As pressure on the healthcare system increases, patients who require surgery experience longer access times to pre- and post-operative appointments and surgery. Hospitals can control their waiting lists by allocating timeslots to the different types of appointments they discern. To inform patients about their appointments in a timely manner, they need to make this decision several weeks in advance. However, the precise consequences of the timeslot allocation on the future waiting list are uncertain, as not all patients follow the same treatment pathway. Furthermore, as these planning decisions are made weeks in advance, they are based on an uncertain prediction of future waiting lists. In this paper, methods are developed with the aim to support hospitals in optimizing their timeslot allocation to reduce patient access times and utilize all available capacity in the outpatient department and operating room. The problem is modelled as a Markov decision process (MDP). However, as the state, decision and outcome spaces grow exponentially in size, even for a single surgeon, an exact solution cannot be determined. We thus compare four alternative solution methods to the static allocation method that is common in hospitals. Least-squares policy iteration is used to find an approximate solution, an (integer) linear program is formulated to solve a deterministic variant of the MDP, several heuristic decision rules are investigated, and a hybrid method is proposed that statically allocates a percentage of timeslots and then dynamically allocates the remaining timeslots with the linear program when sufficient information is available to effectively deal with variability. The solution methods are tested on a case study at the orthopedic care chain of the Sint Maartenskliniek hospital in the Netherlands. Simulation results indicate that in balanced capacity scenarios, static allocation achieves the highest performance when planning more than 4 weeks ahead. In contrast, in unbalanced systems, steering capacity toward patient groups incurring the highest costs yields better outcomes. The hybrid method offers flexibility as it can be adapted to both balanced and unbalanced situations. For the case study, we find that statically allocating 60% of timeslots and dynamically allocating the remainder 4 weeks in advance provides the best results in terms of meeting access time targets and efficient resource utilization.

Introduction: Mathematical and optimisation models are frequently used to improve hospital planning and capacity management. However, the resulting model-derived solutions are rarely evaluated for their adoption within the real-world context of a hospital. Objectives: In this study, we share our experience of an interdisciplinary collaboration between operations research/management science and implementation science, as one way of bridging the gap between technically sound solutions and their practical, sustainable use in healthcare. Methodology: We applied implementation science prospectively to anticipate adoption implications at the design stage of a scheduling tool. Specifically, we used the Consolidated Framework for Implementation Research (CFIR) to identify anticipated barriers and facilitators for adopting a mathematically optimised surgery blueprint schedule within a children’s hospital. Results: Identified anticipated facilitators included strong staff motivation to improve schedules, as well as positive perceptions of an objectively designed mathematical scheduling tool. Barriers included resistance to change among some staff and the demand for more evidence of the schedule’s benefits prior to implementation. We identified a strong culture of retaining autonomy in scheduling decisions, as well as operational adjustments made to current scheduling tools. Practical implications: Applying CFIR prospectively demonstrated how implementation science frameworks could provide a structured way to anticipate adoption challenges and align technical solutions with organisational realities.

In large modular construction projects, such as shipbuilding, multiple similar projects arrive stochastically. At project arrival, a schedule has to be created, in which future modifications are difficult and/or undesirable. Since all projects use the same set of shared resources, current scheduling decisions influence future scheduling possibilities. To model this problem, we introduce the Dynamic Resource Constrained Multi-project Scheduling Problem with Static project Schedules. To find schedules, both a greedy approach and simulation-based approach with varying scenarios are introduced. Although the simulation-based approach schedules projects proactively, the computing times are long, even for small instances. Therefore, a method is introduced that learns from schedules obtained in the simulation-based method and uses a neural network to estimate the objective function value. It is shown that this method achieves a significant improvement in objective function value over the greedy algorithm, while only requiring a fraction of the computation time of the simulation-based method.

The Resource Constrained Project Scheduling Problem with a flexible Project Structure (RCPSP-PS) is a generalization of the Resource Constrained Project Scheduling Problem (RCPSP). In the RCPSP, the goal is to determine a minimal makespan schedule subject to precedence and resource constraints. The generalization introduced in the RCPSP-PS is that, instead of executing all activities, only a subset of all activities has to be executed. We present a model that is based on two graphs: one representing precedence relations and one representing the activity selection structure. The latter defines which subset of activities has to be executed. Additionally, we present theoretical properties of this model and give an exact solution method that makes use of these properties by generating cutting planes and setting bounds on variables. Furthermore, three problem properties are introduced to classify problems in the literature. We compare our model to a model from literature on instances that possess a subset of these three problem properties and find a reduction in computing time. Furthermore, by comparing results on instances that possess all problem properties, it is shown that the computing times are decreased and better lower bounds are found by the cutting planes and variable bounds presented in this paper.

Background: Helicopter emergency medical services (HEMS) are important in many health care systems. In order to best utilize this expensive healthcare service, the location of HEMS bases is key. Concurrency conflicts is a prominent deviation for not completing missions, yet is often overlooked in mathematical modelling. The aim of the present study was to calculate optimal air ambulance base locations when accounting for the potential unavailability of helicopters due to concurrency conflicts. Methods: We used incident data for Norway from 2015. Optimal helicopter base locations were estimated using the Maximum Expected Covering Location Problem (MEXCLP) optimization model, allowing for estimation of the impact of concurrency conflicts by introducing a busy fraction parameter in the model. We explored busy fractions of 0, 0.10, 0.20 and 0.30, representing helicopters on the HEMS bases being busy 0, 10, 20 and 30% of the time, respectively. Both greenfield scenarios and simulations conditioned on the existing base structure were explored. Results: The 428 municipalities had a median (5–95 percentile) of 10 (2–38) incidents. Assuming a helicopter is always available, the existing bases cover an estimated 73.6% of the incidents within 30 min. Increasing the busy fraction in the calculations resulted in a significant decrease in estimated coverage. Re-arranging the currently available 14 helicopters in a greenfield analysis increases coverage to 91.9%. Increasing the busy fraction in the models, the mathematically optimal solutions put increasingly more emphasis on the more densely populated greater Oslo area, removing helicopters from northern Norway and the coastal areas, where population is more spread. Conclusion: The busy fraction significantly impacts the optimal location of air ambulance bases, with higher busy fractions resulting in more helicopters being placed in the more densely populated areas where demand is higher. However, the actual busy fractions reported in the Norwegian HEMS system seem to be of a magnitude small enough to have little impact on the optimal location of HEMS bases and helicopters. To determine the impact of adjusting for non-homogeneous busy fractions across the country more refined busy fraction models are needed.

Ride-hailing companies will face the emergence and gradual expansion of AVs-only zones in urban areas where only automated vehicles (AVs) are allowed to circulate. When owning a mixed fleet (automated and conventional taxis), a ride-hailing company has to determine the optimal fleet size as a function of the gradually expanding coverage of AVs-only zones while taking into account interactions with privately-owned human-driven vehicles. To model this problem, we propose a bi-level framework in which the lower level captures the mixed routing behaviour of the vehicles and the endogenous traffic congestion, and the upper level determines fleet sizes to maximise profit. A parallel genetic algorithm is introduced to solve this bi-level framework, which is embedded with a tailored algorithm for solving the lower-level model. Numerical experiments are conducted on instances based on a small network and the network of the city of Delft, The Netherlands, to demonstrate the performance of the proposed solution method and investigate the impacts of AVs-only zones on traffic and ride-hailing operations. Results indicate that the fleet size of automated taxis increases nonlinearly with the expansion of the AVs-only zone while that of conventional taxis decreases as demand shifts from human-driven vehicles to automated taxis. The fleet size decision depends heavily on the fleet's cost structure, the location and the distribution of parking depots. Furthermore, the existence of an AVs-only zone leads to detours for human-driven vehicles in the early stages, but it will bring major benefits by reducing congestion as its size increases.

Shared automated vehicles (SAV) are expected to benefit the sustainable development of urban regions and alleviate the negative impacts brought by the increasing number of private cars. In this paper, we envision a future scenario where non-pooled SAVs replace private cars and provide public on-demand mobility services to satisfy the mobility needs of a city's residents. To help service providers make profitable fleet sizing and management decisions, we develop a mixed-integer non-linear programming model that considers the congestion effects and the mode choice of urban travellers in different income classes, between SAVs and bicycles. Our model optimises both strategic decisions (fleet size, initial fleet distribution, and service quality level) and operational decisions (trip assignment, vehicle routing, parking, and relocation). Travellers’ preference for both transport modes is described through a binary logit model and congestion effects are described by dynamically varying travel times with respect to traffic flow in a non-linear fashion. In addition, we investigate two types of accept/reject mechanisms (mandatory vs. non-mandatory acceptance) which lead to an endogenously determined acceptance rate that can affect travellers’ willingness to use SAV services. The computational challenge posed by the non-linear and non-convex nature of the model is addressed through reformulation and the use of outer-inner approximation methods combined with a breakpoint generation algorithm. We demonstrate the effectiveness of our proposed method in a case study of the city of Delft in The Netherlands, as well as a scaling analysis on three toy networks with various sizes and demand profiles. A sensitivity analysis of key parameters is carried out to assess system performance. Computational results indicate that fleet sizing decisions are influenced not only by the population's geographical distribution and land use patterns but also by the pricing strategy, unit operating costs of the SAV fleet, network congestion level, and traveller behaviour. When the price rate of using SAVs is low, the fleet sizing decisions can also be influenced by the trip accept/reject mechanism and the travellers’ sensitivity to the service quality level. In addition, a low price of SAV service will attract more users but may not necessarily bring a higher profit because of the increased traffic congestion.

The resource constrained project scheduling problem with a flexible project structure and consumption and production of resources, involves making a selection of activities and scheduling these activities in order to minimize the makespan, subject to precedence and resource constraints. Since finding a feasible selection of activities is NP-hard, we introduce the concept of group graphs and restrict ourselves to instances with an acyclic group graph. For these instances, which represent many practical cases, we show how to make a feasible selection of activities in polynomial time and use this concept to schedule the selected activities using a hybrid differential evolution algorithm. We compare this algorithm with an algorithm from the literature on special cases of instances without consumption and production of resources, and show that our algorithm creates solutions of higher quality. Furthermore, to compare general instances, we develop an ant colony optimization algorithm that performs slightly better on special cases than the algorithm from literature and show that the hybrid differential evolution algorithm outperforms the ant colony optimization algorithm on general instances.

Electric car-sharing systems have attracted large attention in recent years as a new business model for achieving both economic and environmental benefits in urban areas. Among different types, the one considered in this paper is the so-called one-way car-sharing system whereby a user can begin and end a trip at any station of the system. At the same time, the Vehicle-to-Grid (V2G) concept is emerging as a possible innovative solution for smart power grid control. A management system that combines car-sharing system operations and V2G technology is a recent challenge for academia and industry. In this work, a mixed integer linear programming formulation is proposed to find the optimal management of electric vehicles in a one-way car-sharing system integrated with V2G technology. The proposed mathematical model allows finding the optimal start-of-day electric vehicles distribution that maximizes the total revenue obtained from system users and V2G profits through daily electric vehicles charging/discharging schedules. These schedules are based on mean daily users' electric vehicles requests and electricity prices. The model can be applied to evaluate the possible average daily profitability of V2G operations. In order to test the model performance, we applied it to a small-size test network and a real-size test network (the Delft network in the Netherlands). Under the model assumptions, the adoption of V2G technology allows to fully cover the daily charging costs due to users’ trips and to obtain V2G profits by taking advantage of electric vehicles unused time without significantly reducing the satisfied car-sharing system demand. Most of the energy purchased to charge the electric vehicles batteries is provided back to the grid during energy peak load demand, creating benefits also for energy providers.

The era of intelligent transportation with automated vehicles (AVs) is coming. Nonetheless, the transition to this system will be a gradual process. On the one hand, some zones in the city may be dedicated to AVs with a fully intelligent traffic management system geared toward high performance. On the other hand, automated and conventional vehicles may have to be allowed to drive in the remaining zones of the urban network in a transition stage. In this paper, we consider a situation where AVs are deployed by a taxi operating company to serve door-to-door travel requests. Facing this transition period, a strategic flow-based vehicle routing model is developed to determine the optimal fleet size of automated and conventional taxis as a function of the gradually increasing coverage of the AVs-only dedicated area. Traffic congestion is considered through flow-dependent travel times. Two taxi company service regimes are tested: the User Preference Mode (UPM) and the System Profit Mode (SPM). In the UPM, passengers can choose their preferred vehicle type according to their preference. In the SPM, the taxi company will take charge of the vehicle assignment to maximize the system profit. The developed model formulations are applied to a case study of a large toy network. The results give insight into the performance of the heterogeneous taxi system on a hybrid network. Strategies are presented on how to adjust the fleet size of automated and conventional taxis to get the best system profit while satisfying the mobility demand. The SPM can bring more profit to the operating company by reducing the detour and relocation cost of taxis, reducing the salaries for drivers through a bigger fleet size of AVs, and reducing the delay penalty, compared to the UPM.

Combinatorial optimization (CO) problems are at the heart of both practical and theoretical research. Due to their complexity, many problems cannot be solved via exact methods in reasonable time; hence, we resort to heuristic solution methods. In recent years, machine learning (ML) has brought immense benefits in many research areas, including heuristic solution methods for CO problems. Among ML methods, reinforcement learning (RL) seems to be the most promising method to find good solutions for CO problems. In this work, we investigate an RL framework, whose agent is based on self-attention, to achieve solutions for the knapsack problem, which is a CO problem. Our algorithm finds close to optimal solutions for instances up to one hundred items, which leads to conjecture that RL and self-attention may be major building blocks for future state-of-the-art heuristics for other CO problems.

Metaheuristics have been widely used to solve NP-hard problems, with excellent results. Among all NP-hard problems, the Travelling Salesman Problem (TSP) is potentially the most studied one. In this work, a variation of the TSP is considered; the main differences being, edges may have positive or negative costs and the objective is to return a Hamiltonian cycle with cost as close as possible to zero. This variation is called the balanced TSP (BTSP). To tackle this new problem, we present an adaptive variant of the iterated local search metaheuristic featuring also random restart. This algorithm was tested on the MESS2018 metaheuristic competition and achieved notable results, scoring the 5th position overall. In this paper, we detail all the components of the algorithm itself and present the best solutions identified. Even though this metaheuristic was tailored for the BTSP, with small modifications its structure can be applied to virtually any NP-hard problem. In particular, we introduce the uneven reward-and-punishment rule which is a powerful tool, applicable in many contexts where fast responses to dynamic changes are crucial.

Surgery groups are clustered surgery procedure types that share comparable characteristics (e.g. expected duration). Scheduling OR blocks leaves many options for operational surgery scheduling and this increases the variation in usage of both the OR and downstream beds. Therefore, we schedule surgery groups to reduce the options for operational scheduling, ultimately bridging the gap between tactical and operational scheduling. We propose a single step mixed integer linear programming (MILP) approach that approximates the bed and OR usage and a simulated annealing approach. Both approaches are compared on a real-life data set and results show that the MILP performs best in terms of solution quality and computation time. Furthermore, the results show that our model may improve the OR utilization from 71% to 85% and decrease the bed usage variation from 53 beds to 11 beds compared to historical data. To show the potential and robustness of our model, we discuss several variants of the model requiring minor modifications. The use of surgery groups makes it easier to implementation our model in practice and, for operational planners, it is instantly clear where to schedule different types of surgery.

Emergency Medical Services organizations are responsible for providing paramedic crews, vehicles and equipment to transfer patients from one location to another in emergency and non-emergency settings. They must solve difficult scheduling and assignment problems to ensure on-time arrival of patients and the efficient use of health care resources during non-emergency operations. Ambulances can serve both emergency and non-emergency requests but are rarely available to serve non-emergency requests. Therefore, non-emergency requests are the responsibility of Patient Transfer Units. The objective of this study is to develop a mathematical model that will assign Patient Transfer Units to non-emergency patient transfer requests, design a schedule that will minimize travel costs and balance workloads and apply it to a real-world case study. This paper also proposes a framework to utilize historical patient transfer data in the scheduling process. The mathematical model provides decision support for the non-emergency patient transfer scheduling process.

Over the years, several ambulance location models have been discussed in the literature. Most of these models have been further developed to take more complicated situations into account. However, the existing standard models that are often used in case studies have never been compared computationally according to the criteria used in practice. In this paper, we compare several ambulance location models on coverage and response time criteria. In addition to four standard ambulance location models from the literature, we also present two models that focus on average and expected response times. The computational results show that the maximum expected covering location problem (MEXCLP) and the expected response time model (ERTM) perform the best over all considered criteria. However, as the computation times for ERTM are long, the average response time model (ARTM) could be a good alternative. Based on these results, we also propose four alternative models that combine the good coverage provided by MEXCLP and the quick response times provided by ARTM. All four considered models provide balanced solutions in terms of coverage and response times. However, the multiple response times target model (MRTTM) outperforms the other models based on computation time.