K. Kogan et E. Khmelnitsky, TRACKING DEMANDS IN OPTIMAL-CONTROL OF MANAGERIAL SYSTEMS WITH CONTINUOUSLY-DIVISIBLE, DOUBLY CONSTRAINED RESOURCES, Journal of global optimization, 13(1), 1998, pp. 43-59
Citations number
18
Categorie Soggetti
Mathematics,"Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
The paper addresses problems of allocating continuously divisible reso
urces among multiple production activities. The resources are allowed
to be doubly constrained, so that both usage at every point of time an
d cumulative consumption over a planning horizon are limited as it is
often the case in project and production scheduling. The objective is
to track changing in time demands for the activities as closely as pos
sible. We propose a general continuous-time model that states the prob
lem in a form of the optimal control problem with non-linear speed-res
ource usage functions. With the aid of the maximum principle, properti
es of the solutions are derived to characterize optimal resource usage
policies. On the basis of this analytical investigation, numerical sc
heduling methods are suggested and computationally studied.