Production, Manufacturing and LogisticsAn integrated production and preventive maintenance planning model
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 = Nτ 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 = Nτ and T = kτ).
Let nI = ⌊N/k⌋ if the ratio N/k is integer and nI = t⌊N/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:
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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