The shift minimization personnel task scheduling problem is an NP-complete optimization problem that concerns the assignment of tasks to multi-skilled employees with a view to minimize the total number of assigned employees. Recent literature indicates that hybrid methods which combine exact and heuristic techniques such as matheuristics are efficient as regards to generating high quality solutions. The present work employs a constructive matheuristic (CMH): a decomposition-based method where sub-problems are solved to optimality using exact techniques. The optimal solutions of subproblems are subsequently utilized to construct a feasible solution for the entire problem. Based on the study, a time-based CMH has been developed which, for the first time, solves all the difficult instances introduced by Smet et al. (2014) to optimality. In addition, an automated CMH algorithm that utilizes instance-specific problem features has also been developed that produces high quality solutions over all current benchmark instances.
The Traveling Umpire Problem (TUP) is a combinatorial optimization problem concerning the assignment of umpires to the games of a fixed double round-robin tournament. The TUP draws inspiration from the real world multi-objective Major League Baseball (MLB) umpire scheduling problem, but is, however, restricted to the single objective of minimizing total travel distance of the umpires. Several hard constraints are employed to enforce fairness when assigning umpires, making it a challenging optimization problem. The present work concerns a constructive matheuristic approach which focuses primarily on large benchmark instances. A decomposition-based approach is employed which sequentially solves Integer Programming (IP) formulations of the subproblems to arrive at a feasible solution for the entire problem. This constructive matheuristic efficiently generates feasible solutions and improves the best known solutions of large benchmark instances of 26, 28, 30 and 32 teams well within the benchmark time limit. In addition, the algorithm is capable of producing feasible solutions for various small and medium benchmark instances competitive with those produced by other heuristic algorithms. The paper also details experiments conducted to evaluate various algorithmic design parameters such as subproblem size, overlap and objective functions.
Prisoners often require transportation to and from services such as hospital appointments, court proceedings and family visits during their imprisonment. Organising daily prisoners transportation consumes a huge amount of resources. A large fleet of highly protected vehicles, their drivers and security guards must be assigned to all prisoner transports such that all safety and timerelated constraints are satisfied while inter-prisoner (inter-passenger) conflicts are avoided. It is beyond human planners' capabilities to minimize costs while attempting to feasibly schedule all prisoner transportation requests. Whereas the prisoner transportation problem (PTP) bears resemblance with vehicle routing, common software systems for vehicle routing fail to address the intricacies associated with the PTP. A dedicated decision support system is required to both support human planners as well as reduce operational costs. The considerable computational challenge due to problem-specific components (inter-passenger conflicts and simultaneous servicing) also makes the PTP interesting from an academic point of view. We formally introduce the problem by providing mixed integer programming models. We implement exact iterative procedures to solve these formulations and evaluate their performance on small instances. In order to solve instances of a realistic size, we present a heuristic. Academic PTP instances generated and employed for experimentation are made publicly available with a view towards encouraging further follow-up research. The heuristic presented in this paper provides all the necessary components to solve the PTP adequately and sets initial benchmarks for the new public instance set.
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