Showing papers in "OR Spectrum in 2020"

Online routing and scheduling of search-and-rescue teams

Abstract: We study how to allocate and route search-and-rescue teams to areas with trapped victims in a coordinated manner after a disaster. We propose two online strategies for these time-critical decisions considering the uncertainty about the operation times required to rescue the victims and the condition of the roads that may delay the operations. First, we follow the theoretical competitive analysis approach that takes a worst-case perspective and prove lower bounds on the competitive ratio of the two variants of the defined online problem with makespan and weighted latency objectives. Then, we test the proposed online strategies and observe their good performance against the offline optimal solutions on randomly generated instances.

Predicting gasoline shortage during disasters using social media

Abstract: Shortage of gasoline is a common phenomenon during onset of forecasted disasters like hurricanes. Prediction of future gasoline shortage can guide agencies in pushing supplies to the correct regions and mitigating the shortage. We demonstrate how to incorporate social media data into gasoline supply decision making. We develop a systematic approach to examine social media posts like tweets and sense future gasoline shortage. We build a four-stage shortage prediction methodology. In the first stage, we filter out tweets related to gasoline. In the second stage, we use an SVM-based tweet classifier to classify tweets about the gasoline shortage, using unigrams and topics identified using topic modeling techniques as our features. In the third stage, we predict the number of future tweets about gasoline shortage using a hybrid loss function, which is built to combine ARIMA and Poisson regression methods. In the fourth stage, we employ Poisson regression to predict shortage using the number of tweets predicted in the third stage. To validate the methodology, we develop a case study that predicts the shortage of gasoline, using tweets generated in Florida during the onset and post landfall of Hurricane Irma. We compare the predictions to the ground truth about gasoline shortage during Irma, and the results are very accurate based on commonly used error estimates.

A new matheuristic approach for the multi-depot vehicle routing problem with inter-depot routes

Abstract: The multi-depot vehicle routing problem with inter-depot routes is studied in this paper, where vehicles may reset their capacity at any depot during the working day. Due to the complexity of this problem, exact approaches are limited to small-size applications. In order to overcome this limitation, we propose a matheuristic which integrates a mixed integer linear programming formulation with a set of relax-and-fix strategies. This solution approach is shown to be very efficient, and for the first time, large-size benchmarking instances are solved.

Optimal allocation of defibrillator drones in mountainous regions

Abstract: Responding to emergencies in Alpine terrain is quite challenging as air ambulances and mountain rescue services are often confronted with logistics challenges and adverse weather conditions that extend the response times required to provide life-saving support. Among other medical emergencies, sudden cardiac arrest (SCA) is the most time-sensitive event that requires the quick provision of medical treatment including cardiopulmonary resuscitation and electric shocks by automated external defibrillators (AED). An emerging technology called unmanned aerial vehicles (or drones) is regarded to support mountain rescuers in overcoming the time criticality of these emergencies by reducing the time span between SCA and early defibrillation. A drone that is equipped with a portable AED can fly from a base station to the patient’s site where a bystander receives it and starts treatment. This paper considers such a response system and proposes an integer linear program to determine the optimal allocation of drone base stations in a given geographical region. In detail, the developed model follows the objectives to minimize the number of used drones and to minimize the average travel times of defibrillator drones responding to SCA patients. In an example of application, under consideration of historical helicopter response times, the authors test the developed model and demonstrate the capability of drones to speed up the delivery of AEDs to SCA patients. Results indicate that time spans between SCA and early defibrillation can be reduced by the optimal allocation of drone base stations in a given geographical region, thus increasing the survival rate of SCA patients.

Robust post-disaster route restoration

Abstract: Route restoration is considered to be a task of foremost priority in disaster relief. In this paper, we propose a robust optimization approach for post-disaster route restoration under uncertain restoration times. We present a novel decision rule based on restoration time ordering that yields optimal restoration sequencing and propose conditions for complexity reduction in the model and prove probability bounds on the satisfaction of these conditions. We implement our models in a realistic study of the 2015 Gorkha earthquake in Nepal.

A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints

Abstract: In this paper, we consider the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints. For the first time, the concept of partially renewable resources is embedded in the context of projects with general temporal constraints. While partially renewable resources have already broadened the area of applications for project scheduling, the extension by general temporal constraints allows to consider even more relevant aspects of real projects. We present a branch-and-bound procedure for the problem with the objective to minimize the project duration. To improve the performance of the solution procedure, new consistency tests, lower bounds, and dominance rules are developed. Furthermore, new temporal planning procedures, based on forbidden start times of activities, are presented which can be used for any project scheduling problem with general temporal constraints independent on the considered resource type. In a performance analysis, we compare our branch-and-bound procedure with the mixed-integer linear programming solver IBM CPLEX 12.8.0 on adaptations of benchmark instances from the literature. In addition, we compare our solution procedure with the only available branch-and-bound procedure for partially renewable resources. The results of the computational experiments prove the efficiency of our branch-and-bound procedure.

Humanitarian access, interrupted: dynamic near real-time network analytics and mapping for reaching communities in disaster-affected countries

Abstract: In the immediate aftermath of a disaster, local and international aid organisations deploy to deliver life-saving aid to the affected population. Yet pre-disaster road maps and road transportation models do not capture disruptions to the transportation network caused by the disaster or the dynamic changes of the situation, resulting in uncertainty and inefficiency in planning and decision-making. The integration of data in near real time on the status of the road infrastructure in the affected region can help aid organisations to keep track of the rapidly shifting conditions on the ground and to assess the implications for their logistics planning and operations. In this paper, we present a rapid graph-theoretical reachability information system based on a combination of OpenStreetMap and open humanitarian data. The system supports logistics planning in determining road access to affected communities. We demonstrate the results of our approach in a case study on the 2018 earthquake in Papua New Guinea. Our findings show the reachability of affected communities depending on the actual status of the road network, allowing for the prioritization of targeted locations and the identification of alternative routes to get there.

Simultaneous planning for disaster road clearance and distribution of relief goods: a basic model and an exact solution method

Abstract: In recent years, more and more disasters occurred. Additionally, the amount of people affected by disasters increased. Because of this, it is of great importance to perform the relief operations efficiently in order to alleviate the suffering of the disaster victims. Immediately after the occurrence of a disaster, there is an urgent need for delivering relief goods to demand locations and affected regions, respectively. Due to roads being blocked or damaged by debris, some demand locations may be out of reach and therefore the delivery of relief goods is hampered. This paper investigates the basic problem of simultaneously unblocking roads in order to make demand locations accessible and delivering relief goods in order to satisfy demand. Strict deadlines for the delivery of relief goods are considered at the demand locations. A formal problem statement is provided, and its computational complexity is analyzed. Additionally, a mixed integer programming model is developed and an exact solution method based on a branch and bound approach is proposed. A computational study investigating the performance of the model formulation and the branch and bound algorithm is conducted.

Integrating nurse assignment in outpatient chemotherapy appointment scheduling

Abstract: In outpatient chemotherapy, nurses administer the drugs in two steps. In the first few minutes of each appointment, a nurse prepares the patient for infusion (drug administration). During the remainder of the appointment, the patient is monitored by nurses and if needed taken care of. One nurse must be assigned to prepare the patient and set up the infusion device. However, a nurse who is not busy setting up may simultaneously monitor up to a certain number of patients who are already receiving infusion. The prescribed infusion durations are significantly different among the patients on a day at a clinic. We formulate this problem as a multi-criterion mixed integer program. The appointments should be scheduled with start times close to patients’ ready times, balanced workload among nurses, few nurse changes during appointments, and few nurse full-time equivalent (FTE) assigned to the schedule of the day. As the number of nurse FTEs is an output of the model rather than a fixed input, the clinic can use the nursing capacity more efficiently, i.e., with less labor cost. We develop a 3-stage heuristic for finding criterion points with the minimum weighted average deferring time of appointments for the minimum feasible number of nurse FTEs or a desired value above that. By not constraining the number of chairs or beds, we can find solutions with better (dominating) criterion points. Drug preparation, oncologist visit, and the laboratory test can be scheduled based on the drug administration appointment start time. Thus, the drug administration resources are efficiently used with desirable performance in taking the interests and requirements of various stakeholders into consideration: patients, nurses, oncologists, pharmacy, and the clinic.

Blood supply chain: a two-stage approach for tactical and operational planning

Abstract: This work proposes a new integer linear programming model for tactical and operational planning of the blood supply chain. A two-stage approach is developed with a first aggregated stage to establish tactical planning decisions and a second disaggregated stage for the operational level. The model considers multi-products, multi-periods and perishability in a large planning horizon. Inventory levels as well as waste of whole blood and blood-derived products are also modelled. A purchase flow is introduced to handle situations of not enough collection to satisfy demand. The objective is cost minimisation whilst reducing waste and dependence on other regions through purchase. A case study of the South Region of Portugal is explored, demonstrating the possibility of decreased dependency and waste by adjusting allocation of facilities and allowing a more even distribution of activities between processing centres. This is the first study of the kind ever conducted on the Portuguese blood supply chain.

Scheduling personnel for the build-up of unit load devices at an air cargo terminal with limited space

Abstract: This paper addresses the preparation of unit load devices (ULDs) at an air cargo terminal. This process is difficult to plan for many airlines, which face the challenge of assigning a limited number of workers to a limited number of workspaces available for preparing the ULDs, while respecting the requirements imposed by an existing flight schedule. During the preparation of ULDs, the objectives are to comply with the flight schedule, not to exceed the available space at the terminal, and to minimize the maximum workforce employed over time. To support airlines in realizing efficient ULD preparation processes, this paper proposes a mixed-integer linear programming model as well as a generalized set partitioning reformulation of this problem. Based on the latter formulation, we develop different heuristic strategies, some of which are shown to solve this NP-hard problem to near-optimality in a matter of merely 10 s, decisively outperforming a simple rule of thumb frequently used in practice. We also investigate the inherent trade-off between workforce and space utilization.

Centralized resource allocation based on cross-evaluation considering organizational objective and individual preferences

Abstract: Centralized resource allocation is one of important ways for a central organization to control and manage its subordinate organizations. Among various allocation methods based on data envelopment analysis (DEA), the cross-efficiency DEA-based iterative method generates allocation results using peer appraisal which considers the preference from all individual decision-making units (DMUs). However, the planned outputs target from the existing method cannot be achieved under the restrictions of current technology and productivity level. In this study, we propose a new cross-evaluation-based resource allocation approach to address the issue. Our approach not only is preferred by all individual DMUs but also always generates achievable input–output targets. Furthermore, we consider a centralized decision-making case in which an overall goal of whole organization could also be incorporated. The model is also extended to a special case of input resource allocation, namely independent procurement where funds are distributed among DMUs and DMUs use the distributed parts to raise and allocate their own input factors by themselves. Two examples are employed to illustrate our approaches.

Inventory routing for the last mile delivery of humanitarian relief supplies

Abstract: Fast and equitable distribution of the humanitarian relief supplies is key to the success of relief operations. Delayed and inequitable deliveries can result in suffering of affected people and loss of lives. In this study, we analyze the routing operations for the delivery of relief supplies from a distribution center to the dispensing sites. We assume that the relief supplies to be distributed arrive at the distribution center in batches and are consumed at the dispensing sites with a certain daily rate. When forming delivery schedules, we use the ratio of the inventory to the daily consumption rate at the dispensing sites as our decision criterion. This ratio is called the slack and can be considered as the safety stock (when positive) in case of a delay in the deliveries. Negative value for the slack means the dispensing site has stock-outs. Our objective is to maximize the minimum value of this slack among all dispensing sites. This is equivalent to maximizing the minimum safety stock or minimizing the maximum duration of the stock-outs. Due to multi-period structure of the problem, it is modeled as a variant of the Inventory Routing Problem. To address the problem, we propose a general framework which includes clustering, routing and improvement steps. The proposed framework considers the interdependence between all three types of decisions (clustering, routing and resource allocation) and makes the decisions in an integrated manner. We test the proposed framework on randomly generated instances and compare its performance against the benchmark algorithms in the literature. The proposed framework not only outperforms the benchmark algorithms by at least 1% less optimality gap but also provides high-quality solutions with around 2–3% optimality gaps.

Balance in resource allocation problems: a changing reference approach

Abstract: Fairness is one of the primary concerns in resource allocation problems, especially in settings which are associated with public welfare. Using a total benefit-maximizing approach may not be applicable while distributing resources among entities, and hence we propose a novel structure for integrating balance into the allocation process. In the proposed approach, imbalance is defined and measured as the deviation from a reference distribution determined by the decision-maker. What is considered balanced by the decision-maker might change with respect to the level of total output distributed. To provide an allocation policy that is in line with this changing structure of balance, we allow the decision-maker to change her reference distribution depending on the total amount of output (benefit). We illustrate our approach using a project portfolio selection problem. We formulate mixed integer mathematical programming models for the problem with maximizing total benefit and minimizing imbalance objectives. The bi-objective models are solved with both the epsilon-constraint method and an interactive algorithm.

The risk and consequences of multiple breadbasket failures: an integrated copula and multilayer agent-based modeling approach

Abstract: Climate shocks to food systems have been thoroughly researched in terms of food security and supply chain management. However, sparse research exists on the dependent nature of climate shocks on food-producing breadbasket regions and their subsequent cascading impacts. In this paper, we propose that a copula approach, combined with a multilayer network and an agent-based model, can give important insights on how tail-dependent shocks can impact food systems. We show how such shocks can potentially cascade within a region through the behavioral interactions of various layers. Based on our suggested framework, we set up a model for India and show that risks due to drought events multiply if tail dependencies during extremes drought is explicitly taken into account. We further demonstrate that the risk is exacerbated if displacement also takes place. In order to quantify the spatial–temporal evolution of climate risks, we introduce a new measure of multilayer vulnerability that we term Vulnerability Rank or VRank. We find that with higher food production losses, the number of agents that are affected increases nonlinearly due to cascading effects in different network layers. These effects spread to the unaffected regions via large-scale displacement causing sudden changes in production, employment and consumption decisions. Thus, demand shifts also force supply-side adjustments of food networks in the months following the climate shock. We suggest that our framework can provide a more accurate picture of food security-related systemic risks caused by multiple breadbasket failures which, in turn, can better inform risk management and humanitarian aid strategies.

A multi-cover routing problem for planning rapid needs assessment under different information-sharing settings

Abstract: In this paper, we introduce a multi-cover routing problem (MCRP), which is motivated by post-disaster rapid needs assessment operations performed to evaluate the impact of the disaster on different affected community groups. Given a set of sites, each carrying at least one community group of interest, the problem involves selecting the sites to be visited and constructing the routes. In practice, each community group is observed multiple times at different sites to make reliable evaluations; therefore, the MCRP ensures that pre-specified coverage targets are met for all community groups within the shortest time. Moreover, we assume that the completion time of the assessment operations depends on the information-sharing setting in the field, which depends on the availability of information and communication technologies (ICT). Specifically, if remote communication is possible, each assessment team can share its findings with the central coordinator immediately after completing the site visits; otherwise, all teams must return to the origin point to share information and finalize the assessments. To address these different information-sharing settings, we define two MCRP variants with different objectives and present alternative formulations for these variants. We propose two constructive heuristics and a tabu search algorithm to solve the MCRP, and conduct an extensive computational study to evaluate the performance of our heuristics with respect to different benchmark solutions. Our results show that the proposed tabu search algorithm can achieve high-quality solutions for both MCRP variants quickly. The results also highlight the importance of considering the availability of ICT in the field while devising assessment plans.

Exact and heuristic algorithms for scheduling jobs with time windows on unrelated parallel machines

Abstract: This paper addresses scheduling a set of jobs with release dates and deadlines on a set of unrelated parallel machines to minimize some minmax objective. This family of problems has a number of applications, e.g., in discrete berth allocation and truck scheduling at cross docks. We present a novel exact algorithm based on logic-based Benders decomposition as well as a heuristic based on a set partitioning reformulation of the problem. We show how our approaches can be used to deal with additional constraints and various minmax objectives common to the above-mentioned applications, solving a broad class of parallel machine scheduling problems. In a series of computational tests both on instances from the literature and on newly generated ones, our exact method is shown to solve most problems within a few minutes to optimality, while our heuristic can solve particularly challenging instances with tight time windows well in acceptable time.

A two-phase stochastic programming approach to biomass supply planning for combined heat and power plants

Abstract: Due to the new carbon neutral policies, many district heating operators start operating their combined heat and power plants using different types of biomass instead of fossil fuel The contracts with the biomass suppliers are negotiated months in advance and involve many uncertainties from the energy producer’s side The demand for biomass is uncertain at that time, and heat demand and electricity prices vary drastically during the planning period Furthermore, the optimal operation of combined heat and power plants has to consider the existing synergies between the power and heating systems We propose a solution method using stochastic optimization to support the biomass supply planning for combined heat and power plants Our two-phase approach determines mid-term decisions about biomass supply contracts as well as short-term decisions regarding the optimal production of the producer to ensure profitability and feasibility We present results based on ten realistic test cases placed in two municipalities

Endogenous stochastic optimisation for relief distribution assisted with unmanned aerial vehicles

Abstract: Unmanned aerial vehicles (UAVs) have been increasingly viewed as useful tools to assist humanitarian response in recent years While organisations already employ UAVs for damage assessment during relief delivery, there is a lack of research into formalising a problem that considers both aspects simultaneously This paper presents a novel endogenous stochastic vehicle routing problem that coordinates UAV and relief vehicle deployments to minimise overall mission cost The algorithm considers stochastic damage levels in a transport network, with UAVs surveying the network to determine the actual network damages Ground vehicles are simultaneously routed based on the information gathered by the UAVs A case study based on the Haiti road network is solved using a greedy solution approach and an adapted genetic algorithm Both methods provide a significant improvement in vehicle travel time compared to a deterministic approach and a non-assisted relief delivery operation, demonstrating the benefits of UAV-assisted response

A long-term unit commitment problem with hydrothermal coordination for economic and emission control in large-scale electricity systems

Abstract: The paper describes a long-term scheduling problem for thermal power plants and energy storages. In addition, renewable energy sources are integrated by considering the residual demand. Besides the classical minimization of the production costs, emission-related costs are taken into account. Thereby, emission costs are determined by market prices for $$\hbox {CO}_2$$ emission certificates (i.e., using the EU emissions trading system). For the proposed unit commitment problem with hydrothermal coordination for economic and emission control, an enhanced mixed-integer linear programming model is presented. Moreover, a new heuristic approach is developed, which consists of two solution stages. The heuristic first performs an isolated dispatching of thermal plants. Then, a re-optimization stage is included in order to embed activities of energy storages into the final solution schedule. The considered approach is able to find outstanding schedules for benchmark instances with a planning horizon of up to one year. Furthermore, promising results are also obtained for large-scale real-world electricity systems. For the German electricity market, the relationship of $$\hbox {CO}_2$$ certificate prices and the optimal thermal dispatch is illustrated by a comprehensive sensitivity analysis.

Gradual cover competitive facility location

Abstract: A new gradual cover competitive facility location model is proposed and tested. In cover competitive models, it is assumed that up to a certain distance a demand point is attracted to a facility and beyond this distance it is not. The decline in attraction and cover is abrupt. It is either 0 or 1. We propose a gradual decline in attraction from 1 to 0. As the distance increases the attraction and cover decline. The buying power captured by a facility cannot exceed its attraction level, and the total buying power captured by all facilities cannot exceed the buying power available at the demand point. The single-facility location is optimally solved. The largest problem of 1000 demand points is solved in less than one second. The multiple facility version is solved by SNOPT and other solvers.

Evacuation dynamics: a modeling and visualization framework

Abstract: Evacuation mock drills are critical to emergency preparedness and to stress test the infrastructure capacity. Even though drills are expensive in terms of the involved resources, recognizing critical points of the infrastructure can guide decisions to improve the dynamics during a real evacuation, resulting in saving lives. In this paper, we present a modeling and visualization framework that provides useful insight and information of the evacuation dynamics to the decision makers of complex facilities. Using an optimization-based simulation approach, the framework recreates real evacuation scenarios, provides useful statistics of the evacuation dynamics, and allows for what-if analyses. To do so, our framework solves multiple linear optimization models with an underlying network structure that models the topography and resources of the given facility. A dual analysis of the optimization model allows us to identify critical points during an evacuation. In addition, the framework integrates with geographical information systems to produce rich visualizations of the evacuation dynamics. To illustrate the application of this framework, we evaluate two real evacuation scenarios on a university campus, located in Bogota (Colombia), and provide insight to improve the decisions taken by the campus administration.

Balancing partner preferences for logistics costs and carbon footprint in a horizontal cooperation

Abstract: Horizontal cooperation in logistics has gathered momentum in the last decade as a way to reach economic as well as environmental benefits. In the literature, these benefits are most often assessed by aggregating all demand and then optimizing the supply chain at the level of the coalition. However, such an approach ignores the individual preferences of the participating companies and forces them to agree on a unique coalition objective. Companies with different (potentially conflicting) preferences could improve their individual outcome by diverging from this joint solution. In order to prevent such individualistic behavior, we propose an optimization framework that explicitly accounts for the individual partners’ interests. In the models presented in this paper, all partners are allowed to specify their preferences regarding the decrease in logistical costs versus reduced CO $$_{2}$$ emissions. Consequently, all stakeholders are more likely to accept the solution, and the long-term viability of the collaboration is improved. The contribution of our work is threefold. First, we formulate a multi-partner multi-objective location-inventory model. Second, we distinguish two approaches to solve such a multi-partner multi-objective optimization problem, each focusing primarily on a single dimension. The result is a set of Pareto-optimal solutions that support the decision and negotiation process. Third, we propose and compare three different solution techniques to construct a unique solution which is fair and efficient for the coalition. Our numerical experiments not only confirm the potential of collaboration but—more importantly—also reveal valuable managerial insights on the effect of dissimilarities between partners with respect to size, geographical overlap and operational preferences.

Bi-objective optimization problems with two decision makers: refining Pareto-optimal front for equilibrium solution

Abstract: The Pareto-optimality concept in multi-objective optimization theory is different from the Nash equilibrium concept in noncooperative game theory. When the objective holders are independent decision makers, i.e., human entities or organizations, any solution on the Pareto-optimal front is not necessarily an equilibrium point, hence not a valid solution. The solution has to be a Pareto-optimal-equilibrium (POE) point. In this paper, we convert a bi-objective optimization problem into a two-player game problem by introducing “induced games,” and we propose a new refinement method to find a POE point. We prove that at least one such POE point exists for a class of linear bi-objective optimization problems, and we develop an algorithm to find it. We discuss that the innovative approach considered in this paper is of real future interest to some industrial and social applications. One such example is also presented.

A column generation-based decomposition and aggregation approach for combining orders in inland transportation of containers

Abstract: A significant portion of the total cost of the intermodal transportation is generated from the inland transportation of containers. In this paper, we design a mixed integer linear programming (MILP) model for combining orders in the inland, haulage transportation of containers. The pickup and delivery process of both 20 and 40 foot containers from the terminals to the customer locations and vice versa are optimized using heterogeneous fleet consisting of both 20 ft and 40 ft trucks/chasses. Important operational constraints such as the time window at order receivers, the payload weight of containers and the regulation of the working hours are considered. Based on an assignment problem structure, this MILP solves efficiently to optimality for problems with up to 120 orders. To deal with larger instances, a decomposition and aggregation heuristic is designed. The basic idea of this approach is to decompose order locations geographically into fan-shaped subareas based on the angle of the order location to the port baseline, and solve the sub problems using the proposed MILP model. To balance the fleet size amongst all subgroups, column generation is used to iteratively adjust the number of allocated trucks according to the shadow-price of each truck type. Based on decomposed solutions, orders that are “fully” combined with others are removed and an aggregation phase follows to enable wider combination choices across subgroups. The decomposition and aggregation solution process is tested to be both efficient and cost-saving.

The multi-mode resource investment problem: a benchmark library and a computational study of lower and upper bounds

Abstract: The multi-mode resource investment problem (MRIP) is the multi-mode extension of the resource investment problem, which is also known under the name resource availability cost problem. It is a project scheduling problem with a given due date as well as precedence and resource constraints. The goal is to find a precedence feasible schedule that minimises the resource costs of the allocated resources. To compute these costs, the maximum resource peak is considered regarding renewable resource types, whereas the sum of allocated nonrenewable resource units is used in the case of nonrenewable resources. Many practical and complex project scheduling settings can be modelled with this type of problem. Especially with the usage of different processing modes, time and cost compromises can be utilised by the project manager. In the literature, some procedures for the MRIP have been investigated; however, the computational experiments in these studies have not been carried out on common benchmark instances. This makes a fair comparison of methods difficult. Therefore, we generated novel instances specifically designed for this problem and published them on the website https://riplib.hsu-hh.de . On this website, the instances as well as best-known solution values are available and researchers can also contribute their findings. We investigate these novel instances by proposing and evaluating lower bounds for the MRIP. Additionally, we analyse the proposed instances by applying heuristic as well as exact methods. These experiments suggest that most of the instances are challenging and further research is needed. Finally, we show some computational complexity properties of the NP-hard MRIP.

Mathematical models to improve the current practice in a Home Healthcare Unit

Abstract: This paper addresses a home healthcare routing problem in which doctors and nurses visit patients at their homes to provide services. We consider a real-world home healthcare service arising in a particular hospital in Spain. Doctors and nurses are distributed in teams and travel by taxi; taxis transport a pre-defined set of workers who travel together the whole route. The objective is to minimise the transportation costs related to the total taxi journey time, including travelling and waiting costs. The paper presents a mathematical model that considers these current policies and permits the problem to be solved optimally. The paper also explores, after reviewing the hospital’s current model, the benefits that can be obtained by changing some of the current policies of the hospital. In this way, a new model is proposed based on two sustainable strategies that can be extended to other home service fields: (1) workers can walk between houses and (2) the workers transported by a taxi may change during the route. A complex nonlinear mathematical model is presented, and a metaheuristic is designed to provide quality solutions. Computational tests on a set of instances based on real-world data estimate the gap between the solutions of both models.

Railway crew scheduling with semi-flexible timetables

Abstract: We investigate the impact of coordinating the timetable and the crew schedule in an operational freight railway system Usually, those problems are solved sequentially—resulting in suboptimal schedules for train drivers due to large idle times between two train rides We seek to coordinate the timetable and the crew schedule on the operational level by adding flexibility to the timetable We introduce small time windows that allow to shift entire trains forwards and backwards by discrete time periods We present a mathematical model and solve it with a column generation heuristic We test our model on three real datasets of a major European Freight Railway Operator and show that significant reduction in idle time and cost can be achieved

Strategyproof auction mechanisms for network procurement

Abstract: Deferred-acceptance auctions can be seen as heuristic algorithms to solve $${{\mathcal {N}}}{{\mathcal {P}}}$$ -hard allocation problems. Such auctions have been used in the context of the Incentive Auction by the US Federal Communications Commission in 2017, and they have remarkable incentive properties. Besides being strategyproof, they also prevent collusion among participants. Unfortunately, the worst-case approximation ratio of these algorithms is very low in general, but it was observed that they lead to near-optimal solutions in experiments on the specific allocation problem of the Incentive Auction. In this work, which is inspired by the telecommunications industry, we focus on a strategic version of the minimum Steiner tree problem, where the edges are owned by bidders with private costs. We design several deferred-acceptance auctions (DAAs) and compare their performance to the Vickrey–Clarke–Groves (VCG) mechanism as well as several other approximation mechanisms. We observe that, even for medium-sized inputs, the VCG mechanisms experiences impractical runtimes and that the DAAs match the approximation ratios of even the best strategy-proof mechanisms in the average case. We thus provide another example of an important practical mechanism design problem, where empirics suggest that carefully designed deferred-acceptance auctions with their superior incentive properties need not come at a cost in terms of allocative efficiency. Our experiments provide insights into the trade-off between solution quality and runtime and into the additional premium to be paid in DAAs to gain weak group-strategyproofness rather than just strategyproofness.

Coherent combination of probabilistic outputs for group decision making: an algebraic approach

Abstract: Current decision support systems address domains that are heterogeneous in nature and becoming progressively larger. Such systems often require the input of expert judgement about a variety of different fields and an intensive computational power to produce the scores necessary to rank the available policies. Recently, integrating decision support systems have been introduced to enable a formal Bayesian multi-agent decision analysis to be distributed and consequently efficient. In such systems, where different panels of experts independently oversee disjoint but correlated vectors of variables, each expert group needs to deliver only certain summaries of the variables under their jurisdiction, derived from a conditional independence structure common to all panels, to properly derive an overall score for the available policies. Here we present an algebraic approach that makes this methodology feasible for a wide range of modelling contexts and that enables us to identify the summaries needed for such a combination of judgements. We are also able to demonstrate that coherence, in a sense we formalize here, is still guaranteed when panels only share a partial specification of their model with other panel members. We illustrate this algebraic approach by applying it to a specific class of Bayesian networks and demonstrate how we can use it to derive closed form formulae for the computations of the joint moments of variables that determine the score of different policies.