jrp gallego

jrp gallego - IEOR4000 Production Management Lecture 3...

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Unformatted text preview: IEOR4000: Production Management Lecture 3 Professor Guillermo Gallego September 23, 2003 Lecture Plan 1. The Joint Replenishment Problem 2. The Economic Lot Scheduling Problem 1 The Joint Replenishment Problem The Joint Replenishment Problem (JRP) arises in a manufacturing setting when a machine requires a major setup to produce a set of products and a minor setup for each item included in the set. For example, the major setup may consist on placing the die into the machine and to adjust it to get good parts, while the minor setups may consist in opening and closing cavities in the die to produce different variants of the product. The JRP also arises in a distribution setting where multiple items can be shipped together, the cost per shipment is fixed, and there are in addition fixed, item dependent, costs for picking and processing. Notice that an order with a minor setup cost cannot be placed unless the major setup cost is also incurred. However, once the major setup cost is incurred then any item can be ordered by simply incurring its minor setup cost. The relevant questions are: What is the optimal time between major setups? What is the optimal time between setups for each item? When the major setup cost is zero the problem reduces to the case of independent items studied before. When the major setup cost is very large then all the items will be forced to order together. Thus, a manager that insists on ordering all items infrequently and together may be subconsciously charging the system a large major setup cost for his time. In most cases the major setup cost is large enough to force us to consolidate some, but not all, orders. Let λ i demand rate for item i = 1 ,...,n, h i holding cost rate for item i = 1 ,...,n, K i fixed minor setup cost for item i = 1 ,...,n, K fixed major setup cost. For convenience, we set H i = 0 . 5 h i λ i . As stated, the solution can be exceedingly complicated because orders need to be coordinated to account for the major setup cost. Rather than studying this more general problem, we will restrict attention to a type of policy that seems to be quite constraining, but in fact is not. Specifically, we assume that there exists a base planning period β (day, shift, week, or month), where β is expressed in years, and that major setups occur as a non-negative integer power-of-two multiple of β . Finally, we assume that the policy that is followed is stationary. That is, the only solutions that will be considered assume that the time between setups, either major or minor, is always the same. It helps to envision the solution before we delve into the details. There will be a set of items C ⊂ { 1 ,...,n } that will order together and will pay for the major setup cost. You can think of C as the set of items that want to order frequently. The other items will then order only when the set C orders. Thus, for example, if the set of items C orders every month, then other items will order either every month, every two months, every four months, etcetera.either every month, every two months, every four months, etcetera....
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This note was uploaded on 04/19/2011 for the course IEOR 4000 taught by Professor Vineetgoyal during the Spring '11 term at Columbia.

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jrp gallego - IEOR4000 Production Management Lecture 3...

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