Effects of Demand / Lead Time Variability Safety Stock level s Expected demand at average demand rate d Place order Receive order L Variable demand QUESTION: How much inventory is needed during lead time L? KEY POINT: s is larger when there is uncertainty about demand or L
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Effects of Demand / Lead Time Variability
Safety Stock level
s
Expected demand ataverage demand rate d
Placeorder
Receiveorder
L
Variable demand
QUESTION: How much inventory is
needed during lead time L?
KEY POINT: s is larger when there is uncertainty
about demand or L
Summary of Inventory ModelsUse EOQ model
•When: inventory level drops to 0 if lead time is 0 L·D if lead time L > 0•How much: EOQ formula, Q* = sqrt(2D ·K / h)
Use EOQ model•When: inventory level drops to 0 if lead time is 0 L·D if lead time L > 0•How much: EOQ formula, Q* = sqrt(2D ·K / h)
Use (s, S) model•When: inventory position drops below s s = AVG·L + z·STD ·sqrt(L)•How much: EOQ formula, Q* = sqrt(2AVG ·K / h) (S = s+Q*)
Use (s, S) model•When: inventory position drops below s s = AVG·L + z·STD ·sqrt(L)•How much: EOQ formula, Q* = sqrt(2AVG ·K / h) (S = s+Q*)
Is demand rate Is demand rate deterministic?deterministic?
YesYes
NoNo
Risk Pooling• (safety) stock based on standard deviation
– square root law: stock for combined demands usually less than the combined stocks
• Centralizing inventory control reduces safety stock, hence average inventory level for the same service level.
(This phenomenon is called risk pooling)
• works best for – negatively correlated demand.
– high coefficient of variation, which increases required safety stock.
• other kinds of risk pooling: across markets, products, time
Risk Pooling Example• Consider two systems:
Warehouse 1
Warehouse 2
Market 1
Market 2
Supplier
Decentralized System:Two warehouses,each serving one customer
WarehouseMarket 1
Market 2
SupplierCentralized System:One warehouse,serving both customers
Questions: Q1: For the same service level, which system will require more inventory?Q2: For the same total inventory level, which system will have better service?
Example
AVG STD SS s Q SAverage
Inventory
Warehouse 1 39.3 13.2 25.08 65 132 197 91
Warehouse 2 38.6 12.0 22.8 62 131 193 88
CentralizedWarehouse
77.9 20.7 39.35 118 186 304 132
Decentralized system: total SS = 47.88
total avg. invent. = 179
Safety Stock SS = z ·STD · L
Reorder Point s = AVG·L + SSOrder Quantity Q = sqrt(2K·AVG/h)Order-up-to-level S = s + QAverage Inventory SS + Q/2
WarehouseMarket 1
Market 2
d1+d2: (, 2)
Calculating demand variability of centralized systemCalculating demand variability of centralized system
Warehouse 1
Warehouse 2
Market 1
Market 2
d1: (1, 12)
d2: (2, 22)
2 = 1
2 + 22 + 212,
where -1 12
= 12 + 2
2 + 212,
where -1 1
: correlation coefficient of d1, d2
1+ 2 1+ 2
Conclusions: 1. Stdev of aggregated demand is less than the sum of stdev of individual demands2. If demands are independent or negatively correlated, the std of aggregated demand is much less
Conclusions: 1. Stdev of aggregated demand is less than the sum of stdev of individual demands2. If demands are independent or negatively correlated, the std of aggregated demand is much less
1. If d1, d2 positively correlated, > 02. If d1, d2 are independent, = 03. If d1, d2 negatively correlated, < 0
= 1 + 2
= ??
1+2
10-1
22
21
P.C.N.C. Ind.
DecentralizedCentralized
Inbound transportation cost (from factories to warehouses)
Facility/Labor cost
Outbound transportation cost (from warehouses to retailers)
Sport Obermeyer Case 1. Identification of major issues in the supply chain. 2. Recommendation on ordering units of each style during
initial phase of production.(using sample data in Exhibit 10; assume all ten styles in the sample problem are made in Hong Kong, and that Obermeyer's initial production commitment must be at least 10,000 units; ignore price differences among styles in your initial analysis.)
3. Recommendation of operational changes to lower risk and improve performance.
4. How should Obermeyer management think (both short-term and long-term) about sourcing in Hong Kong vs. China?
The Supply Chain
Lining Fabric
Lining Fabric
Shell Fabric
Shell Fabric
Insulation Materials
Insulation Materials
SnapsSnapsZippersZippers
OthersOthers
Cut/Sew
Distribution Center
Retailers
Textile Suppliers
Obermeyer
Obersport
Retailers
Speculative vs. Reactive Capacity
Initial Forecast
Orders
Speculative Production Capacity
Reactive Production Capacity
Scenario Outcome
Excess inventory
Stock out
End of Season Problem
•Loss of 8%/unit ~ $9
•Limited capacity effects (could have used that capacity to produce something that stocked out
•Loss of profit (24%/unit) ~ $27
Increasing Reactive Capacity
New Info / 2nd prod’n order
Increase Total CapacityAdditional Reactive capacity
Decrease Lead TimesAdditional Reactive capacity
Obtain Information EarlierAdditional Reactive capacity
New Info
Base case
Material LT Prod’n LT Delivery LT
Mar/93
Nov/92
Jun/93 Sept/93
Aug/93
1st Prod’n Order
Original Reactive capacitySpeculative production capacity
The Forecast Process: Input for Production Planning
• Independent versus consensus forecasts
• Aggregation of expert estimates
– Average of expert estimates is a proxy for the mean of
the demand distribution
– Standard deviation among expert estimates is a proxy for
half the standard deviation of demand distribution
• Forecast updates
Which Units are Safest to Build First?
• Highest demand– More likely that unit will sell
• Less variable (lower /)
• Less expensive– Lower overage costs – In speculative capacity, you are worried about
being over – being under not a problem, because you can always use reactive capacity
Risk-Based Production Planning: Accurate Response
• how to develop initial probabilistic forecast of demand?
• risk measures? assess _________ and _________ costs
• determine appropriate initial production quantities:– produce ___________________ units early
• “read” early demand indicators• update demand forecast• determine final production quantities
What Obermeyer did
• Early Write program gets sales info one month in advance of Las Vegas Show.
• More stocking of raw materials in Hong Kong.
• Risk-based production planning with forecast uncertainties captured by independent expert estimates used.
• Try to extend risk-based production planning concept to raw materials production.
• Increase commonality of zipper by 5-fold. Increase raw materials sharing across styles.
– Supplier receives POS data from retailers– Supplier use it to improve its own forecasting and production scheduling – but retailer still prepares its own orders
• Continuous Replenishment (CR) – Supplier replenishes retailers– Supplier receives POS data and use it to prepare shipments at previously agreed upon intervals to maintain specific levels of inventory
• Vendor Managed Inventory (VMI)– Supplier replenishes retailers– Suppliers have the total control over replenishment decisions
Why does RSP have those advantages? Why does RSP have those advantages?
Without RSP: sequential, myopic optimization
Supplier Retailer
CustomerSupplier
Information flow
With RSP (particularly, VMI): Joint optimization
Information flow
Retailer optimizes its operations first. Then supplier optimizes its operations subject to the constraints imposed by the retailer.
Retailer optimizes its operations first. Then supplier optimizes its operations subject to the constraints imposed by the retailer.
Supplier optimizes its operations and the retailer’s. This is system-wide.
Supplier optimizes its operations and the retailer’s. This is system-wide.
Example of RSP SuccessExample of RSP Success
• VF Corporation’s Market Response System:
– The VF Corporation, which has many well known brand names (including Wrangler, Lee, Girbaud, and many others), began its VMI program in 1989.
– Currently, about 40 percent of its production is handled using some type of automatic replenishment scheme.
– This is particularly notable because the program encompasses 350 different retailers, 40,000 store locations, and more than 15 million replenishment levels.
– VF’s program is considered one of the most successful in the apparel industry.
– Shut down its VMI effort about one year after its inception
– Buyers were not spending any less time on reorders than they did before
– Issue: buyers didn’t trust suppliers -- continued to carefully monitor inventories and deliveries and to intervene at hint of trouble.
– Suppliers did little to allay these fears; suppliers did not deal well with promotions -- delivery levels were often unacceptably low during these periods of peak demand.
• Return Percentage in the Offline World (Online world has much higher percentages)
Industry
Magazine Publishing (50%)
Book Publishers (20-30%)
Book Distributors (10-20%)
Greeting Cards (20-30%)
Catalog Retailers (18-35%)
Computer Manufacturers (10-20%)
CD-ROMs (18-25%)
Consumer Electronics (4-5%)
Source: Rogers and Tibben-Lembke
3eF: Why Need for Reverse Logistics?3eF: Why Need for Reverse Logistics?
Case: Tale of Two Electronic Distributors 1. What is the value proposition offered by AESCO & ESCI?
Why might an OEM prefer to buy from a distributor rather than directly from a manufacturer?
2. What must AESCO and ESCI do to grow?
3. How are broad industry trends (consolidation, globalization, and the Internet) likely to affect each of these distributors?
Case Discussion
AESCO & ESCI: general description of business model.
value addition to SC channel? (elimination a la Dell direct model always good?)
role of distributor in general in SC risk-pooling (safety stock) break-bulk and mixing (allowing smaller order quantities) closer to buyer, emergency (expedited) shipments one-stop shop value-added services (e.g., some assembly, design) coordinate SC activities and reduce manufacturing costs specialized: matching inventory shortages and surpluses