Energy-aware lot sizing problem: Complexity analysis and exact algorithms

The single-item lot sizing problem under a periodic energy limitation is considered in this paper. Identical and parallel capacitated machines constitute the production system, each one consuming a certain amount of energy when being switched on, when reserved, and when producing. We consider a cost...

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Vydané v:International journal of production economics Ročník 203; s. 254 - 263
Hlavní autori: Rapine, Christophe, Goisque, Guillaume, Akbalik, Ayse
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.09.2018
Elsevier [1991-....]
Predmet:
Capacitated parallel machines
Complexity
Computer Science
Energy
Lot sizing problem
Operations Research
Polynomial time algorithm
Capacitated parallel machines
Polynomial time algorithm
Energy
Lot sizing problem
Complexity
complexity
capacitated parallel machines
polynomial time algorithm
energy
ISSN:0925-5273, 1873-7579
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Shrnutí:The single-item lot sizing problem under a periodic energy limitation is considered in this paper. Identical and parallel capacitated machines constitute the production system, each one consuming a certain amount of energy when being switched on, when reserved, and when producing. We consider a cost for starting-up the machines, a reservation cost to keep the machines ready for production, in addition to classical lot sizing costs, such as, joint setup cost, unit production cost and unit holding cost, all being time-dependent. Besides the classical lot sizing decisions of how much and in which periods to produce, we have to decide the number of machines to switch on and to switch off in each period. We show that this problem is NP-hard even under restricted conditions. In contrast, assuming stationary energy parameters, we propose two polynomial time dynamic programming algorithms to solve the problem to optimality. The first algorithm is proposed for the case with null setup cost, null reservation cost and null reservation energy consumption, and runs in O(M5T4) time, with M being the number of machines and T the number of periods. We show that we can extend this algorithm to solve the generalized version of the problem in time complexity O(M6T6). •The single-item lot sizing problem with a limited energy consumption is considered.•The production system is constituted of identical, parallel capacitated machines.•Energy is consumed by machine start-ups, machine reservations and production.•We establish the NP-hardness of the problem.•We develop polynomial time algorithms for stationary energy parameters.
ISSN:0925-5273
1873-7579
DOI:10.1016/j.ijpe.2018.06.020