Dynamic control of production systems with varying service capacity.

Abstract

The challenge of making operational decisions in the face of a varying service capacity has both a historical and a contemporary significance. In manufacturing systems, it has long been known that making sound machine maintenance and replacement decisions can greatly improve the efficiency of the system. At the same time, a dynamic workforce due to priorities elsewhere in the system presents new and difficult decision-making scenarios. In this thesis we present new insights into these problem areas. The agile, temporary workforce problem models the phenomenon of <italic> floaters</italic>: agile workers (or machines) that can be dynamically reassigned to alleviate congestion in the system. Considered is a two-station tandem queueing system. Neither queue is equipped with dedicated servers. Instead, three scenarios for the fluctuations of workforce level are considered. In the first, a decision-maker can increase/decrease the capacity as deemed appropriate; the <italic>unrestricted</italic> case. In the other two cases, workers arrive randomly and can be rejected or allocated to either station. In one case the number of workers can then be reduced (the <italic>controlled capacity reduction </italic> case). In the other they leave randomly (the <italic>uncontrolled capacity reduction</italic> case). Under server collaboration assumptions, it is shown that in each scenario all workers should be allocated to one queue or the other (never split between queues) and that they should serve exhaustively at a particular queue according to an index rule. This extends previous studies on flexible systems to the case where the capacity varies over time. In the unrestricted case it is then shown that the optimal number of workers is non-decreasing in the number of customers in either queue. In the other cases, the optimal capacity increase/decrease decisions may not be monotone in the number of workers. The machine maintenance problem considers one server that deteriorates over time and has a reduction in productivity. The decision-maker decides when to perform maintenance, which may be done preemptively before catastrophic failures. Similar to classic maintenance models, the information available to the decision-maker includes the deterioration state of the server, <italic> s</italic>. Unlike classic models, the information also includes the number of customers in the queue, <italic>q</italic>. Considered are both repair models, with random repair times, and replacement models, with fixed costs but instantaneous repairs. It is shown in general that the optimal maintenance policies are monotone in <italic>s</italic>. Surprisingly, the switching-curve policies for the repair model are not always monotone in <italic>q</italic>.