Production rate control of an unreliable manufacturing cell with adjustable capacity

Abstract

This article addresses the production control problem of an adjustable capacity unreliable manufacturing cell responding to a single product type demand. The manufacturing cell is composed of an unreliable machine, called the ‘central machine’. Due to availability fluctuations, the central machine may fall short of meeting the long-term demand rate. In order to quickly adjust the production capacity and thus meet the demand, a reserve machine is called upon in support if the finished product inventory level drops below a specific threshold. Such a machine involves higher production costs compared with the central one. This article aims to determine the optimal production control policy for the involved machines in order to minimise production, inventory and backlog costs over an infinite horizon. This article proposes a continuous dynamic programming formulation of the problem and adopted a numerical scheme to solve the optimality conditions equations. The optimal production policy is shown to be described by a state dependent hedging point policy (SDHPP). To determine the optimal control policy parameters, an experimental approach based on design of experiments, simulation modelling, and response surface methodology is proposed. Several sensitivity analyses have been carried out and have shown the robust behaviour of the developed policy facing expected variations of the system parameters. The results also show that the proposed SDHPP policy outperforms classical stand-by and parallel machines based control policies. The usefulness of the proposed approach is outlined for more complex situations where the system must deal with non-exponential failure and repair time distributions.

Keywords:

• production rate control
• adjustable capacity
• HJB equation
• state dependent hedging point policy (SDHPP)
• simulation