Production Planning of a Failure-Prone Manufacturing System under Different Setup Scenarios

Abstract

This paper presents a control problem for the optimization of the production and setup activities of an industrial system operating in an uncertain environment. This system is subject to random disturbances (breakdowns and repairs). These disturbances can engender stock shortages. The considered industrial system represents a well-known production context in industry and consists of a machine producing two types of products. In order to switch production from one product type to another, a time factor and a reconfiguration cost for the machine are associated with the setup activities. The parts production rates and the setup strategies are the decision variables which influence the inventory and the capacity of the system. The objective of the study is to find the production and setup policies which minimize the setup and inventory costs, as well as those associated with shortages. A modeling approach based on stochastic optimal control theory and a numerical algorithm used to solve the obtained optimality conditions are presented. The contribution of the paper, for industrial systems not studied in the literature, is illustrated through a numerical example and a comparative study.

Maintenance and setup planning in manufacturing systems under uncertainties

“…The end result is the development of a new form of HJB equations for more realistic contexts in manufacturing. This contribution is elaborated by comparing the results obtained to those of HJB equations previously developed by Boukas and Kenne (1997), Hajji et al (2004) and Kibouka et al (2016). The model presented in this paper is based on extensions of the hypotheses used in the previous works (Elhafsi and Bai, 1997;Boukas and Kenne, 1997;Hajji et al, 2004).…”

“…and setup planning different hypotheses started in Polotski et al (2015). As compared to the paper by Kibouka et al (2016), setup was always performed in operational mode, the current work analyzes the situation when setup can be performed in any mode; thus allowing to increase the machine availability by executing setup and corrective maintenance in parallel if possible and needed.…”

“…Note that x þ i ¼ max (0, x i ), x À i ¼ max(−x i , 0); c þ i and c À i are the inventory and backlog costs for part-type i per unit of product per unit of time, respectively. As shown in Kibouka et al (2016), given that the setup cost is consumed at the beginning of the operation, the instantaneous cost as a function of the setups, denoted by R(. ), is therefore given by the following expression:…”

“…This research is based on the works of Boukas and Kenne (1997) and Hajji et al (2004). Furthermore, it extends the work of Kibouka et al (2016) to the case of systems where the setup is permitted at all modes of the machine, and when the setup does not necessarily restore the machine to its operational mode.…”

“…This paper is a continuation of the works of Boukas and Kenne (1997), Hajji et al (2004) and Kibouka et al (2016), is to find the optimal production and setup policies that minimize setup, inventory and shortage costs, in order to improve the MHCP. The paper is based on the development of optimal policies, taking into account the interactions between the deterministic setup procedure and random events ( failures and repairs) in the problem formulation.…”