Conference Agenda

Assemble-to-order (ATO) strategies are widely used in various industries. Despite their popularity, ATO systems remain challenging, both analytically and computationally. We study a general ATO problem modeled as an infinite horizon Markov decision process. In particular, we consider a system with mixed-Erlang distributed component production/leadtimes, and Poisson demand for products. Demand is lost if not immediately satisfied. As the optimal policy of such system is computationally intractable, we develop two heuristic policies based on decomposition methods: component-based and product-based. In order to evaluate the performance of the heuristics, we develop a tight lower bound using an Approximate Linear Programming approach that relies on a judicial choice of basis-functions, for approximating the optimal value function. Our results show that the heuristics perform within only few Average Percentage Deviation (ADP) from the lower bound and even a smaller ADP when compared to systems where the optimal policy could be obtained. Moreover, we show that our component-based decomposition heuristic only scales linearly with the number of components in the ATO system, and therefore is suitable for solving large-scale ATO systems.

A significant proportion of machine scheduling models assume that machines are available over the whole planning horizon without any restrictions. However, in the real world, machines need to be maintained from time to time, which has a direct impact on the processing of jobs. For this reason, we consider machines whose availability depends on their maintenance state.

This talk considers the problem of scheduling maintenance activities (MAs) for a given sequence of jobs on a single machine, with the goal of minimising the expected total completion time. The maintenance state deteriorates as the jobs are processed. Each individual job deteriorates the machine by a certain amount, which is subject to a continuous probability distribution. If the deterioration exceeds the maintenance level, a costly emergency maintenance activity must be performed to repair the machine and ensure that processing can continue.

Further, the single machine under consideration is assumed to be transparent. This means that the current maintenance level of the machine can be read out between any two jobs in the sequence. Therefore, the user can decide whether or not to perform a MA based on the information of the actually realised deteriorations and the resulting maintenance level. The main technique used to develop a decision policy is an approximate dynamic program (ADP). During the talk we will present the developed approach and some numerical results on the performance of the decision policy resulting from the ADP compared to different benchmark policies.