Minimising the total weighted tardiness for non-identical parallel batch processing machines with job release times and non-identical job sizes

This paper investigates a scheduling problem of non-identical parallel batch processing machines (PBPMs) with job release times and non-identical job sizes, in which jobs come from compatible product families, to minimise the total weighted tardiness (TWT). Only a few studies on PBPM problems aimed at minimising the TWT are concerned with compatible product families. A mixed integer programming (MIP) model is formulated, and a multi-MIP approach is proposed based on this model. Given the computational difficulty in directly solving the multi-MIP approach, several heuristics are developed based on dispatching rules, dynamic programming methods, and simulated annealing (SA) algorithms. Computational results reveal that the proposed SA algorithms can obtain the optimal solutions for 99.8% of the tested small-scale (n = 10) problems and they significantly outperform the dispatching rule heuristics because the solution space is enlarged by the composite list and swapping method. [Received 11 May 2011; Revised 9 September 2011; Revised 31 December 2011; Accepted 16 January 2012]