Realistic Problem Instances Research Articles

Scheduling of Automated Wet-Etch Stations with One Robot in Semiconductor Manufacturing via Constraint Answer Set Programming

Scheduling and optimization have a central place in the research area of computing because it is increasingly important to achieve fully automated production processes to adjust manufacturing systems to the requirements of Industry 4.0. In this paper, we demonstrate how an automated wet-etch scheduling problem for the semiconductor industry can be solved by constraint answer set programming (CASP) and its solver called clingcon. A successful solution to this problem is achieved, and we found that for all tested problems, CASP is faster and obtains smaller makespan values for seven of the eight problems tested than the solutions based on mixed integer linear programming and constraint paradigms. The considered scheduling problem includes a robot for lot transfers between baths. CASP is a hybrid approach in automated reasoning that combines different research areas such as answer set programming, constraint processing, and Satisfiability Modulo Theories. For a long time, exact methods such as constraint programming have displayed difficulties in solving real large-scale problem instances. Currently, the performance of state-of-the-art constraint solvers is comparatively better than a decade ago, and some complex combinatorial problems can be better solved. These theoretical and technical achievements open new horizons for declarative programming applications such as logistics.

Integrating human infrastructure in post-disaster critical lifeline restoration scheduling

Critical societal services, such as health care, are offered from facilities that are supported by civil lifelines. In disaster events, restoration of the damaged lifeline elements and facilities is necessary for restoring societal function. It is generally presumed that the critical societal services are intact as long as the buildings from which they are provided are functioning and have operating supporting lifelines. This paper recognizes that the services require not only a functioning space for supporting related operations, but also depend on the presence of skilled personnel. For this purpose, a mathematical technique for modeling this human infrastructure as a civil lifeline is proposed. This human infrastructure lifeline modeling approach is integrated into a stochastic program that seeks an optimal schedule of post-event restoration actions across lifelines to minimize the amount of time that civil lifeline elements, including personnel, and the critical societal services they support are nonfunctioning. The model is cast in a real-time setting, where situational awareness increases over time as information is obtained either endogenously via the repair crews or by way of exogenously provided information from other sources (e.g., inspectors, emergency responders, drones, remote sensing). The approach is also useful in estimating critical societal systems resilience. Numerical experiments were conducted on a synthetic, yet realistic problem instance to illustrate the capabilities of the proposed techniques and investigate the importance of adequately capturing the multi-faceted role of personnel in post-disaster service capacity restoration.

Solving large-scale electricity market pricing problems in polynomial time

In centralized wholesale electricity markets worldwide, market operators use mixed-integer linear programming to solve the allocation problem. Prices are typically determined based on the duals of relaxed versions of this optimization problem. The resulting outcomes are efficient, but market operators must pay out-of-market uplifts to some market participants and incur a considerable budget deficit that was criticized by regulators. As the share of renewables increases, the number of market participants will grow, leading to larger optimization problems and runtime issues. At the same time, non-convexities will continue to matter, e.g., due to ramping constraints of the generators required to address the variability of renewables or non-convex curtailment costs. We draw on recent theoretical advances in the approximation of competitive equilibrium to compute allocations and prices in electricity markets using convex optimization. The proposed mechanism promises approximate efficiency, no budget deficit, and computational tractability. We present experimental results for this new mechanism in the context of electricity markets, and compare the runtimes, the average efficiency loss of the method, and the uplifts paid with standard pricing rules. We find that the computations with the new algorithm are considerably faster for relevant problem sizes. In general, the computational advantages come at the cost of efficiency losses and a price markup for the demand side. Interestingly, both are small with realistic problem instances. Importantly, the market operator does not incur a budget deficit and the uplifts paid to market participants are significantly lower compared to standard pricing rules.

Modeling of sustainable integrated supply chains under the consideration of European Union regulations

AbstractThis work introduces a multi-period, multi-commodity, inventory-routing problem with strategic fleet scheduling decisions, under the consideration of speed limits, as well as strict European Union regulations on truck drivers’ working and driving time. To address the new problem, a mixed integer linear programming model was developed. Several artificial but realistic problem instances were randomly generated following relative guidelines from the open literature, to validate and assess the performance of the novel mathematical model. Furthermore, in an effort to produce useful managerial insights, several sensitivity analyses were performed considering different fluctuation rates on key model parameters.

A branch-and-cut approach to solve the Fault Diagnosis Problem with Lazy Spread and imperfect system information

This paper presents a new approach to solving the Fault Diagnosis Problem with Lazy Spread (FDPL) that arises in many fault-tolerant real-world systems with few opportunities for maintenance during their operations and significant failure interactions between the subsystems/components. As opposed to cascading faults that spread to most of the system almost instantaneously, FDPL considers fault-resistant systems where the spread of failures is relatively slow (lazy), i.e., only a small fraction of the components are faulty at the time of inspection, and accurate diagnosis of the faulty components is of critical importance to restore system performance and stop further damage. Introducing an extra level of difficulty, FDPL needs to be solved under imperfect (missing and wrong) system information in most real-world settings. To address this challenging prediction problem, we use graph theory concepts to develop an integer programming formulation and devise an efficient branch-and-cut algorithm for its solution. Extensive numerical experiments on realistic problem instances attest to the superior performance of our approach in terms of both computational efficiency and prediction accuracy compared to the state-of-the-art in the literature.

Enhanced methods for the weight constrained shortest path problem

AbstractThe classic problem of constrained pathfinding is a well‐studied, yet challenging, network optimization problem with a broad range of applications in various areas such as communication and transportation. The weight constrained shortest path problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost‐optimum path with limited weight/resource usage. Given the bi‐criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi‐objective search. This article leverages the recent state‐of‐the‐art techniques in both constrained pathfinding and bi‐objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state‐of‐the‐art algorithms in both time and space metrics. This article also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomized graphs how bucket‐based queues without tie‐breaking can effectively improve the algorithmic performance of exhaustive A*‐based bi‐criteria searches.

Wind farm layout optimization under uncertainty

Wind power is a major source of green energy production. However, the energy generation of wind power is highly affected by uncertainty. Here, we consider the problem of designing the cable network that interconnects the turbines to the substation in wind farms, aiming to minimize both the infrastructure cost and the cost of the energy losses during the wind farm’s lifetime. Nonetheless, the energy losses depend on wind direction and speed, which are rarely known with certainty in real situations. Hence, the design of the network should consider these losses as uncertain parameters. We assume that the exact probability distribution of these parameters is unknown but belongs to an ambiguity set and propose a distributionally robust two-stage mixed integer model. The model is solved using a decomposition algorithm. Three enhancements are proposed given the computational difficulty in solving real problem instances. Computational results are reported based on real data.

Analyzing the benefits of a city hub: An inventory and routing perspective

Collaboration is one of the crucial elements in city logistics and it is often pursued by the introduction of two- or multi-echelon systems using one or more intermediate consolidation points, such as Urban Consolidation Centers (UCCs), city depots, city hubs, etc. Our literature review shows that the study of inventory aspects in such a context is relatively unexplored. Therefore, this paper studies the effect of using a UCC or city hub in a B2B city logistics system in terms of both inventory and routing aspects. A multi-period optimization model is proposed to support the operational decisions in urban B2B distribution when using a city hub. We study the effect of introducing a city hub by comparing our model with a baseline model in which urban retailers operate without a city hub. The model accounts for the complexity of urban logistics by considering a heterogeneous vehicle fleet, the option to perform multiple trips per day, and strict customer time windows. A metaheuristic algorithm based on Large Neighborhood Search (LNS) is used to solve the route optimization problem for realistic problem instances. Extensive numerical experiments are conducted according to an experimental design and a statistical analysis. Results indicate that the introduction of a city hub leads to significant reductions in operational costs and societal impacts (e.g., loading degree, number of urban trips, traveled distances). Our analysis shows that these savings are significantly impacted by the problem context (e.g., replenishment policy, number of retailers, number of suppliers, and holding cost). For example, how retailers make replenishment decisions significantly impacts the costs of the overall system and the potential savings. The most cost-efficient replenishment method is often not the most interesting one from a societal perspective. Finally, from a city’s perspective, a sufficient number of retailers and suppliers should participate in the system to maximize consolidation opportunities. However, in relative terms, the largest potential savings by introducing a city hub are reached when not too many suppliers are included and suppliers have a relatively limited number of customers to serve.

A decision support framework for optimal vaccine distribution across a multi-tier cold chain network

In this paper, we present a decision support framework for optimizing multiple aspects of vaccine distribution across a multi-tier cold chain network. We propose two multi-period optimization formulations within this framework: first to minimize inventory, ordering, transportation, personnel and shortage costs associated with a single vaccine; the second for the case when multiple vaccines with differing efficacies and costs are available for the same disease. We use the case of the Indian state of Bihar and COVID-19 vaccines to illustrate the implementation of the framework. We present computational experiments including what-if scenario and sensitivity analyses to demonstrate: (a) the organization of the model outputs; (b) how the models can be used to assess the impact of cold chain point storage capacities, transportation vehicle capacities, and manufacturer capacities on the optimal vaccine distribution pattern; and (c) the impact of vaccine efficacies and associated costs such as ordering and transportation costs on the vaccine selection decision informed by the model. We then demonstrate how robust optimization versions of the single vaccine model, with box and budgeted uncertainty sets, outperform the deterministic version under multiple levels of uncertainty in key model parameters. Finally, we also consider the computational expense of the framework for realistic problem instances, and suggest multiple preprocessing techniques to reduce computational runtimes. Our study presents public health authorities and other stakeholders with a vaccine distribution and capacity planning tool for multi-tier cold chain networks.

Hub Network Design Problem with Capacity, Congestion, and Stochastic Demand Considerations

Our study introduces the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decisions and congestion cost effect into the problem and allowing dynamic routing for origin-destination (OD) pairs. Connecting strategic and operational level decisions, HNDC jointly decides hub locations and capacity acquisitions by considering the expected routing and congestion costs. A path-based mixed-integer second-order cone programming (SOCP) formulation of the HNDC is proposed. We exploit SOCP duality results and propose an exact algorithm based on Benders decomposition and column generation to solve this challenging problem. We use a specific characterization of the capacity-feasible solutions to speed up the solution procedure and develop an efficient branch-and-cut algorithm to solve the master problem. We conduct extensive computational experiments to test the proposed approach’s performance and derive managerial insights based on realistic problem instances adapted from the literature. In particular, we found that including hub congestion costs, accounting for the uncertainty in demand, and whether the underlying network is complete or incomplete have a significant impact on hub network design and the resulting performance of the system. Funding: This work was supported by Türkiye Bilimsel ve Teknolojik Araştırma Kurumu [Grant 218M520]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.0112 .

A Quantum Algorithm for the Sub-graph Isomorphism Problem

We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number of qubits that scales logarithmically with the number of vertices of the graphs; and (2) on a new ansatz that can efficiently probe the permutation space. Simulations are then presented to showcase the approach on graphs up to 16 vertices, whereas, given the logarithmic scaling, the approach could be applied to realistic sub-graph isomorphism problem instances in the medium term.

The Bicycle Network Improvement Problem

Using a bicycle for commuting is still uncommon in US cities, although it brings many benefits to both the cyclists and to society as a whole. Cycling has the potential to reduce traffic congestion and emissions, increase mobility, and improve public health. To convince people to commute by bike, the infrastructure plays an important role, since safety is one of the primary concerns of potential cyclists. This paper presents a method to find the best way to improve the safety of a bicycle network for a given budget and maximize the number of riders that could now choose bicycles for their commuting needs. This optimization problem is formalized as the Bicycle Network Improvement Problem (BNIP): it selects which roads to improve for a set of traveler origin-destination pairs, taking both safety and travel distance into account. The BNIP is modeled as a mixed-integer linear program that minimizes a piecewise linear penalty function of route deviations of travelers. The MIP is solved using Benders decomposition to scale to large instances. The paper also presents an in-depth case study for the Midtown area in Atlanta, GA, using actual transportation data. The results show that the Benders decomposition algorithm allows for solving realistic problem instances and that the network improvements may significantly increase the share of bicycles as the commuting mode. Multiple practical aspects are considered as well, including sequential road improvements, uneven improvement costs, and how to include additional data.

Novel method for welding gantry robot scheduling at shipyards

ABSTRACT Welding is the most critical operation in the shipbuilding process and has a significant influence on the production cost and quality of ships. Therefore, the welding operation must be optimised. This paper presents a real-world welding gantry robot scheduling problem at shipyards, in which three gantry robots function in parallel. Welding gantry robots cannot cross each other and should operate over a certain distance to avoid collisions. To minimise the makespan, the welding tasks given by line segments should be evenly distributed among the three gantry robots. The welding tasks assigned to each robot should be optimally sequenced to minimise the completion time, including the waiting time required to prevent collisions with neighbouring robots. In addition, long welding edges are split, and the split small length edges are assigned to the gantry robots. This paper proposes a mixed-integer linear programming model, three-stage solution approach, and variable neighbourhood search algorithm to solve this problem. Experimental tests conducted on 20 real problem instances revealed that the proposed approach can reduce the makespan by 14% on average when compared with the conventional method.

Weight Constrained Path Finding with Bidirectional A*

Weight constrained path finding, known as a challenging variant of the classic shortest path problem, aims to plan cost optimum paths whose weight/resource usage is limited by a side constraint. Given the bi-criteria nature of the problem (i.e., the presence of cost and weight), solutions to the Weight Constrained Shortest Path Problem (WCSPP) have some properties in common with bi-objective search. This paper leverages the state-of-the-art bi-objective search algorithm BOBA* and presents WC-BA*, an exact A*-based WCSPP method that explores the search space in different objective orderings bidirectionally. We also enrich WC-BA* with two novel heuristic tuning approaches that can significantly reduce the number of node expansions in the exhaustive search of A*. The results of our experiments on a large set of realistic problem instances show that our new algorithm solves all instances and outperforms the state-of-the-art WCSPP algorithms in various scenarios.

Clustering-based iterative heuristic framework for a non-emergency patients transportation problem

IntroductionNon-emergency patient transportation (NEPT) services are particularly important nowadays due to the aging population and contagious disease outbreaks (e.g., Covid-19 and SARS). In this work, we study a NEPT problem with a case study of patient transportation services in Hong Kong. The purpose of this work is to study the discomfort and inconvenience measures (e.g., waiting time and extra ride time) associated with the transportation of non-emergency patients while optimizing the operational costs and utilization of NEPT ambulances. MethodsA mixed-integer linear programming (MILP) formulation is developed to model the NEPT problem. This MILP model contributes to the existing literature by not only including the patient inconvenience measures in the objective function but also illustrating a better trade-off among different performance measures through its specially customized formulation and real-life characteristics. CPLEX is used to find the optimal solutions for the test instances. To overcome the computational complexity of the problem, a clustering-based iterative heuristic framework is designed to solve problems of practical sizes. The proposed framework distinctively exploits the problem-specific structure of the considered NEPT problem in a novel way to enhance and improve the clustering mechanism by repeatedly updating cluster centers. ResultsThe computational experiments on 19 realistic problem instances show the effective execution of the solution method and demonstrate the applicability of our approach. Our heuristic framework observes an optimality gap of less than 5% for all those instances where CPLEX delivered the result. The weighted objective function of the proposed model supports the analysis of different performance measures by setting different preferences for these measures. An extensive sensitivity analysis performed to observe the behavior of the MILP model shows that when operating costs are given a weightage of 0.05 in the objective function, the penalty value for user inconvenience measures is the lowest; when the weightage value for operating costs varies between 0.8 and 1.0, the penalty value for the same measures is the highest. ConclusionsThis research can assist decision-makers in improving service quality by balancing operational costs and patient discomfort during transportation.

Exact and meta-heuristic approaches for the production leveling problem

In this paper, we introduce a new problem in the field of production planning, called the production leveling problem. The task is to assign orders to production periods such that the load in each period and for each product type is balanced, capacity limits are not exceeded, and the orders’ priorities are taken into account. Production leveling is an important intermediate step between long-term planning and the final scheduling of orders within a production period, as it is responsible for selecting good subsets of orders to be scheduled within each period. We provide a formal model of the problem and study its computational complexity. As an exact method for solving moderately sized instances, we introduce a mixed integer programming (MIP) formulation. For solving large problem instances, metaheuristic local search is investigated. A greedy heuristic and two neighborhood structures for local search are proposed in order to apply them using simulated annealing. Furthermore, three possible extensions that arise from the application in practice are described and implemented, both within the MIP model and within simulated annealing. We make publicly available a set of realistic problem instances from the industry as well as from random instance generators. The experimental evaluation on our test sets shows that the proposed MIP model is well suited for solving instances with up to 250 orders. Simulated annealing produces solutions with less than 3% average optimality gap on small instances, and scales well up to thousands of orders and dozens of periods and product types. The metaheuristic method presented herein is already being successfully used in the industry.

Arc Routing with Electric Vehicles: Dynamic Charging and Speed-Dependent Energy Consumption

Concerns about greenhouse gas emissions and government regulations foster the use of electric vehicles. Several recently published articles study the use of electric vehicles (EVs) in node-routing problems. In contrast, this article considers EVs in the context of arc routing while also addressing practically relevant aspects that have not been addressed sufficiently so far. These include dynamic charging of EVs while driving, speed-dependent energy consumption, and nonlinear charging functions that depend on the battery’s state of charge and the charging time. A generic way of dealing with these aspects is introduced through the concept of an energy-indexed graph, which is used to derive an integer linear programming formulation and a solution framework based on branch and cut. Efficient construction heuristics and a local search for approximately solving large-scale instances are proposed. A computational study is performed on realistic problem instances. Besides analyzing the performance of all proposed methods, the obtained results also provide insights into strategic decisions related to the battery size and the amount of charging facilities.

Benchmark of quantum-inspired heuristic solvers for quadratic unconstrained binary optimization

Recently, inspired by quantum annealing, many solvers specialized for unconstrained binary quadratic programming problems have been developed. For further improvement and application of these solvers, it is important to clarify the differences in their performance for various types of problems. In this study, the performance of four quadratic unconstrained binary optimization problem solvers, namely D-Wave Hybrid Solver Service (HSS), Toshiba Simulated Bifurcation Machine (SBM), Fujitsu Digital Annealer (DA), and simulated annealing on a personal computer, was benchmarked. The problems used for benchmarking were instances of real problems in MQLib, instances of the SAT-UNSAT phase transition point of random not-all-equal 3-SAT (NAE 3-SAT), and the Ising spin glass Sherrington-Kirkpatrick (SK) model. Concerning MQLib instances, the HSS performance ranked first; for NAE 3-SAT, DA performance ranked first; and regarding the SK model, SBM performance ranked first. These results may help understand the strengths and weaknesses of these solvers.

Hybrid Approach for Solving Multi-Objective Hybrid Flow Shop Scheduling Problems with Family Setup Times

Solving industrial scheduling problems remains challenging despite the heavy research efforts in the last decade due to the introduction of new technologies in the context of industry 4.0. Such problems must be solved with light execution time to support near-real-time decision-making processes. In addition, the majority of real industrial Hybrid Flow Shop (HFS) scheduling problems must be solved to minimize multi-objective values that are conflicting in nature. Such problems are proven to be NP-hard. Therefore, in this paper, a hybrid multi-objective approach is presented for solving HFS scheduling problems. The hybrid technique is based on the Non-Dominated Sorting Genetic Algorithms three (NSGA III). The design of the hybrid approach is based on the use of multi-populations that are used to control different allocation-, sequencing-algorithms, and decision points over time. The problems are solved to minimize the makespan, the total number of family major setup times, the total tardiness, and the total number of penalties. The computational results show that the presented approach marginally outperforms other techniques that are published in the related literature for solving two-stage and four-stage HFS scheduling problems. Both problems are derived from real use-cases with real problem instances.

Industrial-size job shop scheduling with constraint programming

The job shop scheduling problem is one of the most studied optimization problems to this day and it becomes more and more important in the light of the fourth industrial revolution (Industry 4.0) that aims at fully automated production processes. For a long time exact methods like constraint programming had problems to solve real large-scale problem instances and methods of choice were to be found in the area of (meta-) heuristics. However, developments during the last decade improved the performance of state-of-the-art constraint solvers dramatically, to the point that they can be applied also on large-scale instances. The presented work’s main target is to elaborate the performance of state-of-the-art constraint solvers with respect to industrial-size job shop scheduling problem instances. To this end, we analyze and compare the performance of two cutting-edge constraint solvers: OR-Tools, an open-source solver developed by Google and recurrent winner of the MiniZinc Challenge, and CP Optimizer, a proprietary constraint solver from IBM targeted at industrial optimization problems. In order to reflect real-world industrial scenarios with heavy workloads like found in the semi-conductor domain, we use novel benchmarks that comprise up to one million operations to be scheduled on up to one thousand machines. The comparison is based on the best makespan (i.e. completion time) achieved and the time required to solve the problem instances. We test the solvers on single-core and quad-core configurations.