Minimizing patients total clinical condition deterioration in operating theatre departments.

The operating theatre is the most crucial and costly department in a hospital due to its expensive resources and high patient admission rate. Efficiently allocating operating theatre resources to patients provides hospital management with better utilization and patient flow. In this paper, we tackle both tactical and operational planning over short-term to medium-term horizons. The main goal is to determine an allocation of blocks of time on each day to surgical specialties while also assigning each patient a day and an operating room for surgery. To create a balance between improving patients welfare and satisfying the expectations of hospital administrators, we propose six novel deterioration rates to evaluate patients total clinical condition deterioration. Each deterioration rate is defined as a function of the clinical priorities of patients, their waiting times, and their due dates. To optimize the objective functions, we present mixed integer programming (MIP) models and two dynamic programming based heuristics. Computational experiments have been conducted on a novel well-designed and carefully chosen benchmark dataset, which simulates realistic-sized instances. The results demonstrate the capability of the MIP models in finding excellent solutions (maximum average gap of 4.71% across all instances and objective functions), though, requiring large run-times. The heuristic algorithms provide a time-efficient alternative, where high quality solutions can be found in under a minute. We also analyse each objective function's ability in generating high quality solutions from different perspectives such as patients waiting times, the number of scheduled patients, and operating rooms utilization rates. We provide managerial insights to the decision makers in cases where their intention is to meet KPIs and/or maintaining trade-offs between patients and administrators expectations, more fair assignments, or ensuring that the most urgent patients are taken care of first

Car sequencing with constraint-based ACO

Hybrid methods for solving combinatorial optimization problems have become increasingly popular recently. The present paper is concerned with hybrids of ant colony optimization and constraint programming which are typically useful for problems with hard constraints. However, the original algorithm suffered from large CPU time requirements. It was shown that such an integration can be made efficient via a further hybridization with beam search resulting in CP-Beam-ACO. The original work suggested this in the context of job scheduling. We show here that this algorithm type is also effective on another problem class, namely the car sequencing. We consider an optimization version, where we aim to optimize the utilization rates across the sequence. Car sequencing is a notoriously difficult problem, because it is difficult to obtain good bounds via relaxations. We show that stochastic sampling provides superior results to well known lower bounds for this problem when combined with CP-Beam-ACO

A biased random key genetic algorithm with rollout evaluations for the resource constraint job scheduling problem

The resource constraint job scheduling problem considered in this work is a difficult optimization problem that was defined in the context of the transportation of minerals from mines to ports. The main characteristics are that all jobs share a common limiting resource and that the objective function concerns the minimization of the total weighted tardiness of all jobs. The algorithms proposed in the literature for this problem have a common disadvantage: they require a huge amount of computation time. Therefore, the main goal of this work is the development of an algorithm that can compete with the state of the art, while using much less computational resources. In fact, our experimental results show that the biased random key genetic algorithm that we propose significantly outperforms the state-of-the-art algorithm from the literature both in terms of solution quality and computation time

The Maximum Happy Induced Subgraph Problem: Bounds and Algorithms

In this paper we consider a combinatorial optimisation problem that takes as input a graph in which some of the vertices have been preassigned to colours. The aim is to then identify the largest induced subgraph in which all remaining vertices are able to assume the same colour as all of their neighbours. This problem shares similarities with the graph colouring problem, vertex cut problems, and the maximum happy vertices problem. It is NP-hard in general. In this paper we derive a number of upper and lower bounds and also show how certain problem instances can be broken up into smaller subproblems. We also propose one exact and two heuristic algorithms for this problem and use these to investigate the factors that make some problem instances more difficult to solve than others

Car sequencing with constraint-based ACO

Hybrid methods for solving combinatorial optimization problems have become increasingly popular recently. The present paper is concerned with hybrids of ant colony optimization and constraint programming which are typically useful for problems with hard constraints. However, the original algorithm suffered from large CPU time requirements. It was shown that such an integration can be made efficient via a further hybridization with beam search resulting in CP-Beam-ACO. The original work suggested this in the context of job scheduling. We show here that this algorithm type is also effective on another problem class, namely the car sequencing. We consider an optimization version, where we aim to optimize the utilization rates across the sequence. Car sequencing is a notoriously difficult problem, because it is difficult to obtain good bounds via relaxations. We show that stochastic sampling provides superior results to well known lower bounds for this problem when combined with CP-Beam-ACO

Constraint-based ACO for a shared resource constrained scheduling problem

We consider a scheduling problem arising in the mining industry. Ore from several mining sites must be transferred to ports to be loaded on ships in a timely manner. In doing so, several constraints must be met which involve transporting the ore and deadlines. These deadlines are two-fold: there is a preferred deadline by which the ships should be loaded and there is a final deadline by which time the ships must be loaded. Corresponding to the two types of deadlines, each task is associated with a soft and hard due time. The objective is to minimize the cumulative tardiness, measured using the soft due times, across all tasks. This problem can be formulated as a resource constrained job scheduling problem where several tasks must be scheduled on multiple machines satisfying precedence and resource constraints and an objective to minimize total weighted tardiness. For this problem we present hybrids of ant colony optimization, Beam search and constraint programming. These algorithms have previously shown to be effective on similar tightly-constrained combinatorial optimization problems. We show that the hybrid involving all three algorithms provides the best solutions, particularly with respect to feasibility. We also investigate alternative estimates for guiding the Beam search component of our algorithms and show that stochastic sampling is the most effective

Strip packing with hybrid ACO: Placement order is learnable

This paper investigates the use of hybrid meta-heuristics based on ant colony optimization (ACO) for the strip packing problem. Here, a fixed set of rectangular items of fixed sizes have to be placed on a strip of fixed width and infinite height without overlaps and with the objective to minimize the height used. We analyze a commonly used basic placement heuristic (BLF) by itself and in a number of hybrid combinations with ACO. We compare versions that learn item order only, item rotation only, both independently, and rotations conditionally upon placement order. Our analysis shows that integrating a learning meta-heuristic provides a significant performance advantage over using the basic placement heuristic by itself. The experiments confirm that even just learning a placement order alone can provide significant performance improvements. Interestingly, learning item rotations provides at best a marginal advantage. The best hybrid algorithm presented in this paper significantly outperforms previously reported strip packing meta-heuristics

Finding happiness: an analysis of the maximum happy vertices problem

The maximum happy vertices problem involves determining a vertex colouring of a graph such that the number of vertices assigned to the same colour as all of their neighbours is maximised. This problem is trivial if no vertices are precoloured, though in general it is NP-hard. In this paper we derive a number of upper and lower bounds on the number of happy vertices that are achievable in a graph and then demonstrate how certain problem instances can be broken up into smaller subproblems. Four different algorithms are also used to investigate the factors that make some problem instances more difficult to solve than others. In general, we find that the most difficult problems are those with relatively few edges and/or a small number of precoloured vertices. Ideas for future research are also discussed