311_session_23_newsvendor practices

311_session_23_newsvendor practices - Demand Uncertainty...

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1 Demand Uncertainty Newsvendor Model BUAD311 Session 23 Hiroshi Ochiumi
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2 Today What if demand is not constant? Newsvendor Model Trade-offs Objective function Solving – decision tree Solving – marginal analysis Examples
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3 Uncertain Demand What are the relevant trade-offs? Overstock Demand is lower than the available inventory Inventory holding cost Shortages Demand is higher than the available inventory Why do we have shortages? What is the effect of shortages?
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4 The Magnitude of Shortages (Out of Stock)
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5 What are the Reasons?
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6 Consumer Reaction
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7 What can be done to minimize shortages? Better forecast Produce to order and not to stock Is it always feasible? Have large inventory levels Order the right quantity What do we mean by “the right” quantity?
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8 Uncertain Demand What is the objective? Minimize (maximize) the expected cost (profits). What are the decision variables? Purchase quantity, or inventory level.
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9 What are the Relevant Costs? S: Set-up cost (per order) h: Holding cost (per unit per period) c: Purchasing cost (per unit) v: Salvage value (per unit) The value of salvage, at the end of the horizon, for excess inventory p: Revenue per unit g: Goodwill cost
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10 News Vendor Model Assumptions Demand is random Distribution of demand is known No initial inventory Set-up cost is equal to zero Single period Zero lead time Linear costs: Purchasing (production) Salvage value Revenue Goodwill
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11 Example 1: Beer Distributor A retailer knows that the demand for beer during the Super Bowl can be either high (8 units) or low (4 units). How many units should the retailer stock? Do we need more information to answer this question?
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12 Example 1: Beer Distributor The answer depends on the probability of each event happening and on the costs. Suppose: Probability of demand being equal to 4 is 0.4. Probability of demand being equal to 8 is 0.6. Salvage value is $1 per unit Purchasing cost is $3 per unit Revenue is $12 per unit Goodwill cost is $0 per unit We will maximize expected profit.
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13 Example 1: Beer Distributor Profit = Sales Revenue + Salvage Revenue – Purchase Cost Purchase 4 units: E[Profit] = 4*12 – 4*3 = $36 Purchase 8 units: E[Profit] = 0.4*(4*12-8*3+1*4) + 0.6*(8*12-8*3) = $54.4 Therefore, it is better to purchase 8 units.
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14 Observations When demand exceeds the amount purchased, we pay an “underage” or “shortage” cost of 12-3=$9. When demand is lower that the
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This note was uploaded on 12/18/2009 for the course BUAD 311 at USC.

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311_session_23_newsvendor practices - Demand Uncertainty...

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