Minimizing non-decreasing separable objective functions for the unit-time open shop scheduling problem
نویسندگان
چکیده
منابع مشابه
Minimizing non-decreasing separable objective functions for the unit-time open shop scheduling problem
In this paper we study both the nonpreemptive and preemptive versions of the popular unit-time open shop scheduling problem. For the set of feasible schedules, we construct the linear description of the convex hull of the vectors of the job completion times. Based on the properties of the resulting scheduling polyhedron, we show that the problem of constructing an optimal schedule minimizing an...
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v ∈ ∂f(w) ⇐⇒ ∃wn → w, f(wn)→ f(w),vn ∈ ∂̂f(wn),vn → v. Clearly, ∂̂f(w) ⊆ ∂f(w) for all w. If f is (resp. continuously) differentiable at w, then ∂̂f(w) (resp. ∂f(w)) coincides with the usual derivative. From the definition it follows that if w is a local minimizer, then 0 ∈ ∂̂f(w) and 0 ∈ ∂f(w), which generalizes the familiar Fermat’s rule. In the main text, we are interested in finding some w so t...
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ژورنال
عنوان ژورنال: European Journal of Operational Research
سال: 2005
ISSN: 0377-2217
DOI: 10.1016/j.ejor.2004.04.014