Stochastic Optimal Capacity Management in Reconfigurable Manufacturing Systems

Abstract

This paper presents an optimal policy, based on Markov decision theory for the capacity management problem in a firm facing stochastic market demand. The firm implements a reconfigurable manufacturing system and faces a delay between the times capacity changes are ordered and the times they are delivered. Optimal policies are presented as optimal boundaries representing the optimal capacity expansion and reduction levels. To increase the robustness of the optimal policy to unexpected events, the concept of feedback control is applied to address the capacity management problem. It is shown that feedback provides sub-optimal solutions to the capacity management problem which are more robust under unexpected disturbances in market demand and unexpected events.

Capacity adjustment based on reconfigurable machine tools – Harmonising throughput time in job-shop manufacturing

“…Control theoretic approaches base on a controller model (single-or double-loop) to dynamically control capacities of single work stations [18][19][20]. Up to now, approaches of reconfigurable manufacturing systems tend to remain on a rather abstract modelling level [21,22].…”

Mathematical Models for Manufacturing Systems Capacity Planning and Expansion – An Overview

“…1. Distributions of the market demand [12] The capacity management dynamics evolves in discrete time. It is assumed that there is delay time from when the capacity is ordered until it can be utilized, shown by T. The dynamic capacity evolution is represented by: ) ; min(…”

“…2. Optimal Capacity Management Policy [12] Optimal thresholds levels L and U are obtained numerically by solving Equations (4). It is also shown that there exists optimal lower and upper limits for L and U shown by L*, and U* and the sufficient condition for a policy to be optimal is to be located within these two limits.…”

Impact of reconfiguration characteristics for capacity investment strategies in manufacturing systems

“…The optimal control theory based works by Asl and Ulsoy (2003), Matta et al (2007) develop an optimal policy where reconfiguration periods are considered in a single product with random demand environment. In the model proposed by Matta et al (2007), the ramp up is limited to a maximum of 50% of the available period.…”