Browsing by Subject "Optimal Control"

Now showing 1 - 3 of 3

Open Access
Continuous time control of make-to-stock production systems
(2010) Bulut, Önder
We consider the problem of production control and stock rationing in a make-tostock production system with multiple servers –parallel production channels--, and several customer classes that generate independent Poisson demands. At decision epochs, in conjunction with the stock allocation decision, the control specifies whether to increase the number of operational servers or not. Previously placed production orders cannot be cancelled. We both study the cases of exponential and Erlangian processing times and model the respective systems as M /M /s and M /Ek /s make-to-stock queues. We characterize properties of the optimal cost function, and of the optimal production and rationing policies. We show that the optimal production policy is a state-dependent base-stock policy, and the optimal rationing policy is of state-dependent threshold type. For the M /M /s model, we also prove that the optimal ordering policy transforms into a bang-bang type policy when we relax the model by allowing order cancellations. Another model with partial ordercancellation flexibility is provided to fill the gap between the no-flexibility and the full-flexibility models. Furthermore, we propose a dynamic rationing policy for the systems with uncapacitated replenishment channels, i.e., exogenous supply systems. Such systems can be modeled by letting s --the number of replenishment channels-- go to infinity. The proposed policy utilizes the information on the status of the outstanding replenishment orders. This work constitutes a significant extension of the literature in the area of control of make-to-stock queues, which considers only a single server. We consider an arbitrary number of servers that makes it possible to cover the spectrum of the cases from the single server to the infinite servers. Hence, our work achieves to analyze both the exogenous and endogenous supply leadtimes.
Open Access
An optimal solution for the multi-agent rendezvous problem appearing in cooperative control
(2008) Kölmek, Fatih
The multi-agent rendezvous problem appearing in cooperative control is considered in this thesis. There are various approaches to this topic as the objectives and problem set-ups vary in real-life rendezvous problems. Some of the applications can be given as the coordination of autonomous mobile robots or unmanned air vehicles (UAVs) for joint tasks, and motion planning for vehicle convoys. The problem is basically on providing a rendezvous for mobile agents at a specified or unspecified destination. What makes the topic interesting is maintaining a coordination between the mobile agents so that the agents reach the rendezvous point simultaneously. Early or late arrivals are not desired. An energy optimal solution is obtained for the problem. Imperfect road conditions, obstacles, internal problems of the agents or similar disturbances are also tried to be handled. As these factors are included in the problem, it is assumed that the agents communicate between each other at specified time instants exchanging information about their expected arrival times in order to maintain a common rendezvous time among the team. The solution is initially derived for rendezvous in one-dimensioned space. Then, the problem configuration is altered for two-dimensioned motions, and the target point is assumed to be moving in order to extend the solution to possible practical applications. The effect of increasing disturbance on the control input and time delays in the communication are also discussed.
Open Access
Optimal timing of an energy saving technology adoption
(2011) Harmankaya, Mehmet Fatih
In this thesis, we use two stage optimal control techniques to analyze the optimal timing of energy saving technology adoptions. We assume that the physical capital goods sector is relatively more energy intensive than consumption goods sector. First, we solve a benchmark problem without exogenously growing energy saving technology frontier. In such a case, the economy sticks either to the initial technology or immediately switches to a new technology, depending on the growth rate advantage compared to the obsolescence and adjustment costs. In the second step, we introduce exogenously growing energy saving technology frontier. The anticipated level of the technology provides incentives to delay the adoption and generates an interior switching time. Finally, we analyze numerically the e§ects of the speed of adjustment to the new technology, growth rate of technology, subjective time preference and planning horizon on the optimal timing of technology adoption.