Analysis of the Uncapacitated Dynamic Lot Size Problem

In this paper we provide worst case error bounds for several heuristics for the uncapacitated dynamic lot size problem. We propose two managerially oriented procedures and show that they have a relative worst case error bound equal to two, and develop similar analyses for methods known as the "Silver and Meal" heuristics, the part period balancing heuristics, and economic order quantity heuristics (expressed in terms of a time supply of demand).We also present results on aggregation and partitioning of the planning horizon

Computational complexity of the capacitated lot size problem

HD28 .M414 no.1271-, 81,

Analysis of the uncapacitated dynamic lot size problem

HD28 .M414 no.1282-, 82,

Linear Gate Assignment: a Fast Statistical Mechanics Approach

This paper deals with the problem of linear gate assignment in two layout styles: onedimensional logic array, and gate matrix layout. The goal is to find the optimal sequencing of gates in order to minimize the required number of tracks, and thus to reduce the overall circuit layout area. This is known to be an NP-Hard optimization problem, for whose solution no absolute approximation algorithm exists. Here we report the use of a new optimization heuristic derived from statistical mechanics - the microcanonical optimization algorithm, µO - to solve the linear gate assignment problem. Our numerical results show that µO compares favorably with at least five previously employed heuristics: simulated annealing, the unidirectional and the bidirectional Hong construction methods, and the artificial intelligence heuristics GM_Plan and GM_Learn. Moreover, in a massive set of experiments with circuits whose optimal layout is not known, our algorithm has been able to match and even to improve, b..

Approximation Methods for the Uncapacitated Dynamic Lot Size Problem

We provide worst case error bounds for several approximation methods (heuristics, product aggregation, and partitioning of the planning horizon) for the uncapacitated dynamic lot size problem. We propose two managerially oriented heuristics and show that they have a relative wont case error bound equal to two, and develop similar analyses for methods known as the least cost per unit heuristic, the part period balancing heuristic, and an economic order quantity heuristic (expressed in terms of a time supply of demand). We also show how errors introduced by partitioning of the planning horizon in multi-product multi-facility problems are bounded by product set-up costs, and how errors introduced by product aggregation are bounded by set-up costs, holding costs, and demands. The latter results suggest methods for product aggregation that minimize the worst case error bounds.inventory/production: lot sizing