Optimal production policy for economic production lot-sizing model with preventive maintenance

ABSTRACT

In this study, we determine the optimal manufacturing quantity for an economic production lot-sizing model with a defective rate and preventive maintenance for a manufacturing machine. We investigate the properties of economic manufacturing quantity to minimize expected costs during the production run when a random defective rate for that product is considered using an in-control condition and an out-of-control condition. If a manufacturing machine produces a proportion of defective items which is larger than the lot tolerance percent defective, then a machine shifts from an in-control condition to an out-of-control condition, and it should have a maintenance service to decrease the possibility that it will produce imperfect-quality products. A research model is developed to determine optimal manufacturing quantity and optimal production time when a defective rate and maintenance service are considered. Numerical examples are given for the applicability of the methodology derived in the paper.

KEYWORDS:

• Economic production lot-size
• in-control condition
• lot tolerance percent defective
• out-of-control condition
• preventive maintenance
• random defective rate

Nomenclature

pdf, cdf	=	Probability density function, cumulative distribution function, respectively
EMQ	=	Economic manufacturing quantity
ECR	=	Expected cost rate
NHPP	=	Non-homogeneous Poisson process
LTPD	=	Lot tolerance percent defective, $l_0$
CM, PM	=	Corrective maintenance, preventive maintenance, respectively
P, Q, D	=	Production rate, production lot size and annual demand, respectively
Y	=	Defective rate which is the proportion of defective items among total manufacturing products.
$t_p:$	=	Time to produce a lot Q, i.e., $t_p=\frac{Q}{P}$
$c_m:$	=	Minimal repair cost
$c_r:$	=	Rework cost
$c_c:$	=	Scrapped cost
$c_s:$	=	Set-up cost for each production cycle
$c_h:$	=	Holding cost per unit for a year
$c_{pm}:$	=	Preventive maintenance cost
$k:$	=	Number of preventive maintenance services
$\gamma :$	=	Percentage of imperfect quality items
$\theta :$	=	Random portion of the imperfect quality items are scrapped
$\eta :$	=	PM cycle
$f(\cdot ),F(\cdot ),\bar{F}(\cdot ),h(\cdot ):$	=	pdf, cdf, survival function and intensity function of time, respectively
$f_{pm}(\cdot ),F_{pm}(\cdot ),{\bar{F}}_{pm}(\cdot ),h_{pm}(\cdot ):$	=	pdf, cdf, survival function and intensity function of time, respectively, when a PM service is considered.
$f_X(\cdot ),F_X(\cdot ),{\bar{F}}_X(\cdot ):$	=	pdf, cdf, and survival function of shifted time X from in-control condition to out-of-control condition
$g(\cdot ),G(\cdot ),\bar{G}(\cdot ):$	=	pdf, cdf, survival function, respectively, of defective rate
$L(t_p):$	=	Length of production run of the product when the rate between the time with the production lot size and production rate $Q/P$ is equal to $t_p$
$q(\cdot ),Q(\cdot ),\bar{Q}(\cdot )$	=	pdf, cdf, survival function, respectively, of $L(t_p)$
$N_{l_0}(a,b):$	=	Number of failures that has been taken place in the interval (a,b) when the LTPD is equal to $l_0$

Acknowledgements

The author is very grateful to the editor and anonymous referees for their valuable and constructive comments and suggestions which greatly improved the final version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2017R1E1A1A03069903).

Notes on contributors

Minjae Park

Minjae Park is an associate professor in the school of business administration at Hongik University, Seoul, Republic of Korea. His research interests include reliability modeling, maintenance policy, quality management, mean shift detection, optimization, and applied statistics.