Generalized preemption models for single-machine dynamic scheduling problems

In the extensive scheduling literature, job preemption, if allowed, implies that the processing of a partly completed job is temporarily halted and later resumed at the same point. However, little attention has been given to problems where job preemption is allowed under the condition that either some startup time delay must be incurred or some fraction of work must be repeated if preemption occurs. We generalize the notion of job preemption by using models representing these conditions. The models are applied to studying the dynamic single-machine scheduling problems of minimizing total flow time, and of minimizing maximum lateness, subject to arbitrary and unknown job ready dates. On-line optimal dispatching rules, which consider only available - as opposed to look-ahead - information, are developed. These rules determine, on arrival or completion of each job, which available job should next be processed by the machine. A special case of our models, the preempt-repeat scenario, where preempted jobs must be totally repeated, is suggested as heuristic for the equivalent non-preemptive static problem where all ready dates are known and given. A computational study is performed to determine the potential benefits of reducing startup time delays or work repetition fractions in the context of continuous improvement of manufacturing systems.     

Quantifying phenotypic plasticity of berry traits using an allometric-type approach: A case study on anthocyanins and sugars in berries of Cabernet Sauvignon

In this paper we advance a novel allometric-type approach to quantify the stability of key berry traits viz. anthocyanins and sugars. To test the concept, we used data from Cabernet Sauvignon grown in a hot environment of South Australia. Sources of variation in berry traits included water supply, fruit load, seasonal conditions and their interactions. Anthocyanins and sugars were measured in berry samples taken 7–8 times between veraison and harvest. Rates and durations of accumulation of anthocyanins and sugars per berry were derived from a bi-linear model between amount of compound and thermal time. We develop a framework based on 'α' a parameter representing the slope of the regression between rate and duration in a log-log scale. This relationship accommodates three conditions viz. (a) potentially plastic, rate-driven trait (α–1), (b) potentially plastic, duration-driven trait (α < –1), and (c) a stable trait, whereby variation in rate and variation in duration cancel each other (α=–1). Under our experimental conditions, amount of anthocyanins (range of variation 148%) was more plastic than amount of sugars per berry (range of variation 37%). The slope α captured the differential plasticity of these traits: α was significantly greater than –1 for anthocyanins and statistically undistinguishable from –1 for sugars. The rate-dominated accumulation of anthocyanins explained the relatively large variation in this constituent whereas the tightly coupled, inverse relationship between duration and rate (α–1) explained the relative stability of sugars per berry. We conclude that our allometric-type relationship between rate and duration allows for the quantification of cultivar-environment specific plasticity of important berry traits.     

Effect of reduced irrigation on growth,yield, ripening rates and water relations of Chardonnay vines grafted to five rootstocks

Background and Aims: In the first decade of the 21st century, drought within the Murray–Darling Basin has reduced the amount of water available for irrigation. We investigated whether the response of vines to reduced irrigation was modified by rootstock. Methods and Results: Reduced irrigation (5 versus 8 ML/(ha·year)) was applied to Chardonnay vines grafted to five rootstocks (Ramsey, 140 Ruggeri, 1103 Paulsen, 110 Richter and K51‐40) for four seasons. It decreased the yield from 29.3 to 26.7 kg/vine, and increased the irrigation water use index (IWUI) from 4.7 to 6.6 t/(ha·ML), but gains in this index declined as the trial progressed. The values of mid‐afternoon leaf water potential were not affected by reduced irrigation, but leaf CO₂ assimilation declined from 13.1 to 11.7 µmol/(m²·s). These effects were independent of rootstock. Reduced irrigation did not increase soil salinity (ECe) or vine tissue Na and Cl concentrations. Vines on Ramsey and 1103 Paulsen rootstocks had higher yields, 32.2 and 30.0 kg/vine, respectively, and the highest IWUIs, 5.9 and 5.5 t/(ha·ML). In two of the three seasons, reducing irrigation did not affect the rates of ripening (°Brix/growing degree days) excepting vines on 1103 Paulsen. Ripening rates varied by 1.5‐fold between seasons. Conclusion: The yield and growth responses of Chardonnay vines to a 35% reduction in irrigation were not modified by rootstock. Significance of the Study: Reducing irrigation did not lead to a build‐up of soil salts. The response of vines to reduced irrigation on rootstocks rated as having good drought tolerance was the same as that for vines on a rootstock rated as having poor drought tolerance.