Abstract. The paper is a survey devoted to job scheduling problems with resource allocation. We present the results available in the scientific literature for commonly used models of job processing times and job release dates, i.e., the models in which the job processing time or the job release date is given as a linear or convex function dependent on the amount of the additional resource allotted to the job. The scheduling models with resource dependent processing times or resource dependent release dates extend the classical scheduling models to reflect more precisely scheduling problems that appear in real life. Thus, in this paper we present the computational complexity results and solution algorithms that have been developed for this kind of problems.
Mohs micrographic surgery (MMS) is a treatment method aiming at thorough, personalized eradication of skin cancers by mean of staged excision of tissues surrounding the tumor with complete (100%) histopathological examination of their margins. In many MMS laboratories, the excised tissue is divided, shaped, frozen in a cryostat with a heat extractor and positioned manually (with the block on the object disc) in an articulated cryostat chuck during cutting. However, these activities may be difficult, time-consuming and associated with the risk of imprecise tissue sectioning. Development of a laboratory device allowing for processing of large tissue specimens, with the function of mechanical, mathematically steered positioning of the tissue block surface directly to the microtome knife cutting place, eliminating the need for manual adjustment. The prototype device was designed and manufactured. Its functioning was tested on 513 histological slides produced during 212 operations of skin cancers using MMS. The depth of the first complete sections and the diameter of sections were measured. Complete sections were obtained at an average depth of 81.60 μm (min. 20 μm, max. 180 μm, SD = 29.15), whereas the average diameter of sections was 18.11 mm (min. 4 mm, max. 42 mm, SD = 9.10). The histological processing of large specimens with mathematically based positioning of the tissue surface in relation to the cryotome knife cutting plane is precise, fast and easy. The device can be useful in those MMS centers which continue to employ manual setting of the cryostat chuck or share the cryostat with other users, which prevents fixing the chuck position (including large hospital settings). It may also be helpful in centers using a cryostat with a fixed chuck, for the correction of minimal inaccuracies of its preset position.
In this article a survey of studies on scheduling problems with a common due window assignment and earliness/tardiness penalty functions is presented. A due window is a generalization of the classical due date and describes a time interval in which a job should be finished. If a job is completed before or after the due window, it incurs an earliness or a tardiness penalty, respectively. In this survey we separately analyse the classical models with job-independent and job-dependent earliness/tardiness penalty functions and some other more complicated models. We describe the computational complexity of the problems and the main features of the approaches developed to solve them. Particular attention is paid to practical applications of the analysed models. As turns out, some complicated models combining classical scheduling problems with, e.g., learning and aging effects have no reasonable practical justification in the literature.
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