مدل برنامه ریزی غیرخطی غیرصفر عدد صحیح برای اندازه نیروی کار تعمیر و نگهداری

This paper formulates a non-linear integer programming model to solve a maintenance workforce sizing problem with a productivity improvement goal. This problem is modelled in a bi-objective framework that minimises the number of maintenance personnel while maximising their productivity levels. Inputs into the optimisation model include monthly and routine maintenance periods, volume of production, contingency maintenance time, use factor and priority factor among others. The model has been validated with real-life detergent factory data, demonstrating its potential usefulness. A principal novelty of the model is the inclusion of use factor, which captures how often maintenance technicians are busy on the job with respect to assigned tasks, including unanticipated high maintenance workload. The model has been solved using a branch and bound algorithm. The impact of workforce structure and workers’ salaries on model’s performance has been studied and sensitivity analysis carried out to investigate the changes to the optimal solution as a result of changes in the input data. The results show a reduction in the number of maintenance workforce personnel in comparing values with and without use factor in the model. The model’s ability to obtain global optimal result depends on the value of the minimum routine maintenance time within each maintenance section. Also, the model is shown to be sensitive to priority factor, which captures the appropriate ratio of full- and part-time workers under the same category. The model provides both an easy-to-use practical tool for maintenance managers and supervisors as well as a scientific tool for determining optimal maintenance workforce size for a manufacturing plant.

Workforce sizing in manufacturing industries (Duffuaa and Raouf, 1992 and Mosely et al., 1998) across the globe has received more attention than before in recent times due to the turbulent business environment, which generated stiff competition among industries and the purchasing power of customers that has declined, thus leading to reduced purchases of companies’ products. Consequently, organisations are unable to keep large workforces and need to downsize for survival and the maintenance of business profitability (Naveh et al., 2007 and Hargaden and Ryan, 2011). This development, which requires a careful planning for the workforce has also spread to service systems such as retailing, aircraft (Al-Sugair, 1994, Alfares, 1997 and Alfares, 1999), hospital buildings (Al-Zubaidi and Christer, 1997), information technology (Dixit et al., 2009 and Chouhan and Goyal, 2010). The research scope brought about by the need to downsize, restructure or re-engineer the workforce system has gone beyond engineering to take advantage of other fields (i.e. psychology) for maximum benefit to the workforce and the system. In engineering systems, especially in maintenance engineering, different studies sought to address maintenance workforce problems (Roberts and Escudero, 1983a, Roberts and Escudero, 1983b, Galpio et al., 1993, Al-Sugair, 1994, Alfares, 1997 and Mosely et al., 1998). An important attribute of these studies is that they were conducted in developed countries where government policies are usually consistent over long period. In these studies the data used in testing models are usually obtained in environments where they are conducted with special attributes of such environments. However, since environments are different in developing countries, some of these data may not be applicable. Human factors (Dorn, 1996 and Shepherd and Kraus, 1997), training policies (Iraturi et al., 1995, Brusco and Johns, 1996 and Shepherd and Kraus, 1997), decision support systems (Dixit et al., 2009) and motivation (Maloney and McFillen, 1987) are the major considerations in modelling workforce problems and may largely be at variance in developing countries. Over the years, several factors and influences have affected workforce considerations and one event that has significant effect on this experience/trend is the last global economic meltdown in 2008, which had catastrophic effects on business survival. This occurrence led to drastic reduction in the number of employees maintained in small-medium- and large-scale organisations world-wide, particularly in economies that depend on the importation of raw materials for their industries. This reduction has been aided using multi-skilled approach (Williamson, 1992a, Williamson, 1992b, Brusco and Johns, 1996, Bechtold, 1988, Stanley, 1997, Burleson et al., 1998, Gomar et al., 2002 and Bamber et al., 2003). Williamson (1992a) considered the optimisation of maintenance of AIDE facilities using multi-skill approach. Varying productivity and training policies as they affect multi-skilled workforce were examined by Brusco and Johns (1996). Stanley (1997) investigated benefits, impediments and limitation of multi-skilled workforce utilisation strategies in construction. The strategies involved in the use of multi-skilled workforce with respect to the construction sector were the focus of Burleson et al. (1998). All these multi-skilling studies are also having their problems (Van den Beukel and Molleman, 2002); they fail to address prioritisation and use factor in workforce assignments. Research and practice on workforce sizing is further encouraged due to a number of factors, including heightened workers absenteeism, poor product demand, poor machine utilisation, poor skilling attitudes, technological discontinuity and turnover of staff that are experienced in industries during this current turbulent business experience. The use of scientific workforce sizing tools may result in a reduced need for downsizing by organisations. The remaining sections of this paper are organised as follows: Section 2 presents the literature review, Section 3 deals with the model development while Section 4 presents model application and the discussion of results is presented in Section 5. The conclusion of this study is in Section 6.

This study used a non-zero integer programming model in solving workforce sizing problem in a maintenance function for a detergent production company in Lagos, Nigeria. The developed model focused on minimising number of maintenance workforce and maximisation of their productivity. The formulated problem was solved using goal programming technique (Taha, 1982). The results obtained showed that the incorporation of use factor in the proposed model yielded a reduction of the number of maintenance technicians when the use factor was incorporated into the model compared with when it was without the use factor. This resulted in a 6.86 reduction in the total cost of maintenance technicians at f=2. The optimal total cost of maintenance technician was N 699,220 with the electrical section contributing 11.7% of this cost while 25.9% and 62.3% were contributed by the instrumentation and mechanical sections, respectively. Further research of the current work can be made by increasing the objectives and constraints in this work to make the model more robust. For instance, penalty for delay in production activities, which resulted from maintenance problem, minimisation of employee turnover, maximisation of employee benefits and the effects of product re-branding could be investigated. Also, new products and government policies concerning salaries agreement could all be incorporated into a new model in future. Similarly, this model can be applied in other manufacturing processes with different production systems. For instance, in a job shop where products are manufactured according to highly fluctuating orders, several adjustments to the model proposed here could be made to make it applicable. Other applications in non-manufacturing industries could be made with modifications of functional constraints. Also, the results obtained and the nature of the problem that was formulated shows that there is possible future research with soft computing techniques (i.e. particle swarm optimisation, support vector machines and differential evolution) in dealing with the problem. For a company that engages in 100% sub-contracting, there is no control of the workforce by the company that engages the contractors and hence, applying the model in that situation by the host company may be challenging and even ineffective. Finally, extension of the proposed model is possible with production plan, and other activities that have direct connections with maintenance activities. The main contribution of the current study is from two perspectives. First, we present the maintenance workforce sizing or crew size determination scenario from a viewpoint at variance with previous studies in literature. The productivity of the maintenance workforce sizing is analysed from the perspective of optimisation as well as combined branch and bound, integer and non-linear programmes for the first time in the maintenance workforce sizing literature. Second, the concept of use factor in managing workers in worksystems that was considered by Charles-Owaba (2002) for the first time in literature is demonstrated in a new form as applied to maintenance workforce sizing modelling and applications.