Unit08 - Inventory_Management
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Transcript of Unit08 - Inventory_Management
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Dr. Rameez Khalid, PMP, CQSSBB Faculty, Department of Management
Institute of Business Administration, Karachi
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Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Inventory: a stock or store of goods
Inventory
2
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Types of Inventories
Raw materials & purchased parts Partially completed goods called
work in progress (WIP) Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)
Unit-8: Inventory Management [email protected] 3
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Types of Inventories
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers
Unit-8: Inventory Management [email protected] 4
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Functions of Inventory
To meet anticipated demand To smooth production requirements To decouple operations To protect against stock-outs To take advantage of order cycles To help hedge against price increases To permit operations To take advantage of quantity discounts
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Objective of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service
Costs of ordering and carrying inventory
Inventory turnover is the ratio of: average cost of goods sold to average inventory investment.
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A system to keep track of inventory A reliable forecast of demand Knowledge of lead times Reasonable estimates of
Holding costs Ordering costs Shortage costs
A classification system
Effective Inventory Management
Unit-8: Inventory Management [email protected] 7
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Inventory Counting Systems
Periodic System (T or P System) Physical count of items made at periodic intervals
Perpetual Inventory System (Q System) System that keeps track of removals from inventory continuously, thus monitoring current levels of each item
Unit-8: Inventory Management
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Inventory Counting Systems (Contd)
Two-Bin System - Two containers of inventory; reorder when the first is empty
Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached
0
214800 232087768
Unit-8: Inventory Management [email protected] 9
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Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory
Shortage costs: costs when demand exceeds supply
Key Inventory Terms
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Holding Costs
Obsolescence Insurance Extra staffing Interest Pilferage Damage Warehousing Etc.
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Ordering/Setup Costs
Supplies/Freight Incoming QC Order processing Clerical support Etc.
Unit-8: Inventory Management [email protected] 12
Clean-up costs Re-tooling costs Adjustment costs Etc.
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ABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly.
A - very important B - mod. important C - least important
0 20 40 60 80
100
0 50 100 % of Inventory Items
% A
nnua
l $ U
sage
A
B C
Class % $ Vol % Items A 80 15 B 15 30 C 5 55
Unit-8: Inventory Management
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Inventory
Process stage
Demand Type
Number & Value Other
Raw Material WIP Finished Goods Independent
Dependent
A Items B Items C Items
Maintenance Dependent Operating
Inventory Classifications
Unit-8: Inventory Management [email protected] 14
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Cycle Counting
A physical count of items in inventory
Cycle counting management
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?
Unit-8: Inventory Management [email protected] 15
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Fixed order-quantity models Economic order quantity (EOQ) Economic production quantity (EPQ)
or Production order quantity (POQ) Quantity discount
Probabilistic models Fixed order-period models
Help answer the inventory planning questions!
Inventory Models
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Economic order quantity (EOQ) model The order size that minimizes total annual cost
Economic production model
Quantity discount model
Economic Order Quantity Models
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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
Assumptions of EOQ Model
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The Inventory Cycle
Profile of Inventory Level Over Time
Quantity on hand
Q
Receive order
Place order
Receive order
Place order
Receive order
Lead time
Reorder point
Usage rate
Time
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Total Cost
Annual carrying cost
Annual ordering cost
Total cost = +
TC = Q 2 H D Q
S +
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Cost Minimization Goal
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
Annu
al C
ost
(optimal order quantity)
TC Q H DQ
S 2
Holding Costs
22
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Deriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
Q = 2DSH
= 2(Annual Demand )(Order or Setup Cost )Annual Holding CostOPT
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Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
Q
2 H D Q
S =
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EOQ A local distributor for a national tire company
expects to sell approx. 9,600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year.
a. EOQ? b. How many Orders? c. Length of an order cycle? d. Total Annual Cost?
25
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Production done in batches or lots Capacity to produce a part exceeds the parts
usage or demand rate Assumptions of EPQ are similar to EOQ except
orders are received incrementally during production
Economic Production Quantity (EPQ)
Unit-8: Inventory Management [email protected] 27
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EOQ EPQ Model When To Order
Reorder Point (ROP)
Time
Inventory Level
Lead Time
Optimal Order Quantity (Q*)
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EPQ Model Inventory Levels Inventory Level
Time Supply Begins
Supply Ends
Production portion of cycle
Demand portion of cycle with no supply
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EPQ Model Inventory Levels
Time
Inventory Level
Production Portion of Cycle
Imax Max. Inventory Q(1- u/p)
Q*
Supply Begins
Supply Ends
Inventory level with no demand
Demand portion of cycle with no supply
Unit-8: Inventory Management [email protected] 30
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Economic Run Size
Q DSH
pp u
02
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D = Demand per year S = Setup cost H = Holding cost u = Demand per day p = Production per day
EPQ Model Equations
Optimal Order Quantity
Setup Cost
Holding Cost
= = -
= *
= *
=
Q H* u
p
Q
D Q
S
p *
1
(
0.5 * H * Q - u p
1
) - u p 1
( )
2*D*S
( ) Maximum inventory level
Imax
32
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EPQ A toy manufacturer uses 48,000 rubber wheels
per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year.
a. EPQ or POQ or Optimal Run Size? b. Minimum Total Annual Cost? c. Cycle Time? d. Run Time?
33
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Answers how much to order & when to order Allows quantity discounts
Reduced price when item is purchased in larger quantities
Other EOQ assumptions apply Trade-off is between lower price & increased
holding cost Buyers Goal:
Select the order quantity that will minimize the total cost.
Quantity Discount Model
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Total Costs with Purchasing Cost
Annual carrying cost
Purchasing cost TC = +
Q 2 H
D Q
S TC = +
+ Annual ordering cost
PD +
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Total Costs with PD C
ost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing cost doesnt change EOQ
37
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Case1: Constant Holding Costs
OC
EOQ Quantity
Tota
l Cos
t
TCa
TCc
TCb Decreasing Price
HC a,b,c
38
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Quantity Discount When D = 816 cases per year, S =$12, and
H=$4 per case per year, determine for the following discounts:
a. Optimal Order Quantity? b. Total Cost?
Range Price 1 to 49 $20 50 to 79 18 80 to 99 17 100 or more 16
39
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Quantity Discount
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Case2: Holding Cost as Percentage of Purchase Price
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Quantity Discount When D = 4000 switches per year, S =$30,
and H=0.40P per unit per year, determine for the following discounts:
a. Optimal Order Quantity? b. Total Cost?
Range Price 1 to 499 $0.90 500 to 999 0.85 1000 or more 0.80
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Case2: Holding Cost as Percentage of Purchase Price
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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 and/or lead time.
Service Level - Probability that demand will not exceed supply during lead time.
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Determinants of the Reorder Point
The rate of demand The lead time Demand and/or lead time variability Stock-out risk (safety stock)
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ROP and Safety Stock
Safety stock
reduces risk of
Stock-out during lead
time
ROP = d x LT
= Expected Demand during Lead time + Safety Stock
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ROP and Safety Stock
ROP = expected demand during LT + Safety Stock
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ROP and Safety Stock Service Level = 100% - Stock-out Risk
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ROP and Safety Stock
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51
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Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory
levels Risk of stockout Fill rate the percentage of demand filled by the
stock on hand
Fixed-Order-Interval Model
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Time
Inventory Level Target maximum
Period Period Period
Fixed Period Model When to Order?
54
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Benefits: Items from same supplier may yield savings in:
Ordering Packing Shipping costs
May be practical when inventories cannot be closely monitored
Disadvantages: Requires a larger safety stock Increases carrying cost Costs of periodic reviews
Fixed-Interval Model
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Too much inventory Tends to hide problems Easier to live with problems than to eliminate
them Costly to maintain
Wise strategy Reduce lot sizes Reduce safety stock
Operations Strategy
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REFERENCES
Operations Management William J. Stevenson
Operations Management Barry Render & Jay Heizer
Solution: Slide#25 = a. 300 tires; b. 32; c. 9 working days; d. $4800 Slide#33 = a. 2400 wheels; b. $1800; c. 12 days; d. 3 days Slide#39 = a. 100 cases; b. TC100=$13354 Slide#42 = a. 1000 switches; b. TC1000=$3480