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ABSTRACT: We consider deterministic mixed-line flow shop systems that are composed of controllable and uncontrollable machines. Arrival times and completion deadlines of jobs are assumed to be known, and they are processed in the order they arrive at the machines. We model these flow shops as serial networks of queues operating under a non-preemptive first-come-first-served policy, and employ max-plus algebra to characterize the system dynamics. Defining completion-time costs for jobs and service costs at controllable machines, a non-convex optimization problem is formulated where the control variables are the constrained service times at the controllable machines. In order to simplify this optimization problem, under some cost assumptions, we show that no waiting is observed on the optimal sample path at the downstream of the first controllable machine. We also present a method to decompose the optimization problem into convex subproblems. A solution algorithm utilizing these findings is proposed, and a numerical study is presented to evaluate the performance improvement due to this algorithm.
IEEE Transactions on Automatic Control 03/2010; · 2.11 Impact Factor
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ABSTRACT: We consider an optimization problem for deterministic flow shop systems of traditional machines with service costs penalizing small service times. A regular completion-time cost is also included so as to complete jobs as early as possible. The service times are assumed to be initially controllable, i.e., they are set at the startup time. Assuming convexity of the cost functions, we formulate a convex optimization problem after linearization of the max constraints. The numeric solution of this problem demands a large memory limiting the solvable system sizes. In order to relieve the memory bottleneck, some waiting characteristics of jobs served in fixed-service-time flow shop systems are exploited to result in a simpler equivalent convex optimization problem. These characteristics and the benefit of CNC machines are demonstrated in a numerical example. We also show that the simplifications result in significant improvements in solvable system sizes and solution times.
IEEE Transactions on Automatic Control 01/2009; · 2.11 Impact Factor
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ABSTRACT: We consider an optimal control problem for the hybrid model of a deterministic flow shop system, in which the jobs are processed in the order they arrive at the system. The problem is decomposed into a higher-level discrete-event system control problem of determining the optimal service times, and a set of lower-level classical control problems of determining the optimal control inputs for given service times. We focus on the higher-level problem which is nonconvex and nondifferentiable. The arrival times are known and the decision variables are the service times that are controllable within constraints. We present an equivalent convex optimization problem with linear constraints. Under some cost assumptions, we show that no waiting is observed on the optimal sample path. This property allows us to simplify the convex optimization problem by eliminating variables and constraints. We also prove, under an additional strict convexity assumption, the uniqueness of the optimal solution and propose two algorithms to decompose the simplified convex optimization problem into a set of smaller convex optimization problems. The effects of the simplification and the decomposition on the solution times are shown on an example problem.
IEEE Transactions on Automatic Control 01/2008; · 2.11 Impact Factor
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ABSTRACT: We consider a two-stage serial hybrid system for which the arrival times are known and the service times are controllable. We derive some optimal sample path characteristics, in particular, we show that no buffering is observed between stages. The original non-smooth optimal control problem is first transformed into a convex optimization problem which is then simplified by the no buffer property. Further simplifications are possible for the bulk arrival case
American Control Conference, 2006; 07/2006
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ABSTRACT: We consider threshold-based admission control policies for traffic
in fixed-route circuit-switched networks, and develop a scheme for
adjusting the threshold parameters online so that, as operating
conditions in the network change, the thresholds "adapt" with the
objective of minimizing a weighted sum of call blocking probabilities.
An algorithm for estimating online the sensitivity of the call blocking
metric with respect to thresholds is presented. The formal optimization
problem over the set of discrete threshold parameters is solved by means
of a conversion to an optimization problem over a set of auxiliary
real-valued parameters. Such threshold-based policies, though
conservative at low traffic rates, have the advantage of being simple to
implement, distributed in nature, adaptive, and not requiring explicit
distributional modeling assumptions. Numerical results included in the
paper indicate that at higher traffic rates these simple policies yield
the same performance as more complex and less flexible call admission
schemes
IEEE Transactions on Automatic Control 07/2002; · 2.11 Impact Factor
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ABSTRACT: We consider stochastic discrete optimization problems where the decision variables are nonnegative integers and propose a generalized surrogate problem methodology that modifies and extends previous work in Ref. 1. Our approach is based on an online control scheme which transforms the problem into a surrogate continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both the actual and surrogate system states. In contrast to Ref. 1, the proposed methodology applies to arbitrary constraint sets. It is shown that, under certain conditions, the solution of the original problem is recovered from the optimal surrogate state. Applications of this approach include solutions to multicommodity resource allocation problems; in these problems, exploiting the convergence speed of the method, one can overcome the obstacle posed by the presence of local optima.
Journal of Optimization Theory and Applications 06/2002; 114(1):97-132. · 1.06 Impact Factor
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ABSTRACT: We consider optimal control problems for hybrid systems with a
separable cost structure allowing us to decompose them into two
components: a lower-level component with time-driven dynamics
(describing the physical state of the system) interacting with a
higher-level component with event-driven dynamics (describing the
changes in the operating modes of the system). We develop a hybrid
controller which aims at jointly optimizing the performance of both
hierarchical components. We demonstrate this approach on two problems: a
linear system switching from one operating mode to another and a
multistage manufacturing system. In the first problem, the main
difficulty is due to the coupling of the physical states across modes,
whereas in the second it is due to the nondifferentiable event-driven
dynamics
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on; 02/2000
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ABSTRACT: We consider stochastic discrete optimization problems where the
decision variables are non-negative integers. We propose and analyze an
online control scheme which transforms the problem into a
“surrogate” continuous optimization problem and proceeds to
solve the latter using standard gradient-based approaches while
simultaneously updating both actual and surrogate system states.
Convergence of the proposed algorithm is established and it is shown
that the discrete state neighborhood of the optimal surrogate state
contains the optimal solution of the original problem. Numerical results
are included in the paper illustrating the fast convergence properties
of this approach
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on; 02/1999
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ABSTRACT: Extending previous work for an optimal control problem of a
single-stage system, we consider a two-stage manufacturing system where
each job has a physical state characterized by time-driven dynamics and
a temporal state by event-driven dynamics. We derive necessary
conditions for optimality and develop some new algorithms for explicit
solution of the problem that make use of Bezier approximation
techniques. In addition, we establish some properties of the optimal
control sequence that have interesting implications
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on; 02/1999
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ABSTRACT: We consider a single-stage manufacturing system where the physical
state of each job is characterized by time-driven dynamics and its
temporal state by event-driven dynamics. Extending an earlier analysis
of a deterministic model for this system, we study a stochastic model
where there are controllable parameters that affect the service
processing speed. When job arrivals are represented through a Poisson
process, the service time required to attain a desired physical state is
exponentially distributed (dependent on a controllable processing
speed), and the cost associated with inventory level is non-decreasing
convex, we show that there exists a threshold policy on the inventory
level for selecting the optimal process speed. For a discrete-time model
with geometrically distributed arrivals and deterministic service times,
similar results are derived
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on; 02/1999
