Integer Linear Model Research Articles

Multi-resource constrained elective surgical scheduling with Nash equilibrium toward smart hospitals

This paper focuses on the elective surgical scheduling problem with multi-resource constraints, including material resources, such as operating rooms (ORs) and non-operating room (NOR) beds, and human resources (i.e., surgeons, anesthesiologists, and nurses). The objective of multi-resource constrained elective surgical scheduling (MESS) is to simultaneously minimize the average recovery completion time for all patients, the average overtime for medical staffs, and the total medical cost. This problem can be formulated as a mixed integer linear multi-objective optimization model, and the honey badger algorithm based on the Nash equilibrium (HBA-NE) is developed for the MESS. Experimental studies were carried out to test the performance of the proposed approach, and the performance of the proposed surgical scheduling scheme was validated. Finally, to narrow the gap between the optimal surgical scheduling solution and actual hospital operations, digital twin (DT) technology is adopted to build a physical-virtual hospital surgery simulation model. The experimental results show that by introducing a digital twin, the physical and virtual spaces of the smart hospital can be integrated to visually simulate and verify surgical processes.

A heuristic algorithm to improving the coil slitting process in the steel industry

Abstract The steel industry is constantly facing problems and challenges that require optimisation to improve the production process. We present an algorithm to address a major challenge, the slitting problem, for a specific Spanish company. This problem arises when large steel coils need to be cut into smaller strips. Given the highly heterogeneous stock (coils come from previous operations), selecting the most suitable coils and defining the cutting patterns become very complicated due to operational and customer constraints. The company aims to reduce the leftovers and increase the service level (the difference between the weight requested by the customer and the weight supplied). The algorithm is currently in production and was validated using the company’s data and compared with an exact model. Results significantly improved the company’s operations, achieving a 50% reduction in leftovers and a much better service level in minutes, as opposed to the hours the company previously required. Although there are Mixed Integer Linear Optimization models that provide an optimal solution in small cases, they are not a viable alternative for the company because they require excessive computational time (even, in some cases, to obtain feasible solutions) and use overly expensive commercial solvers.

Optimum design of wind turbine foundation according to rebar detailing

This research proposes a Mixed Integer Linear Programming model to assist structural engineers in the reinforcement detailing phase of circular foundations, with a specific focus on wind tower foundations, aiming to optimise the design process and, consequently, reduce the costs associated with constructing these elements. After analysing the internal forces in circular foundations, the designer must define the calculation sections to determine the required area of steel and select the diameter of the steel bars and their positioning in the base. This determination is often based on the designer's experience, which can lead to choices that unnecessarily increase costs, thus justifying the creation of a model to optimise this process. The proposed model consists of three phases: the first involves a non-linear regression to obtain an equation that represents the bending moments at any point in the foundation; the second applies a linear quadratic model to choose the ideal layout of the calculation sections; and the third uses a binary integer linear model to determine the ideal diameter of the bars and their consequent positioning. This search for optimality must comply with the restrictions imposed by normative criteria, including maximum bar lengths and rebar lap splices, maintaining good constructability based on standardisation. Validation tests were conducted with confirmed cases using the proposed model, resulting in an average reduction of 10.72 % in the value of the rebar weight due to the model's second stage and a decrease of 12.28 % in the best case during the final step. It can, therefore, be concluded that the proposed model is viable for application in circular foundation projects, leading to savings in the total weight of steel used in the foundations.

A two-echelon multi-trip vehicle routing problem with synchronization for an integrated water- and land-based transportation system

This study focuses on two-echelon synchronized logistics problems in the context of integrated water- and land-based transportation (IWLT) systems. The aim is to meet the increasing demand in city logistics as a result of the growth in transport activities, including parcel delivery, food delivery, and waste collection. We propose two models, a novel mixed integer linear joint model, and a logic-based Benders’ decomposition (LBBD) model, for a two-echelon problem under realistic settings such as multi-trips, time windows, and synchronization at the satellites with no storage and limited resource capacities. The objective is to optimize transfers and satellite assignments, thereby reducing overall logistics costs for street vehicles and vessels. Computational experiments demonstrate that the LBBD model is more robust in terms of solution quality and solution time on average while the added value of the LBBD is more evident when solving large-scale instances with 100 customers, reducing the overall costs by 10.6% on average and significantly reducing the fleet costs on both networks. Furthermore, we assess the effect of changing cost parameters and satellite locations in the proposed IWLT system–analyzing system behavior and suggesting potential improvements–and evaluate several system alternatives in city logistics–consisting of different transportation network designs (single- and two-echelon), vehicle types, and operational constraints. On average, the proposed two-echelon IWLT system reduces the number of kilometers traveled by vehicles at street level by ranging from 20% to 30% compared to a typical single-echelon service design that relies solely on trucks.

A Multi‐Trip Vehicle Routing Problem With Release Dates and Interrelated Periods

ABSTRACTThis article proposes a new multi‐trip vehicle routing problem variant, originally motivated by a practical application, namely a car components distribution to repair centers (warehouses). The problem is named the multi‐trip vehicle routing with release dates and interrelated periods (MTVRP‐RDIP). The routes may start at different pre‐defined periods, called departure periods, and may have different durations. Thus, two routes that start at different periods may be active at the same period, leading to the so‐called interrelated periods. Moreover, a route may only start at a period if a vehicle is available, and the availability of the vehicle depends not only on the existing vehicles but also on the active routes at that time period. The clients are classified according to their importance and represent warehouses that require car components that are made available throughout the time horizon, thus leading to the consideration of release dates. Delays in satisfying client orders and not serving orders in the time horizon result in penalty costs that must be minimized. The objective to minimize also includes routing costs and vehicle utilization costs. Two metrics are defined to compute an order's delay, each leading to a different mixed integer linear model. Computational results showed that one model clearly outperforms the other and even this one is only suited to address the smallest instances. A matheuristic based on a rolling‐horizon process that iteratively solves the better‐performing model with fewer periods was designed to tackle the largest instances. The matheuristic can provide feasible solutions for all test instances in an efficient manner that are, on average, better than the ones provided by the model in most of the compared key performance indicators.

Optimized Noise Suppression for Quantum Circuits

Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on noise characterization, mitigation, and suppression. Crucially, these methods must also be efficient in terms of their classical and quantum overhead. Here, we efficiently characterize and mitigate crosstalk noise, which is a severe error source in, for example, cross-resonance based superconducting quantum processors. For crosstalk characterization, we develop a simplified measurement experiment. Furthermore, we analyze the problem of optimal experiment scheduling and solve it for common hardware architectures. After characterization, we mitigate noise in quantum circuits by a noise-aware qubit routing algorithm. Our integer programming algorithm extends previous work on optimized qubit routing by swap insertion. We incorporate the measured crosstalk errors in addition to other, more easily accessible noise data in the objective function. Furthermore, we strengthen the underlying integer linear model by proving a convex hull result about an associated class of polytopes, which has applications beyond this work. We evaluate the proposed method by characterizing crosstalk noise for two chips with up to 127 qubits and leverage the resulting data to improve the approximation ratio of the Quantum Approximate Optimization Algorithm by up to 10% compared with other established noise-aware routing methods. Our work clearly demonstrates the gains of including noise data when mapping abstract quantum circuits to hardware native ones. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue on Quantum Computing. Funding: This work was supported by Bavarian state government; Bayerische Staatsministerium für Wirtschaft, Landesentwicklung und Energie. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0551 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0551 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Data-driven collaborative healthcare resource allocation in pandemics

Severe shortages of healthcare resources are major challenges in pandemics, especially in their early stages. To improve emergency management efficiency, this paper proposes a novel rolling predict-then-optimize framework that includes three interactive modules, i.e., data-driven demand prediction, healthcare resource allocation, and parameter rolling update. Such a framework uses historical data to dynamically update the control parameters of the proposed Net-SEIHRD model, which predicts the healthcare needs of each region by jointly considering government interventions and cross-regional travel behaviors. Based on the forecasted healthcare resource demand in real-time, an optimization model is then formulated to realize coordinated resource allocation across multiple regions by minimizing the total generalized cost. To facilitate model solving, the proposed mixed integer nonlinear programming model is converted into an equivalent mixed integer linear model by using some linearization techniques. Finally, the proposed method is applied to the SARS-CoV-2 emergency response and collaborative allocation of healthcare resources in Shanghai, China. The results show that the proposed prediction model can effectively predict the peak and scale of the spread of the virus. Compared with the traditional LM and SEIHR models, the prediction accuracy of the Net-SEIHRD model is improved by 10.76% and 24.11%, respectively. Moreover, coordinated relief activities across regions, such as patient transfer and drug-sharing can improve the efficiency of pandemic control and save social costs.

Modelling and optimization of a distributed flow shop group scheduling problem with heterogeneous factories

In this paper, we solve a distributed flow shop group scheduling problem with heterogeneous factories, which we call the distributed heterogeneous flow shop group scheduling problem (DHFGSP). The objective is to minimize the energy consumption cost of the critical factory (the factory with the highest energy consumption cost among all factories). Although the DHFGSP is very meaningful for today’s production situation, it has not captured attention so far. Firstly, in this paper, a mixed integer linear model is developed. Secondly, four heuristic methods are presented based on specific scheduling rules and energy consumption cost criteria features. Thirdly, an effective iterative greedy algorithm based on Q-learning (Q_PIG) is proposed. In the Q_PIG, a family ordering rule is proposed to exchange with families in other factories to explore better quality solutions during the local search. Moreover, a Q-learning algorithm is embedded to select operations (family operations or job operations) for the current solution. The embedding of Q-learning enables the current solution to execute high-quality operations. Comprehensive experiments show that the Q_PIG is very effective for the problem solved.

Planning municipal drainage infrastructure maintenance operations with finite available crews: pragmatic optimization approach

This paper proposes a streamlined approach to addressing the problem of allocating finite crew resources to concurrent jobs in the context of municipal drainage infrastructure maintenance. The problem was defined from the perspective of a project manager involved in planning such operations on a day-by-day basis. The problem statement was then transformed into a simplified Integer Linear Programming optimization model. Performance metrics were devised to evaluate the optimization model’s effectiveness. A heuristic algorithm representing the decision-making process by a seasoned planner in the partner company was also developed. Both methods were applied to a case study and contrasted based on the same performance metrics. The findings underscored substantial optimization benefits in rendering decision support in resource-constrained drainage construction operations planning. In conclusion, this research presents an alternative strategy for navigating the complexities inherent in finite crew resource allocation on multiple concurrent drainage projects; lends a cost-effective optimization solution to improving the utilization of finite available crews while satisfying service demands from multiple clients to the largest extent possible.

Fixed Automated stations location and UAVs routing problems in urban road Networks: A tailored Branch-&-price algorithm

Unmanned aerial vehicles (UAVs) serve as vital tools for collecting real-time traffic data, enabling rapid responses to events, and optimizing traffic management based on their cost-effectiveness, high flexibility, and wide coverage range advantages. The urban UAV cruising problem primarily focuses on selecting the locations of fixed automated station (FAS) and optimizing UAVs’ cruising routes. This paper introduces a strategy where UAVs can take off and land on different FASs to enhance urban UAVs’ cruising efficiency. Firstly, the problem is formulated as an integrated linear integer model (FU-ILP) which simultaneously determines the locations of FASs and the routes of UAVs. The objective is to minimize redundant cruising distance and cruising cycle time. The FU-ILP model takes into account UAV‘s flight capabilities, FAS’s signal coverage range, power requirements, and battery charging. Moreover, we design a tailored branch-and-price (TB&P) algorithm to decompose the FU-ILP model, which can reduce the variable scale for solving larger-scale cases. Finally, we test the model and the algorithm on the Sioux Falls Test Network. The TB&P algorithm improves computational efficiency by nearly 80%. Moreover, our strategy yields superior results compared to the strategy where UAVs must return to their take-off FASs for recharging. We also demonstrate that increasing the number of UAVs does not reduce redundant cruising distance in the whole network, but it can shorten the cruising cycle. These policy conclusions also apply to the case of Xiongan. This provides a basis for managers to calculate the minimum UAV’s configuration based on the cities’ actual cruising frequency requirements.

Low-carbon operation strategy of virtual power plant considering progressive demand response

Adapting virtual power plants (VPPs) to the development of new power systems has gradually become a trend. Meanwhile, the economical and effective use of demand-side resources in VPPs has become a research hotspot in the field of new energy. This paper proposes a low-carbon operation strategy with progressive demand response (DR). A DR model id established by evaluating the scheduling potential of low-carbon and flexible loads and the DR transfer of different users motivated by incentive mechanisms. Because the changing carbon price in carbon trading also affects the response transfer amount, it is beneficial to reduce the operating cost of the energy system by using consumers’ surplus value according to consumer psychology to guide energy users to participate in DR. Finally, wind, light, user load data and VPP internal unit output are optimized in rolling mode over multiple time scales, and the optimal adjustment results of the previous day are taken as the basis. At the same time, the output deviation penalty function is added to further reduce the system cost. The nonlinear model of DR cost is transformed into a mixed integer linear model, which is modeled on MATLAB software and solved by a CPLEX optimization solver. The case analysis shows that the progressive DR strategy may increase the total operating cost of the system, but reduce the cost of the carbon emission. The proposed model and method can not only improve the feasibility and effectiveness of market supervision strategy, but also provides a useful reference for operators and demand-side users in energy systems to choose strategies.

A robust optimisation approach of train timetabling for freight transportation using high-speed railway

To ensure reliable services for high-speed freight rail transport, we address the issue of robust freight train timetabling by incorporating buffer times. Unlike passenger trains with prescribed timetables, high-speed freight train timetables need to be scheduled from the beginning and integrated into existing passenger schedules. To achieve reliable high-speed rail freight services, we introduce robust parameters that determine the buffer times for train operations and station stops. Using these, we develop an integer linear robust model aimed at maximizing timetable robustness, considering given control parameters, while minimizing travel and deviation times. We employ an integer Benders decomposition algorithm to solve this model efficiently. Our robust optimization method is validated through experiments using data from the Chengdu-Chongqing high-speed railway, demonstrating the efficacy and efficiency of our model and algorithm, especially in balancing efficiency and robustness.

A dynamic bi-objective optimization model for a closed loop supply chain design under environmental policies

Given the increasing focus on sustainability and environmental policy constraints, companies are required to redesign their supply chains. This paper explores the optimization of a closed loop supply chain (CLSC) network under both economic and environmental considerations. To achieve this, a bi-objective mixed integer linear model was developed. The proposed model identifies the optimal selection of CLSC facilities and manages both forward and reverse flows between them. The economic objective is reached by minimizing the total CLSC costs, while the environmental objective is satisfied by reducing CO2 emissions throughout the network. Products can be returned throughout their entire life cycle, which is why our model incorporates a dynamic aspect by considering product life cycle phases as time periods for the decision horizon. The model was tested through numerical experiments using a meta-heuristic approach based on the non-dominated sorting genetic algorithm NSGA-II. This algorithm produces a set of Pareto-optimal solutions that balance both objectives effectively. The results showed good performance in terms of computational time and optimization. Pareto solutions offered various options for managers and decision makers aiming for a sustainable closed loop supply chain design.

Predicting disease recurrence in patients with endometriosis: an observational study

BackgroundDespite surgical and pharmacological interventions, endometriosis can recur. Reliable information regarding risk of recurrence following a first diagnosis is scant. The aim of this study was to examine clinical and survey data in the setting of disease recurrence to identify predictors of risk of endometriosis recurrence.MethodsThis observational study reviewed data from 794 patients having surgery for pelvic pain or endometriosis. Patients were stratified into two analytic groups based on self-reported or surgically confirmed recurrent endometriosis. Statistical analyses included univariate, followed by multivariate logistic regression to identify risk factors of recurrence, with least absolute shrinkage and selection operator (Lasso) regularisation. Risk-calibrated Supersparse Linear Integer Models (RiskSLIM) and survival analyses (with Lasso) were undertaken to identify predictive features of recurrence.ResultsSeveral significant features were repeatedly identified in association with recurrence, including adhesions, high rASRM score, deep disease, bowel lesions, adenomyosis, emergency room attendance for pelvic pain, younger age at menarche, higher gravidity, high blood pressure and older age. In the surgically confirmed group, with a score of 5, the RiskSLIM method was able to predict the risk of recurrence (compared to a single diagnosis) at 95.3% and included adenomyosis and adhesions in the model. Survival analysis further highlighted bowel lesions, adhesions and adenomyosis.ConclusionsFollowing an initial diagnosis of endometriosis, clinical decision-making regarding disease management should take into consideration the presence of bowel lesions, adhesions and adenomyosis, which increase the risk of endometriosis recurrence.

Efficiency-oriented vehicle relocation of shared autonomous electric fleet in station-based car-sharing system

Long waiting delays for users and significant imbalances in vehicle distribution are bothering traditional station-based one-way electric car-sharing system operators. To address the problems above, a “demand forecast-station status judgement-vehicle relocation” multistage dynamic relocation algorithm based on the automatic formation cruising technology was proposed in this study. In stage one, a novel trip demand forecast model based on the long short-term memory network was established to predict users' car-pickup and car-return order volumes at each station. In stage two, a dynamic threshold interval was determined by combining the forecast results with the actual vehicle distribution among stations to evaluate the status of each station. Then vehicle-surplus, vehicle-insufficient, vehicle-normal stations, and the number of surplus or insufficient vehicles for each station were counted. In stage three, setting driving mileage and carbon emission as the optimization objectives, an integer linear programming mathematical model was constructed and the optimal vehicle relocation scheme was obtained by the commercial solver Gurobi. Setting 43 stations and 187 vehicles in Jiading District, Shanghai, China, as a case study, results showed that rapid vehicle rebalancing among stations with minimum carbon emissions could be realized within 15 min and the users’ car-pickup and car-return demands could be fully satisfied without any refusal.

A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy

PurposeThis paper aims at developing a multi-objective mathematical model of circular economy that integrates key concept of leasing as a strategy in addition to reuse, refurbishing, primary recycling, secondary recycling and disposal.Design/methodology/approachThis paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.FindingsThe results show that the leasing of the products improves the economic function in addition to the known environmental improvements. The proposed model also shows that the circular economy can generate the jobs for the unskilled people at different locations.Research limitations/implicationsThe proposed model can be further improved by considering the non-linearity due to economy of scale at various centers and in transportation. The model can be further extended to make it multi-period model.Practical implicationsThe proposed model of circular economy can be used by the organizations as a policy tool to decide the optimum number of collection centers, disassembly centers, refurbishing centers, recycling centers and disposal centers and their optimum locations and allocations. The organizations can also trade-off among economic, environmental and social benefits of their proposed decisions in circular economy.Originality/valueThe originality of the proposed mathematical model is consideration of leasing as a strategy to have better control over the supply chain for circularity; considering the training of unskilled people for backward supply chain jobs and accounting for primary recycling and secondary recycling separately for economical computation.

Multi-objective optimization for perishable product dispatch in a FEFO system for a food bank single warehouse

One of the main challenges of food bank warehouses in developing countries is to determine how to allocate perishable products to beneficiary agencies with different expiry dates while ensuring food safety, meeting nutritional requirements, and minimizing the shortage. The contribution of this research is to introduce a new multi-objective, multi-product, and multi-period perishable food allocation problem based on a single warehouse management system for a First Expired-First Out (FEFO) policy. Moreover, it incorporates the temporal aspect, guaranteeing the dispatch of only those perishable products that meet the prescribed minimum quality standards. A weighted sum approach converts the multi-objective problem of minimizing a vector of objective functions into a scalar problem by constructing a weighted sum of all the objectives. The problem can then be solved using a standard constrained optimization procedure. The proposed mixed integer linear model is solved by using the CPLEX solver. The solution obtained from the multi-objective problem allows us to identify days and products experiencing shortages. In such cases, when there is insufficient available inventory, the total quantity of product to be dispatched is redistributed among beneficiaries according to a pre-established prioritization. These redistributions are formulated as integer programming problems using a score-based criterion and solved by an exact method based on dynamic programming. Computational results demonstrate the applicability of the novel model for perishable items to a real-world study case.

Integrated corridor management by cooperative traffic signal and ramp metering control

AbstractThis paper formulates a cooperative traffic control methodology that integrates traffic signal timing and ramp metering decisions into an optimization model to improve traffic operations in a corridor network. A mixed integer linear model is formulated and is solved in real time within a model predictive controller framework, where the cell transmission model is used as the system state predictor. The methodology is benchmarked in a case study corridor in San Mateo, CA, in VISSIM with two optimization scenarios, namely, optimal metering and optimal signal control, and two simulation scenarios with a preset metering plan and no metering. The numerical results show that integrated traffic signal and ramp metering control reduces delays, stops, and travel times of the corridor by up to 33.1%, 36%, and 16.4%, respectively, compared to existing benchmark conditions. With appropriate weights prioritizing freeway or arterial street operations, the integrated control balances traffic congestion between the arterial street and the freeway.

Design of a mathematical model for staff planning in an emergency department

The emergency department plays a fundamental role in hospitals and critically affects a hospital's overall efficiency. Inadequate staff planning in emergency departments generates high costs, overcrowding, and patient dissatisfaction due to long waiting times, possibly putting the patient's health and life at risk. This research designed two mixed integer linear programming mathematical models. The first determined the optimal number of physicians required per shift and weekday in an adult emergency department to minimize the deviation between available and required capacity. The results of the optimization model would reduce by 16.07 % the required medical office staff per week, from 56 physicians in the current situation to 47, reducing staffing costs without impacting waiting times. Moreover, the overall physician utilization would be 95.01 % compared to 77.79 % in the current situation, indicating an adequate distribution of physicians on each shift of each day according to patient demand. These results contribute to the problem of high medical staff costs and overcrowding without sacrificing timeliness and quality of care. In contrast, the second model that minimized the number of physicians considering capacity constraints would increase the staff by 7.14 % concerning the current situation. This research was based on a model presented in the literature, but the objective function included the deviation variables as unrestricted in sign and a constraint to ensure that they were positive. The first model designed is presented as a tool to support emergency department managers in the medium-term planning of medical staff, ensuring an optimal solution to this problem

A Forward–Backward Simheuristic for the Stochastic Capacitated Dispersion Problem

In an effort to balance the distribution of services across a given territory, dispersion and diversity models typically aim to maximize the minimum distance between any pair of facilities. Specifically, in the capacitated dispersion problem (CDP), each facility has an associated capacity or level of service, and the objective is to select a set of facilities so that the minimum distance between any pair of them (dispersion) is maximized, while ensuring a user-defined level of service. This problem can be formulated as a linear integer model, where the sum of the capacities of the selected facilities must match or exceed the total demand in the network. Real-life applications often necessitate considering the levels of uncertainty affecting the capacity of the nodes. Failure to account for this uncertainty could lead to low-quality or infeasible solutions in practical scenarios. However, research addressing the stochastic version of the CDP is scarce. This paper introduces two models for the CDP with stochastic capacities, incorporating soft constraints and penalty costs for violating the total capacity constraint. The first model includes a probabilistic constraint to ensure the required level of service with a certain probability, while the second model introduces a soft constraint with penalty costs for violations. To solve both variants of the model, a forward–backward simheuristic algorithm is proposed. Our approach combines a metaheuristic algorithm with Monte Carlo simulation, enabling the efficient handling of the random behavior of node capacities and obtaining reliable solutions regardless of their probability distribution.