A Manpower allocation model of job specialization

A major copier machine company in Hong Kong presently faces the problem of providing effective servicing and repairing support to its four service regions. Due to the shortage of skilled technicians and the variety of jobs to be handled by technicians of differing skill levels, its Service Department appears to be understaffed, experiencing substantial daily backlogs. This study concentrates on a new perspective of operation: the assignment of technicians at each skill level to specialize in a single type of job in one of the four regions. The objective is to maximize the overall daily number of completed service calls. A mathematical model is developed to handle this specialized allocation problem, where the average travel time (forming part of the coefficient of one of the model's variables) of a technician servicing a type of job in a region is dependent on the decision variables - the composition of the whole team. This results in what we call a mixed integer non-linear programme with variable coefficients. An exact solution is obtained by an iterative algorithm with an overall dynamic programming approach. Sample numerical results are also reported.