Hybridizing discrete- and continuous-time models for batch sizing and scheduling problems

Siqun Wang, Monique Guignard
2006 Computers & Operations Research  
This paper proposes a new hybrid technique called "partial parameter uniformization" to hybrid discrete-and continuous-time models for batch sizing and scheduling problems. The uniformization method simpli...es a problem by ignoring the di¤erent values of some parameters that the problem can take, which can facilitate the solution of some complex combinatorial optimization problems. Good feasible solutions can then be obtained at relatively low computational cost for the Westenberger and
more » ... h Benchmark problems, as well as for the newer problems of Blömer and Günther. Various discrete-time and continuous-time MILP (Mixed Integer Linear Programming) formulations have been built and utilized for capacitated batch sizing and scheduling problems in process industries. Initially, discrete-time formulations (with time-indexed variables) were proposed (see, for instance, [Kondili, Pantelides and Sargent (1993)], [Guignard, Spielberg and Yan (1996)], [Yan (1996)], [Blömer and Günther (1998)], [Wang (1998)], and [Guignard and Wang (1998)] ). The major advantage of discrete-time models is the capability of considering complex job ‡ows, handling resource constraints and inventory situations. The major problems with this approach, however, are (1) the large size of the MILP model (especially when each job processing time is di¤erent) and (2) the approximation of the actual points in time horizon when the events take place. Given the weaknesses of the discrete-time representations, researchers in this ...eld have recently started to look into continuous-time formulations (with continuous variables for time points or time ¤
doi:10.1016/j.cor.2004.11.013 fatcat:werx4dxqibetrbcc24mkn54squ