TY - JOUR

T1 - A combinatorial approach to a class of parallel-machine, continuous-time scheduling problems

AU - Kogan, Konstantin

AU - Khmelnitsky, Eugene

AU - Levner, Eugene

PY - 2002/3

Y1 - 2002/3

N2 - The paper analyzes a manufacturing system with N non-identical, parallel machines continuously producing one product type in response to its demand. Inventory and backlog costs are incurred when tracking the demand results in inventory surpluses and shortages respectively. In addition, the production cost of a machine is incurred when the machine is not idle. The objective is to determine machine production rates so that the inventory, backlog, and production costs are minimized. For problems with demand defined as an arbitrary function of time, numerical methods are suggested to approximate an optimal solution. The complexity of the approximation methods is polynomial, while finding an exact optimal solution requires exponential time. In a case when production is to cope with a special form of a single-mode, K-level piece-wise constant demand, we prove, with the aid of the maximum principle, that the exact optimal solution can be found as a combination of analytical and combinatorial tools in O(KN2(max{K,2N})2) time.

AB - The paper analyzes a manufacturing system with N non-identical, parallel machines continuously producing one product type in response to its demand. Inventory and backlog costs are incurred when tracking the demand results in inventory surpluses and shortages respectively. In addition, the production cost of a machine is incurred when the machine is not idle. The objective is to determine machine production rates so that the inventory, backlog, and production costs are minimized. For problems with demand defined as an arbitrary function of time, numerical methods are suggested to approximate an optimal solution. The complexity of the approximation methods is polynomial, while finding an exact optimal solution requires exponential time. In a case when production is to cope with a special form of a single-mode, K-level piece-wise constant demand, we prove, with the aid of the maximum principle, that the exact optimal solution can be found as a combination of analytical and combinatorial tools in O(KN2(max{K,2N})2) time.

UR - http://www.scopus.com/inward/record.url?scp=0036498123&partnerID=8YFLogxK

U2 - 10.1023/A:1012475430060

DO - 10.1023/A:1012475430060

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AN - SCOPUS:0036498123

SN - 0740-817X

VL - 34

SP - 223

EP - 231

JO - IIE Transactions (Institute of Industrial Engineers)

JF - IIE Transactions (Institute of Industrial Engineers)

IS - 3

ER -