Student version - Ch5 - part 4

Student version - Ch5 - part 4 - MGMT 361 Operations...

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MGMT 361 Operations Management (OM) 1 Chapter 5 Inventory Management part 4

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Models involving probability distributions Earlier models (EOQ, EPQ, etc) had deterministic demand: no shortages were permitted. 100% service level. Now we will consider probabilistic demand models: occasional shortages service level<= 100% No. Model type 5 When to reorder fixed amount Q: re-order point model (Q system, continuous Review) 6 How much to order at a fixed time: Fixed order interval model (P system, periodic review) 7 Single period model (Newsvendor) 2
3 Filling Gas When do you fill your car with gas? Whenever the gas tank is empty (or ¼ full), fill up gas tank Q system, continuous review Every Tuesday / Wednesday (when gas is cheap) fill up gas tank P system, periodic review

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To look at our first example of how this works, we will assume that: Lead time is fixed. Shortages are made up by backordering. Order OUL – IP units at the review time. Demand may vary from day to day and shortages can occur occasionally while we wait for an order to arrive. 4 P - System: P eriodic Review System (fixed interval order system) – ‘A system where an item’s inventory position is reviewed p eriodically, at a fixed interval ( P ), rather than continually. Such a system can simplify delivery scheduling because a routine is established.’ On the review day, an order is placed so that the inventory position (IP) is raised to a specified value: order-up-to level (OUL).
OUL = 600, OI = 4 days 5 Day Opening Receipt Order Withdraw Closing IL IP IL IP 1 210 0 120 2 0 80 3 130 4 80 5 90 6 110 7 135 8 80 9 120 Total 210 Example 6.1: P system 480 90 480 10 400 390 10 400 270 270 0 270 270 190 190 0 190 190 100 510 390 90 410 0 100 510 -10 400 410 -10 400 265 265 0 265 265 185 185 0 185 185 415 65 480 800 1215 945 LT = 2 days, Opening stock = 210, no receipts on day 1, 2 Verify formulas Closing IL(Y) = Opening IL(X) + Receipt – Withdrawal Closing IP(Y) = Opening IP(X) + Order – Withdrawal Lead time L T Time between placing and receiving order. On Hand Inventory O H Physical stock Inventory Level IL IL = OH – Quantity on backorder Inventory Position IP IP = IL + Quantity in transit

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6 Time LT OUL 0rder-up-to level 6 Periodic Review System (P system) OI Q 1 Q 3 Q 2 OI is fixed. On the review day, order Q = OUL – IP . We need to raise OUL and increase the value of Q 1 So, we need to consider demand over OI + LT units of time. This is called the protection period. Order interval is fixed, order quantity varies. Notice that if we want to avoid shortage after period 2
Q and P systems: Demand/unit time: N[ , ] , Lead Time: L T , Order Interval: OI , Service Level: SL, Protection period PP = (OI + LT) Q system (Fixed Q) P system (Fixed Order interval (OI)) Optimal policy Order Q units when IP ROP Prob (LT demand ≤ ROP)≥SL Order (OUL – IP) units on review date. Decision

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Student version - Ch5 - part 4 - MGMT 361 Operations...

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