1. Purchasing & Materials Management The Newsvendor Model

2. 新加坡国立大学商学院 Setting the Stage Supply Chain with Retailer and Supplier – In advance of observing demand, retailer buys from supplier at unit cost c – Retailer sells to market at price p (p > c) – Retailer has to decide how many units to buy 2

3. 新加坡国立大学商学院 Sequential Decisions Determine Stocking Quantity 3 Consideration: – Additional unit to be purchased should generate positive (or non-negative) profit – Cost of x-th unit: c – Expected revenue: p Pr[Demand ≥ x] – Expected profit: p Pr[Demand ≥ x] – c – Interpretation: Do I take the next bet? Buy n units if: – p Pr[Demand ≥ m] – c ≥ 0 for m ≤ n – p Pr[Demand ≥ n+1] – c < 0

4. 新加坡国立大学商学院 Things to Note 4 1.Pr[Demand ≥ x] is a decreasing function of x (… think about it) 2.Pr[Demand ≤ x] is the cumulative distribution function – For a “continuous random variable” (e.g.: normal, uniform, exponential), … – … Pr[Demand ≥ x] = 1 - Pr[Demand ≤ x] … otherwise… – … Pr[Demand ≥ x] = 1 - Pr[Demand < x]

5. 新加坡国立大学商学院 Things to Note 5 3.To estimate a normal distribution, simply calculate the average and standard deviation. – Note that demand distributions may be far from normal – Demand distributions may be seasonal so demand from a given month/quarter over a few years may be used – Demand may evolve over time with demographic changes such as population, income, etc.

6. 新加坡国立大学商学院 Exercises 6 What is the impact of property 1 (from the previous slides) on calculation? (After finding the first unit for which expected profit is negative…) How does the criterion change if there is a salvage value s for all unsold units?