James R. Perkins

Stable, distributed, real-time scheduling of flexible manufacturing/assembly/diassembly systems

The authors consider general flexible manufacturing/assembly/disassembly systems with the following features: (i) there are several types, each with given processing time requirements at a specified sequence of machines; (ii) each part type needs to be produced at a prespecified rate; (iii) parts may incur variable transportation delays when moving from one machine to another; (iv) set-up times are required whenever a machine changes from a production run of parts of one type to a run of another type; (v) some part types may also need assembly or disassembly; and (vi) a proportion of parts of a part type may require separate routing on exiting from a machine, for reasons including, but not limited to, poor quality. The authors exhibit a class of scheduling policies implementable in real time in a distributed way at the various machines, which ensure that the cumulative production of each part type trails the desired production by no more than a specific constant. The buffers of all the machines are guaranteed to be bounded, and the system can thus operate with finite buffer capacities. >

Distributed scheduling of flexible manufacturing systems: stability and performance

We consider a manufacturing system producing several part-types on several machines. Raw parts are input to the system. Each unit of a given part-type requires a predetermined processing time at each of several machines, in a given order. A setup time is required whenever a machine switches from processing one part-type to another. For a single machine system with constant demand rates, we present a class of generalized round-robin scheduling policies for which the buffer level trajectory of each part-type converges to a steady state level. Furthermore, for all small initial conditions, we show that these policies can be Pareto-efficient with respect to the buffer sizes required. Allowing the input streams to have some burstiness, we derive upper bounds on the buffer levels for small initial conditions. For non-acyclic systems, we consider a class of policies which are stable for all inputs with bounded burstiness. We show how to employ system elements, called regulators, to stabilize systems. Using the bounds for the single machine case, we analyze the performance of regulated systems implementing generalized round-robin scheduling policies. >

Scheduling multiple part-types in an unreliable single-machine manufacturing system

Quadratic approximations to the differential cost-to-go function, which yield linear switching curves, have been extensively studied in the literature. In this paper, we provide solutions to the partial differential equations associated with the components of the steady-state probability density function of the buffer levels for two part-type, single-machine flexible manufacturing systems under a linear switching curve (LSC) policy. When there are more than two part-types, we derive the probability density function, under a prioritized hedging point (PHP) policy by decomposing the multiple part-type problem into a sequence of two part-type problems. The analytic expression for the steady-state probability density function is independent of the cost function. Therefore, for average cost functions, we can compute the optimal PHP policy or the more general optimal LSC policy for two part-type problems.

Failure-prone production systems with uncertain demand

We consider a failure-prone manufacturing system with bursty demand arrivals. We prove that the hedging-point policy is optimal for this problem and provide analytical expressions to compute the hedging point. This allows us to compare our exact results to simpler approximations. We also show that our result leads to the solution for the constant demand rate problem, under an appropriate scaling of the demand process. We also provide a necessary and sufficient condition under which the just-in-time (JIT) policy is optimal for the case of linear, absolute value instantaneous cost.

Stable distributed real-time scheduling of flexible manufacturing/assembly/disassembly systems

The authors propose a dynamic model of the manufacturing environment which allows a real-time, distributed approach to scheduling. They first consider a single machine, and then they consider an interconnection of machines called a distributed clear-a-fraction policy which results in an acyclic system such as a flow shop. Finally, they treat a general manufacturing system with no restrictions on interconnections, using a clear-a-fraction policy with backoff, which can be shown to be stable.<<ETX>>

Optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs

We consider a single, failure-prone machine, producing multiple part-types The objective is to minimize the expected sum of quadratic buffer costs. In general, the optimal solution to this problem is unknown. However, by restricting the allowable set of control policies to the class of prioritized hedging point (PHP) policies, we are able to determine simple, analytical expressions for the optimal hedging points. We also provide some results for choosing the optimal priority ordering.

Stable scheduling policies for broadcast channels

We present a class of scheduling policies for an N-user broadcast channel and show that the system is stable in the mean through the use of a Lyapunov argument.

Optimal resource allocation in new product development projects: a control-theoretic approach

Considers problems motivated by the dynamic allocation of limited heterogeneous resources in new product development (NPD) projects. The interchangeability of resources and simultaneous resource sharing are defining characteristics of NPD processes. A continuous flow model is introduced that incorporates these features. For problems without activity precedence constraints, a linear program is presented which yields the minimum completion time for all activities. A dynamic, rule-based algorithm is shown to be optimal for two resources processing a multiple-activity arrival stream. For problems with precedence constraints, some special cases are solved, and structural properties of the class of optimal controls for the general problem are discussed.

On the optimality of myopic production controls for single-server, continuous-flow manufacturing systems

In this note, we consider a broad class of dynamic scheduling problems associated with a single-server, multiclass, continuous-flow manufacturing system. Using a general framework, we provide conditions under which the solution to these problems is the implementation of a class of production controls called myopic scheduling policies. The proof of optimality, which is intuitively appealing, applies to more general production models than existing proofs in the literature, which typically either use the maximum principle or solve the Hamilton-Jacobi-Bellman (HJB) equation. We also present several counter-examples that explicitly illustrate the potential limitations of myopic scheduling policies.

The role of queue length information in congestion control and resource pricing

We consider a single-user congestion problem with a packet loss constraint viewed as a stochastic control problem. Using a precise nonlinear model of the queue with a time-varying Markovian service rate, we show that the optimal controller is a bang-bang type solution. Additionally, we show that a stochastic problem with a quality of service (QoS) constraint can also be viewed as an unconstrained stochastic problem where the user is forced to pay a price for QoS violations.