Operations
10
473.31
Fall 2015
Bruce Duggan
Providence University College
Summary
• Two main classes of demand:
o independent demand
o dependent demand
• Independent demand is the focus of this chapter
o based on statistics
• In the fixed-order-quantity and fixed-time-period models, the influence of
service level was shown on safety stock and reorder point determinations.
• inventory reduction requires a knowledge of the operating system
• A major goal of most firms today is to reduce inventory
Learning Objectives Review
1. What is the strategic role of inventory and where do you position it in
the supply chain?
2. What are the different reasons for keeping inventory?
3. What are the different costs of creating and holding inventory?
4. Discuss how the type of inventory system logic that is appropriate for an
item depends on the type of demand for that item.
5. Calculate the appropriate order size when a one-time purchase must be
made.
Learning Objectives Review
6. What is the economic order quantity and how do you calculate it?
7. Discuss fixed-order-quantity and fixed-review-period models, including ways
to determine safety stock when there is variability in demand.
8. What is Pareto (ABC) analysis of inventory?
9. What is inventory counting and what is its relationship to inventory accuracy?
Definitions
Inventory
• “the stock of any item or resource used in an organization”
• it can include:
o raw materials
o finished products
o component parts
o Supplies
o work-in-process
An inventory system is the set of policies and controls that monitor levels of
inventory and determines what levels should be maintained, when stock
should be replenished, and how large orders should be
Definitions
An Inventory System
• “the set of policies and controls that monitor levels of inventory and
determine
o what levels should be maintained
o when stock should be replenished, and
o how large orders should be”
LO1
Supply Chain Inventories
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Inventory Systems
Single-period Inventory model
• used when making a one time purchasing decision
Fixed-order-quantity model (Q-model)
• a model where the amount requisitioned is fixed and the actual ordering is
triggered by inventory dropping to a specified level of inventory
• also called Economic Order Quantity (EOQ)
Fixed-time-period model (P-model)
• a model that specifies inventory is ordered at the end of a predetermined
time period
Purposes of Inventory
1. To maintain independence of operations
2. To meet variation in product demand
3. To allow flexibility in production scheduling
4. To provide a safeguard for variation in raw material delivery time
5. To take advantage of economic purchase order size
Inventory Costs
1. Holding (or carrying) costs
• include the costs for
• storage facilities
• handling
• insurance
• pilferage
• breakage
• obsolescence
• depreciation
• taxes, and
• the opportunity cost of capital
2. Setup (or production change) costs
• include the costs for arranging specific
equipment setups
Inventory Costs
3. Ordering (or order preparation) 4. Shortage costs
costs
• the cost of
•
the managerial and clerical
costs to prepare the purchasing
order such as:
•
cost of someone placing an order
•
counting items, and
•
calculating order sizes
•
lost profits
•
lost customers, and
•
lateness penalties
Independent vs Dependent Demand
Independent demand
• the demands for various items
that are unrelated to each other.
Dependent demand
• the need for any one item is a
direct result of the need for some
other item, usually an item of
which it is a part.
Single-Period Inventory Model
Cu
10.1: P £
Co + Cu
Where :
This model states that we
should continue to increase
the size of the inventory so
long as the probability of
selling the last unit added is
equal to or greater than the
ratio of: Cu/Co+Cu
Co = Cost per unit of demand overestimated
Cu = Cost per unit of demand underestimated
P = Probability that the unit will be sold
Single Period Model Example
Our college basketball team is playing in a tournament game this weekend.
Based on our past experience we sell on average 2,400 shirts with a standard
deviation of 350. We make $10 on every shirt we sell at the game, but lose
$5 on every shirt not sold. How many shirts should we make for the game?
Solution:
• Cu = $10 and Co = $5
• P ≤ $10 / ($10 + $5) = .667
Z.667 = .432 (use NORMSINV(.667) or Appendix E)
• therefore we need 2,400 + .432(350) = 2,551 shirts
Multiperiod Inventory Systems
Multiperiod Inventory Systems
Fixed-Order-Quantity Models Assumptions
• Demand for the product is constant and uniform throughout the period.
• Lead time is constant.
• Price per unit of product is constant.
• Inventory holding cost is based on average inventory.
• Ordering or set-up cost are constant.
• All demands for the product will be satisfied. (No backorders are allowed.)
LO6
Fixed-Order-Quantity Models
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Basic Fixed-Order Quantity (EOQ) Model Formula
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Fixed-Order-Quantity Models
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EOQ Example Problem Data
EOQ Example Solution
Lot Size vs. Set-up Cost
Fixed-Order-Quantity Model with Safety Stock
Fixed-Order-Quantity Model with Safety Stock
Fixed-Order-Quantity Model with Safety Stock
Fixed-Order-Quantity Model with Safety Stock
Example
Fixed-Time-Period Model
Fixed-time-period model (P-model)
• inventory is ordered at the end of a predetermined time period.
Inventory is counted only at particular times, such as every week or
every month.
Fixed-Time-Period Model with Safety Stock
Fixed-Time-Period Model with Safety Stock
Fixed-Time-Period Model with Safety Stock Example
EXAMPLE 10.5: QUANTITY TO ORDER
Daily demand for a product is 10 units with a
standard deviation of 3 units. The review period is 30
days, and lead time is 14 days. Management has set
a policy of satisfying 98 percent of demand from
items in stock. At the beginning of this review
period, there are 150 units in inventory.
How many units should be ordered?
Fixed-Time-Period Model with Safety Stock Example
Inventory Control and Supply Chain
Management
Inventory turn
• a key measure that relates inventory control to company performance
• Inventory turn = Cost of goods sold / Average inventory value
Inventory Control and Supply Chain Management
Inventory Control and Supply Chain
Management - Example
Inventory Control and Supply Chain
Management - Example
ABC Classification System
Items kept in inventory are not of equal importance in terms of:
• dollars invested
• profit potential
• sales or usage volume
• stock-out penalties
So, identify inventory items based on percentage of total
dollar value, where “A” items are roughly top 15 %, “B”
items as next 35 %, and the lower 65% are the “C” items
ABC Classification System Example
ABC Classification System Example
ABC Classification System Example
Inventory Accuracy and Cycle Counting
Inventory accuracy
• how well the inventory records agree with physical count.
Cycle Counting
• is a physical inventory-taking technique in which inventory is counted on a
frequent basis rather than once or twice a year
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End of Chapter 10
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