Binary Integer Programming Model Research Articles

Solving the project scheduling problem with dependent resource constraints

ABSTRACT Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints.

How to optimize service-oriented cloud manufacturing

Within the context of Industry 4.0, service-oriented cloud manufacturing has emerged as a paradigm of significant interest, noted for enhancing manufacturing efficacy through integration, flexibility, and customization. The challenges of service selection and optimization, alongside transportation optimization, are pivotal for the effective implementation of service-oriented cloud manufacturing. This study explores an integrated problem that incorporates both sequential and parallel structures. To address this intricate issue, a binary-integer programming model is proposed, aiming to minimize the cumulative costs, including both manufacturing and transportation expenses. The validity and effectiveness of the proposed model are demonstrated through a real-world case study in mold manufacturing. Analysis of the experimental results provides managerial insights, which could inform the implementation and improvement of service-oriented cloud manufacturing strategies.

Valorant Haven Strategy Using BIP and Weighted Graph

Strategy in a competitive video game is needed to reach a successful game, for example, Valorant. Route planning is one of the strategies in playing games. In consideration of making a new strategy, this research develops a binary integer programming (BIP) model to generating optimal route depending on passable paths, travel time, kills, and survivability. By using POM QM for Windows to compute the model, we obtained optimal modified routes that can be combined in the role and agent composition.

High-speed train timetable optimization based on space–time network model and quantum simulator

Timetable scheduling is a combinatorial optimization problem that presents formidable challenges for classical computers. This paper introduces a pioneering methodology for addressing the high-speed train timetabling problem through quantum computing. Initially, a comprehensive binary integer programming model, grounded in the space–time network, is proposed (M1). To manage the intricacy of model M1, a knapsack problem reformulation is employed to establish a simplified binary integer programming model (M2). Both M1 and M2 are subsequently converted into quadratic unconstrained binary optimization (QUBO) models to harness the potential of quantum computing. Several techniques, including the Gurobi solver, simulated annealing, and the coherent Ising machine (CIM) quantum simulator, are deployed to solve the model across four distinct scenarios of varying complexity. The findings indicate that CIM quantum simulator outperforms the simulated annealing method in terms of solution quality for medium-scale problems.

Improved artificial bee colony algorithm-based channel allocation scheme in low earth orbit satellite downlinks

In low earth orbit (LEO) constellations, channel utilization is low owing to variations in the traffic distributions between beams. LEO satellites improve channel utilization via the full-band multiplexing technology. However, such satellites produce significant inter-beam interference. Additionally, this inter-beam interference becomes more aggravated owing to the requirements of multiple satellite coverage. To resolve this issue, we propose a LEO channel allocation scheme based on an improved artificial bee colony (IABC) algorithm. This scheme considers the difference in inter-beam communication traffic and the limitation of co-channel interference. A binary integer-programming model and IABC algorithm allocate channels to maximize the system throughput. The channel allocation matrix corresponds to a feasible solution in the IABC algorithm. The simulation results verify the excellent performance of the proposed scheme in terms of the throughput, blocking rate, and propagation delay compared with the performance of traditional schemes.

Single-machine scheduling with periodic maintenance and learning effect

This paper discusses a single-machine scheduling problem with periodic maintenance activities and position-based learning effect to minimize the makespan. To obtain exact solutions of small-scale problems, one new two-stage binary integer programming model is formulated. In addition, a branch and bound algorithm combining boundary method and pruning rules is also proposed. According to the property of the optimal solution, a special search neighborhood is constructed. A hybrid genetic-tabu search algorithm based on genetic mechanism with tabu technique as an operator is proposed to solve medium-scale and large-scale problems. Moreover, to improve the efficiency of genetic algorithm and hybrid genetic-tabu search algorithm, Taguchi method is used for parameter tuning. Furthermore, computational experiments are carried out to compare the efficiency and performance of these algorithms.

Adaptive large neighborhood search algorithm for multi-stage weapon target assignment problem

Weapon target assignment (WTA) is a critical operational research topic that can be applied to plentiful military fields. A new variant of WTA, the multi-stage WTA problem, is investigated, which is to assign limited weapons to all targets in multiple attacking phases. The attacking flexibility for targets in different stages is considered, and a binary nonlinear integer programming model is developed to formulate the problem. An improved adaptive large-scale neighborhood search (ALNS) algorithm is proposed. First, a priority-based encoding strategy is designed to facilitate the feasible solution generating and solution space exploring. Then, six specific neighborhood structures are designed to generate 15 operators through their combination. The simulated annealing mechanism is integrated to avoid getting trapped in local optima. Moreover, an adaptive learning strategy is employed to improve the exploration capability. Both exact methods and metaheuristics are compared with the ALNS algorithm by instances with different scales. Experimental results show that, for most situations, the ALNS algorithm can obtain higher-quality solutions in a shorter time.

A Binary Integer Programming Model for Personnel Scheduling: A Case Study at Fast-Food Restaurant in Johor

This study is about analysing the current practice of the personnel scheduling at a well-known fast-food restaurant, as the post-pandemic situation slightly change their operating system. Therefore, the personnel scheduling needs to be modified according to the real-time situation using the binary integer programming (BIP) model. Based on the observation made, the problem of the study is to modify the working schedule with a proper break time for each staff to give them a fair working time, keep the workstations occupied during their operating hours and to maintain the restaurant as a healthy workplace. Therefore, after a background study on the topic and data collection made from a fast-food restaurant done, a one-day schedule is prepared to determine the number of staffs working in a day and scheduled the staff’s break period. A new schedule is obtained that meets all constraint’s requirements by solving the model using Microsoft Excel Solver. The new schedule minimized the number of staffs working in a day to 11 staff as compared to 12 staff in the current schedule. In conclusion, the proposed mathematical model can serve a fast and accurate solution for minimizing the personnel size and helps each staff to have a reasonable working hour with sufficient break time.

Reconstruction of LoD-2 Building Models Guided by Façade Structures from Oblique Photogrammetric Point Cloud

Due to the façade visibility, intuitive expression, and multi-view redundancy, oblique photogrammetry can provide optional data for large-scale urban LoD-2 reconstruction. However, the inherent noise in oblique photogrammetric point cloud resulting from the image-dense matching limits further model reconstruction applications. Thus, this paper proposes a novel method for the efficient reconstruction of LoD-2 building models guided by façade structures from an oblique photogrammetric point cloud. First, a building planar layout is constructed combined with footprint data and the vertical planes of the building based on spatial consistency constraints. The cells in the planar layout represent roof structures with a distinct altitude difference. Then, we introduce regularity constraints and a binary integer programming model to abstract the façade with the best-fitting monotonic regularized profiles. Combined with the planar layout and regularized profiles, a 2D building topology is constructed. Finally, the vertices of building roof facets can be derived from the 2D building topology, thus generating a LoD-2 building model. Experimental results using real datasets indicate that the proposed method can generate reliable reconstruction results compared with two state-of-the-art methods.

An integrated approach for selecting design parameters in smart product-service system conceptual design

Nowadays, with the rapid development of cyber physical systems, IoT, and artificial intelligence, more and more attention has been paid to adapting the combination of smart, connected products and their generated services. Among these, smart product-service system (SPSS) with the unique features of smartness, connection, value co-creation, and data-driven has been widely concerned. Therefore, based on axiomatic design theory, the mapping from function domain to physical domain is a critical process in SPSS's conceptual design and the selecting of design parameters in physical domain has great impact on meeting multi-stakeholders’ benefits. Nevertheless, despite a few works on requirement conversion, it is not clear about the mapping mechanism under the target of value co-creation. Aiming to fill this gap, an integrated SPSS conceptual design method is proposed to solve the cross-domain mapping problem. It decomposes and reorganizes SPSS's function requirements with requirement development laws in TRIZ and divides the physical domain into product-related domain and service-related domain. Design parameters would be selected and evaluated by domain experts based on fuzzy comprehensive evaluation from different dimensions, which could represent the benefit of multi-stakeholders. Next, a binary integer programming (BIP) model with restrictions from different stakeholders would be constructed, which could be regarded as a multi-objective optimization problem. To solve the BIP model, the genetic algorithm is used and the optimal design parameters combination could be generated as the output of this process. Finally, a case study is carried out to demonstrate the feasibility and advantages of the integrated approach for cross-domain mapping in SPSS conceptual design.

Proposed Optimization Algorithm for Solving CCTV Camera Placement

The installation of CCTV cameras monitoring the street sections of one of the most visited areas of Manila may serve as deterrence against theft, crime, abduction, and even act of lasciviousness. Furthermore, the redundant orientations of some of the units in the system were recognized as possible inhibitors of the efficiency of the local surveillance system. In line with this, the study proposed a model for CCTV camera placement in Intramuros by representing the community as a graph in a 2-dimensional space. The paper presents a two-phase approach in determining the best placements of CCTV cameras. Phase I took care of the ideal installation spots as a set-covering problem while Phase II identified the optimal CCTV orientation using the Proposed algorithm. In Phase I, a binary integer programming model was formulated and solved using the data solver function of Microsoft Excel. The designed algorithm in Phase II was based on greedy heuristics utilizing the results in Phase I to identify the optimal orientation of the CCTV units. Findings suggest that out of the seventeen candidate locations, nine of them are optimal for CCTV installation. A total of twenty-three CCTV units are required to cover all the entry and exit points of the streets in district 5 of Intramuros. The proposed algorithm produced two optimal solutions A and B. Comparison with the existing CCTV system in the district and discussions on each optimal installation suggested that result B is better than A. Recommendations on the results of the study were addressed to the authorities of district 5 for immediate implementation.

A method to find the optimum routes and stations for bus rapid transit in urban areas

Public transportation (PT) is an essential system for cities to achieve sustainability. However, determination of proper locations for PT stations and finding suitable routes are critical decisions. The aim of the present study is to propose a novel method to determine bus rapid transit (BRT) stations and routes in cities, using a fuzzy inference system (FIS) and binary integer programming (BIP). In the proposed method, first, a set of potential locations for BRT stations is selected based on engineering judgement. Then, by considering several variables and with the help of FIS, a weight is calculated for each location. Subsequently, the optimum corridors for BRT are identified with BIP. The objective function of the BIP model is to maximise the sum of the stations’ weights (involving the most suitable locations for BRT stations), while ensuring that the maximum number of passengers can travel each route. Constraints related to technical, social and economic considerations are also taken into account. To control the model efficiency, the outputs are compared with the stations and corridor suggested by experts. Based on the results, the most important features of the developed model are its simplicity, its ability to consider various factors, a short running time and its high level of accuracy.

Bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance with a dynamic speed-scaling technique

Nowadays, industries contribute to a substantial consumption of energy. This consumption leads to significant greenhouse gas emissions, energy dependence and ever-increasing costs for manufacturers. Controlling consumption and improving energy efficiency in industry are therefore major challenges in terms of environmental issues. In this context, this article examines an energy-efficient bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance activities problem to minimize both makespan and total energy consumption. The parallel machines are speed-scaling. To solve the problem, we propose a bi-objective mixed integer linear programming (MILP) model. Since the problem involves assigning jobs to machines and selecting an appropriate processing speed level for each job, we characterize each individual by two vectors: a job-machine assignment vector and a speed vector. To the best of our knowledge, no papers considering both production scheduling and Preventive Maintenance periods with minimizing the bi-objective makespan and the total of energy consumption. The gap between theory and practice prevents the satisfying performance of the schedules in industry. The purpose of this paper is to establish a joint model for integrating the production and PM scheduling to optimize the bi-objective of the total of energy consumption (TEC) and makespan (Cmax) simultaneously; and to make the theory applied in practice more efficaciously. The performance of the proposed mixed binary integer programming model is evaluated based on the exact method of Branch and Bound integrated on the CPLEX solver plus analyses using MATLAB software. A study of the results proved the performance of the model developed.

Integrated train routing and timetabling problem in a multi-station high-speed railway hub

ABSTRACT With multiple stations being built in the high-speed railway hub, how to schedule trains among stations is of great significance. This paper studies the integrated train routing and timetabling problem in a multi-station high-speed railway hub. Based on a specific bi-level network, a binary integer programming model using cumulative flow variables is proposed to minimize the total cost of trains and passengers. An extended Alternating Direction Method of Multipliers (ADMM) algorithm is developed to decompose the model into train and passenger subproblems. The performance of the algorithm is investigated on small-scale and large-scale networks. Compared with the commonly used Lagrangian Relaxation (LR) algorithm, the results indicate that the extended ADMM obtain better solutions with less iterations, where the lower bound decreases by 3.79% and iterations are reduced by 83.54%. Another comparative experiment shows the total cost of the optimization scheme is 16.22% lower than that of the current fixed scheme.

The location routing problem for cooling shelters during heat waves

Given the increasing frequency, duration, and intensity of heat waves around the globe, more research is needed on the allocation and operations of cooling shelters for efficient heat mitigation. To address this need, this study considers a cooling shelter operating system that uses shuttle buses to transport heat-vulnerable people and presents a binary integer programming model for the multi-depot location routing problem (LRP) that decides optimal locations of cooling shelters and routes of shuttle buses simultaneously with the objective of minimizing the total operating cost for full accommodation of the heat-vulnerable population. Since the LRP is NP-hard, we further present the simulated annealing to efficiently derive a near-optimal solution. We then validate the proposed methodology with an application to the 14 administrative regions of Ulsan Metropolitan City in the Republic of Korea to assign heat-vulnerable residents and provide them with ride services to the associated cooling shelters. The overall results demonstrate the proposed methodology's competitive performance compared with the traditional two-phased solution approach that separately solves the location problem and routing problem. In particular, our results show that the proposed methodology can save up to 49,000 USD in addressing the cooling shelter location routing problem compared to the two-phased solution approach. Subsequently, a sensitivity analysis is conducted regarding three factors that are likely to impact the effectiveness and efficiency of cooling shelter operations: shuttle bus capacity, traveling cost, and maximum walking distance. Our research provides recommendations for policymakers to carry out the best heat mitigation strategy for their unique circumstances and reduce heat-related illness and death.

An Efficient Binary Integer Programming Model for Residency Time-Constrained Cluster Tools With Chamber Cleaning Requirements

Cluster tools play a significant role in the entire process of wafer fabrication. As the width of circuits in semiconductor chips shrinks down to less than 10nm, strict operational constraints are imposed on the operations of cluster tools in order to ensure the quality of processed wafers. Particularly, wafer residency time constraints and chamber cleaning requirements are commonly seen in etching, chemical vapor deposition, coating processes, etc. They make the scheduling problem of cluster tools more challenging. This work aims to provide a solution for dual-arm cluster tools with wafer residency time constraints and chamber cleaning requirements. To do so, it proposes a novel virtual wafer-based scheduling method. By this method, under a steady state, a PM processes either a real or virtual wafer at a time. When a PM processes a virtual one, its chamber can perform a cleaning operation. In this way, we can meet not only the strict residency time constraints for real wafers, but also innovatively meet chamber cleaning requirements. Based on such a novel scheduling method, an efficient binary integer programming model is established to optimize the throughput of cluster tools. Finally, experiments are performed to show the efficiency and effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —To ensure wafer quality in semiconductor manufacturing, engineers have to impose wafer residency time constraints and chamber cleaning requirements on the operations of cluster tools. In order to tackle their scheduling problem with these constraints, this work proposes a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for time-constrained cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a PM processes a virtual wafer, a chamber cleaning operation can be performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. To do so, this work establishes an efficient binary integer programming model to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has a high practical value to numerous semiconductor manufacturers.

CARSP: A Smart Parking System Based on Doubly Periodic Rolling Horizon Allocation Approach

Blind search for available parking space is accountable for most traffic congestion, accident, and pollution in cities, which severely impact people’s life. Parking management based on an online smart parking system is practical to alleviate parking problems in which parking allocation is the core. However, existing researches are weak at satisfying allocation effect and speed simultaneously when solving large-scale dynamic parking allocation problem. To address this problem, we firstly construct an online “Collection-Allocation-Response” smart parking system (CARSP) to offer parking services to users and rent parking spaces from owners so as to obtain revenue for system managers. We then propose a novel Doubly Periodic Rolling Horizon allocation approach (DPRH) that circularly conduct allocation within a short period and reallocation within a long period. We formulate a narrow allocation model (without reallocation) and broad allocation model (with reallocation), both of which are binary integer programming models with the objective of maximizing system integrated benefit. We design seven performance metrics to evaluate the overall allocation effect and speed of CARSP based on DPRH. According to the three-day district-level instance in Beijing, CARSP based on DPRH performs excellently in balancing allocation effect and speed. This study is meaningful for constructing and optimizing an online smart parking system.

A binary integer programming (BIP) model for optimal financial turning points detection

PurposeThis paper aims to detect the most profitable, i.e. optimal turning points (TPs), from the history of time series using a binary integer programming (BIP) model. TPs prediction problem is one of the most popular yet challenging topics in financial planning. Predicting profitable TPs results in earning profit by offering the opportunity to buy at low and selling at high. TPs detected from the history of time series will be used as the prediction model’s input. According to the literature, the predicted TPs’ profitability depends on the detected TPs’ profitability. Therefore, research for improving the profitability of detection methods has been never given up. Nevertheless, to the best of our knowledge, none of the existing methods can detect the optimal TPs.Design/methodology/approachThe objective function of our model maximizes the profit of adopting all the trading strategies. The decision variables represent whether or not to detect the breakpoints as TPs. The assumptions of the model are as follows. Short-selling is possible. The time value for the money is not considered. Detection of consecutive buying (selling) TPs is not possible.FindingsEmpirical results with 20 data sets from Shanghai Stock Exchange indicate that the model detects the optimal TPs.Originality/valueThe proposed model, in contrast to the other methods, can detect the optimal TPs. Additionally, the proposed model, in contrast to the other methods, requires transaction cost as its only input parameter. This advantage reduces the process’ calculations.

A heuristic approach to integrate train timetabling, platforming, and railway network maintenance scheduling decisions

Train timetabling, platforming, and network maintenance scheduling are three highly interdependent problems that are crucial in the planning of railway operations, and each is normally addressed separately. In this paper, we simultaneously optimize these problems for a high-speed railway network that is comprised of multiple railway lines and stations. We model the railway network on a mesoscopic level and formulate a 0–1 binary integer programming model that minimizes the total train weighted running cost and any deviation from ideal maintenance task start times. A heuristic procedure, which dynamically updates the available time windows for each of the trains, is used to control the number of train paths in the mathematical model. The mathematical model is repeatedly solved, and at each iteration we gradually modify the set of train paths available. Four different strategies to modify train time windows are used in the train path modification step and their selection depends on the solution to the mathematical model. Computational results for three networks of different sizes conclusively demonstrate that there is not only benefit in integrating these problems, with improvements of as much as 30%, but also that the proposed solution approach is highly effective. Compared to the commercial solver CPLEX, the proposed approach is able to more quickly find better quality solutions within a given time limit.

An optimisation Model for minimising Totes exchange in VLM and SBS/RS integrated System

Warehouses and distribution centres are based on integrated material handling solutions. Most of the research papers in intralogistics are only concerned with one system to analyse and optimise the addressed system's performance, such as maximum throughput performance, minimum total cost, maximum energy efficiency, etc. This paper presents a concept to justify the proposed VLM and SBS/RS integrated system and a binary integer programming (BIP) model that minimises totes exchange between the two storage systems. The results show that the minimal number of exchanges between VLM and SBS/RS was achieved in a case study with a longer order list (T = 1600) and a highly dependent SKU's Pareto relationship (20-50).