In this chapter, the authors show the main aspects and implications of automatic sizing, including yield. Different strategies for accelerating performance estimation and design space search are addressed. The analog sizing problem is converted into a nonlinear optimization problem, and the design space is explored using metaheuristics based on genetic algorithms. Circuit performance is estimat...

We show for the general dynamic lot sizing model how minimal forecast horizons may be detected by a slight adaptation of an earlier 0(n log n) or 0(n) forward solution method for the model. A detailed numerical study indicates that minimal forecast horizons tend to be small, that is, include a small number of orders. We describe a new planning approach to ensure stability of the lot sizing deci...

This paper gives a status report and describes the future work directions of a systematic research effort to develop and validate methods for structural sizing of an airframe designed with the use of composite materials and active controls. This research program includes procedures for computing aeroelastic loads, static and dynamic aeroelasticity, analysis and synthesis of active controls, and...

This paper studies convex optimization and modelling for component sizing and optimal energy management control of hybrid electric vehicles. The novelty in the paper is the modeling steps required to include a battery wear model into the convex optimization problem. The convex modeling steps are described for the example of battery sizing and simultaneous optimal control of a series hybrid elec...

We consider a capacitated production-inventory problem in both discreteand continuous-time, stationary settings. In the discretetime setting we analyze the infinite horizon capacitated dynamic lot-sizing problem, find the optimal solution and characterize its properties. For the continuous-time setting we formulate a new problem, which we claim to be an appropriate counterpart of the above disc...

We develop a competitive pricing model which combines the complexity of time-varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carryi...

The optimal sizing of a small autonomous hybrid power system can be a very challenging task, due to the large number of design settings and the uncertainty in key parameters. This problem belongs to the category of combinatorial optimization, and its solution based on the traditional method of exhaustive enumeration can be proved extremely time-consuming. This paper proposes a binary genetic al...

We introduce a heuristic method for finding good, feasible solutions for multiproduct lot sizing problems with general assembly structures, multiple constrained resources, and nonzero setup costs and setup times. We evaluate the performance of this heuristic by comparing its solutions to optimal solutions of small randomly generated problems and to time-truncated Optimization Subroutine Library...

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the socalled Facility Location formulation, the Shortest Route formulation, and the Inventory and Lot Sizing formulation with (`, S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integ...

We study the classical multistage lot sizing problem that arises in distribution and inventory systems. A celebrated result in this area is the 94% and 98% approximation guarantee provided by power-of-two policies. In this paper, we propose a simple randomized rounding algorithm to establish these performance bounds. We use this new technique to extend several results for the capacitated lot si...