Data-driven Algorithm for Scheduling with Total Tardiness

In this paper, we investigate the use of deep learning for solving a classical NP-Hard single machine scheduling problem where the criterion is to minimize the total tardiness. Instead of designing an end-to-end machine learning model, we utilize well known decomposition of the problem and we enhance it with a data-driven approach. We have designed a regressor containing a deep neural network that learns and predicts the criterion of a given set of jobs. The network acts as a polynomial-time estimator of the criterion that is used in a single-pass scheduling algorithm based on Lawler's decomposition theorem. Essentially, the regressor guides the algorithm to select the best position for each job. The experimental results show that our data-driven approach can efficiently generalize information from the training phase to significantly larger instances (up to 350 jobs) where it achieves an optimality gap of about 0.5%, which is four times less than the gap of the state-of-the-art NBR heuristic

A Hybrid ant colony optimization algorithm for solving a highly constrained nurse rostering problem

Distribution of work shifts and off days to nurses in a duty roster is a crucial task. In hospital wards, much effort is spent trying to produce workable and quality rosters for their nurses. However, there are cases, such as mandatory working days per week and balanced distribution of shift types that could not be achieved in the manually generated rosters, which are still being practiced. Hence, this study focused on solving those issues arising in nurse rostering problems (NRPs) strategizing on a hybrid of Ant Colony Optimization (ACO) algorithm with a hill climbing technique. The hybridization with the hill climbing is aiming at fine-tuning the initial solution or roster generated by the ACO algorithm to achieve better rosters. The hybrid model is developed with the goal of satisfying the hard constraints, while minimizing the violation of soft constraints in such a way that fulfill hospital’s rules and nurses’ preferences. The real data used for this highly constrained NRPs was obtained from a large Malaysian hospital. Specifically, three main phases were involved in developing the hybrid model, which are generating an initial roster, updating the roster through the ACO algorithm, and implementing the hill climbing to further search for a refined solution. The results show that at a larger value of pheromone, the chance of obtaining a good solution was found with only small penalty values. This study has proven that the hybrid ACO is able to solve NRPs with good potential solutions that fulfilled all the four important criteria, which are coverage, quality, flexibility, and cost. Subsequently, the hybrid model is also beneficial to the hospital’s management whereby nurses can be scheduled with balanced distribution of shifts, which fulfill their preferences as well