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Medientyp: E-Artikel Titel: Deterministic and stochastic scheduling with teamwork tasks Beteiligte: Cai, Xiaoqiang; Zhou, Xian Erschienen: Wiley, 2004 Erschienen in: Naval Research Logistics (NRL), 51 (2004) 6, Seite 818-840 Sprache: Englisch DOI: 10.1002/nav.20021 ISSN: 0894-069X; 1520-6750 Schlagwörter: Management Science and Operations Research ; Ocean Engineering ; Modeling and Simulation Entstehung: Anmerkungen: Beschreibung: <jats:title>Abstract</jats:title><jats:p>We study a class of new scheduling problems which involve types of teamwork tasks. Each teamwork task consists of several components, and requires a team of processors to complete, with each team member to process a particular component of the task. Once the processor completes its work on the task, it will be available immediately to work on the next task regardless of whether the other components of the last task have been completed or not. Thus, the processors in a team neither have to start, nor have to finish, at the same time as they process a task. A task is completed only when all of its components have been processed. The problem is to find an optimal schedule to process all tasks, under a given objective measure. We consider both deterministic and stochastic models. For the deterministic model, we find that the optimal schedule exhibits the pattern that all processors must adopt the same sequence to process the tasks, even under a general objective function <jats:italic>GC</jats:italic> = <jats:italic>F</jats:italic>(<jats:italic>f</jats:italic><jats:sub><jats:italic>1</jats:italic></jats:sub>(<jats:italic>C</jats:italic><jats:sub><jats:italic>1</jats:italic></jats:sub>), <jats:italic>f</jats:italic><jats:sub><jats:italic>2</jats:italic></jats:sub>(<jats:italic>C</jats:italic><jats:sub><jats:italic>2</jats:italic></jats:sub>), … , <jats:italic>f</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub>(<jats:italic>C</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub>)), where <jats:italic>f</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>(<jats:italic>C</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>) is a general, nondecreasing function of the completion time <jats:italic>C</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub> of task <jats:italic>i</jats:italic>. We show that the optimal sequence to minimize the maximum cost <jats:italic>MC</jats:italic> = max <jats:italic>f</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>(<jats:italic>C</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>) can be derived by a simple rule if there exists an order <jats:italic>f</jats:italic><jats:sub><jats:italic>1</jats:italic></jats:sub>(<jats:italic>t</jats:italic>) ≤ … ≤ <jats:italic>f</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub>(<jats:italic>t</jats:italic>) for all <jats:italic>t</jats:italic> between the functions {<jats:italic>f</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>(<jats:italic>t</jats:italic>)}. We further show that the optimal sequence to minimize the total cost <jats:italic>TC</jats:italic> = ∑ <jats:italic>f</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>(<jats:italic>C</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>) can be constructed by a dynamic programming algorithm. For the stochastic model, we study three optimization criteria: (A) almost sure minimization; (B) stochastic ordering; and (C) expected cost minimization. For criterion (A), we show that the results for the corresponding deterministic model can be easily generalized. However, stochastic problems with criteria (B) and (C) become quite difficult. Conditions under which the optimal solutions can be found for these two criteria are derived. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004</jats:p>