Control and optimal control of assemble to order manufacturing systems under heavy traffic

We consider the problem of reducing the response time of fork-join systems by maintaining the workload balanced among the processing stations. The general problem of modeling and finding an optimal policy that reduces imbalance is quite difficult. In order to circumvent this difficulty, the heavy traffic approach is taken, and the system dynamics are approximated by a reflected diffusion process. This way, the problem of finding an optimal balancing policy that reduces workload imbalance is set as a stochastic optimal control problem, for which numerical methods are available. Some numerical experiments are presented, where the control problem is solved numerically and applied to a simulation. The results indicate that the response time of the controlled system is reduced significantly using the devised control.

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Optimal and Approximately Optimal Control Policies for Queues in Heavy Traffic

SIAM Journal on Control and Optimization ◽

10.1137/0327066 ◽

1989 ◽

Vol 27 (6) ◽

pp. 1293-1318 ◽

Cited By ~ 44

Author(s):

Harold J. Kushner ◽

K. M. Ramachandran

Keyword(s):

Optimal Control ◽

Heavy Traffic ◽

Control Policies

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Approximations and Optimal Control for State-Dependent Limited Processor Sharing Queues

Stochastic Systems ◽

10.1287/stsy.2021.0087 ◽

2022 ◽

Author(s):

Varun Gupta ◽

Jiheng Zhang

Keyword(s):

Optimal Control ◽

Average Cost ◽

Concurrency Control ◽

Heavy Traffic ◽

Control Policy ◽

Original System ◽

Diffusion Control ◽

Service Rate ◽

Processor Sharing ◽

State Dependent

The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs that can share the server concurrently, with the rest of the jobs waiting in a first-in-first-out (FIFO) buffer. A desirable control scheme should strike the right balance between efficiency (operating at a high service rate) and parallelism (preventing small jobs from getting stuck behind large ones). We use the framework of heavy-traffic diffusion analysis to devise near optimal control heuristics for such a queueing system. However, although the literature on diffusion control of state-dependent queueing systems begins with a sequence of systems and an exogenously defined drift function, we begin with a finite discrete PS server and propose an axiomatic recipe to explicitly construct a sequence of state-dependent PS servers that then yields a drift function. We establish diffusion approximations and use them to obtain insightful and closed-form approximations for the original system under a static concurrency limit control policy. We extend our study to control policies that dynamically adjust the concurrency limit. We provide two novel numerical algorithms to solve the associated diffusion control problem. Our algorithms can be viewed as “average cost” iteration: The first algorithm uses binary-search on the average cost, while the second faster algorithm uses Newton-Raphson method for root finding. Numerical experiments demonstrate the accuracy of our approximation for choosing optimal or near-optimal static and dynamic concurrency control heuristics.

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THE GREATEST SOLUTION IN THE INEQUALITY OF K X X LX WITH K 2 ISnn;L 2 ISnn;X 2 ISnm ARE A COMPLETE IDEMPOTENT SEMIRINGS OF INTERVAL

Jurnal Matematika Thales ◽

10.22146/jmt.56567 ◽

2021 ◽

Vol 2 (2) ◽

Author(s):

Eka Susilowati

Keyword(s):

Optimal Control ◽

Manufacturing Systems ◽

Industrial Applications ◽

Model Matching ◽

Idempotent Semiring ◽

Matching Problem ◽

Idempotent Semirings ◽

Adjusted Model

The greatest solution of an inequality KX X LX to solve the optimalcontrol problem for P-Temporal Event Graphs, which is to nd the optimal control thatmeets the constraints on the output and constraints imposed on the adjusted model prob-lem (the model matching problem). We give the greatest solution K X X L Xand X H with K; L;X;H matrices whose are entries in a complete idempotent semir-ings. Furthermore, the authors examine the existence of a sucient condition of theprojector in the set of solutions of inequality K X X L X with K; L;X matrixwhose entries are in the complete idempotent semiring. Projectors can be very necessaryto synthesize controllers in manufacturing systems that are constrained by constraintsand some industrial applications. The researcher then examines the requirements forthe presence of the greatest solution was called projector in the set of solutions of theinequality K X X L X with K; L;X matrices whose are entries in an completeidempotent semiring of interval. Researchers describe in more detail the proof of theproperties used to resolve the inequality K X X L X. Before that, we givethe greatest solution of the inequality KX X LX and X G with K; L;X;Gmatrices whose are entries in an complete idempotent semiring of interval

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