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Lecture 5

# 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
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
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.
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
The Cost Function [ ] [ ] ( ) expected overage cost + shortage cost

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

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