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Chapter 11

Chapter 11. Coordinated Replenishment at a Single Stocking Point. Coordinated Replenishment at a Single Stocking Point. The items are all stocked at the same location and they share a common supplier or mode of transportation or production facility. Advantages .

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Chapter 11

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  1. Chapter 11 Coordinated Replenishment at a Single Stocking Point

  2. Coordinated Replenishment at a Single Stocking Point The items are all stocked at the same location and they share a common supplier or mode of transportation or production facility.

  3. Advantages • Savings on unit purchase cost: discounts due to high quantities • Savings on unit transportation cost • Savings on ordering cost: several items on a single order • Ease of scheduling

  4. Disadvantages • Possible increase in average inventory level • Increase in system control costs: more difficult than individual item control • Reduced flexibility

  5. Deterministic Case A: setup cost associated with a replenishment of the family ai: minor setup cost associated with including item i in a replenishment of the family Assumptions • All assumptions of EOQ are valid • Coordination of items is allowed to reduce the setup costs

  6. Deterministic Case Decision rule T: time interval between replenishment of a family mi: number of T intervals that the replenishment quantity of the item i will last (e.g. mi=2Qi=2TD)

  7. Deterministic Case m1=1 m2=2 m3=1 Q3 Q2 Q1 T 2T 3T 4T

  8. Deterministic Case Decision rule The integer mi’s must be selected to minimize Di: demand rate of item i vi: unit variable cost of item i n: number of items in the family Once the best mi’s are known

  9. Deterministic Case Procedure Step 1: Number the items such that is smallest for item 1. Set m1=1. Step 2: Evaluate rounded to the nearest integer greater than zero. Step 3: Evaluate T* using the formula given before. Step 4: Determine Qivi=miDiviT*

  10. Example 4 different sized containers with A=$40 and r=0.24$/$/yr

  11. Probabilistic Demand Case Probabilistic demand greatly complicates the problem in a coordinated control context. Questions to be answered: • R=? • When to reorder the group? • How much to order? • How to allocate the order among items?

  12. Probabilistic Demand Case Some item in the family will trigger the order, other items will be above their reorder levels. This complicates the matter in two ways: • More difficult to ascertain the average inventory level of an item. • Service implications of any particular s are much more difficult to evaluate than individual item case.

  13. Probabilistic Demand Case (S,c,s) or Can-Order Systems Continuous review system for controlling coordinated items. si: must-order point for item i ci: can-order point for item i Si: order-up-to level for item i Whenever an item i’s inventory position drops to or below si, it triggers a replenishement that raises item i’s level to Si. Any other item j with inventory position at or below cj is included in the replenishment.

  14. Probabilistic Demand Case (S,c,s) or Can-Order Systems t1: Item i triggers an order. t2: Another item triggers an order. Item i is not included since its inventory position is above ci. t3: Another item triggers an order. Item i is included since its inventory position is below ci. Si ci si t1 t2 t3

  15. Probabilistic Demand Case A Periodic Review System • Outperforms can-order systems. • Easier to compute. • Allocate A in small amounts to products that are produced most frequently, keeping the expected time to the next replenishment for these products in balance.

  16. Probabilistic Demand Case A Periodic Review System Step 1: Compute Runout time =

  17. Probabilistic Demand Case A Periodic Review System Step 2: Choose the product with the smallest time supply (runout time), call it product 1. Allocate 1 of A to product 1. Increase 1 until T1 and T2 are equal. Then, increase 1 until T1 and T2 are equal to T3. Continue until A is allocated, i.e.

  18. Probabilistic Demand Case A Periodic Review System Total setup cost for an item = Ti values are equal for all products that have i>0 (base period/base cycle)

  19. Probabilistic Demand Case A Periodic Review System Step 3: Compute the cycle of other items that are not purchased every cycle to a multiple of the base cycle. Use powers of 2 multiples of the base cycle (21,22,23,...). Step 4: SS and S are determined by using (R,S) system where R is the cycle time for each product.

  20. Example 4 products from the same supplier A=$20, ai=$3, r=0.24$/$/yr, L=1 week, 1 year=50 weeks

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