Upload
anirudh-menon
View
1.178
Download
1
Tags:
Embed Size (px)
DESCRIPTION
Citation preview
1
Inventory BA 339
2
3
Inventory Definitions
Inventory vs. Inventory systemDependent vs. Independent
environmentsTypes
Safety StockAnticipation InventoryHedge inventory (unusual events)Transportation or Pipeline Inventory
4
Purposes of Inventory
1. Independence of operations.
2. Variation
Product demand
Material Delivery Time
3. Scheduling flexibility
4. Volume Discounts
5. Material price fluctuations
5
Inventory Costs
Holding (or carrying) costs
Setup (or production change) costs
Ordering costs.
Shortage costs.
6
Inventory Systems
Rules to manage inventory, specifically: timing (when to order) sizing (how much to order)
Continuous Review or Fixed-Order Quantity Models (Q)Event triggered (Example: running out of
stock) Periodic Review or Fixed-Time Period Models (P)
Time triggered (Example: Monthly sales call by sales representative)
7
Comparison of Periodic and Continuous Review Systems
Periodic Review Fixed order intervals Variable order sizes Convenient to
administer Inventory position only
required at review
Continuous Review Varying order intervals Fixed order sizes (Q) Allows individual review
frequencies Possible quantity discounts Lower, less-expensive
safety stocks
8
Inventory costs C = Unit cost or production cost: the
additional cost for each unit purchased or produced.
H = Holding costs: cost of keeping items in inventory(cost of lost capital, taxes and insurance for storage, breakage, etc., handling and storing)
S = Setup or ordering costs: a fixed cost incurred every time you place an order or a batch is produced.
9
Total costs of carrying inventory
Assumptions demand is constant and uniform throughout the
period for your products (5 cases per day) Price per unit is constant for the period ($16/case) Inventory holding cost is based on an average cost.
Total Inventory Policy Cost annually= annual purchase cost + annual order cost + annual holding cost
10
Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998
Cost Minimization Goal
Ordering Costs
HoldingCosts
QOPT
Order Quantity (Q)
COST
Annual Cost ofItems (DC)
Total Cost
11
Total cost of Inventory Policy
= annual purchase cost (annual demand * Cost/item)+ annual order cost (annual # orders * Cost to order)+ annual holding cost (average units held*cost to carry one unit)
12
HQ
SQ
DCDTC
2*
D = yearly demand of unitsC = cost of each unitQ = quantity orderedS = cost to place orderH = average yearly holding cost for each unit = storage+interest*CD/Q = number of orders per yearQ/2 = average inventory held during a given period assuming with start with Q and drop to zero before next order arrives (cycle inventory).
Total Inventory Cost Equation
13
Deriving the EOQ :Economic Order Quantity
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero
Cost Holding Annual
Cost) Setupor der Demand)(Or 2(Annual =
H
2DS = EOQQ
14
EOQ Model--Basic Fixed-Order Quantity Model (Q)
R = Reorder pointQ = Economic order quantityL = Lead time
L L
Q QQ
R
Time
Numberof unitson hand
15
The Reorder Point
Reorder point = (average period demand)*Lead Time periods= d * L
16
Another EOQ Example
Annual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15
Determine the economic order quantity & reorder point.
17
Minor Deviations Here
What causes minor deviations from the ideal order size?
Assumptions behind the regular EOQ Model?
18
Variations in lead time
If we have variations in lead time, how should we change the reorder point so we rarely run out?
Reorder Point = Average demand during lead time(d*L) + safety stock (Z* L)
where: d = average daily (or weekly) demandL = Lead time (matching days or weeks)L = standard deviation of demand during lead time. D = standard deviation of demand (days or weeks).
LDL
19
Service Level or % of time inventory will meet demand during lead time
Z Value Resulting Service Level
1.28 90%
1.65 95%
2.33 99%
3.08 99.9%
20
Example
Annual Demand = 1000 units 250 work days in the year
d=1000/250 = 4 units/day Q= 200 units
L=9 days L = 3 units
z=2 (97.7% likelihood that we won’t run out during lead time)
Reorder point= d*L +z*L = (4*9) + (2*3) = 42 units
21
P Method (periodic review)
You have a predetermined time (P) between orders (sales rep comes by every 10 days) or the average time between orders from EOQ = Q/D
How much should you order to bring inventory level up to some predetermined level, R where:
R = restocking level Current Inventory position = IP Order Quantity= R-IP
22
Restocking Level Needs to meet most demand situations R= Restocking level
= Average demand during lead time & review period+ safety stock= P+L + z* P+Lwhere:P+L = average demand during lead time and review period z = # of standard dev from mean above the average demand (higher z is lower probability of running out). RP+L = standard deviation of demand during lead time + review period
23
ABC Inventory Management
Based on “Pareto” concept (80/20 rule) and total usage in dollars of each item.
Classification of items as A, B, or C based on usage.
Purpose is to set priorities on effort used to manage different SKUs, i.e. to allocate scarce management resources.
SKU: Stock Keeping Unit
24
ABC Inventory Management
‘A’ items: 20% of SKUs, 80% of dollars‘B’ items: 30 % of SKUs, 15% of dollars‘C’ items: 50 % of SKUs, 5% of dollarsThree classes is arbitrary; could be any
number.Percents are approximate.Danger: dollar use may not reflect
importance of any given SKU!
25
Item
Annual Usage in
Units Unit Cost Dollar Usage
Percentage of Total
Dollar Usage
1
5,000 $ 1.50 $ 7,500 2.9%
2
1,500 8.00 12,000 4.7%
3
10,000 10.50 105,000 41.2%
4
6,000 2.00 12,000 4.7%
5
7,500 0.50 3,750 1.5%
6
6,000 13.60 81,600 32.0%
7
5,000 0.75 3,750 1.5%
8
4,500 1.25 5,625 2.2%
9
7,000 2.50 17,500 6.9%
10
3,000 2.00 6,000 2.4%
Total $ 254,725 100.0%
Example of SKU list for 10 items
26
ABC Chart for SKU List
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
3 6 9 2 4 1 10 8 5 7
Item No.
Pe
rce
nt
Usa
ge
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
Cu
mu
lati
ve %
Usa
ge
Percentage of Total Dollar Usage Cumulative Percentage
A B C
27
ABC Application
Jewelry StoreFine Dining RestaurantOutdoor RetailerLarge Department Store