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Joint production and maintenance strategy for economic production quantity model with imperfect production processes

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Abstract

In this study, an economic production quantity (EPQ) model is generalized by considering maintenance and production programs for an imperfect process involving a deteriorating production system with increasing hazard rate. There are two types of preventive maintenance (PM), namely imperfect PM and perfect PM. The probability that perfect PM is performed depends on the number of imperfect maintenance operations performed since the last renewal cycle. Following a failure, the delayed repair performs some restorations and reduces production rate to restore the system into an operating state (in-control state), but leaves its lower production rate until perfect PM is performed. That is, the production run period not always starts in normal production rate. This study considers backorders, as well as loss of inventory due to the lower production rate. For the EPQ model, the optimum run time, which minimizes the total cost, is discussed. Various special cases are considered, including the maintenance learning effect. Finally, a numerical example is presented to illustrate the effects of PM ability, repair cost and production decreasing rate on total costs and production period.

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Abbreviations

T :

Time of each production run

T 1 :

Period of production stoppage and inventory depletion; \({T_1 =(\frac{p}{d}-1)T}\)

*:

Implies an optimum value

p :

Normal production rate in units per year

Q :

Production lot

d :

Demand rate in units per year; p > d

α :

Production decreasing rate after delayed repair

\({\bar{{P}}_j }\) :

Probability that the first j PM are imperfect PM; \({\bar{{P}}_0 =1}\)

p j :

Probability that PM is perfect following the (j − 1) imperfect PM; \({p_j =\bar{{P}}_{j-1} -\bar{{P}}_j }\)

\({\{\bar{{P}}_j \}}\) :

Sequence of \({\bar{{P}}_j ,j=0,1,2, \ldots }\)

q j :

Probability that the j-th PM is an imperfect PM; \({q_j =\bar{{P}}_j /\bar{{P}}_{j-1}}\)

θ j :

Probability that the j-th PM is a perfect PM; θ j = 1 − q j

M :

Number of PM preceding the first perfect PM

R m :

Cost of each PM

R s :

Setup cost for each production run

R ms :

Sum of R m and R s ; R ms = R m + R s

R r :

Delayed repair cost of time lapse between failure and perfect PM per unit of time including rework cost

R b :

Backorder cost per unit

R h :

Holding cost per unit per year of the product

\({J( {T;\{ {\bar{{P}}_j }\}})}\) :

Expected total production cost for the EPQ model

X :

Time to failure of a new unit

F(t):

Failure distribution function of X

f(t):

Failure density function associated with F(t)

\({\bar{{F}}(t)}\) :

Survival function associated with F(t)

r :

The learning rate

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Authors and Affiliations

  1. Department of Information Science and Management Systems, National Taitung University, 684 Chunghua Rd., Sec. 1, Taitung, Taiwan, ROC

    Gwo-Liang Liao

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  1. Gwo-Liang Liao
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Correspondence to Gwo-Liang Liao.

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Liao, GL. Joint production and maintenance strategy for economic production quantity model with imperfect production processes. J Intell Manuf 24, 1229–1240 (2013). https://doi.org/10.1007/s10845-012-0658-1

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  • DOI: https://doi.org/10.1007/s10845-012-0658-1

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