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Chapter 10

Chapter 10. Style Goods and Perishable Items. Style Goods and Perishable Items. Decision situations The newsvendor The Christmas tree vendor The cafeteria manager The farmer. Features of the Problem . Short season How much of each SKU to order prior to the season?

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Chapter 10

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  1. Chapter 10 Style Goods and Perishable Items

  2. Style Goods and Perishable Items Decision situations • The newsvendor • The Christmas tree vendor • The cafeteria manager • The farmer

  3. Features of the Problem • Short season • How much of each SKU to order prior to the season? • Prior to the season or during the early part of the season, there may be one or more opportunities for replenishment. • Forecasts of demand include considerable uncertainty due to the long inactive period. • If demand during season exceeds the stock, there are underage costs. • Lost sales • Added cost of acquiring at a high unit value

  4. Features of the Problem • If demand is less than the stock, there are overage costs • Salvage value is low • It is expensive to carry the inventory to the next season • Markdowns or transfers • Style goods are often substitutable • Sales are influenced by promotional activities ignore

  5. Unconstrained, Single Item, News Vendor Problem Profit Maximization v= acquisition cost ($/unit) p= revenue per sale ($/unit) B= penalty for not satisfying the demand ($/unit) g= salvage value ($/unit) Q= quantity to be stocked (units) px<(x0)= the probability that the total demand x takes a value less than x0

  6. Unconstrained, Single Item, News Vendor Problem

  7. Unconstrained, Single Item, News Vendor Problem

  8. Unconstrained, Single Item, News Vendor Problem Normally Distributed Demand

  9. Example The Ski Bum, a small discount retailer of ski equipment, faces the difficult task of ordering a particular line of ski gloves in the month of May, well before the ski season begins. The selling price for these gloves is $50.30 per pair, while the cost to the retailer is only $35.10. The ratiler can usually buy additional gloves from competitors at their retail price of $60. Gloves left over at the end of the short selling season are sold at a special discount price of $25 per pair. The owner and manager of the store assumes that demand is approximately normally distributed with a mean of 900 gloves and a standard deviation of 122 gloves.

  10. Unconstrained, Single Item, News Vendor Problem Fixed Charge to Place the Order Initial Inventory

  11. Unconstrained, Single Item, News Vendor Problem Discrete Demand When discrete units are used, the best Q value is the smallest Q value that satisfies

  12. Example A farmer raises cattle and sells the beef at the weekly farmer’s market in a uniform size of 5 kg at a price of $30. The demand in the last twenty market sessions: 1,3,3,2,2,5,1,2,4,4,2,3,4,1,5,2,2,3,1,4. The farmer stores the processed beef in a freezer on his farm. He estimates the value of a 5-kg unit to be $19 after he removes it from the freezer and gets to the market. Once the beef is brought to the market, he chooses not to take it home and refreeze it. Therefore, any leftover beef at the market he sells to a local butcher at a discount price of $15 per 5-kg unit. There is no additional cost associated with not satisfying a demand.

  13. The Single-Period, Constrained, Multi-Item Problem • More than one type of SKU to be stocked for a single period’s demand • Independent demands • Space or budget constraints on the group of items Examples: • Several different newspapers sharing a limited space or budget in a corner newsstand • A buyer for a style goods department of a retail outlet who has a budget limitation for a group of items

  14. The Single-Period, Constrained, Multi-Item Problem A solution procedure for the case of a restriction on the total dollar value of the units stocked Notation: n: number of different items ipx<(x0): Probability that total demand for item i is less than x0 vi= acquisition cost of item i ($/unit) pi= selling price of item i ($/unit) Bi= penalty for not satisfying the demand of item i ($/unit) gi= salvage value of item i ($/unit) W= budget available for allocation among the stocks of n items ($)

  15. The Single-Period, Constrained, Multi-Item Problem Step1: Select an initial positive value of the multiplier M. Step 2: Determine each Qi to satisfy Step 3: Compare with W If QiviW, we are through If Qivi<W, return to Step 2 with a smaller value of M If Qivi>W, return to Step 2 with a larger value of M M is the value of adding one more dollar to the budget W.

  16. The Single-Period, Constrained, Multi-Item Problem For the case of normal demand

  17. The Single-Period, Constrained, Multi-Item Problem Example: W=$70,000, Normally distributed demand

  18. The Single-Period, Constrained, Multi-Item Problem Example: increase M increase M

  19. The Single-Period, Constrained, Multi-Item Problem Example: decrease M

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