In many manufacturing problems, the total lead time taken to manufacture a product is an important consideration. Long lead times impose costs due to higher work-in-process inventory, increased uncertainty about requirements, larger safety stocks and poorer performance to due dates. Traditional lot sizing models ignore lead time related costs, although there are systematic relationships between lot sizes and lead times. This paper examines these relationships and their implications for lot sizing and work-in-process inventories, for batch manufacturing shops with queues.

https://www.jstor.org/stable/pdfplus/2631860.pdf

Lot Sizes, Lead Times and In-Process Inventories

Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems

We consider a class of weighted gradient methods for distributed resource allocation over a network. Each node of the network is associated with a local variable and a convex cost function; the sum of the variables (resources) across the network is fixed. Starting with a feasible allocation, each node updates its local variable in proportion to the differences between the marginal costs of itself and its neighbors. We focus on how to choose the proportional weights on the edges (scaling factors for the gradient method) to make this distributed algorithm converge and on how to make the convergence as fast as possible. We give sufficient conditions on the edge weights for the algorithm to converge monotonically to the optimal solution; these conditions have the form of a linear matrix inequality. We give some simple, explicit methods to choose the weights that satisfy these conditions. We derive a guaranteed convergence rate for the algorithm and find the weights that minimize this rate by solving a semidefinite program. Finally, we extend the main results to problems with general equality constraints and problems with block separable objective function.

/pdf/optimal-scaling-of-a-gradient-method-for-distributed-472n51e0o2.pdf

Optimal Scaling of a Gradient Method for Distributed Resource Allocation

Decentralized algorithms are examined for optimally distributing a divisible resource in a distributed computer system. To study this problem in a specific context, the problem of optimal file allocation is considered. In this case, the optimization criteria include both the communication cost and average processing delay associated with a file access. The algorithms examined have their origins in the field of mathematical economics. They are shown to have several attractive properties, including their simplicity and distributed nature, the computation of feasible and increasingly better resource allocations as the result of each iteration, and, in the case of file allocation, rapid convergence. Conditions are formally derived under which the algorithms are guaranteed to coverage, and their convergence behavior is additionally examined through simulation. >

/pdf/a-microeconomic-approach-to-optimal-resource-allocation-in-qlv3mkw1jo.pdf

A microeconomic approach to optimal resource allocation in distributed computer systems

Networked control systems often send information across the communication network in a periodic manner. The selected period, however, must assure adequate system performance over a wide range of operating conditions and this conservative’ choice may result in significant over-provisioning of the communication network. This observation has motivated the use of sporadic transmission across the network’s feedback channels. Event-triggering represents one way of generating such sporadic transmissions. In event-triggered feedback, a sensor transmits when some internal measure of the novelty in the sensor information exceeds a specified threshold. In particular, this means that when the gap between the current and the more recently transmitted sensor measurements exceeds a state-dependent threshold, then the information is transmitted across the channel. The state-dependent thresholds are chosen in a way that preserves commonly used stability concepts such as input-to-state stability or \({\mathcal L}_2\) stability. This approach for threshold selection therefore provides a systematic way of triggering transmissions that provides some guarantees on overall control system performance. While early work in event-triggering focused on control applications, this technique can also be used in distributed estimation and distributed optimization. This chapter reviews recent progress in the use of state-dependent event-triggering in embedded control, networked control systems, distributed estimation, and distributed optimization.

/pdf/event-triggered-feedback-in-control-estimation-and-57vg8si8nx.pdf

R. Suri

Papers

A Class of Center-Free Resource Allocation Algorithms 1

New Techniques for Modelling and Control of Flexible Automated Manufacturing Systems