Robust capacity planning for accident and emergency services

Accident and emergency departments (A&E) are the first place of contact for urgent and complex patients. These departments are subject to uncertainties due to the unplanned patient arrivals. After arrival to an A&E, patients are categorized by a triage nurse based on the urgency. The performance of an A&E is measured based on the number of patients waiting for more than a certain time to be treated. Due to the uncertainties affecting the patient flow, finding the optimum staff capacities while ensuring the performance targets is a complex problem. This paper proposes a robust-optimization based approximation for the patient waiting times in an A&E. We also develop a simulation optimization heuristic to solve this capacity planning problem. The performance of the approximation approach is then compared with that of the simulation optimization heuristic. Finally, the impact of model parameters on the performances of two approaches is investigated. The experiments show that the proposed approximation results in good enough solutions

Fertilizer application management under uncertainty using approximate dynamic programming

Finding the right amount of fertilizer for the plants in different maturity levels is a dynamic and stochastic problem due to the uncertainties in the weather conditions and yields. Besides, two conflicting objectives of multiple stakeholders, maximizing the yield and minimizing the environmental impact should be considered together. This paper proposes a mathematical model based on stochastic dynamic programming to find the fertilization levels in a citrus orchard for a finite planning period. Due to the size of the problem, we develop an Approximate Dynamic Programming (ADP) algorithm to obtain the best policy. The data for the case study is collected through literature sources and from farmers in southern Turkey where the income from orchards are unstable and groundwater pollution is observed. We find that ADP performs better than static and dynamic heuristics in a wide range of parameters. Extensive sensitivity analysis indicates that if the penalty for the leaching is computed per acre of orchard, this may lead to excessive fertilizer use in large orchards. Finally, the increase in the standard deviation of rainfall due to the global warming is expected to cause up to 22% drop in the yield

Robust capacity planning for sterilisation department of a hospital

Sterile services departments are special units designed to perform sterilisation operations in an efficient way within a hospital. The delays in sterilisation services cause significant disruptions on surgery schedules and bed management. To prevent the delays, an upper time limit can be imposed on the time spent in the sterilisation services. In this paper, we propose a mathematical modelling approach for the optimum capacity planning of a sterilisation service unit considering the uncertainties in the sterilisation process. The model aims to find the optimum capacity on four tandem steps of the sterilisation whilst at the same time minimising the total cost and keeping the maximum time in the system below a limit. Assuming general distributions for service and interarrival times, an approximation structure based on robust optimisation is used to formulate the maximum time spent in the system. We analysed the structural property of the resulting model and found that the relaxed version of the model is convex. The real data from a large sterilisation services unit is used for computational experiments. The results indicated that the approximation fits well against the simulated maximum time in the system. Other experiments revealed that an upper limit of 7 hours for the sterilisation services balances the cost vs. robustness trade-off

Dynamic Capacity Planning of Hospital Resources under COVID-19 Uncertainty using Approximate Dynamic Programming

COVID-19 pandemic has resulted in an inflow of patients into the hospitals and overcrowding of healthcare resources. Healthcare managers increased the capacities reactively by utilizing expensive but quick methods. Instead of this reactive capacity expansion approach, we propose a proactive approach considering different realizations of demand uncertainties in the future due to COVID-19. For this purpose, a stochastic and dynamic model is developed to find the right amount of capacity increase in the most critical hospital resources. Due to the problem size, the model is solved with Approximate Dynamic Programming. Based on the data collected in a large tertiary hospital in Turkey, the experiments show that ADP performs better than a benchmark myopic heuristic. Finally, sensitivity analysis is performed to explore the impact of different epidemic dynamics and cost parameters on the results.</p

Fertilizer application management under uncertainty using approximate dynamic programming

Finding the right amount of fertilizer for the plants in different maturity levels is a dynamic and stochastic problem due to the uncertainties in the weather conditions and yields. Besides, two conflicting objectives of multiple stakeholders, maximizing the yield and minimizing the environmental impact should be considered together. This paper proposes a mathematical model based on stochastic dynamic programming to find the fertilization levels in a citrus orchard for a finite planning period. Due to the size of the problem, we develop an Approximate Dynamic Programming (ADP) algorithm to obtain the best policy. The data for the case study is collected through literature sources and from farmers in southern Turkey where the income from orchards are unstable and groundwater pollution is observed. We find that ADP performs better than static and dynamic heuristics in a wide range of parameters. Extensive sensitivity analysis indicates that if the penalty for the leaching is computed per acre of orchard, this may lead to excessive fertilizer use in large orchards. Finally, the increase in the standard deviation of rainfall due to the global warming is expected to cause up to 22% drop in the yield.</p

Dynamic and flexible staff deployment in accident and emergency departments using simulation-based optimization

Accident and emergency departments experience overcrowding due to staff shortages as well as to variations in patient arrivals and the time required to treat them. Several policies have been developed by hospitals to ensure that patients are not put at clinical risk during overcrowding. These policies suggest flexing nurses from different duties to the overcrowded section. However, the policies do not indicate the details of when exactly the flexing should be activated. We develop a mathematical model to find the optimum levels of triage and treatment queue lengths after which flexing should be activated. The performance indicators of the department are the waiting time targets and the disturbance due to nurse flexing. Because of the lack of closed-form formulations, we propose simulation optimization to solve the problem. By analyzing the model structure, we develop an efficient search procedure of the discrete solution space. We show the application of the proposed method using the data of a large hospital in the UK under different parameter settings. The results show that hospital management should focus on increasing the number of treatment nurses rather than flexing the nurses, and the queue of the service stream that requires tighter staffing should be controlled by an upper limit

Dynamic surgery management under uncertainty

Real-time surgery management involves a complex and dynamic decision-making process. The duration of surgeries in many cases cannot be known until the surgery has actually been completed. Furthermore, disruptions such as equipment failure or the arrival of a non-elective surgery can occur simultaneously. Thus, the assignment of surgeries needs to be updated, as and when disruptions occur, to minimize their effects. In this paper, we present a stochastic dynamic programming approach to the surgery allocation problem with multiple operating rooms under uncertainty. Given an elective list for the day, the dynamic optimization model minimizes the number of surgeries not carried out by the end of the shift and the total waiting times of patients during the day weighted according to their urgency level. Due to the curse of dimensionality, we apply an approximate dynamic programming algorithm to solve the stochastic dynamic surgery management model. Computational experiments are designed to demonstrate the performance of the proposed algorithm and its applicability to practical settings. The results show that the approximate dynamic programming algorithm provides a good approximation to the optimum policy and leads to some managerial insights