Joint optimization of economic production quantity and preventive maintenance with considering multi-products and reserve time

Journal of Industrial Engineering and Management JIEM, 2017 – 10(3): 431-443 – Online ISSN: 2013-0953 – Print ISSN: 2013-8423 https://doi.org/10.3926/jiem.2270 Joint Optimization of Economic Production Quantity and Preventive Maintenance with Considering Multi-Products and Reserve Time Xuejuan Liu , Binrong Wang Donlinks School of Economics and Management, University of Science and Technology Beijing (China) , Received: March 2017 Accepted: May 2017 Abstract: Purpose: We deal with the problem of the joint determination of optimal economic production quantity (EPQ) and optimal preventive maintenance (PM) for a system that can produce multiple products alternately. The objective is to find the optimal number of production cycles and the PM policy simultaneously by minimizing the cost model. Design/methodology/approach: Considering the products go through the system in a sequence and a complete run of all products forms a production cycle. In each cycle, beyond production time we also consider some reserve time for maintenance and setup, shortage and overproduction may occur. We study the integrated problem based on two PM policies, and explain the situation with the other PM policies. The delay – time concept is used to model PM decisions. Findings: Using the integrated EPQ and PM model, we can calculate the optimal production planning and PM schedule simultaneously, especially we consider multiple products in each production cycle, which is more practical and economic than previous works. Originality/value: In modern companies, the production planning and maintenance schedule share the same system, and traditional research about two activities is separated, that always generate conflicts, such as inadequate or excessive maintenance, and shortages, etc., so we develop the integrated EPQ and PM model to avoid these undesirable effects. -431- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2270 Keywords: economic production quantity, preventive maintenance, delay-time, inventory, product quality 1. Introduction Traditionally, in modern companies, optimal production planning and optimal maintenance schedule are always studied separately, conflict is generated inevitably since the two activities share the same system. To avoid shortages, improper maintenance, or the other harmful effect caused by separated planning about production and maintenance, lots of researches of integrated production and maintenance are developed. Those researches can be categorized into two classes, the first one is about the integrated EPQ and maintenance model (Liu, Wang & Peng, 2015a), which is mainly based on the continuous modes of production, the second one is about the integrated capacitated lot sizing problem (CLSP) and maintenance model (Fitouhi & Nourelfath, 2014; Liu, Wang & Peng, 2015b), which is mainly based on the discrete modes of production. In this paper, we focus only on the first direction, and study the joint optimal EPQ and PM schedule in finite planning horizon for a multi-product system. There are some related researches about integrated EPQ and PM problems. For instance, Lee and Rung (2000) studied lot-sizing policies in multi-stage serial production systems with the systems prone to failures. They concluded that the lot sizes in the unreliable systems could be smaller or larger than those in the classical EPQ model. Giri and Dohi (2004) proposed a net present value approach to determine the EPQ for an unreliable production system over an infinite planning horizon. Sami (2008) considered a system that deteriorates with an increasing failure rate, and proposed a model to determine the optimal number of the production runs and the PM schedule that minimize the long-term average cost. Chakraborty, Giriand and Chaudhuri (2008) presented a EPQ model for an unreliable production system in which the production facility may shift from an “in-control” state to an “out-of-control” state at any random time and may ultimately break down afterwards. Chakraborty, Giriand and Chaudhuri (2009) developed integrated production, inventory and maintenance models to study the joint effects of process deterioration, machine breakdown and inspections on the optimal lot-sizing decisions. Jafari and Makis (2015) developed the joint optimization of EPQ and PM policy for a production facility subject to deterioration and condition monitoring, and they proposed the proportional hazards model to consider condition monitoring information as well as the age of the production facility, the deterioration process is determined by the age and covariate values, the covariate process is modeled as a continuous-time Markov process, this work is extended by Jafari and Makis (2016), they modeled the covariate process as a Semi-Markov decision process. Bouslah, Gharbi and Pellerin (2016) studied the integrated design of -432- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2270 production, continuous sampling inspection and preventive maintenance of a deteriorating production system. The abovementioned works are more reasonable than the classical EPQ model as the system deterioration and maintenance are considered, however all these models are restricted to the one product case. Liu et al. (2015a) proposed an integrated EPQ and PM model for multi-products system, in this paper we will develop further research about the work they studied. We consider the reserve time which is decided by production planners for maintenance and system setup, the reserve time may be not exact since the production planner set it based on the history data and experiences, so the idle time or shortage may occur, this situation exists in reality but has not been studied in Liu et al. (2015a), we extend their work by considering the reserve time in this paper. In a finite planning horizon, several types of product should be produced according to their lot sizes, the demand for each product is fixed, and each product is produced once in a production cycle. PM is carried out at some set-up points for less interruption to the production. We also consider the unqualified products in the cost model. Our objective is to determine the optimal lot size for each product and the optimal PM policy, in reality, smaller lot sizes lead to smaller inventory costs, but more setup costs and more opportunities for PM, and vice versa, so it is necessary to model the integrated EPQ and PM schedule. In this paper, we use the delay–time concept to model the PM policy for the system, this concept has been widely applied in maintenance modeling and optimization (Wang, 2012), many case studies have shown the validity of the delay-time-based models (Fu, Wang & Shi, 2012; Wu & Wang, 2011). The delay–time concept considers the failure process as a two stage process: the first stage from new to an initial point of the defect, usually referred to as the normal stage, in this stage, the defect (...truncated)