Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands
In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are b...
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| Veröffentlicht in: | Management science Jg. 30; H. 3; S. 344 - 357 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Linthicum
INFORMS
01.03.1984
Institute of Management Sciences Institute for Operations Research and the Management Sciences |
| Schriftenreihe: | Management Science |
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| ISSN: | 0025-1909, 1526-5501 |
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| Abstract | In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries. |
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| AbstractList | In many practical applications of multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries. In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries. Frequently, considerable cost savings can be achieved for multi-item inventory systems by coordinating the replenishment of groups of items. The problem of determining optimal coordination or replenishment orders is considered for a multi-item inventory system operating under continuous review. Replenishment of each group of items requires a lead time and results in a major setup cost. Minor setup costs are added by including any given item in a replenishment order. In addition, inventory holding costs are incurred, along with penalty costs for demand which cannot be satisfied with on-hand inventory. An algorithm is presented for minimizing the long-range average costs of inventory replenishment, subject to the constraint that on-hand inventory satisfies a fraction of demand. The algorithm uses a heuristic decomposition procedure to transform the multi-item problem into single-item subproblems, which are solved using a specialized policy iteration technique. |
| Author | Groenevelt, H Tijms, H. C Federgruen, A |
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| Copyright | Copyright 1984 The Institute of Management Sciences Copyright Institute for Operations Research and the Management Sciences Mar 1984 |
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| Snippet | In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for... In many practical applications of multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for... Frequently, considerable cost savings can be achieved for multi-item inventory systems by coordinating the replenishment of groups of items. The problem of... |
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| SubjectTerms | Algorithms Approximation Average cost Carrying costs compound Poisson demand processes coordinated replenishments Coordination Cost control Costs Decision making models Decision theory Decomposition Excess demand Heuristic Heuristics Integers Inventories Inventory control Inventory management Lead Lead compounds Measures multi-item inventory systems Order quantity Poisson process policy-iteration algorithm Random variables service level constraint |
| Title | Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands |
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