A FUZZY LINGUISTIC APPROACH OF PREVENTIVE MAINTENANCE SCHEDULING COST OPTIMISATION

The simultaneous scheduling of resource-constrained maintenance and operations is an emerging theory that is attracting the attention of both researchers and practitioners. The purpose of this paper is to capture the uncertainty in the development of a model that schedules both preventive maintenance and operational activities. Fuzzy logic is employed to transform the human expertise into IF-THEN rules. The approach has the advantage of revealing semantic uncertainty with the associated non-specifying measures. The methodology applied tracks the error values in terms of results in linguistic variable. The result obtained indicates the feasibility of tracking the uncertain measures in the model discussed. Thus, the study may be applicable to both production system and transportation organizations that are engaged in both maintenance and operational activities. The research has serious implication in terms of the ability to monitor the imprecision that were introduced in the previous models. This obviously provides a more reliable framework for researchers and practitioners interested in maintenance scheduling operation. The paper is new in that, it demonstrates the application of fuzzy logic in a form that was never documented. INTRODUCTION Many organization worldwide are shifting their focus from the traditional way of running the business to a modern and pro-active approach that guarantees the continued existence of the business. Traditionally, businesses are managed with the sole aim of making profit. This viewpoint is fading away in view of the emerging business improvement concepts that has dominated organizational practices worldwide. Such concepts include business process reengineering, total quality management, etc. As such the customer is at the central focus of the company’s objective with the aim of satisfying and exceeding customers' requirements. This condition has created intense competition among rival organizations. Therefore, for businesses to stay afloat, customer satisfaction should be the central focus. While satisfying the customer, the profit maximization objective of company would automatically be achieved since an increased customer patronage is envisaged. In an effort to continue in business, company managers are re-engineering their processes for efficiency and effectiveness. The maintenance culture is one of the subsystems of the organization that has received an increased attention in recent times. Fortunately the viewpoint of the maintenance function as a “bottomless pit of expenses” is fading away. Maintenance is now viewed as a “value adding activity” to the organization. In other to improve efficiency of operations, proper scheduling of facilities should be done. In scheduling facilities, optimal approaches are sought for such that minimum cost is expended on activities and maximum results obtained. Until recently most approaches utilized in maintenance scheduling are near optimal (see Anily et al., 1998, 1999). This is largely due to the non-polynomial problem that usually exists in problem formulation. KATHMANDU UNIVERSITY JOURNAL OF SCIENCE, ENGINEERING AND TECHNOLOGY VOL.I, No.III, JANUARY, 2007. 2 Fortunately, Charles Owaba (2002) has recently proposed a breakthrough methodology that uses the basic principles of Gantt Charting. Since the development of the original model numerous efforts have been made by authors in extending its framework. Such extensions have incorporated a reviewed cost dimensions, and alternative consideration without the use of Gantt charting principles. Unfortunately, none of the articles have considered the uncertain nature of the problem semantic uncertainty in the model framework is an important concern that is worthy of analytical investigation (Oke, 2004a,b). This important gap in the maintenance scheduling literature is addressed in the current work. In particular, the fuzzy logic concept is applied to the simultaneous scheduling of resourceconstrained maintenance and operations. The linguistic variables are used to substitute for the key-parameters and variable of the Gantt charting model. The model that evolves from the current research is of immense benefits both to the academic community and the industry. With the model, the real value of measure could be easily captured while the decisions based on the modeling information will be more reliable than the former model that does not contain fuzzy logic concepts. Literature review: The maintenance scheduling literature has a variety of applications (Zurn and Quintana, 1975; Wang et al., 2002; Walker et al., 2001a,b). These diverse applications include aircraft maintenance, process industry, vehicle fleet maintenance, railway track maintenance, power generation, pavement maintenance, highway maintenance, refinery and production facilities (Alfares, 1999; Ashayeri, et al., 1996; de Campos and Belhot, 1994; Gunn and Lee, 1991; Lee, 1991; Lake et al., 2000, 2001; Lake and Ferreira, 2001; Creemers et al., 1994). An attempt to codify the maintenance scheduling literature portrays a line of inquiry that has grown in volume and in depth. Despite the immense resources allocated to the study of maintenance scheduling during the past 30 years, a more intensive study into some deep structures is still required. Subsequently, a number of theoreticians proposed models for scheduling maintenance (Zurn and Quintana, 1977; Stremel and Jenkins, 1981; Stremel, 1981; Ram and Olumolade, 1987; Duffuaa and Al-Sltan, 1997). Duffuaa and Ben-Daya (1994) proposed a model, which is similar to that of Hariga in that it focused on non-identical production units (Duffuaa and Ben-Daya, 1994). The model is developed for the joint overhaul problem by incorporating the cost of production, and the cost of coordination. The model obtains lower costs of two examples. Among the deficiencies of these models is the fact that no evidence of machine dominance concept is considered. Cheung and Hui (2004) investigated a chemical production site from the perspective of loss minimization. The paper proposes a multi-period mixed integer linear programming (MILP) model as an aid to optimize short-term maintenance schedule. In a study by El-Sharkh and El-keib (2003), the concept of a fuzzy evolutionary programming-based solution methodology for security-constrained generator maintenance scheduling was explored. The paper presents the fuzzy model with uncertainties in the load and fuel and maintenance costs. The technique results are fuzzy optimal cost range that reflects the problem uncertainties. It solves a decomposed maintenance model of two interrelated subproblems, namely the maintenance and the security-constrained economic dispatch problem. Dieulle et. al. (2003) focused on the development of a new probabilistic method based on the semi-regenerative property of the evolution process. In order to calculate the long-time expected cost per unit of time, the authors use a recent result generalizing the well-known theorem that expresses KATHMANDU UNIVERSITY JOURNAL OF SCIENCE, ENGINEERING AND TECHNOLOGY VOL.I, No.III, JANUARY, 2007. 3 the cost criterion as equal to the ratio of the expected cost on renewal cycle over the expected cycle duration. Numerical experiments show that there exists a set of parameters (the critical threshold and the parameters of maintenance scheduling function) which lead to a minimal cost. El-Sharkh and El-Keib (2000) considered an evolutionary programming (EP) based technique to the unified model of the maintenance scheduling (MS) problem of power generation and transmission systems. The Hill-climbing technique (HCT) is used in conjunction with the EP to find a feasible solution in the neighbourhood of the new feasible solutions during the solution process. The work by Kobbacy et al. (1997) is concerned with the development of a realistic preventive maintenance (PM) scheduling model. A heuristic approach for implementing the semi-parametric proportional hazard model (PHM) to schedule the next preventive maintenance interval on the basis of the equipment’s full condition history was introduced. These models are then used within a simulation framework to schedule the next preventive maintenance interval. The results indicate a higher availability for the recommended schedule than the availability resulting from applying the optimal PM intervals as suggested by using the conventional stationary models. Olorunniwo and Izuchukwu (1991) applied the concept of maintenance improvement factors to preventive and overhaul maintenance. The authors developed mathematical models that are used to generate preventive and overhaul maintenance schedules. Examples are provided to demonstrate the sensitivity of the schedules to model parameters. Ashayeri et al. (1996) reported on simultaneous planning of preventive maintenance and production in a process industry environment. The authors developed a mixed integer linear programming model. The model scheduling production jobs and preventive jobs, while minimizing costs associated with production back orders, corrective maintenance and preventive maintenance. The model takes into account the probability of a breakdown given by the last maintenance period. The formulation of the model is flexible so that it can be adapted for several production situations. However, the deterministic model discussed does not afford insight into the nature of deterioration of machines. A common form of machine deterioration is stochastic but many studies have assumed linear deterioration for ease of modeling. Model framework: From the original proposal by Charles-Owaba (2002) the problem is defined as follows: Given a set of machines for preventive maintenance and operations in T contiguous periods, limited periodic maintenance capacity (Aj), limited budgetary allocation (Ba); limited manpower resources (Mr); duration (Bir) per maintenance visit, arrival period Kij); and the number of visits per machine (