A manpower allocation problem with layout considerations

In this study we investigate the problem of assigning tasks to operators in a facility characterized by longitudinal parallel machines such as in a shop floor served by an overhead travelling crane. Given a master production schedule (MPS) the objective is to assign all the jobs scheduled on the machines (i.e., the tasks) to the operators in order to fill to capacity the available workforce minimizing the distance between operators and tasks. In the model we assume that one task, i.e., a particular production job processed by a particular machine, must be entirely completed by a single operator. Different levels of automation of the machines are considered, from manual machines that require a permanent employee to highly-automated machines where a single operator can oversee several machines. During the setup time or repair time of a machine the operator is considered free to operate on the remaining tasks assigned to him, if any. On the basis of the MPS the number of operators is pre-defined in the long-term planning horizon taking in consideration a fixed mean transfer time between the tasks, that are the different production jobs on different machines. This value has a huge uncertainty because it is highly influenced by the tasks allocation. In fact a simultaneous multiple allocation means a continuous back and forth of the operator between his assigned machines. The objective of the model is the maximization of the operators utilization through minimizing the operator-task distances. The backlogged work is not admitted, therefore each day is independent of the other days, so a daily staffing is modelled. The study arises from a specific real-world problem but it could be easily extended to other contexts in which the operator-task allocation is subject to spatial-layout considerations. In general, non-optimized operators' travel times may result in production losses, i.e., machine blocking and work in progress.