Production, Manufacturing and Logistics
An integrated production and preventive maintenance planning model

https://doi.org/10.1016/j.ejor.2006.06.032Get rights and content

Abstract

We are given a set of items that must be produced in lots on a capacitated production system throughout a specified finite planning horizon. We assume that the production system is subject to random failures, and that any maintenance action carried out on the system, in a period, reduces the system’s available production capacity during that period. The objective is to find an integrated lot-sizing and preventive maintenance strategy of the system that satisfies the demand for all items over the entire horizon without backlogging, and which minimizes the expected sum of production and maintenance costs. We show how this problem can be formulated and solved as a multi-item capacitated lot-sizing problem on a system that is periodically renewed and minimally repaired at failure. We also provide an illustrative example that shows the steps to obtain an optimal integrated production and maintenance strategy.

Introduction

There exists an extensive literature addressing the issue of production planning and an equally broad literature tackling maintenance planning questions. Production planning models seek typically to balance the costs of setting up the system with the costs of production and materials holding, while maintenance models attempt typically to balance the costs and benefits of sound maintenance plans in order to optimize the performance of the production system. In both domains, issues of production modeling and maintenance modeling have experienced an evident success both from theoretical and applied viewpoints. Paradoxically the issue of combining production and maintenance plans has received much less attention. The large part of the production planning models assumes that the system will function at its maximum performance during the planning horizon, and the large part of the maintenance planning models disregards the impact of maintenance on the production capacity and does not explicitly consider the production requirements. Actually, apart from the preventive maintenance actions that can be scheduled during down times, any unplanned maintenance action disturbs the production plan. It is therefore crucial that both production and maintenance aspects related to a production system are concurrently considered during the elaboration of optimal production and maintenance plans.

The purpose of this paper is to develop a combined production and maintenance model in a batch production system context. The main objective of the proposed model is to determine an integrated production and maintenance plan that minimizes the expected total production and maintenance costs over a finite planning horizon. The model takes into account the fact that the production system may fail randomly. A minimal repair is performed at failure and a periodic replacement is carried out periodically (Barlow and Hunter, 1960). According to this maintenance policy, the system failure rate remains undisturbed by any repair at failure between the periodic replacements (Barlow and Proschan, 1996). They are thus incorporated in the production–planning model through the definition of available production capacity in each period. In other words, the available production capacity in each period is a function of the system’s effective capacity and the expected lost capacity due to preventive and corrective maintenance actions.

The remainder of this paper is organized as follows: in Section 2 a brief review of literature is presented. In Section 3 a mathematical model for integrated production and maintenance planning is developed. An algorithm to find the best integrated production and maintenance plan is presented in Section 4. Section 5 presents an illustrative example to show how the proposed algorithm works as well as the coherence of the obtained results from the mathematical model. Some possible extensions and remarks are discussed in the conclusion.

Section snippets

Brief literature review

The issue of unreliable production systems has been considered at different levels of production planning, and especially at the operational (scheduling) level. A larger part of scheduling problems discussed in the literature assumes that the maintenance periods are known in advance at the time when jobs are to be scheduled (Qi et al., 1999, Graves and Lee, 1999). It can be shown that these scheduling problems are reducible to scheduling problems with machine availability constraints, and that

The mathematical model

We are given a planning horizon H =  including N periods of fixed length τ, and a set of products P to be produced during this planning horizon. For each product i  P a demand dit is to be satisfied in each period t  H. We assume that the production system has a known nominal capacity denoted by Cmax and that each maintenance action consumes a certain percentage of this capacity. Thus, we assume that each planned preventive and unplanned maintenance action consumes, respectively, Lp = aCmax and Lr = 

A solution algorithm

To solve the above mathematical programming problem (PPM) we assume, without loss of generality, that the length of the planning horizon H as well as the length of the preventive maintenance cycle T are given in multiples of the basic planning period duration τ (i.e., H =  and T = ).

Let nI = N/k⌋ if the ratio N/k is integer and nI = tN/k + 1 otherwise (where ⌊N/k⌋ is the highest integer smaller or equal than N/k).

The maintenance and planning model (PPM) can now be rewritten as follows:

PPMr:Minimize

An illustrative example

Let us consider the following planning horizon composed of 8 production periods, each with an available maximal capacity of Cmax = 15. Two products are to be produced in lots so that the demands are satisfied. Table 1, Table 2 show the setup, production and holding costs for each product and the periodic demands of each product respectively.

Table 3 shows the optimal plan for the two products without taking into account the capacity lost in maintenance (assuming that the system will not fail and

Conclusion

A joint production and maintenance planning model for a production system subject to random failures has been proposed. This model takes, explicitly, into account the reliability parameters of the system and its capacity in the development of the optimal production plan. At failure, a minimal repair is carried out to restore the system into the operating state without changing its failure rate function. The system is also replaced preventively at predetermined instants, regardless of its state

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    It should be noted that modeling the production scheduling under uncertainties is problem-dependent. Due to the high nonlinearity of jobs’ completion time when the time consumption of maintenance activities is taken into account, minimizing the expected total production cost is a general consideration in the existing maintenance and production scheduling problems [29–39]. Our motivation is, therefore, to develop a new integrated production planning and preventive maintenance scheduling optimization model to minimize the expectation of the total production cost, and it is the first time to consider the impact of stochastic machine failures on production synchronization in the integrated optimization problem.

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