Determining Optimal Level of Product Availability

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Determining Optimal Level of Product Availability
? ???(1) Determining Optimal Level of Product
Availability

• Optimal Matching of Supply and Demand (III)

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Supply Chain Decision-Making Framework
Competitive strategy
Supply chain strategy
Supply chain structure
Inventory
Transportation
Facilities
Information
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Outline

• Determining optimal level of product availability
• Ordering under capacity constraints
• Levers to improve supply chain profitability
• Contracts

• Single order in a season
• Continuously stocked items

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Mattel, Inc. Toys R Us
Mattel was hurt last year by inventory cutbacks
at Toys R Us, and officials are also eager to
avoid a repeat of the 1998 Thanksgiving weekend.
Mattel had expected to ship a lot of merchandise
after the weekend, but retailers, wary of excess
inventory, stopped ordering from Mattel. That led
the company to report a 500 million sales
shortfall in the last weeks of the year ... For
the crucial holiday selling season this year,
Mattel said it will require retailers to place
their full orders before Thanksgiving. And, for
the first time, the company will no longer take
reorders in December, Ms. Barad said. This will
enable Mattel to tailor production more closely
to demand and avoid building inventory for orders
that don't come. - Wall Street Journal, Feb.
18, 1999
Microsoft?
barbiecollections
Wikipedia
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stephaniefierman.com
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Key Questions

• How much should Toys R Us order given demand
  uncertainty?
• How much should Mattel order?
• Will Mattels action help or hurt profitability?
• What actions can improve supply chain
  profitability?

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Factors Affecting Optimal Level of Product
Availability

• Cost of overstocking

• The loss incurred for each unsold unit

• Cost of understocking

• The margin lost for each lost sale unit

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A Newsboy Problem
Microsoft?
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Parkas at L.L. Bean
Cost per parka 45 Sale price per parka
100 Discount price per parka 50 Holding and
transportation cost to outlet 10
llbean.com

• Profit from selling parka
• (cost of understocking) 100-45 55
• Cost of overstocking 4510-50 5

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How much to order? Parkas at L.L. Bean
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Parkas at L.L. Bean

• Expected demand 10 (00) parkas
• Expected profit from ordering 10 (00) parkas

• Expected profit from extra 100 parkas

5500 ? P (demand ? 1100) 500 ? P (demand lt 1100)
5500 ? 0.49 500 ? 0.51 2440
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How much to order? Parkas at L.L. Bean
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Parkas at L.L. Bean

• Expected demand 10 (00) parkas
• Expected profit from ordering 10 (00) parkas

• Expected profit from extra 100 parkas

5500 ? P (demand ? 1100) 500 ? P (demand lt 1100)
5500 ? 0.49 500 ? 0.51 2440
49,900
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Parkas at L.L. Bean

• Expected demand 10 (00) parkas
• Expected profit from ordering 10 (00) parkas

49,900

• Expected profit from extra 100 parkas

5500 ? P (demand ? 1100) 500 ? P (demand lt 1100)
5500 ? 0.49 500 ? 0.51 2440
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Parkas at L.L. Bean

• Expected demand 10 (00) parkas
• Expected profit from ordering 10 (00) parkas

49,900

• Expected profit from extra 100 parkas

5500 ? P (demand ? 1100) 500 ? P (demand lt 1100)
5500 ? 0.49 500 ? 0.51 2440
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How much to order? Parkas at L.L. Bean
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Parkas at L.L. Bean

• Expected demand 10 (00) parkas
• Expected profit from ordering 10 (00) parkas

49,900
100

• Expected profit from extra 100 parkas

1200
1200
5500 ? P (demand ? 1100) 500 ? P (demand lt 1100)
5500 ? 0.49 500 ? 0.51 2440
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Parkas at L.L. Bean
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Parkas at L.L. Bean

• Optimal order quantity is 1300 parkas, which
• provides a CSL of 92
• The fill rate achieved if 1300 parkas are ordered

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How much to order? Parkas at L.L. Bean
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Parkas at L.L. Bean

• Optimal order quantity is 1300 parkas, which
• provides a CSL of 92
• The fill rate achieved if 1300 parkas are ordered

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Optimal level of service

• p sale price
• s outlet or salvage price
• c purchase price
• CSL Probability that demand will be at or below
  
• reorder point At optimal order
  size,

Expected Marginal Benefit from raising order
size (1-CSL)(p - c)
Expected Marginal Cost CSL(c - s).
(1-CSL)Cu CSL? Co,
CSL Cu / (Cu Co)1/1(Co /Cu)
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Parkas at L.L. Bean

• Expected demand 10 (00) parkas
• Expected profit from ordering 10 (00) parkas

49,900

• Expected profit from extra 100 parkas

5500 ? P (demand ? 1100) 500 ? P (demand lt 1100)
5500 ? 0.49 500 ? 0.51 2440
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Optimal level of service

• p sale price
• s outlet or salvage price
• c purchase price
• CSL Probability that demand will be at or below
  
• reorder point At optimal order
  size,

Expected Marginal Benefit from raising order
size (1-CSL)(p - c)
Expected Marginal Cost CSL(c - s).
DemandltN
(1-CSL)Cu CSL? Co,
(1-CSL)Cu CSL? Co,
CSL Cu / (Cu Co)
CSL Cu / (Cu Co)
1/1(Co /Cu)
CUUnder Stock.
?p-c
COOver Stock
?c-s
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Optimal Order Size(O) and Fill Rate under
Optimal Order Size

• Optimal Order Size (O)

• Fill rate at O

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Order Quantity for a Single Order

• Co Cost of overstocking 5
• Cu Profit from sale Cost of understocking
  55

• O Optimal order size

Optimal Order Quantity 13
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Optimal level of product availability

• Expected profit

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Expected Profit, Overstock and Understock under O

• Expected overstock

• Expected understock

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Example Sportmart

• The manager at Sportmart has to decide on the
  number of skis to purchase for the winter season.
  Considering past demand data and weather
  forecasts for the year, management has forecast
  demand to be normal distributed with a mean 350
  and a standard deviation 100. Each pair of skis
  costs c100 and retails for p250. Any unsold
  skis at the end of the season are disposed of for
  85. Assume that it costs 5 to hold a pair of
  skis in inventory for the season.
• Evaluate the number of
• skis that the manager
• should order to maximize
• expected profits.

• Cu p c 250 -100 150
• Co 100 80 20
• CSL Cu / (Cu Co) 0.88
• O NORMINV(0.88, 350, 100) 468
• Expected profits 49,146
• Expected overstock 108
• Expected understock 8

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Continuously Stocked Items Optimal Safety
Inventory Levels

• CSL Probability of not stocking out in a cycle
  with current level of safety stock Cycle
  Service Level
• ROP Reorder point
• D Average demand per unit time
• ? Standard deviation of demand per unit time
• ss Safety stock
• Cu Cost of stock out per unit
• h Holding cost as a fraction of product cost
  per unit time
• C Unit cost
• H Cost of holding one unit for one year hc
• S Fixed cost associated with each order
• Q Economic order quantity

Microsoft?
Microsoft?
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Optimal Safety Inventory Levels for Backlogged

• CSL 1- HQ/CuD

• Example D 100 gallons/week ? 20 unit cost
  3
• h 0.2 H 0.6/gal./year L 2
  weeks
• Q 400 ROP 300, DL DL 200,

• What is the imputed cost of stocking out?
• CSLF(ROP, DL, ?L) F(300,200,28.3) 0.9998
• Cu 0.6?400/(1-0.9998) ?5200 230.8

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Optimal Safety Inventory Levels for Lost Sales
Backlogged CSL 1- HQ/CuD

• CSL 1- HQ/(HQ CuD)

• Follow the previous example, given Cu 2.

• What is optimal CSL?
• CSL 1-0.6 ?400/(0.6 ?4002 ?5200) 0.98

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Levers for Increasing Supply Chain Profitability

• Decreasing the costs of overstocking and
  understocking
• Reducing the demand uncertainty

Microsoft?
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The Ways to decreasing the costs of overstocking
and understocking

• Increase salvage value sell to outlet, sell to
  different regions

• Decrease margin lost from stockout
• 1.backup sourcing
• 2.purchase from market
• 3.rain check
• 4.discount

Microsoft?
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Impact of Co/Cu on Optimal CSL
CSL
1
Co/Cu
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The Ways to Reduce Demand Uncertainty

• Improved forecasting to lower uncertainty
• Quick response reduce lead time to increase
  number of orders per season
• Postponement of product differentiation
• Tailored sourcing

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How to Estimate Demand Distribution?

• Historical data Time series forecasting
• Dependent factors Regression, causal forecasting
• Expert opinion Buying committee

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Impact of Improving Forecasts
Example A buyer at Bloomingdales responsible for
purchasing dinnerware with Xmas
pattern. Demand Normally
distributed with a mean of D 350 and standard
deviation of ?D 150 Purchase
price 100 Retail price 250
Disposal value 80
Microsoft?
Microsoft?
How many units should be ordered as ?D changes?
Cu 250 100 150, Co 100 80 20
CSL ? 150/(150 20) 0.88
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Impact of Improving Forecasts
Example A buyer at Bloomingdales responsible for
purchasing dinnerware with Xmas
pattern. Demand Normally
distributed with a mean of D 350 and standard
deviation of ?D 150 Purchase
price 100 Retail price 250
Disposal value 80
How many units should be ordered as ?D changes?
Cu 250 100 150, Co 100 80 20
CSL ? 150/(150 20) 0.88
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Variation of Profit and Inventories with Forecast
Accuracy
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Whats Quick Response?

• A widely used strategy

• By general merchandise, soft-lines retailers and
  manufacturers
• To reduce retail out-of-stocks, forced markdown,
  merchandising system and operating costs

• A partnership strategy

• Suppliers and retailers work together to respond
  more rapidly to consumer needs
• By sharing POS information to jointly forecast
  future demand for replenishable items, and to
  continuously monitor trends to detect
  opportunities for new items

• A JIT strategy

Microsoft?
Microsoft?

• Spread through the supply chain and seamlessly
  linked at each stage by electronic data
  interchange

Microsoft?
Microsoft?
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4 ??????Microsoft Office 2007?????,??Microsoft ??????????46?52?65??????
4 ??????Microsoft Office 2007?????,??Microsoft ??????????46?52?65??????
4 ??????Wikipedia (http//zh.wikipedia.org/wiki/FileToysrus.png),????2012/5/17,???????46?52?65??????
4 ??????stephaniefierman??(http//stephaniefierman.com/mattels-missed-opportunity.phpcomments),????2012/2/22????????46?52?65??????
7 ??????Microsoft Office 2007?????,??Microsoft ??????????46?52?65??????
8 ??????llbean.com??(http//www.llbean.com/llb/shop/32?pagellbean-sale ),????2012/1/11????????46?52?65??????(?????????,???????????)
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