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Research output: Contribution to Journal/Magazine › Journal article
Research output: Contribution to Journal/Magazine › Journal article
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TY - JOUR
T1 - Dynamic resource allocation in a multi-product make-to-stock production system
AU - Hodge, D J
AU - Glazebrook, K D
PY - 2011/4
Y1 - 2011/4
N2 - We consider optimal policies for a production facility in which several (K) products are made to stock in order to satisfy exogenous demand for each. The single machine version of this problem in which the facility manufactures at most one product at a time to minimise inventory costs has been much studied. We achieve a major generalisation by formulating the production problem as one involving dynamic allocation of a key resource which drives the manufacture of all products under an assumption that each additional unit of resource allocated to a product achieves a diminishing return of increased production rate. A Lagrangian relaxation of the production problem induces a decomposition into K single product problems in which the production rate may be varied but is subject to charge. These reduced problems are of interest in their own right. Under mild conditions of full indexability the Lagrangian relaxation is solved by a production policy with simple index-like structure. This in turn suggests a natural index heuristic for the original production problem which performs strongly in a numerical study. The paper discusses the importance of full indexability and makes proposals for the construction of production policies involving resource idling when it fails.
AB - We consider optimal policies for a production facility in which several (K) products are made to stock in order to satisfy exogenous demand for each. The single machine version of this problem in which the facility manufactures at most one product at a time to minimise inventory costs has been much studied. We achieve a major generalisation by formulating the production problem as one involving dynamic allocation of a key resource which drives the manufacture of all products under an assumption that each additional unit of resource allocated to a product achieves a diminishing return of increased production rate. A Lagrangian relaxation of the production problem induces a decomposition into K single product problems in which the production rate may be varied but is subject to charge. These reduced problems are of interest in their own right. Under mild conditions of full indexability the Lagrangian relaxation is solved by a production policy with simple index-like structure. This in turn suggests a natural index heuristic for the original production problem which performs strongly in a numerical study. The paper discusses the importance of full indexability and makes proposals for the construction of production policies involving resource idling when it fails.
KW - Backordering
KW - Dynamic programming
KW - Dynamic resource allocation
KW - Index heuristic
KW - Lagrangian relaxation
KW - Make-to-stock policy
KW - Queueing control
U2 - 10.1007/s11134-011-9217-2
DO - 10.1007/s11134-011-9217-2
M3 - Journal article
VL - 67
SP - 333
EP - 364
JO - Queueing Systems
JF - Queueing Systems
SN - 0257-0130
IS - 4
ER -