Integer Programming Research Articles

Strategy for optimizing outpatient access for chronic patients in a health insurance company

ABSTRACT The last decades have been marked by significant population transformations in several nations. The demographic transition, resulting from the significant reduction in birth rates and the increase in life expectancy, has resulted in a further ageing population. Knowing how to prioritize and optimize the allocation of resources becomes, therefore, a prerequisite for managers decision-making. Strategies that reduce hospital costs while improving the quality of care are essential for the sector, mainly because they allow integrated processes and greater accessibility to users. Proximity and ease of access to health services are essential to ensure continuity of care and improve patient engagement with suggested treatment. The objective of this article is to demonstrate a viable solution for the allocation of chronic patients in the outpatient units of a Brazilian health insurance company in a regionalized manner and based on a set of criteria and restrictions. The study used Integer Programming, an optimization technique of Operations Research, to determine the outpatient units. As a result, it was possible to identify and suggest practical improvements in the care coordination process, offering a concrete contribution to the effectiveness and operational efficiency of the decision-making process.

Multi-objective intermodal transportation planning with real-life application

ABSTRACT This paper explores the optimal route selection problem within an intermodal transportation network that comprises road, rail, sea, and inland waterways. Initially, we propose a multi-objective integer linear programming model that aims to minimize total cost, transport time, and carbon emissions. Subsequently, we apply two multi-objective programming approaches: Fuzzy Goal Programming and Compromise Programming. These approaches are implemented in a real-life case study, aiming to determine the optimal intermodal transportation route from Türkiye (Denizli) to Germany (Duisburg). Four out of the six methods suggest the same road and maritime pathway. Furthermore, this model has the potential to aid decision-makers in selecting routes based on customer requirements and serve as a valuable tool for policymakers in establishing an efficient intermodal transport network.

Optimization on linear integer programming model for a grain multimodal transport system

Optimization on linear integer programming model for a grain multimodal transport system

Traveling Salesman Problem with Backend Information Processing

This paper introduces the Traveling Salesman Problem (TSP) with Backend Information Processing (bTSP), which integrates backend processing times into path planning to minimize the makespan. The study develops a mixed integer linear programming formulation and conducts a theoretical analysis to understand the relationship between the TSP and the bTSP. The results show that an optimal solution for the bTSP can be efficiently derived by leveraging the connection to the standard TSP.

Faster Integer Programming

A new analysis proves that all integer programs theoretically could be solved much faster than previously guaranteed.

Addressing staffing challenges through improved planning: Demand-driven course schedule planning and instructor assignment in higher education

This paper presents a novel decision support system (DSS) to address the University Course Timetabling Problem (UCTP). The solution decomposes the NP-complete UCTP into two sub-problems, allowing a structured approach to addressing the complexities inherent in the UCTP process. A mixed integer linear programming (MILP) model is proposed to integrate academic year course schedule planning and instructor assignment, accommodating various constraints to meet student demands. The model optimizes the number of course sections and strategically schedules instructors, aiming to reduce the number of new and distinct courses assigned to them. Historical data from an academic department encompassing multiple disciplines, including Computer Information Systems, Business Management, and Business Analytics, at a large public university in the U.S. is used to develop the model, and the results are compared with the actual course schedule and instructor assignment. The results demonstrate that the proposed DSS would result in a 14 % reduction in the number of course sections offered, translating to approximately $130,000 in annual savings. Additionally, it could significantly reduce the number of new courses assigned to instructors by up to 81 % and the number of distinct course sections assigned to them by 29 %.

Adaptive large-neighbourhood search for optimisation in answer-set programming

Answer-set programming (ASP) is a prominent approach to declarative problem solving that is increasingly used to tackle challenging optimisation problems. We present an approach to leverage ASP optimisation by using large-neighbourhood search (LNS), which is a meta-heuristic where parts of a solution are iteratively destroyed and reconstructed in an attempt to improve an overall objective. In our LNS framework, neighbourhoods can be specified either declaratively as part of the ASP encoding or automatically generated by code. Furthermore, our framework is self-adaptive, i.e., it also incorporates portfolios for the LNS operators along with selection strategies to adjust search parameters on the fly. The implementation of our framework, the system ALASPO, currently supports the ASP solver clingo, as well as its extensions clingo-dl and clingcon that allow for difference and full integer constraints, respectively. It utilises multi-shot solving to efficiently realise the LNS loop and in this way avoids program regrounding. We describe our LNS framework for ASP as well as its implementation, discuss methodological aspects, and demonstrate the effectiveness of the adaptive LNS approach for ASP on different optimisation benchmarks, some of which are notoriously difficult, as well as real-world applications for shift planning, configuration of railway-safety systems, parallel machine scheduling, and test laboratory scheduling.

Model Predictive Control of a Stand-Alone Hybrid Battery-Hydrogen Energy System: A Case Study of the PHOEBUS Energy System

Model predictive control is a promising approach to robustly control complex energy systems, such as hybrid battery-hydrogen energy storage systems that enable seasonal storage of renewable energies. However, deriving a mathematical model of the energy system suitable for model predictive control is difficult due to the unique characteristics of each energy system component. This work introduces mixed integer linear programming models to describe the nonlinear multidimensional operational behavior of components using piecewise linear functions. Furthermore, this paper develops a new approach for deriving a strategy for seasonal storage of renewable energies using cost factors in the objective function of the optimization problem while considering degradation effects. An experimentally validated simulation model of the PHOEBUS Energy System is utilized to compare the performance of two model predictive controllers with a hysteresis band controller such as utilized for the real-world system. Furthermore, the sensitivity of the model predictive controller to the prediction horizon length and the temporal resolution is investigated. The prediction horizon was found to have the highest impact on the performance of the model predictive controller. The best-performing model predictive controller with a 14-day prediction horizon and perfect foresight increased the total energy stored at the end of the year by 18.9% while decreasing the degradation of the electrolyzer and the fuel cell.

Solving a class of two-stage stochastic nonlinear integer programs using value functions

Solving a class of two-stage stochastic nonlinear integer programs using value functions

Optimizing supply chain networks using mixed integer linear programming (MILP)

Mixed Integer Linear Programming (MILP) has emerged as a powerful tool for optimizing complex supply chain networks. This paper explores the theoretical foundations of MILP, including the integration of integer variables and advanced solution techniques such as branch-and-bound and branch-and-cut algorithms. Through detailed modeling of production planning, network design, and transportation logistics, MILP enables companies to achieve significant cost reductions and operational efficiencies. We present case studies from retail, manufacturing, and pharmaceutical sectors to illustrate the practical applications of MILP. These examples demonstrate how MILP optimization can lead to reductions in production and inventory costs, improved customer satisfaction, and enhanced service levels. The findings underscore the value of MILP in addressing the multifaceted challenges of modern supply chain management.

Optimizing supply chain networks using mixed integer linear programming (MILP)

Mixed Integer Linear Programming (MILP) has emerged as a powerful tool for optimizing complex supply chain networks. This paper explores the theoretical foundations of MILP, including the integration of integer variables and advanced solution techniques such as branch-and-bound and branch-and-cut algorithms. Through detailed modeling of production planning, network design, and transportation logistics, MILP enables companies to achieve significant cost reductions and operational efficiencies. We present case studies from retail, manufacturing, and pharmaceutical sectors to illustrate the practical applications of MILP. These examples demonstrate how MILP optimization can lead to reductions in production and inventory costs, improved customer satisfaction, and enhanced service levels. The findings underscore the value of MILP in addressing the multifaceted challenges of modern supply chain management.

Research on Topology Optimization of Building Digital Supply Chain Based on Genetic Neural Network

In order to maximize the benefit of building supply chain, the topology optimization method of building digital supply chain based on genetic neural network is studied. According to the overall structural characteristics of the building digital supply chain, customer demand data, supplier sales data, manufacturer production management data, and environmental policy exception data are collected to form a building digital supply chain data set. As input data, a building digital supply chain demand prediction model based on improved genetic LSTM neural network is constructed. Capture the needs of the building digital supply chain; according to the demand of suppliers, manufacturers and customers in building digital supply chain, a nonlinear 0–1 mixed integer programming model based on the newsboy model is established. According to the various information provided by the supplier, the ant colony algorithm is used to calculate the optimal supplier. After all suppliers are identified, the topology of the digital supply chain is constructed. So far, the optimization of the supply chain has been completed. The experimental data show that this method can accurately predict the demand of construction projects, the maximum error is less than 1.5%, and can obtain the best supplier selection results. Compared with before optimization, the profit of the structural digital supply chain after topology optimization increases the most.

Robustness-Based Approach for Slack Time Optimization in Tram Timetables

AbstractConsidering the unique interplay of trams with road traffic, this study explored the issue of instability in tram operations—a prominent medium-capacity rail transit. Our goal was to design a timetable slack time optimization method for scheduling slack time to improve the stability of tram operations. To facilitate this, we derived the travel/dwelling time distribution from historical data, which assisted in estimating interference times and evaluating the requisite slack time. We then developed an integer programming model to calculate both the punctuality rate and expected delay under varying travel times, enabling the creation of alternative slack time schemes. Using a unique tram operation simulation logic, we assessed the operational efficiency and reliability of these alternate schemes based on specific operational indicators. The results suggest that our novel approach to timetable optimization significantly enhances the tram’s adaptability to disruptions, directly improving the passenger experience and tram competitiveness. This work offers a robust framework for timetable optimization for semi-independent right-of-way public transportation.

On the Complexity of Proving Polyhedral Reductions

We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer constraints between the marking of places. In addition to defining an automated proof method, this paper aims to better characterize polyhedral reductions, and to give an overview of their application to reachability problems. Our approach relies on encoding the equivalence problem into a set of SMT formulas whose satisfaction implies that the equivalence holds. The difficulty, in this context, arises from the fact that we need to handle infinite-state systems. For completeness, we exploit a connection with a class of Petri nets, called flat nets, that have Presburger-definable reachability sets. We have implemented our procedure, and we illustrate its use on several examples.

Typical daily scenario extraction method based on key features to promote building renewable energy system optimization efficiency

Given its intrinsic volatility and randomness, the effective design of a building renewable energy system (BRES) necessitates long-period, short-step boundaries. Nevertheless, this poses computational burdens. In this context, time-series aggregation (TSA) emerges as a valuable approach, which involves obtaining a set of typical scenarios to substitute original time series. Numerous studies have focused on mathematical algorithms to minimize the deviation between typical scenarios and original time series. However, the premise of enhancing model-solving efficiency by extracting typical scenarios is to ensure the optimality of planning. Henceforth, identifying and quantifying key features in the original time series that significantly influence the planning, and further extracting need to be addressed. This paper proposes a typical day extraction method based on key features, named the feature-based method. Key features are summarized through an extensive literature review and then quantitatively expressed through different indicator models. Finally, a feature-based mixed integer linear programming (MILP) model is established for extraction. To evaluate the effectiveness of the feature-based method, it is applied to design a BRES and compared with traditional TSA methods such as Averaging Method (AM) and k-means. Results indicate that the feature-based method can effectively retain key features, thereby achieving more efficient and accurate designs.

Simultaneous costs minimizing in electricity and gas micro-grids with the presence of distributed generation

Distributed generation can actively participate in the day-ahead markets, real-time power balance, and wholesale gas markets to achieve various goals, such as supplying gas to various electric power generation plants. A multi-objective network with two types of loads is considered in this paper. The reason for the simultaneous optimization of these two networks is that these two energy carriers are dependent on each other and gas is needed to produce electricity, so this issue can be addressed with a multi-objective function. The simulation carried out in this article is coded in GAMS software as a mixed integer linear programming (MILP). The efficiency of gas turbines and fuel cells in this article is dependent on their working point, and considering the exact model of these resources and the relationships related to the calculation of their fuel consumption is non-linear. On the other hand, a binary variable has been used to show the charging and discharging state of the storage and the on-and-off state of the gas turbines. Therefore, the problem considered in this article is a MILP problem. The results of this article are the proper planning of charging and discharging of the energy storage system with the proper planning of the power generation of different energy sources considering the network loads in two optimized and non-optimized scenarios.

Multi-objective robust optimization for optimal operation of gas-electricity networks with the penetration of integrated P2G and electric vehicle parking lots

Energy is considered one of the most important human needs. Therefore, various energy resources are exploited to meet human needs. Among all available resources, electricity and natural gas have accounted for the largest share in meeting these needs. Accordingly, management of these resources is one of the most important issues in different societies. This paper presents a multi-objective optimization model for optimal management and operation of the power distribution network and natural gas network as well as reducing carbon emissions. In this modeling, the natural gas network and distribution power network are connected through two electric vehicle parking lots (EVPLs) and two gas-fired units (GFUs), and these two EVPLs and GFUs exchange energy with each other. The EVPLs are equipped with various facilities including power-to-gas (P2G) systems and natural gas storage that facilitate energy exchange between the two networks. The modeling presented in this article is based on mixed integer linear programming, so the nonlinear equations including power flow equations, the Weymouth equation and the cost functions of GFUs are also linearized using various methods. It should be noted that the price of purchased electricity poses uncertainty which is modeled using robust optimization techniques. The proposed model is tested on the 33-bus power distribution network and the 20-node natural gas network. The results show that the presence of EVPLs significantly reduces the operational costs of the natural gas network and power distribution network and carbon emissions.

Scheduling of memory chips for final testing on parallel machines considering power constraints and deteriorating effects

This paper delves into the intricate scheduling strategies crucial for the final testing phase of memory chip manufacturing within the semiconductor industry and other related sectors. It specifically addresses the complex serial-batching scheduling problem, where memory chips are tested on parallel machines under power constraints and chip deterioration effects. The processing time for each chip is significantly influenced by both the cumulative processing time of preceding chips and the power requirements for testing. We formulate this real-world optimization problem using a mixed integer nonlinear programming model. Exact solutions for small instances are obtained using a commercial solver. However, due to the model's complexity, we also develop heuristic solutions to efficiently handle larger instances. Based on the derivation of structural properties, we develop two tailored heuristic algorithms to determine the schedule for the final testing of memory chips. Additionally, we propose a refined Variable Neighborhood Search algorithm (VNS-H) that seamlessly integrates five local search strategies with two supplementary heuristic algorithms, dynamically alternating between them to ensure a balance between computational efficiency and the quality of the solutions obtained. Additionally, we establish a lower bound to validate the effectiveness of these solutions, particularly for large-scale instances. To validate the efficacy and robustness of our proposed metaheuristic algorithm, we conduct a rigorous comparison of the VNS-H algorithm with five other metaheuristic algorithms that have promising performance in various optimization problems. The results highlight the superior performance of the VNS-H algorithm. In small-scale instances, our VNS-H algorithm achieves an average makespan that is 5.52% lower compared to the original VNS. For large-scale instances, the VNS-H algorithm reduces the average makespan by 13.46% compared to VNS. Finally, we discuss the managerial implications of our findings, providing insights specifically tailored to semiconductor manufacturing enterprises based on the outcomes of this study.

A two-step linear programming approach for repeater placement in large-scale quantum networks

Thanks to the applications such as Quantum Key Distribution and Distributed Quantum Computing, the deployment of quantum networks is gaining great momentum. A major component in quantum networks is repeaters, which are essential for reducing the error rate of qubit transmission for long-distance links. However, repeaters are expensive devices, so minimizing the number of repeaters placed in a quantum network while satisfying performance requirements becomes an important problem. Existing solutions typically solve this problem optimally by formulating an Integer Linear Program (ILP). However, the number of variables in their ILPs is O(n2), where n is the number of nodes in a network. This incurs infeasible running time when the network scale is large. To overcome this drawback, this paper proposes to solve the repeater placement problem by two steps, with each step using a linear program of a much smaller scale with O(n) variables. Although this solution is not optimal, it dramatically reduces the time complexity, making it practical for large-scale networks. Moreover, it constructs networks that have higher node connectivity than those by existing solutions, since it deploys slightly more number of repeaters into networks. Our extensive experiments on both synthetic and real-world network topologies verified our claims.

An efficient branch‐and‐bound algorithm to optimize a function over a nondominated set

AbstractThis study introduces an algorithm based on the branch‐and‐bound approach for optimizing a main function over the nondominated set of a multiobjective integer programming (MOIP) problem. Initially, is optimized within the feasible solution set of the MOIP. A new efficiency test combining Benson's test with is then developed using an auxiliary optimization program. This program provides both an efficient solution and a lower bound for . Moreover, this solution is the best one for when compared to its alternative solutions for MOIP. Subsequently, efficient cuts are incorporated into the criteria space to eliminate dominated points. Furthermore, the algorithm is tailored to handle scenarios where the objective involves optimizing a linear combination of multiobjective programming criteria over the nondominated set. The study concludes by showcasing the superior performance of the proposed two algorithms through comparison with existing approaches on well‐known problem instances from the literature.