Integer Linear Programming Model Research Articles

Operation estimation on multiple public transport timetables integrated with vehicle scheduling in practice

ABSTRACT Even-headway and even-load timetables have been in practice for the past 50 years. The former stipulates constant departures to cultivate users’ habits accordingly, whereas the latter is oriented from demand regulations aiming to further reduce waiting times. However, striking the balance between operation reliability (derived from even-headway timetabling) and an on-demand response to passenger fluctuation (referring to even-load timetabling) requires addressing major challenges presented by peak or alternatively off-peak demands. Our work addresses this imbalance by comparable estimation. The focused problem involves timetabling, vehicle scheduling, fleet size, and operation reliability based on an identical modeling framework simultaneously involving the three models. Nonetheless, their compatibility warrants a unified measure estimation. Hence, a mixed integer linear programming model is built. Finally, multiple timetabling performance comparisons are observed by the Auckland public transport system yielding sensitivity analysis.

UAV-rider coordinated dispatching for the on-demand delivery service provider

Fast response is critical to the success of the on-demand delivery service providers. Recently, more and more on-demand delivery service providers have started trying to use UAVs/drones to cope with the increasing challenges due to delivery service-sensitive demand. In this study, we propose a novel UAV-rider coordinated on-demand delivery model from the perspective of the on-demand delivery service provider. The objective aims to provide cost-effective delivery solutions by introducing the UAV/drone fleets into the current rider-only on-demand delivery system. A mixed integer linear programming (MILP) model is formulated to solve the problem, which is verified by the solver Cplex. To further analyze the impacts of the integration of UAVs on the riders’ deployment in practice, we develop a modified adaptive large neighborhood search (ALNS) algorithm to solve real business large-scale instances. The mechanism of how to improve the operational efficiency of the delivery service provider by integrating UAVs and the best-coordinated mode between UAVs and riders is discussed by conducting real-data-based numerical experiments. The results show that, for the case with a small number of orders in a dispatch cycle, the pure UAV model is best for the on-demand delivery service provider. When there are a large number of orders received in one dispatch cycle, the UAV-rider coordinated model is the best one to achieve cost-effective solutions. Some useful managerial insights are obtained through extensive experiments.

Optimizing vehicle route, schedule, and platoon formation considering time-dependent traffic congestion

Vehicle platooning, a strategy where vehicles drive in close formations, has emerged as a promising approach to reduce fuel consumption. This study presents a comprehensive model of the time-dependent vehicle platooning problem, which synchronously considers routing, scheduling, and platoon formation to minimize total fuel costs in a network affected by time-dependent traffic congestion. We first propose a mixed integer linear programming model to address this problem. To solve the problem, we develop two solution methods: a tabu search method and a platoon clustering algorithm. Through numerical experiments, we demonstrate the effectiveness of our mathematical model and the efficiency of the proposed algorithms. Our findings provide insights into the operational aspects of platooning and reveal that time-dependent traffic congestion can reduce the fuel-saving effects of platooning. This study underscores the importance of considering time-dependent traffic congestion in route planning and scheduling to ensure the effectiveness of vehicle platooning.

Agri-food supply chain optimization through a decentralized production process in the olive oil industry

A tactical/operational model is proposed to assist decision-making in harvest planning and olive oil production planning of the different producers in the rural sector, considering allocation and transportation decisions of the kilograms of olives to the production plant with temporary relocation decisions of the mobile olive oil mills through decentralized production activities in the agri-food supply chain. A Mixed Integer Linear Programming model is presented that maximizes the profit of small farmers in the production process of single-varietal extra virgin olive oil. The decisions are based on the geographical dispersion of the different olive growers and the oil concentration of the olive varieties in a certain period, which depends on the climatic conditions of each sector where the olives are cultivated. The mathematical programming model is applied in Coquimbo, Chile, using actual data collected from previous harvest seasons. The computational results of the optimization model indicate that transportation decisions impact olive harvesting and oil production decisions. It is concluded that cooperatives of small producers in the rural sector increase overall profits and reduce transportation costs and the number of kilometers traveled by at least 41% through a decentralized production process with mobile production plants.

An efficient bi-objective optimization approach for the optimal design of omnichannel supply chain distribution networks with sustainability

ABSTRACT This article studies a bi-objective omnichannel supply chain network design (SCND) problem, while simultaneously minimizing the overall supply chain (SC) cost and associated environmental emissions. A novel bi-objective mixed integer linear programming model is formulated, then an efficient optimization approach is proposed for the problem. Experimental studies on a case study and 210 random testing instances were conducted to evaluate the performance of the proposed model and approach. For the case study, 10 Pareto-optimal solutions were obtained within 1.9 s. For the random testing instances, the average number of Pareto-optimal solutions and computational time were 10.19 and 18.85 s, respectively. The overall results show that the proposed method is efficient and outperforms the adapted non-dominated sorting genetic algorithm II on test instances. Computational results indicate that this approach could assist decision makers in making good decisions, with considerable SC cost saving and carbon emission reductions in different situations.

Combinatorial Benders decomposition for single machine scheduling in additive manufacturing with two-dimensional packing constraints

This paper addresses a single-machine scheduling problem in additive manufacturing (AM). We focus on the direct metal laser sintering (DMLS) technology of an AM process, where parts can be produced simultaneously in a batch. In this problem, we consider simultaneously the assignment of parts to batches and the packing of parts onto two-dimensional surfaces of the build chamber to minimize the makespan objective. To solve this problem, a mixed integer linear programming model is formulated, and an approximation algorithm is proposed, followed by an exact algorithm based on combinatorial Benders decomposition method with various Benders cuts and acceleration strategies (Algorithm CBD). Finally, we conduct a comprehensive computational study to verify the efficiency of our proposed Algorithm CBD. The computational results show that our proposed Algorithm CBD can effectively solve the test instances with different sizes.

Optimal dispatch of integrated electricity and heating systems considering the quality-quantity regulation of heating systems to promote renewable energy consumption

The integrated electricity and heating system (IEHS) can improve energy efficiency and promote renewable energy consumption. When quality-quantity regulation (QQR) is adopted, namely adjusting hydraulic and thermal conditions of heating system, the increase in operation flexibility is more remarkable. However, present IEHS dispatch models considering QQR overlook hydraulic characteristics of valves and variable frequency pumps resulting in inexecutable dispatch results easily and hindering IEHS’s flexibility potential. Furthermore, loop networks and the access of multiple heat sources in heating systems may lead to flow reversal, but current research adopts a fixed flow direction which suppresses the potential of flow reversal to improve flexibility. In this paper, we propose an IEHS dispatch model considering QQR to promote renewable energy consumption, which considers hydraulic characteristics of valves and variable frequency pumps, and flow reversal. Specifically, we introduce two binary flow direction labels for every branch in heating system model and then the IEHS dispatch model which can deal with flow reversal is established. A sequential solution process combining linear and nonlinear optimization is formulated to overcome the non-convex feature of IEHS dispatch model. Specifically, piecewise linearization and piecewise McCormick relaxation are combined to handle complex nonlinear terms in the dispatch model. Therefore, a mixed integer linear programming model is obtained and solved, of which results are used as initial values for nonlinear optimization. Results in the case study show that operation cost is decreased by 0.97% and renewable power consumption rate is increased from 83.31% to 84.42% after considering valve adjustment. Operation cost is further decreased by 6.06% and renewable power consumption rate is increased to 94.04% after considering flow reversal.

Transport capacity analysis for sharing-corridor metro lines under virtual coupling

In this study, a method is proposed to analyze the capacity improvement ability of using virtual coupling technology to the sharing-corridor metro lines for solving the problem of capacity bottleneck. A mixed integer linear programming model is developed to optimise the train timetable of sharing-corridor lines under the assumption of using the virtual coupling technology, considering the constraints related to train timetabling, virtual coupling technology, and passenger assignment, with the objective to improve the service quality. The model adopts the departure times, arrival times, and whether each train service is planned as virtually coupled, with its adjacent front one or the following one, as decision variables. Furthermore, a method is proposed to evaluate the capacity utilization referring to UIC 406 and considering the feature of virtual coupling technology. The experiments on Shanghai Metro Line 3 and Line 4 are implemented to verify the effectiveness on transport capacity and passenger service quality of the proposed method. The results show that using virtual coupling technology can launch eight more train services during morning peak hours and at most reduce passengers’ waiting time by 73.8 s.

Computing the l,k-Clique Metric Dimension of Graphs via (Edge) Corona Products and Integer Linear Programming Model

Let G be a graph with n vertices and CG=X:X is an l-clique of G. A vertex v∈VG is said to resolve a pair of cliques X,Y in G if dGv,X≠dGv,Y where dG is the distance function of G. For a pair of cliques X,Y, the resolving neighbourhood of X and Y, denoted by RGX,Y, is the collection of all vertices which resolve the pair X,Y. A subset S of VG is called an l,k-clique metric generator for G if RGX,Y∩S≥k for each pair of distinct l-cliques X and Y of G. The l,k-clique metric dimension of G, denoted by l−cdimkG, is defined as minS:S is an l,k-clique metric generator of G. In this paper, the l,k-clique metric dimension of corona and edge corona of two graphs are computed. In addition, an integer linear programming model is presented for the l,k-clique metric basis for a given graph G and its l-cliques.

An Integer Linear Programming Model to Optimize Coding DNA Sequences By Joint Control of Transcript Indicators.

A Coding DNA Sequence (CDS) is a fraction of DNA whose nucleotides are grouped into consecutive triplets called codons, each one encoding an amino acid. Because most amino acids can be encoded by more than one codon, the same amino acid chain can be obtained by a very large number of different CDSs. These synonymous CDSs show different features that, also depending on the organism the transcript is expressed in, could affect translational efficiency and yield. The identification of optimal CDSs with respect to given transcript indicators is in general a challenging task, but it has been observed in recent literature that integer linear programming (ILP) can be a very flexible and efficient way to achieve it. In this article, we add evidence to this observation by proposing a new ILP model that simultaneously optimizes different well-grounded indicators. With this model, we efficiently find solutions that dominate those returned by six existing codon optimization heuristics.

Integrated Optimisation Model of Daily Freight Train Scheduling and Dynamic Railcar Routing Based on a Two-Layer Space-Time Network

This paper focuses on daily freight train scheduling and dynamic railcar routing problems for rail freight transportation at the operational level.  Two mixed integer linear programming models that adopted different strategies were formulated based on a continuous two-layer time-space network. We simultaneously considered the benefits of railroad company and service quality when setting the objective function. By solving the  models, we can distribute the dynamic railcar flows to the train paths in the basic train timetable to obtain the daily train operation plan over a short time horizon (e.g. a day), which will be helpful for dispatchers to make decisions such as the empty railcar distribution and car routing (trip planning). Finally, we compared two models on a part of the Chinese railroad network. The results show that the second model can effectively improve the efficiency of railroad freight transportation.

Service blockage on the downlink in large-scale satellite optical networks: a multi-downlink scheduling for routing selection

Over years of space laser communication technology advances, satellite optical networks (SONs) have emerged as a pivotal component in 6 G networks. Satellite services are transmitted from the global view, undergoing transmission through SONs, and being downloaded to the targeted areas. However, the transmission capacity of satellites passing through the areas where users are concentrated may be insufficient to download services transmitted worldwide. This problem exists in various kinds of satellite networks and may cause a large amount of service congestion. In this paper, we propose a multi-downlink delivery routing selection (MDD-RS) strategy to study the total utilization of transmission capacity of SONs. We construct an integer linear programming (ILP) model to establish an optimal case study for minimal network capacity occupation. Also, we design an online option, MDD-RS heuristic algorithm, dynamically calculating path routes, considering bandwidth allocation and resource constraints. A comparative analysis against the conventional single-downlink scheme reveals superior performance of the MDD-RS heuristic algorithm, with a reduction in blocking probability of 0.129 and an improvement in bandwidth utilization of 0.032.

Cost-based distributionally robust tourist attraction recommendation with demand uncertainty

Tourist attraction recommendation (TAR) problem has gained attention due to its potential to enhance tourist services. Existing studies focus on meeting tourists’ individual needs, but overlook the tour operator’s interests as the TAR service provider. The TAR problem is more challenging due to the high variability of customer demand, which is difficult to predict accurately beforehand. This paper examines TAR in response to random changes in tourist demand, aiming to minimize transportation costs, cooperation expenses between tour operators and attractions, ticket booking fees, and promotion costs, where ambiguity set is defined by means, mean absolute deviations, and the support set. Firstly a distributionally robust model is proposed to identify suitable attractions for cooperation, along with determining the associated costs of ticket booking, promotion, and tourist transportation, while considering chance constraint on the service level. Subsequently, the model is reformulated into a tractable mixed integer linear programming model using duality theory. Numerical experiments illustrate that the proposed model outperforms both the stochastic programming model and the deterministic model in terms of risk level by out-of-sample test. In particularly, considering uncertainty and distributional ambiguity can make the model more accurate and credible.

A Sustainable Multi-Objective Model for Capacitated-Electric-Vehicle-Routing-Problem Considering Hard and Soft Time Windows as Well as Partial Recharging.

Due to the high pollution of the transportation sector, nowadays the role of electric vehicles has been noticed more and more by governments, organizations, and environmentally friendly people. On the other hand, the problem of electric vehicle routing (EVRP) has been widely studied in recent years. This paper deals with an extended version of EVRP, in which electric vehicles (EVs) deliver goods to customers. The limited battery capacity of EVs causes their operational domains to be less than those of gasoline vehicles. For this purpose, several charging stations are considered in this study for EVs. In addition, depending on the operational domain, a full charge may not be needed, which reduces the operation time. Therefore, partial recharging is also taken into account in the present research. This problem is formulated as a multi-objective integer linear programming model, whose objective functions include economic, environmental, and social aspects. Then, the preemptive fuzzy goal programming method (PFGP) is exploited as an exact method to solve small-sized problems. Also, two hybrid meta-heuristic algorithms inspired by nature, including MOSA, MOGWO, MOPSO, and NSGAII_TLBO, are utilized to solve large-sized problems. The results obtained from solving the numerous test problems demonstrate that the hybrid meta-heuristic algorithm can provide efficient solutions in terms of quality and non-dominated solutions in all test problems. In addition, the performance of the algorithms was compared in terms of four indexes: time, MID, MOCV, and HV. Moreover, statistical analysis is performed to investigate whether there is a significant difference between the performance of the algorithms. The results indicate that the MOSA algorithm performs better in terms of the time index. On the other hand, the NSGA-II-TLBO algorithm outperforms in terms of the MID, MOCV, and HV indexes.

A parallel deep adaptive large neighbourhood search algorithm for distributed heterogeneous hybrid flow shops with mixed-model assembly scheduling

ABSTRACT Nowadays, manufacturing enterprises must have fast response and flexible production capabilities to meet personalized and diversified market demands. Mixed-model production and distributed production have become the preferred production methods for enterprises. This article studies a distributed heterogeneous hybrid flow shop scheduling problem with a mixed-model assembly line (DHHFSP-MMAL), which consists of manufacturing and assembly stages. The DHHFSP-MMAL is modelled by a mixed integer linear programming (MILP) model. Three constructive heuristics and a parallel deep adaptive large neighbourhood search (PDALNS) problem are presented. A constructive heuristic with a group strategy is employed to obtain an initial solution. Several deep destroy-and-repair operators are proposed where problem-specific greedy local search methods are applied. The PDALNS assigns weights to destroy-and-repair operators to guide the selection of operators. The parallel computing technique is introduced to increase the efficiency of training. The experiments demonstrate that the PDALNS algorithm is an efficient and effective algorithm for solving the DHHFSP-MMAL problem.

A Triple Bottom Line optimization model for assignment and routing of on-demand home services

‘On-demand home services’ is a fast-growing industry where online platforms match independent service professionals with customers seeking aid for household tasks. In this paper, we study the assignment and routing of service professionals for serving customers of an on-demand home services platform considering the Triple Bottom Line (TBL) criteria for ensuring sustainability in operations. We characterize this as the Home Services Assignment and Routing Problem with the Triple Bottom Line (HSARP-TBL) and implement a Mixed Integer Linear Programming (MILP) model for solving it. We assign service professionals to customers based on their desired time slots and also transport modes for each customer visit by a professional, considering either combinations of public transport or a personal vehicle for each professional’s tour. The objective is to minimize costs due to time window violations and uncovered customers, catering to the economic pillar of the TBL. We incorporate additional constraints related to the TBL by improving customer satisfaction based on the ratings of assigned professionals to customers, with and without subscription (economic), controlling emissions due to transportation of professionals (environmental) and ensuring equity in service allocation and net earnings between professionals (social). For tackling large instances we implement a Hybrid Genetic Search (HGS) algorithm adapting it to our problem setting. We demonstrate that the HGS outperforms the MILP model systematically for large instances in terms of solution value and computational time. Finally, we observe that for some instances, without worsening the primary economic objective, all the TBL indicators can be improved.

How we deal with transition planning as we approach the e-bus era

With the rapid development of new energy, the widespread adoption of electric buses is significant. This paper delves into the environmental impact, economic implications, and strategic planning solutions associated with the proliferation of electric buses. We initiate this process by using bus data from Qingdao, China. Subsequently, using the fuel life cycle method, we carefully examined CO and the pollutant emission characteristics of Qingdao bus fleet before and after electrification. The research results reveal that CO, nitrogen oxides, and VOC emissions have all increased. An economic analysis of electric vehicle adoption in public transportation was conducted in response to the second question. Considering government subsidies, a cost-saving model for electric vehicles per 100 kilometers was constructed. Furthermore, the study found that as the electrification rate increases, the operating costs of electric buses in Qingdao gradually decrease. We developed a comprehensive linear integer programming model to address the third question. The model, aimed at achieving the lowest comprehensive cost while considering various constraints, was solved through the branch and bound method. We applied this model to analyze the optimal plans for completing the conversion of electric buses in Qingdao, Zhengzhou, and Xi’an within a 10-year timeframe. For the fourth question, we have put forward policy recommendations.

Sustainable vehicle allocation decisions under a vertical logistics collaboration setting

Enhancing vehicle utilization through a collaborative logistics approach allows businesses to contribute to the three pillars of sustainability by reducing fuel consumption and emissions, enhancing profit margins, and increasing customer satisfaction. This paper aims to introduce an Integer Linear Programming model for solving a vehicle allocation problem within a proposed vertical logistics collaboration setting. In this collaboration setup, production capacity allocation decisions are jointly made by collaborating customers and the logistics service provider, in order to create a more balanced and profitable logistics plan for all involved parties. Through the application of the proposed mathematical model, our numerical analyses illustrate the effects of the vertical logistics collaboration on the performance of transportation operations, including improved vehicle utilization rate and increased satisfied demand amount. Besides, we analyze the outputs of this operation related to the economic (by focusing on profit growth), environmental (by measuring the reduction in emissions), and social (by assessing the discounted transportation costs for customers) aspects of sustainability. To the best of our knowledge, no current study in the literature has established the vehicle allocation problem in the context of vertical logistics collaboration across all three sustainability pillars at the same time. The model can also serve as a tool for evaluating the potential economic, environmental, and social benefits arising from vertical collaboration and joint projects with customers, along with the support offered to logistics decisions.

Integer Linear Programming Models and Greedy Heuristic for the Minimum Weighted Independent Dominating Set Problem

This paper explores the Minimum Weighted Independent Dominating Set Problem and proposes novel approaches to tackle it. Namely, two integer linear programming formulations and a fast greedy heuristic as an alternative approach are proposed. Extensive computational experiments are conducted to evaluate the performance of these approaches on the established set of benchmark instances for the problem. The obtained results demonstrate that the introduced integer linear programming models are able to achieve optimal solutions on all instances with 100 nodes and significantly outperform existing exact methods on numerous other instances. Additionally, the greedy heuristic exhibits superior performance compared to competing greedy heuristics, particularly on random graphs. These findings suggest promising directions for future research, including the integration of these methods into hybrid algorithms or metaheuristic frameworks.

Combinatorial Benders' decomposition for the constrained two-dimensional non-guillotine cutting problem with defects

This paper studies the constrained two-dimensional non-guillotine cutting problem with defects, in which a set of items of a specific size is cut from a large rectangular sheet with defective areas, with the number of each type of cut item cannot exceed a specified quantity. The objective is to maximise the total value of the cut items. We propose a decomposition approach to address the problem. The process involves decomposing the original problem into a master problem and a subproblem. The master problem is formulated as a one-dimensional contiguous bin packing problem, while the subproblem is an x-Check problem to identify a two-dimensional packing that does not lead to any overlap. The x-Check problem is effectively addressed by using an integer linear programming model. When the x-Check problem proves infeasible, cuts are added to the master problem, and the iteration is repeated until the x-Check finds a feasible solution. Furthermore, we introduce several novel techniques, including valid inequalities, preprocessing techniques, and lifting the cut methods to improve the performance of the algorithm. Extensive computational results show that our method can quickly find the optimal solution for the 5450 instances in the literature.