Joint optimization of quality-based multi-level maintenance and buffer stock within multi-specification and small-batch production

Abstract

This study proposes a comprehensive framework for the joint optimization of maintenance actions and safety stock policies for multi-specification small-batch (MSSB) production. The production system considered consists of multiple machines arranged in a series-parallel configuration. Given the multi-stage nature of the MSSB, a piecewise Gamma process is developed to model the degradation of machines owing to varying product specifications. A quality-based maintenance model is proposed to guide the scheduling of maintenance actions based on the observed product defect rate. The maintenance policy is optimized at two levels: at the machine level, the optimal quality of the produced products is determined, and at the system level, a threshold quality value is established to facilitate the opportunistic maintenance of machines. The relationship between the buffer stock and machine capacity is explicitly modeled to ensure production efficiency. A simulation-based multi-objective algorithm is employed to identify the optimal decision variable levels for the proposed maintenance policy. The numerical results demonstrate that the proposed method effectively balances the conflicting objectives of minimizing the expected operational costs and maximizing production efficiency.

Graphical abstract

Keywords

serial-parallel multi-stage production system / multi-specification and small-batch / multi-level maintenance / quality control / safety stock

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Competing Interests

The authors declare that they have no competing interests.

Notations
$N_s$	Total quantity of production orders
$l_s$	Length of the production cycle of the sth order
$q_{smj}$	Processing intensity of machine $M_{smj}$ in the sth order
$q_{smj}^{\prime }$	Processing intensity of machine $M_{smj}$ after overhaul
$b_{1mj}$	Coefficient of influence of processing technology on machine $M_{smj}$
$b_{2mj}$	Coefficient of influence of processing strength on machine $M_{smj}$
$P_s$	System productivity in the sth order
$D_s$	Market demand rate of the sth order
$p_{smj}$	Production rate of machine $M_{smj}$ in the sth order
$p_{smj}^{\prime }$	Production rate of machine $M_{smj}$ in the sth order after overhaul
${IB}_{\cdot mj}$	Structure importance measure of machine $M_{smj}$
${\tilde{p}}_{smj}\left(t\right)$	Defective rate of machine $M_{smj}$ at time t in the sth order
${\tilde{p}}_{0mj}$	Initial defective rate of machine $M_{smj}$ in a brand new state
${\eta }_{smj},{\lambda }_{smj},{\gamma }_{smj}$	Parameters of quality deterioration in the sth order
${\alpha }_{smj},{\beta }_{smj}$	Shape and scale parameters of gamma process in the sth order
$X_{smj}(t)$	Cumulative gradation level of machine $M_{smj}$ at time t in the sth order
$L_{smj}$	Failure threshold of machine $M_{smj}$ in the sth order
${CR}_{smj}$	Capacity ratio of equipment $M_{smj}$ in the sth order in the mth stage
$t_{smj}^{ohm}$	Duration of overhaul performed on machine $M_{smj}$ in the sth order
$a_{smj}$	ADGP parameter of machine $M_{smj}$ in the sth order
$C_{set}$	Production line replacement cost (preparation cost of production order)
$C_{in}$	Cost of inspection for the system
$c_d$	Cost of loss of defective products per unit item
$c_h$	Inventory cost per unit item per unit time
$c_s$	Shortage cost of an item per unit time
$C_{PM}^{mj}$	Preventive maintenance cost for machine $M_{smj}$
$C_{OM}^{mj}$	Opportunistic maintenance cost for machine $M_{smj}$
$C_{CM}^{mj}$	Corrective maintenance cost for machine $M_{smj}$
$C_{OH}^{mj}$	Overhaul cost for machine $M_{smj}$
${ET}_s$	Effective time rate of the sth order
$g,u,v$	Parameters of evaluation matrix Z
${\mathit{S}}_u$	The relative proximity of the solutions in the Pareto frontier solution set

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