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Inventory Management
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1DSC 335, Fall 2009
Inventory Management
DSC 335
2DSC 335, Fall 2009
DSC 335 Roadmap
Operations Strategy
Process Management
Process strategy/analysis
Capacity analysis/planning
Quality management
Lean systems
Supply Chain Mgmt.
Supply chain dynamics
Inventory management
Case: Kristen’s Cookie
Case: Blanchard
Littlefield Game 1
Littlefield Game 2
Case: A Pain in Chain
Beer game
Decision Making Tools
3DSC 335, Fall 2009
Inventory
Definition: the stock of any item or resource used in an organization
In the forms of Raw materials & component parts Work in process Finished products Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers
4DSC 335, Fall 2009
Inventory Example – a PC Manufacturer
5DSC 335, Fall 2009
How Much Inventory We Need to Manage
In 2006 (nation-wide), the monthly average inventory is Retail: $ 486 B Wholesale: $ 381 B Manufacturing: $ 470 B Total: $1,337 B
6DSC 335, Fall 2009 data from finance.yahoo.com
Inventory
($million)% in Current Assets % in Total Assets
Wal-Mart 32,191 73.46% 23.30%
Target 7,797 50.80% 20.59%
Bestbuy 3,338 41.80% 28.14%
Amazon 877 26.00% 20.10%
Exxon Mobil 9,321 12.71% 4.47%
Boeing 8,105 35.27% 15.65%
GM 21,394 34.44% 4.56%
Ford 10,271 16.32% 3.72%
Toyota 13,799 15.10% 5.64%
Cisco 1,371 5.34% 3.17%
Solectron 1,516 34.84% 28.22%
Dell 576 3.25% 2.49%
Apple 270 1.86% 1.57%
HP 7,750 16.06% 9.45%
Inventory in Balance Sheets
7DSC 335, Fall 2009
Pressure to Cut Inventory
0
30
60
90
120
1980 1985 1990 1995 2000 2004
Wal-Mart Kmart Target
Days of Inventory
8DSC 335, Fall 2009
Sun’s Incentive Compensation to Boost Supply-Chain Performance
Bob Ferrari, a former employee of Sun Microsystems, says Sun is on the cutting edge of incentive compensation. Within Ferrari’s business unit at Sun, compensation metrics was weighted toward the supply chain. “On-time delivery, inventory turns, and customer satisfaction were all tied into pay,” Ferrari says.
– Jennifer Caplan, CFO.com
9DSC 335, Fall 2009
Why Hold Inventory?
10DSC 335, Fall 2009
Why Not to Hold Inventory?
11DSC 335, Fall 2009
Cost of Holding Inventories
Annual holding cost of inventory is 30 to 35% of its value! This means: Retail: $ 486 B Wholesale: $ 381 B Manufacturing: $ 470 B Total: $1,337 B
Total inventory holding cost
= $ 1,337 B * 30% = $ 400 Billion !!
12DSC 335, Fall 2009
Inventory Control
Managerial Objectives for Inventories Minimize the investment/cost tied in inventories. Meet the inventory availability needs of customers.
Inventory control answers two questions. How much to order? When to order?
Coping with uncertainty is challenging. Forecast demand and lead times. Sets stock availability levels (service levels).
13DSC 335, Fall 2009
Economic Order Quantity (EOQ) Model
14DSC 335, Fall 2009
Economic Order Quantity (EOQ) Model
Key Assumption 1 : All aspects are known with certainty Constant demand stream (No demand variability) Constant setup cost per order (independent of size of order) Constant annual holding cost per unit Constant lead time (= zero in the basic setting)
Instant replenish No backorders are allowed
15DSC 335, Fall 2009
Managerial Questions
1. When to order/produce (assuming zero lead time)? When your inventory reaches zero
2. How much to order/produce? Let’s see…
16DSC 335, Fall 2009
How Much Should We Order?
Holding cost Order setup cost Purchase cost
Large order size
Small order size
Time
Inventory
Inventory
Large order size
Small order size
Time
Slope = Demand rate
High
Low
Low
High
Same
Same
17DSC 335, Fall 2009
Economic Order Quantity (EOQ) Model
Data (inputs to the model)
D = Demand rate (units / yr)
c = Cost of purchasing or producing a unit ($ / unit)
S = Setup cost or per order or per production run ($)
H = Annual holding cost per unit of inventory ($ / (unit•yr))
H is often taken as a percentage of the unit cost:
H = ic, where i is annual percentage holding cost
Decision: Q = Quantity of an order (units)
Objective: To minimize the total cost
Let’s see how to compute the total cost …
18DSC 335, Fall 2009
Total Cost (TC)
Number of orders per year = D / Q ( / yr)
Annual ordering cost = (D / Q) S ($ / yr)
Average inventory = Q / 2 (units)
Annual holding cost = (Q / 2) H ($ / yr)
Annual purchase cost = c D ($ / yr)
Slope = D (units/year)Inventory
Q
Time
19DSC 335, Fall 2009
Inventory Management at South Face
Here are some facts about The South Face retail shop:
D: 1200 jackets / year
S: $2,000
c: $200 per jacket
i: 25% / year
What order size (Q) would you recommend for The South Face ?
retailerwarehouse
20DSC 335, Fall 2009
The South FaceNumber of units Number of Annual Annual Annualper order/batch Batches per Setup Cost Holding Cost Total Cost
Q Year: D/Q $ $ $50100150200250260270280290300310320330340350400500600700
21DSC 335, Fall 2009
The South FaceNumber of units Number of Annual Annual Annualper order/batch Batches per Setup Cost Holding Cost Total Cost
Q Year: D/Q $ $ $50 24 48000100 12 24000150 8 16000200 6 12000250 4.8 9600260 4.6 9231270 4.4 8889280 4.3 8571290 4.1 8276300 4 8000310 3.9 7742320 3.75 7500330 3.6 7273340 3.5 7059350 3.4 6857400 3 6000500 2.4 4800600 2 4000700 1.7 3429
22DSC 335, Fall 2009
The South FaceNumber of units Number of Annual Annual Annualper order/batch Batches per Setup Cost Holding Cost Total Cost
Q Year: D/Q $ $ $50 24 48000 1250100 12 24000 2500150 8 16000 3750200 6 12000 5000250 4.8 9600 6250260 4.6 9231 6500270 4.4 8889 6750280 4.3 8571 7000290 4.1 8276 7250300 4 8000 7500310 3.9 7742 7750320 3.75 7500 8000330 3.6 7273 8250340 3.5 7059 8500350 3.4 6857 8750400 3 6000 10000500 2.4 4800 12500600 2 4000 15000700 1.7 3429 17500
23DSC 335, Fall 2009
The South FaceNumber of units Number of Annual Annual Annualper order/batch Batches per Setup Cost Holding Cost Total Cost
Q Year: D/Q $ $ $50 24 48000 1250 49250100 12 24000 2500 26500150 8 16000 3750 19750200 6 12000 5000 17000250 4.8 9600 6250 15850260 4.6 9231 6500 15731270 4.4 8889 6750 15639280 4.3 8571 7000 15571290 4.1 8276 7250 15526300 4 8000 7500 15500310 3.9 7742 7750 15492320 3.75 7500 8000 15500330 3.6 7273 8250 15523340 3.5 7059 8500 15559350 3.4 6857 8750 15607400 3 6000 10000 16000500 2.4 4800 12500 17300600 2 4000 15000 19000700 1.7 3429 17500 20929
24DSC 335, Fall 2009
The South FaceNumber of units Number of Annual Annual Annualper order/batch Batches per Setup Cost Holding Cost Total Cost
Q Year: D/Q $ $ $50 24 48000 1250 49250100 12 24000 2500 26500150 8 16000 3750 19750200 6 12000 5000 17000250 4.8 9600 6250 15850260 4.6 9231 6500 15731270 4.4 8889 6750 15639280 4.3 8571 7000 15571290 4.1 8276 7250 15526300 4 8000 7500 15500310 3.9 7742 7750 15492320 3.75 7500 8000 15500330 3.6 7273 8250 15523340 3.5 7059 8500 15559350 3.4 6857 8750 15607400 3 6000 10000 16000500 2.4 4800 12500 17300600 2 4000 15000 19000700 1.7 3429 17500 20929
25DSC 335, Fall 2009
Ordering Cost
QOPT (optimal order quantity) Q
Q DTC = H+ S
2 QHolding cost
SQD
H2Q
Cost
Lowest Cost
Finding the Optimal Q (EOQ)
26DSC 335, Fall 2009
Calculating EOQ
The EOQ formula:
# orders / year =
Time between orders
EOQ = 2DSH
TBOEOQ = EOQD
DEOQ
27DSC 335, Fall 2009
Example: Application 12.1
Suppose that you are reviewing the inventory policies on an $80 item stocked at a hardware store. The current policy is to replenish inventory by ordering in lots of 360 units. Additional information is:
D = 60 units per week, or 3,120 units per year
S = $30 per order
H = 25% of selling price, or $20 per unit per year
What is the EOQ?
EOQ = =2DS
H= 97 units2(3,120)(30)
20
SOLUTION
28DSC 335, Fall 2009
Current Policy EOQ Policy
(cont’d)
What is the total annual cost of the current policy (Q = 360), and how does it compare with the cost with using the EOQ?
Q = 360 units Q = 97 units
C = 3,600 + 260
C = $3,860
C = (360/2)(20) + (3,120/360)(30)
C = 970 + 965
C = $1,935
C = (97/2)(20) + (3,120/97)(30)
29DSC 335, Fall 2009
(cont’d)
What is the time between orders (TBO) for the current policy and the EOQ policy, expressed in weeks?
TBO360 =
TBOEOQ =
(52 weeks per year) = 6 weeks360
3,120
(52 weeks per year) = 1.6 weeks97
3,120
SOLUTION
30DSC 335, Fall 2009
Notes on EOQ
EOQ is driven by cost minimization Holding cost + Setup cost
Total cost curve is fairly flat near the optimal point EOQ is “robust”, i.e, some errors in parameters estimation will not lead to large cost increase.
At EOQ, Holding cost = Ordering cost Is that always true if holding cost or setup cost take different
forms? Not necessarily.
31DSC 335, Fall 2009
Managerial Insights – Sensitivity Analysis
TABLE 12.1 | SENSITIVITY ANALYSIS OF THE EOQ
Parameter EOQ Parameter Change
EOQ Change
Comments
Demand ↑ ↑ Increase in lot size is in proportion to the square root of D.
Order/Setup Costs ↓ ↓
Weeks of supply decreases and inventory turnover increases because the lot size decreases.
Holding Costs ↓ ↑ Larger lots are justified when holding
costs decrease.
2DSH
2DSH
2DSH
32DSC 335, Fall 2009
Slope= D (units/yr)= d (units/day)
Q
Time
ReorderPoint (ROP)
Receive order
Placeorder
Receive order
Lead time:L (days)
Reorder Point: ROP = dL
What Happens When Lead Time > 0?
Reminder: Keep time units consistent!
33DSC 335, Fall 2009
A cloth item is held in stock at a retail store, c = $0.1 per yard; H = $0.75 per yard/yr; S= $150 per order; D = 10,000 yards/yr. What’s the EOQ? Note: There are 311 operating days per year for the store
Exercise
34DSC 335, Fall 2009
(cont’d) When to Order?
Reorder Point (R): level of inventory at which to place a replenishment order
R = d x L
d = demand rate per period , L = lead time
35DSC 335, Fall 2009
What if demand is uncertain? – Inventory Control Systems
Continuous review (Q) system Also known as Reorder Point (ROP) system Constant amount ordered when inventory declines to
predetermined level Fixed-order-quantity system and
Fixed-time-period system (Periodic review) Order placed for a variable amount after fixed passage of time