: Select the 𝑄𝑖∗ with the lowest total cost.
Example: EOQ under all-unit discount

The demand for a product is 10,000 bottles per month.
The fixed ordering cost incurred at the buyer’s place is
$100 per order and the inventory holding cost is 20%.
The seller uses the following all unit discount scheme.
Quantity breaks

Unit Price
0 – 4,999
$3.00
5,000 – 9,999
$2.96
10,000 and more
$2.92
What is the optimal order quantity or lot size in this case?
Next Week

Production Facility Layouts
◦ Basic production Layouts
◦ Suitable products for each layout
◦ Design of Process Layout
 CRAFT
 Systematic Layout Planning
◦ Design of Assembly Line
 Assembly line balancing
 How to speed up