Minimizing the waiting time for emergency surgery

Hospitals aim to deliver the highest quality of care. One key priority is to schedule emergency surgeries as quickly as possible, because postponing them generally increases a patient’s risk of complications and even death. In this paper, we consider the case that emergency surgeries are scheduled in one of the elective Operating Rooms (ORs). In this situation, emergency patients are operated once an going elective surgery has finished. We denote these completion times of the elective surgeries by ‘break-in-moments’ (BIMs). The waiting time for emergency surgeries can be reduced by spreading these BIMs as evenly as possible over the day. This can be achieved by sequencing the surgeries in their assigned OR, such that the maximum interval between two consecutive BIMs is minimized. In this paper, we discuss several exact and heuristic solution methods for this new type of scheduling problem. However, in practice, emergency surgeries arising throughout the day and the uncertainty of the durations of elective surgeries, may disrupt the initial schedule. As a result, the completion times of the elective surgeries, and therefore, the BIMs change, leading also to a change of the maximum distance between two BIMs. To estimate this effect and investigate the robustness of the created schedules, we conduct a simulation study. Computational results show that the best approaches reduce the waiting time of emergency surgeries by approximately 10%

Modelo matemático para tempo de transformação de prioridades no deslocamento intra-hospitalar

Orientador: Prof. Dr. José Eduardo Pécora JúniorCoorientador: Prof. Dr. Gustavo Valentim LochDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia de Produção. Defesa : Curitiba, 26/05/2021Inclui referências: p. 75-79Área de concentração: Pesquisa OperacionalResumo: O transporte intra-hospitalar de pacientes realizado em macas é um processo importante e que requer atenção pois o tempo desse deslocamento pode influenciar no agravamento do estado de saúde dos pacientes. Existe um número de funcionários (maqueiros) para realizar o deslocamento e cada paciente tem um nível de prioridade para ser deslocado. Cada nível de prioridade tem um tempo máximo em que o paciente deve ser deslocado e quando esse tempo é ultrapassado o paciente recebe uma prioridade mais urgente. Esse tempo se trata do tempo de transformação de prioridades. Baseado na solicitação de um hospital canadense e em um artigo inicial do tema, foi realizada uma expansão do modelo para, após esse tempo limite, o paciente receber um nível de prioridade mais urgente para ser atendido mais rapidamente. O problema abordado será o tempo de espera para deslocamento e foi resolvido como sendo um sistema clássico de máquinas paralelas (parallel machine). Apesar do tema ter algumas abordagens, nenhuma toma como base a transformação de níveis de prioridade na fila de atendimento. Portanto, neste trabalho foi proposto um modelo de programação linear inteira mista para a transformação de prioridades no deslocamento intra-hospitalar utilizando as instâncias propostas de um artigo inicial sobre o tema. Foi realizada a comparação entre 3 tipos de testes (do modelo original, modelo com transformação de prioridades e o modelo desenvolvido nesse trabalho com transformação e melhoria de tempo) e para análise dos resultados vários aspectos foram levados em consideração: maior tempo de término entre as atividades, função objetivo, tempo de atraso médio por prioridade, tempo de resposta por prioridade, tempo ocioso dos maqueiros e atraso por prioridade. Sabe-se que o modelo aqui desenvolvido apresentou melhoras em alguns aspectos e a maior contribuição do estudo foi a sugestão de modificação dos tempos de prioridade, principalmente na prioridade 4 que é a mais urgente, reduzindo assim os atrasos recorrentes. O estudo desses tempos é um dos pontos fundamentais para a tomada de decisão do atendimento do hospital em questão, bem como a busca de um deslocamento sem demoras e atrasos, respeitando a necessidade hospitalar de cada paciente.Abstract: Intra-hospital patient transport on stretchers is an important process that requires attention because the time of this displacement can influence the worsening of the patients' health status. There are a number of employees (stretcher bearers) to perform the displacement and each patient has a priority level to be moved. Each priority level has a maximum time in which the patient must be moved, and when this time is exceeded, the patient receives a more urgent priority. This time is the priority transformation time. Based on a request from a Canadian hospital and an early article on the subject, an expansion of the model was made so that after this time limit, the patient would receive a more urgent priority level to be seen more quickly. The problem addressed will be the displacement waiting time and was solved as a classic parallel machine system. Although the subject has some approaches, none of them is based on the transformation of priority levels in the queue. Therefore, in this work, a mixed integer linear programming model was proposed for the transformation of priorities in intra-hospital displacement using the proposed instances from an initial paper on the subject. A comparison between 3 types of tests (the original model, the model with priority transformation and the model developed in this work with transformation and time improvement) was performed and to analyze the results several aspects were taken into consideration: longest completion time between activities, objective function, average delay time per priority, response time per priority, idle time of waiters and delay per priority. It is known that the model developed here presented improvements in some aspects and the greatest contribution of the study was the suggestion to modify the priority times, especially in priority 4 which is the most urgent, thus reducing recurring delays. The study of these times is one of the fundamental points for decision making in the care of the hospital in question, as well as the search for a displacement without delays and delays, respecting the hospital needs of each patient

Scheduling with safety distances

We investigate the problem of Scheduling with Safety Distances (SSD) that consists in scheduling jobs on two parallel machines without machine idle time. Every job is already assigned to its machine, and we just have to specify an ordering of the jobs for each machine. The goal is to find orderings of the jobs such that the minimum time elapsed between any two job completion times is maximized. We prove that this problem is NP-hard in general and give polynomial time algorithms for special cases. These results combined establish a sharp borderline between NP-complete and polynomial solvable versions of the problem SSD