Susan Cholette DS855 Fall 2006

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Susan CholetteDS855 Fall 2006
Expected demand
Risk of shortage
Service level
Quantity
z
z-scale
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Determining Optimal Level of Product Availability

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Outline

• The importance of the level of product
  availability
  
• Factors affecting the optimal level of product
  availability
  
• Managerial levers to improve supply chain
  profitability
  
• Supply chain contracts and their impact on
  profitability
  
• Setting optimal levels of product availability in
  practice
  
• Digression Introduction to Simulation
• Supply Chain contracts (section 12.4) are ignored
  in this class
  

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What Do We Mean by Optimal?

• Product availability is measured by the cycle
  service level or the fill rate
  
• Product availability affects supply chain
  responsiveness
  
• From previous chapter, recall trade-off
• High levels of product availability ? increased
  responsiveness and higher revenues
  
• High levels of product availability ? increased
  inventory levels and higher costs
  
• Product availability is related to profit
  objectives, and strategic and competitive issues
  (e.g., Nordstroms verses Ross)
  
• We now ask what is the level of fill rate or
  cycle service level that will result in maximum
  supply chain profits?

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Factors Affecting the Optimal Level of Product
Availability

• What is the Cost of over-stocking? Co
• What is the Cost of under-stocking? Cu
• Possible scenarios
• Does the product have a finite duration?
  (trend/spoilage/seasonal)
  
• Yes- i.e. Seasonal items with a single order
  placed for the season
  
• No- i.e. Continuously stocked, stable,
  non-spoilage items
  
• How is demand during a stock-out treated?
• What if all Demand during stock-out is
  backlogged?- i.e. there is a cost for an
  out-of-stock, but the order is not lost
  
• Or.
• What if all Demand during stock-out is
  irretrievably lost?

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One Time Orders for Single-Season Products

• A Season can be as long as a half-year for the
  sale of Skis from late Fall through Spring. Or it
  can be as short as 15 minutes (How many
  hamburgers to prepare in anticipation of
  customers arriving?)
• Commonality is that we place the order before the
  season with no way of ordering extra product if
  demand is better than expected.
  
• Once the season is over, the product has a
  limited (if any) salvage value
  
• BUS786 students may recognize this as the
  newsboy problem - How many daily newspapers to
  stock at the kiosk?
  

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One Time Orders for Single-Season Products
Calculations

• Calculations you may remember from BUS786 (Also
  on sheet 1 Ch12_inv.xls)
  
• Optimal SL Cu/(Cu Co)
• Optimal Order Size Q m zs where z
  NORMSINV(SL)
  
• So how do we get Expected Profit, or E(pr)?
• E(pr) (p-s)mNORMDIST((Q-m)/s,0,1,1)
• (p-s)sNORMDIST(((Q-m)/s,0,1,0)
• - Q(c-s)NORMDIST(Q,m,s,1)
• Q(p-c)(1-NORMDIST(Q,m,s,1))
• Ugh! E(pr) will not be on any 855 quizzes or
  tests!
  

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Setting Service Levels for Continuously Stocked
Items

• More complex than for single-season
• For items that are stock continuously and have
  repeated orders, here are some scenarios (demo
  sheet 2 on ch12_inv.xls)
  
• If we can backlog all demand for out-of-stock
  items (and incur Cost Cu for discount, free
  express shipping, or other services to mollify
  customers)
• Target SL 1-HQ/(DCu)
• If we expect to lose all demand for out-of-stock
  items (What does Cu represent now?)
  
• Target SL 1-HQ/(HQ DCu)
• In this scenario, service levels will be higher
  than with 100 conversion of our backlog, if all
  other parameters are the same
  
• What can we say about the target service level if
  we expect to lose some, but not all of the demand
  for the Out-of-Stock items?
  

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Managerial Levers to Improve Supply Chain
Profitability

• How do we keep product availability high, yet
  decrease inventory costs?
  
• Obvious actions
• Increase salvage value of each unit
• Decrease the margin lost from a shortage (backup
  sourcing)
  
• Improved forecasting
• Quick response (placing a second order)
• Postponement
• Tailored sourcing

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Improved Forecasts

• Improved forecasts result in reduced uncertainty
• Less uncertainty (lower s) results in either
• Lower levels of safety inventory (and costs) for
  the same level of product availability
  
• or
• Higher product availability for the same level of
  safety inventory
  
• or
• Both lower levels of safety inventory and higher
  levels of product availability

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Impact of Improving Forecasts (Example)

• Bloomingdales buys holiday china and sells it
  from October thru December. In January all china
  will be sold in an end-of-season-sale at a huge
  discount
• Demand Normally distributed with a mean of R
  350 and standard deviation of ? 150
  
• Wholesale cost 100
• Retail price 250
• End-of-season sale value 80
• What is Cost of Over-stocking and Cost of
  Under-stocking?
  
• Cu p-c 250-100 150
• Co c s 20
• What is the Optimal Service Level?
• SL Cu/(CuCo) 88
• How many units should be ordered as ?R changes
  and how is expected profit affected?

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Impact of Improving Forecasts

• Also calculated on sheet 1 of Ch12_inv.xls

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Quick Response

• Set of actions taken by managers to reduce lead
  time
  
• Reduced lead time results in improved forecasts
• Typical example of quick response is multiple
  orders in one season for retail items (such as
  fashion clothing)
  
• Buyers can usually make very accurate forecasts
  after seeing sales in the first week or two in a
  season
  
• Multiple orders are only possible if the lead
  time is reduced otherwise there wouldnt be
  enough time to get the later orders before the
  season ends
• Benefits
• Lower order quantities ? less inventory, same
  product availability
  
• Less overstock
• Why would this benefit be especially attractive
  to clothing retailers?
  
• Higher profits

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Quick Response MultipleOrders Per Season

• Sheet 3 of single order calculations done on
  sheet 3 of ch12-inv.xls goes over Saks shawl
  example on p. 356
  
• Caveat- includes complications of holding costs,
  and is beyond scope of this class (even book
  example not performed correctly!)
  
• In order get quantitative predictive effects of
  multiple orders per season, would have to use
  simulation.

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Postponement

• Delay of product differentiation until closer to
  the time of the sale of the product
  
• All activities prior to product differentiation
  require aggregate forecasts more accurate than
  individual product forecasts
  
• Individual product forecasts are needed close to
  the time of sale demand is known with better
  accuracy (lower uncertainty)
  
• Results in a better match of supply and demand
• Valuable in e-commerce time lag between when an
  order is placed and when customer receives the
  order (this delay is expected by the customer and
  can be used for postponement)
• Higher profits, better match of supply and demand

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Value of PostponementExample Benetton

• Demand for sweaters of each of 4 colors
• Mean demand 1,000 SD 500
• For each garment
• Sale price 50
• Salvage value 10
• Production cost using Option 1 (long lead time)
  20
  
• Production cost using Option 2 (uncolored thread)
  22
  
• Allows postponement (dye later) but is more
  costly
  
• What is the value of postponement?
• Expected profit increases from 94,576 to
  98,092
  
• Sheet 5 of ch12-inv shows this example in detail

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Value of Postponementwith Dominant Product

• Color with dominant demand Mean 3,100, SD
  800
  
• Other three colors Mean 300, SD 200
• Expected profit without postponement 102,205
• Expected profit with postponement 99,872
• In this situation it is better to not postpone,
  as higher production costs from postponement
  option dominate the profits
  
• What might be a solution to improve profits?

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Tailored Postponement Example Benetton

• Strategy
• Produce Q1 units for each color using Option 1
  and QA units (aggregate) using Option 2
  
• Tailored postponement allows a firm to increase
  profits by postponing differentiation only for
  products with the most uncertain demand products
  with more predictable demand are produced at
  lower cost without postponement
• Usually too complex to model without resorting to
  simulation

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Tailored Sourcing

• A firm uses a combination of two supply sources
• One is lower cost but is unable to deal with
  uncertainty well
  
• The other is more flexible, and can therefore
  deal with uncertainty, but is higher cost
  
• Analogous to the different production options for
  Red_Tomato tools from Aggregate Planning
  
• The two sources must focus on different
  capabilities
  
• Depends on being able to have one source that
  faces very low uncertainty and can therefore
  reduce costs
  
• Increase profits, better match supply and demand

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Vendor-Managed Inventories (VMI)

• Manufacturer or supplier is responsible for all
  decisions regarding inventory at the retailer
  
• Control of replenishment decisions moves to the
  manufacturer
  
• Requires that the retailer share demand
  information with the manufacturer
  
• Having final customer demand data also helps
  manufacturer plan production more effectively
  
• Side-benefit manufacturer may have better
  information on new products than retailer
  
• Real world Example MGM uses VMI in K-Mart and
  Wal-mart for their Videotapes DVDs SKUs
  
• Potential drawback when retailers sell products
  that are substitutes in customers minds and
  these products are all managed by VMI (i.e. lose
  savings from aggregation of SS of combined
  products)

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Simulation

• Several techniques in this and other chapters
  have suggested simulation
  
• Used to predict results when no closed form
  solution is possible
  
• Used to validate results even when the problem
  seems simple enough to be solved with a couple
  equations!
  
• With advent of cheap computing power, simulation
  is playing a greater role in diverse fields
  
• Available to limited degree in excel (tendency to
  crash program)
  
• Simulation techniques explored in great detail in
  a dedicated class DS851
  
• Goal Run multiple instances of a scenario,
  then determine the average outcome and payoff by
  taking the average of all the scenarios

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Setting Optimal Levels ofProduct Availability in
Practice

• Use an analytical framework to increase profits
• Verify with simulation
• Beware of preset levels of availability
• Use of approximate costs is acceptable
• profit-maximizing solutions are very robust
• Estimate a range for the cost of stocking out
• Ensure that levels of product availability fit
  with the firms competitive strategy

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Simulation Example

• A game costs 5 to play and has 2 outcomes
• Win 10 (original 5 5 more) with 55 chance
• Lose the 5 playing fee with 45 chance
• The expected value of playing this game once is
• E(game) .555 .45(-5) 0.50
• If I have 20 to start and I play the game 30
  times, how much should I expect to take home?
  
• Is it 20 30E(game) 35
• Why or why not?

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Simulation Example

• In general, F(E(x)) not same as E(f(x))
• Our model ignores the possibility of going broke-
  cant play the game if run out of money!
  
• Look at gambling_simulation.xls on website
• Take average of 102 instances of a 30-round game
• Sometimes average return is higher than 35
• More often than not, it is lower than 35
• Is there a right answer for what the simulated
  return is?
  
• Why do we simulate so many times?

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Example Pricing and Sourcing Strategy

• Lands End needs to determine how many cashmere
  sweaters to buy and how deeply to discount
  leftovers
  
• Sweaters sell for 150 each during winter
• Demand is uncertain,
• Assumed to be distributed normally, with m 3000
  and s 1000
  
• Towards the end of Season, the sweaters are
  discounted
  
• Discounted demand is uncertain, but is dependent
  on price
  
• Normal distribution md 1000 5p , sd
  (1000 5p) /3
  
• at p 80, we would average sales of 600
  sweaters, standard dev 200
  
• Whatever is not sold at a discount cannot be kept
  for next year and is donated for a 20 salvage
  value per sweater
  

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Inventory Simulation

• Have a complex situation not solved by a
  closed-form equation Sheet 4 of Ch12_inv.xls or
  Appendix 12F
  
• Two decisions to be modeled
• Simulation set to be at 500 instances
• The more instances, the more confident we are of
  the solution
  
• Is this saying that we are observing demand from
  the winters of 2004 to 2504?
  
• Summary statistics in grey tabulate the results
• Another chart shows the results from 9 different
  strategies
  
• How many instances were calculated, at a minimum
  to come up with this table?
  
• Can we make any definitive claims about the
  superiority of one set of decisions to another ?
  

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Summary of Learning Objectives

• What are the factors affecting the optimal level
  of product availability?
  
• What are the managerial levers that can be used
  to improve supply chain profitability through
  optimal service levels?
  
• What tool is available for modeling complex
  inventory strategies and also to stress-test even
  simple ones?