Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for the TWT and TWET problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm for solving the preemptive relaxation formulated as a mixed integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines, and then we exploit recent advances in solving the non-preemptive single machine TWT and TWET problems for constructing non-preemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances up to 5 machines and 200 jobs.

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Loligo vulgaris is a commercially important squid throughout the Mediterranean region and is a candidate species in biomedical and aquaculture research. Some loligo species (L. opalescens, L. forbesi, Sepiteuthis lessoniana) have now been cultured through some successive generations in closed, recirculating seawater systems. The e¡ects of salinity on hatching European Squid (L. vulgaris Lamarck,1798) eggs were investigated during November 2004. The egg capsules were incubated directly in salinity of 32, 34, 36, 38, 40, 42 and 37 g L À1 (control group) at 19.8 1C (SD 1.2 1C), and a photoperiodicity of 12 h light:12 h dark for 16^23 days before hatching. In all treatments, the eggs were developed and hatched normally after 16^22 days at 32 g L À1 , 17^22 days at 34, 18^21 days at 42 g L À1 ,18^22 days at 36 and 40 g L À 1 ,19^22 days at 37 g L À1 and 19^23 h at 38 g L À1 . In the experiments, the highest hatching rate and hatching success (HS) of the eggs were obtained at 38 g L À1 (hatching rate: 100% (SD 0%) and HS: 96.7% (SD 3.5%)) and the lowest hatching rate at 42 g L À1 (hatching rate: 3% (SD 6%) and HS: 0%). Dorsal mantle lengths (DML) of new hatchlings ranged from 2.08 to 2.80 mm. The present study showed that salinity a¡ects the hatching rate and HS of eggs and ¢rst hatching time and DML of paralarvae in L. vulgaris. The squid eggs at stage 11 (I) can tolerate 5 g L À1 reduction and 3 g L À1 increase in salinity.

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