Large-scale Integer Programming Research Articles

Designing a two-stage model for the resilient agri-food supply chain network under dynamic competition

PurposeSupply chain risk management can effectively reduce the loss of retailers. In this regard, retailers need to consider the competition risks of competitors in addition to the disruption risks. This paper designs a resilient retail supply chain network for perishable foods under the dynamic competition to maximize retailer's profits.Design/methodology/approachA two-stage mixed-integer non-linear model is presented for designing the supply chain network. In the first stage, an equilibrium model that considers the characteristics of perishable foods is developed. In the second stage, a mixed integer non-linear programming model is presented to deal with the strategic decisions. Finally, an efficient memetic algorithm is designed to deal with large-scale problems.FindingsThe optimal the selection of suppliers, distribution centers and the order allocation are found among the supply chain entities. Considering the perishability of agri-food products, the equilibrium retail price and selling quantity are determined. Through a numerical example, the optimal inventory period under different maximum shelf life and the impact of three resilient strategies on retailer's profit, selling price and selling quantity are analyzed.Research limitations/implicationsAs for future research, the research can be extended in a number of directions. First, this paper studies the retail supply chain network design problem under competition among retailers. It can be an interesting direction to consider retailers competing with suppliers. Second, the authors can try to linearize the non-linear model and solve the large-scale integer programming problem by exact algorithm. Finally, the freshness of perishable foods gradually declines linearly to zero as the maximum shelf life approaches, and it would be a meaningful attempt to consider the freshness of perishable foods declines exponentially.Originality/valueThis paper innovatively designs the resilient supply chain network for perishable foods under dynamic competition. The retailer's dynamic competition and resilient strategies are considered simultaneously when designing supply chain network for perishable foods. In addition, this paper gives insights into how to obtain the optimal inventory period and compare the retailer's resilient strategies.

AI-based energy-efficient path planning of multiple logistics UAVs in intelligent transportation systems

In the context of Industry 5.0, artificial intelligence (AI)-based logistics Unmanned Aerial Vehicles (UAVs) have been widely applied in intelligent transportation systems due to their advantages of faster speed, lower cost, more environment-friendly, and less manpower needed. Whereas, most of the existing logistics UAV delivery models have not taken the energy consumption of the logistics UAVs and mixed time windows of the customers, which leads to their models cannot be applied in practical transportation systems. Therefore, we propose to minimize the total energy cost of multiple logistics UAVs during the customized products delivery period for a smart transportation system. Taking the energy consumption variation of the logistics UAVs, mixed time windows of the customers, as well as simultaneous delivery and pick up into consideration, we formulate a cooperative path planning problem via jointly optimizing the route of the logistics UAVs and the service allocation. To solve this large-scale integer programming problem, we employ the Large Neighborhood Search Algorithm (LNS) to accelerate the convergence rate of Genetic Algorithm (GA), and then develop an improved GA based cooperative path planning algorithm (IGCPA). The optimization procedure of the proposed algorithm IGCPA is divided into two phases, using the GA crossover operator and variational operator in the global search phase and LNS operator in the local search phase, and validating the integer programming model and the effectiveness of the solution algorithm based on different scale cases. Finally, abundant simulation results show that the energy cost of IGCPA is reduced by 17.35%, 15.18% and 9.99% compared with GA, LNS and Particle Swarm Optimization (PSO), respectively. Furthermore, the IGCPA is validated using Solomn standard data, which further verifies that the IGCPA can enhance the convergence rate of GA as well as obtain a lower delivery cost. Sensitivity analysis of the maximum UAV load and battery capacity reveals that the distribution cost tends to decrease and then increase as the increase of maximum load and battery capacity.

A Game-Theoretic Approach for the Robust Daily Aircraft Routing Problem

In the operation of airlines, the most important link is determining the route and scheduling of aircraft. The key to this problem is to input the flight segment and aircraft type and finally determine all flight segments for each aircraft. In this paper, we focus on finding feasible, robust scheduling for various uncertainties in the flight process. This paper presents a new robust integer mathematical model based on game theory that considers daily aircraft routing. Then, in order to find the suboptimal solution to a large-scale integer programming problem in a limited amount of time, a heuristic algorithm integrating a column generation algorithm and variable domain search is introduced. In addition, we use the data of a Chinese airline to verify, and the experimental results show that the model proposed by us is more robust than the model in general.

NICE: Robust Scheduling through Reinforcement Learning-Guided Integer Programming

Integer programs provide a powerful abstraction for representing a wide range of real-world scheduling problems. Despite their ability to model general scheduling problems, solving large-scale integer programs (IP) remains a computational challenge in practice. The incorporation of more complex objectives such as robustness to disruptions further exacerbates the computational challenge. We present NICE (Neural network IP Coefficient Extraction), a novel technique that combines reinforcement learning and integer programming to tackle the problem of robust scheduling. More specifically, NICE uses reinforcement learning to approximately represent complex objectives in an integer programming formulation. We use NICE to determine assignments of pilots to a flight crew schedule so as to reduce the impact of disruptions. We compare NICE with (1) a baseline integer programming formulation that produces a feasible crew schedule, and (2) a robust integer programming formulation that explicitly tries to minimize the impact of disruptions. Our experiments show that, across a variety of scenarios, NICE produces schedules resulting in 33% to 48% fewer disruptions than the baseline formulation. Moreover, in more severely constrained scheduling scenarios in which the robust integer program fails to produce a schedule within 90 minutes, NICE is able to build robust schedules in less than 2 seconds on average.

JD.com: Operations Research Algorithms Drive Intelligent Warehouse Robots to Work

JD.com pioneered same-day delivery as a standard service in China’s business-to-consumer e-commerce sector in 2010. To balance the urgent need to meet growing demands while maintaining high-quality logistics services, the company built intelligent warehouses that use analytics to significantly improve warehouse efficiency. The brain of the intelligent warehouse system is the dispatching algorithm for storage rack-moving robots, which makes real-time dispatching decisions among robots, racks, and workstations after solving large-scale integer programs in seconds. The intelligent warehouse technology has helped the company decrease its fulfillment expense ratio to a world-leading level of 6.5%. The construction of intelligent warehouses has led to estimated annual savings of hundreds of millions of dollars. In 2020, JD.com delivered 90% of its first-party-owned retail orders on the same day or on the day after the order was placed. The agility of such intelligent warehouses has allowed JD.com to handle 10 times the normal volume of orders during peak sales seasons and has also helped the company respond quickly to COVID-19 and ensure the rapid recovery of production capabilities.

A Passenger-Centric Approach to Air Traffic Flow Management

Traffic flow management initiatives aim to balance the flows of vehicles in capacity-constrained transportation networks to minimize congestion costs. While existing research has focused on vehicle-centric delay minimization objectives, this may not result in most efficient outcomes from the end users' perspective when travel itineraries involve connections between multiple vehicles. This paper develops an original user-centric approach to traffic flow management. First, an analytical Markov Decision Process is presented to derive structural insights on the drivers of user-centric operations. Second, this paper augments existing air traffic flow management (ATFM) models by explicitly balancing flight delay costs and passenger delays. A large-scale integer programming model is formulated to track the impact of flow management operations on passenger accommodations. An original rolling procedure decomposes the problem over time while ensuring global feasibility, and shown to enable the model's implementation in short computational times. Computational results in the US National Aviation System suggest that this modeling and computational framework can achieve large reductions in passenger delays at comparatively small increases in flight delay costs. Analytical and computational results highlight two major levers of user-centric operations: (i) delay allocation, which determines which flights to delay or prioritize to minimize delay costs, and (ii) delay introduction, which deliberate adds departure holds to avoid passenger misconnections.

A defender-attacker model and algorithm for maximizing weighted expected hitting time with application to conservation planning

ABSTRACTThis article studies an interdiction problem in which two agents with opposed interests, a defender and an attacker, interact in a system governed by an absorbing discrete-time Markov chain. The defender protects a subset of transient states, whereas the attacker targets a subset of the unprotected states. By changing some of the transition probabilities related to the attacked states, the attacker seeks to minimize the Weighted Expected Hitting Time (WEHT). The defender seeks to maximize the attacker’s minimum possible objective, mitigating the worst-case WEHT. Many applications can be represented by this problem; this article focuses on conservation planning. We present a defender–attacker model and algorithm for maximizing the minimum WEHT. As WEHT is not generally a convex function of the attacker’s decisions, we examine large-scale integer programming formulations and first-order approximation methods for its solution. We also develop an algorithm for solving the defender’s problem via mixed-integer programming methods augmented by supervalid inequalities. The efficacy of the proposed solution methods is then evaluated using data from a conservation case study, along with an array of randomly generated instances.

Modeling, Optimization, and Operation of Large-Scale Air Traffic Flow Management on Spark

The nationwide air traffic flow management problem often encounters computational difficulty because it is generally modeled as an integer programming problem that requires computationally expensive optimization algorithms. This paper introduces a customized Spark-based optimization architecture for such large-scale integer programming problems to further speed up the modeling and optimization process, where Spark is a big data cluster-computing platform. First, a novel layered aggregate model is developed for handling flexible rerouting problem, which is not well handled in a previous link transmission model. As an aggregate linear model, the layered aggregate model has the nice features of computational efficiency and scalability, which make it suitable for Apache Spark. By applying a dual decomposition method, the original large-scale problem is decomposed into a number of small subproblems. The optimization proceeds by iteratively solving subproblems and updating Lagrange multipliers. This paper encapsulated the process into the Spark-based data processing model such that the optimization is automatically scheduled to run in parallel. Spark gains efficiency by means of in-memory computing and dynamic schedule allocation. This is demonstrated in the experimental results that are compared to an earlier Hadoop MapReduce-based model, where Hadoop MapReduce is a basic cloud computing framework; the Spark-based model is solved twice as fast as the Hadoop MapReduce-based model.

Optimal duty rostering for toll enforcement inspectors

We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.

Locomotive Planning at Norfolk Southern: An Optimizing Simulator Using Approximate Dynamic Programming

For decades, locomotive planning has been approached using the classical tools of mathematical programming; the result has been very large-scale integer programming models that are beyond the capabilities of modern solvers but still require a host of simplifying assumptions that limit their use for analyzing important planning problems. The primary interest of Norfolk Southern was in developing a model that could assist it with fleet sizing. However, the cumulative effect of the simplifications required to produce a practical integer programming formulation resulted in models that underestimated the required fleet. We use the modeling and algorithmic framework of approximate dynamic programming, which uses an intuitive balance of simulation and optimization with feedback learning, to produce a highly detailed model that calibrates accurately against historical metrics. The result was a model that can be used to plan fleet size and mix, be sensitive to a wide range of operating parameters, and adapt to many scenarios.

A Parallel Branch and Bound Algorithm for Solving Large Scale Integer Programming Problems

Branch and Bound technique is commonly used for intelligent search in fin ding a set of integer solutions within a space of interest. The corresponding binary tree structure provides a natural p arallelism allowing concurrent evaluation of subproblems using parallel computing technology. While the master-worker paradigm is successfully used in many parallel applications as a common framework to implement parallel applications, it has drawbacks when a large number of computing resources are connected via WAN. A supervisor-master-sub-master-worker algorithm has been proposed. From the solved benchmark example this algorithm proved to provide a considerable save of time. Results show that a consistently bette r efficiency can be achieved in solving integer equations, providing reduction of time. The hierarchical supervisor-master-sub-master-worker algorithm sustains good performance revealed from the knapsack problem solved as a benchmark example.

Minimum Length Scheduling With Packet Traffic Demands in Wireless <italic>Ad Hoc</italic> Networks

Traditional approach to the minimum length scheduling problem ignores the packet level details of transmission protocols, meaning that a packet transmission can be divided into several data chunks each of which is transmitted at a different rate due to the difference in the set of concurrently transmitting nodes. This solution requires including packet headers for each data chunk resulting in both an increase in the system overhead and underutilization of the time slots. In this paper, we extend the previous works on minimum length scheduling by considering the transmission of the packets of arbitrary sizes in the time slots of arbitrary lengths. Given the packet traffic demands on the links, we formulate the joint optimization of the power control, rate adaptation and scheduling for minimizing the schedule length of a wireless ad hoc network and demonstrate the hardness of this problem. Upon solving the power control and rate adaptation problem separately, we formulate the scheduling problem as an integer programming (IP) problem where the number of variables is exponential in the number of the links. In order to solve this large-scale IP problem fast and efficiently, we propose Branch and Price Method and Column Generation Method based heuristic algorithms.

A Decomposition Technique For Solving Integer Programming Problems

Dantzig-Wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound due to the non-convexity of an integer problem. In this paper, we develop an algorithm for solving large scale integer program relying on column generation method. We implemented our algorithm for solving Capital budgeting and scheduling type problems. Moreover, we used the Computer Aided System (CAS) AMPL to convert our algorithm into programming codes and illustrated the same problem in our program. We demonstrate our method by illustrating some numerical examples. DOI: http://dx.doi.org/10.3329/ganit.v33i0.17649 GANIT J. Bangladesh Math. Soc.Vol. 33 (2013) 1-11

High-Speed Rail Train Timetabling Problem: A Time-Space Network Based Method with an Improved Branch-and-Price Algorithm

A time-space network based optimization method is designed for high-speed rail train timetabling problem to improve the service level of the high-speed rail. The general time-space path cost is presented which considers both the train travel time and the high-speed rail operation requirements: (1) service frequency requirement; (2) stopping plan adjustment; and (3) priority of train types. Train timetabling problem based on time-space path aims to minimize the total general time-space path cost of all trains. An improved branch-and-price algorithm is applied to solve the large scale integer programming problem. When dealing with the algorithm, a rapid branching and node selection for branch-and-price tree and a heuristic train time-space path generation for column generation are adopted to speed up the algorithm computation time. The computational results of a set of experiments on China’s high-speed rail system are presented with the discussions about the model validation, the effectiveness of the general time-space path cost, and the improved branch-and-price algorithm.

A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs

Large-scale binary integer programs occur frequently in many real-world applications. For some binary integer problems, finding an optimal solution or even a feasible solution is computationally expensive. In this paper, we develop a discrete meta-control procedure to approximately solve large-scale binary integer programs efficiently. The key idea is to map the vector of n binary decision variables into a scalar function defined over a time interval [0; n] and construct a linear quadratic tracking (LQT) problem that can be solved efficiently. We prove that an LQT formulation has an optimal binary solution, analogous to a classical bang-bang control in continuous time. Our LQT approach can provide advantages in reducing computation while generating a good approximate solution. Numerical examples are presented to demonstrate the usefulness of the proposed method.

A fast algorithm for kernel 1-norm support vector machines

This paper presents a fast algorithm called Column Generation Newton (CGN) for kernel 1-norm support vector machines (SVMs). CGN combines the Column Generation (CG) algorithm and the Newton Linear Programming SVM (NLPSVM) method. NLPSVM was proposed for solving 1-norm SVM, and CG is frequently used in large-scale integer and linear programming algorithms. In each iteration of the kernel 1-norm SVM, NLPSVM has a time complexity of O(ℓ3), where ℓ is the sample number, and CG has a time complexity between O(ℓ3) and O(n′3), where n′ is the number of columns of the coefficient matrix in the subproblem. CGN uses CG to generate a sequence of subproblems containing only active constraints and then NLPSVM to solve each subproblem. Since the subproblem in each iteration only consists of n′ unbound constraints, CGN thus has a time complexity of O(n′3), which is smaller than that of NLPSVM and CG. Also, CGN is faster than CG when the solution to 1-norm SVM is sparse. A theorem is given to show a finite step convergence of CGN. Experimental results on the Ringnorm and UCI data sets demonstrate the efficiency of CGN to solve the kernel 1-norm SVM.

Container Slot Co-Allocation Planning with Joint Fleet Agreement in a Round Voyage for Liner Shipping

In the liner shipping market carriers share container slots to offer better service and realize economies of scale. This paper studies slot co-allocation planning for a joint fleet in a round trip for a shipping alliance in the liner shipping industry. In particular, a conceptual model is developed based on joint fleet and slot co-allocation management. The factors affecting slot co-allocation planning are explored in detail. A large-scale integer programming model is formulated to guide carriers in an alliance in pursuing an optimal slot co-allocation strategy. In contrast to the existing research, this approach leads to a more accurate representation of the situation for cooperative services in the liner shipping market. Extensive numerical experiments based on a true Asia-Europe cooperative route of COSCO and HANJIN show that the proposed model can be efficiently solved by LINGO11.0 for the case study. The computational results suggest that the mechanism and model can be used to benefit carriers in making better decisions in shipping cooperation services.

A Compressed Sensing Based Basis-pursuit Formulation of the Room Algorithm

Regulatory on off minimization (ROOM) is a popular metabolic modeling strategy for obtaining the fluxes of various metabolic reactions in a mutant. It is based on minimization of the number of flux changes with respect to the wild-type. The ROOM approach involves solving an integer programming problem. In ROOM, the number of integer decision variables is equal to the number of reactions in the metabolic network under consideration. Typically, metabolic networks of interest are genome scale implying that the number of reactions in the network and hence the number of integer decision variables is large. The ROOM approach thus has inherent difficulties associated with large scale integer programming problems. In the current work, motivated by the emerging area of compressed sensing, we propose a reformulation, known as basis-pursuit, of the ROOM algorithm. The proposed formulation is an L1 norm minimization problem and is thus convex in nature. The proposed approach is used to obtain the flux profiles for various mutants of the Synechocystis species strain PCC 6803. The results are compared with the existing ROOM approach. It is observed that the proposed algorithm performs better in most cases. Use of compressed sensing based formulation creates exciting possibilities of efficiently reformulating various other metabolic network analysis problems.

Converging upon basic feasible solutions through Dantzig–Wolfe decomposition

We derive an important property for solving large-scale integer programs by examining the master problem in Dantzig–Wolfe decomposition. In particular, we prove that if a linear program can be divided into subproblems with affinely independent corner points, then there is a direct mapping between basic feasible solutions in the master and original problems. This has implications for integer programs where the feasible region has integer corner points, ensuring that integer solutions to the original problem will be found even through the decomposition approach. An application to air traffic flow scheduling, which motivated this result, is highlighted.

Feedback Control of the National Airspace System

DOI: 10.2514/1.51203 This paper proposes a general modeling framework adapted to the feedback control of traffic flows in Eulerian modelsof the NationalAirspace System. It is shown thatthe problems of scheduling androuting aircraft flowsin the NationalAirspaceSystemcanbeposedasthecontrolofanetworkofqueueswithload-dependentservicerates.Focus can then shift to developing techniques to ensure that the aircraft queues in each airspace sector, which are an indicator of the air traffic controller workloads, are kept small. This paper uses the proposed framework to develop control laws that help prepare the National Airspace System for fast recovery from a weather event, given a probabilistic forecast of capacities. In particular, the model includes the management of airport arrivals and departures subject to runway capacity constraints, which are highly sensitive to weather disruptions. I. Introduction T HE frequent occurrence of air traffic delays in the National Airspace System (NAS), along with the projected increase in demand, motivate the scheduling of flight operations to better use available system resources. The process of planning operations to balancetheavailablecapacityandthedemandforresourcesisknown asTrafficFlowManagement(TFM).Thistaskiscurrentlyconducted manually by air traffic controllers (ATC), and contributes significantlytotheirworkload.Tomeettheincreasingtrafficdemand,there is a desire to introduce a greater level of automation and decision support for air traffic management. Research on the TFM problem has traditionally focused on developing open-loop policies for scheduling aircraft operations. Because of the typical travel times of cross-country flights, openloop traffic flow management policies need to be determined 5– 6 hours ahead of the time of operations. Such policies prescribe the positionofeachaircraftinthesystemateachinstant,andareobtained by solving large-scale integer programs [1,2]. This approach is difficult to scale to the scheduling of approximately 40,000 flights a day, and typically does not address the many sources of uncertainty present in the system. Weather, in particular, is a major source of disruption that requires constant adjustment of the schedules. For instance, 66% of all NAS delays in 2009 were attributed toweather. ‡ Moreover, open-loop traffic flow management algorithms require precise weather forecasts several hours ahead of time, which are arguably beyond the limits of even state-of-the-art weather forecasting tools [3]. The disturbance attenuation properties of feedback control make closed-loop control policies for the NAS very attractive. Attempts have been made to introduce some feedback in the decision algorithmswhilestilltryingtooptimizeeachaircrafttrajectory[4,5]. More recently, researchers have started developing new models that are more tractable for the purpose of control, which only record aircraft counts in specific control volumes of airspace rather than follow individual aircraft. These aggregate flow models, called