Lecture 5 - Statistical Reorder Point Models When your...

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Statistical Reorder Point Models When your pills get down to four, Order more. 1 – Anonymous, from Hadley & Whitin
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EOQ Assumptions 1. Instantaneous production. 2. Immediate delivery. 3. Deterministic demand . newsvendor and (Q,r) relax this one lags can be added to EOQ or other models EPL model relaxes this one 2 4. Constant demand. 5. Known fixed setup costs. 6. Single product or separable products. WW model relaxes this one can use constraint approach multiple product cases
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Inventory control subject to uncertain demand Newsvendor model Lot size-reorder point systems Service levels in (Q,R) systems Cycle service level (CSL) Fill rate (fr)
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The Newsvendor Approach Assumptions A single period (Extension to multiple periods possible) Random demand with known distribution Cost per unit of leftover inventory (overage cost c o ) Cost per unit of unsatisfied demand (shortage cost c s ) s Objective: Minimize the sum of expected shortage and overage costs 4 s Tradeoff: If we order too little, we incur a shortage cost; if we order too much we incur a an overage cost Examples: newspapers or other items with rapid obsolescence Christmas trees or other seasonal items capacity for short-life products
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Single- and Multi- Period Models • In a single-period model , items are received in the beginning of a period and sold during the same period. The unsold items are not carried over to the next period. (ANY EXAMPLES?) • The unsold items may be a total waste, or sold at a duced rice reduced price • The revenue generated (if any) by the unsold items is called the salvage value. • In the single-period model, there remains only one question to answer: how much to order.
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Single- and Multi- Period Models • In a multi-period model , all the items unsold at the end of one period are available in the next period. • If in a multi-period model orders are placed at regular intervals e.g., once a week, once a month, etc, then there is only one question to answer: how much to order. • However, we discuss Q , R models in which it is assumed that an order may be placed anytime. – there are two questions: how much to order and when to order.
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Single-Period Models • Let’s define: • Loss resulting from the items unsold (overage cost) c o = Purchase price - Salvage value • Profit resulting from the items sold (underage cost) Selling price urchase price c s = Selling price - Purchase price • The Question Given costs of overage/underage and the probabilities of various demand sizes how many units will be ordered?
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Newsvendor Model Notation demand. of function density ) ( ) ( .) continuous (assumed demand of function on distributi cumulative ), ( ) ( variable. random a units), (in demand = = = = x G dx d x g x X P x G X 8 ariable. decision v the is this units); (in quantity /order production shortage. of unit per dollars) (in cost over. left unit per dollars) (in cost = = = Q c c s o
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The Cost Function [ ] [ ] ( ) expected overage cost + shortage cost
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This note was uploaded on 04/25/2010 for the course IE 654 taught by Professor Smith during the Spring '10 term at 카이스트, 한국과학기술원.

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Lecture 5 - Statistical Reorder Point Models When your...

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