scholarly journals Optimality Conditions for Inventory Control

2016 ◽  
pp. 14-45 ◽  
Author(s):  
Eugene A. Feinberg
Keyword(s):  
Optimality Conditions ◽  
Inventory Control

A NEW MODEL OF RESOURCE PLANNING FOR OPTIMAL PROJECT SCHEDULING

2007 ◽  
Vol 12 (2) ◽  
pp. 255-266 ◽  
Author(s):  
Andrey Valuev
Keyword(s):  
Optimality Conditions ◽  
Inventory Control ◽  
Project Scheduling ◽  
Decomposition Method ◽  
Classical Model ◽  
Resource Planning ◽  
Optimum Amount ◽  
Industrial Systems ◽  
Internal Resources ◽  
Precedence Conditions

It is well known that not only the classical model of PERT/CPM but its later improvements treat a resource planning in the project scheduling in a very limited way. Using them it is possible to calculate the optimum amount of resources taken from outside or financial expenses for separate operations but it is quite impossible to share internal resources between parallel operations. Instead of these models a new one is introduced. It combines relationships concerning sharing resources‐capacities and works dynamics and perhaps other ones that express the use of materials and funds, inventory control and so on. Non‐strict work precedence conditions may be used as well. The model as a whole slightly differs from the model of resource planning in complex industrial systems proposed by the author and retains its general properties, notably the form of optimality conditions. A decomposition method of the project optimum fulfillment is proposed.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Sign in / Sign up

Export Citation Format

Share Document