Two-phase Solution Approach Research Articles

Railway line planning with passenger routing: Direct-service network representations and a two-phase solution approach

The railway line planning problem (LPP) plays a crucial role in determining the quality of services provided to passengers, as well as operation costs borne by railway companies. In periodic railway LPPs, it is common to consider passenger transfers between train lines to realize a general passenger travel cost setting in the railway system. While detecting passenger transfers requires incorporating passenger routing into mathematical formulations, thereby significantly complicating the problem. Studies on transfer-included LPPs are generally based on the Change&Go network that is constructed based on a pre-given line pool, which however is usually non-exhaustive due to computational intractability. To efficiently include passenger transfers in large-scale railway LPPs, this paper proposes a novel extended direct-service network representation of LPP, where lines are dynamically generated within the optimization process, and part of passenger transfers between lines can be precisely captured without the need for explicit modeling of passengers’ distribution on specific lines. A two-phase solution approach based on the representation is designed. The first phase formulates LPP with part of transfers as a path-based service network design model, solved using a branch-price-and-cut algorithm. The second phase conducts a neighborhood search around the first-phase solution to seek better ones when considering all passenger transfers. Numerical results showcase the good performance of the two-phase solution approach. It delivers optimal solutions in 18 out of 24 test instances for a small case and achieves optimality gaps within 2.85% across all small instances. The large case study of China’s Shandong high-speed railway network whose line pool size reaches millions demonstrates the scalability of the approach and its advantage over the traditional Change&Go method with partial line pools and an exact model developed in the paper.

Two-Phase Fuzzy Real-Time Approach for Fuzzy Demand Electric Vehicle Routing Problem with Soft Time Windows

Environmental concerns have called for several measures to be taken within the logistics and transportation fields. Among these measures is the adoption of electric vehicles instead of diesel-operated vehicles for personal and commercial-delivery use. The optimized routing of electric vehicles for the commercial delivery of products is the focus of this paper. We study the effect of several practical challenges that are faced when routing electric vehicles. Electric vehicle routing faces the additional challenge of the potential need for recharging while en route, leading to more travel time, and hence cost. Therefore, in this work, we address the issue of electric vehicle routing problem, allowing for partial recharging while en route. In addition, the practical mandate of the time windows set by customers is also considered, where electric vehicle routing problems with soft time windows are studied. Real-life experience shows that the delivery of customers’ demands might be uncertain. In addition, real-time traffic conditions are usually uncertain due to congestion. Therefore, in this work, uncertainties in customers’ demands and traffic conditions are modeled and solved using fuzzy methods. The problems of fuzzy real-time, fuzzy demand, and electric vehicle routing problems with soft time windows are addressed. A mixed-integer programming mathematical model to represent the problem is developed. A novel two-phase solution approach is proposed to solve the problem. In phase I, the classical genetic algorithm (GA) is utilized to obtain an optimum/near-optimum solution for the fuzzy demand electric vehicle routing problem with soft time windows (FD-EVRPSTW). In phase II, a novel fuzzy real-time-adaptive optimizer (FRTAO) is developed to overcome the challenges of recharging and real-time traffic conditions facing FD-EVRPSTW. The proposed solution approach is tested on several modified benchmark instances, and the results show the significance of recharging and congestion challenges for routing costs. In addition, the results show the efficiency of the proposed two-phase approach in overcoming the challenges and reducing the total costs.

Optimal predictive selective maintenance for fleets of mission-oriented systems

ABSTRACT In many settings, fleets of assets must perform series of missions with in-between finite breaks. For such fleets, a widely used maintenance strategy is the fleet selective maintenance (FSM). Under resource constraints, the FSM problem selects an optimal subset of feasible maintenance actions to be performed on a subset of components to minimise the maintenance cost while ensuring high system reliability during the upcoming mission. The majority of extant FSMP models are focussed on traditional physics-based reliability models. With recent advances in Machine Learning (ML) and Deep Learning (DL) algorithms, data-driven methods have shown accuracy in predicting remaining useful life (RUL). This paper proposes a predictive FSM strategy for fleets of complex and large multicomponent systems. It relies on a concurrent ML/DL and optimisation approach where a clustering algorithm is used to determine the health states of components and a probabilistic RUL prognostics model is used for component reliability assessment. An optimisation model is developed to solve the predictive FSM problem to ensure high reliability of all systems within the fleet. An efficient two-phase solution approach is developed to solve this complex optimisation problem. Numerical experiments show the validity of the approach and highlight the improved maintenance plans achieved.

AlexNet Classifier and Support Vector Regressor for Scheduling and Power Control in Multimedia Heterogeneous Networks

In this paper, the downlink transmission of a two-tier heterogeneous network (HetNet) is considered in which a macro base station (MBS) serves the macro users using orthogonal frequency division multiple access (OFDMA) and small base stations (SBSs) serve the small-cell users through multi-carrier non-orthogonal multiple access (MC-NOMA) and joint transmission (JT). In particular, assuming the subcarriers are already allocated to macro users, the problem of scheduling (i.e., joint user association and subcarrier allocation) and power control is studied with the goal of maximizing the total users perceived quality-of -experience (QoE) for small-cell users, while a minimum data rate for macro users is guaranteed. To solve the joint optimization problem, a near-optimal and computationally efficient two-phase solution approach is proposed based on the tools from optimization and machine learning (ML). In the first phase, the optimization problem is solved to obtain the scheduling decisions and transmit power variables. In the second phase, the optimized scheduling decisions and transmit power variables serve as training samples for an AlexNet classifier and support vector regressor (SVR), respectively. Simulation results reveal that the integration of JT into MC-NOMA, outperforms the conventional MC-NOMA scheme by up to 24%, 19%, and 21% for the web, video and audio multimedia services, respectively.

Hybrid MCDM and simulation-optimization for strategic supplier selection

Supplier selection for strategic items requires a comprehensive framework dealing with qualitative and quantitative aspects of a company’s competitive priorities and supply risk, decision scope, and uncertainty. In order to address these aspects, this study aims to tackle supplier selection for strategic items with a multi-sourcing, taking into account multi-criteria, incorporating uncertainty of decision-makers judgment and supplier–buyer parameters, and integrating with inventory management which the past studies have not addressed well. We develop a novel two-phase solution approach based on integrated multi-criteria decision-making (MCDM) and multi-objective simulation-optimization (S-O). First, MCDM methods, including fuzzy AHP and interval TOPSIS, are applied to calculate suppliers’ scores, incorporating uncertain decision makers’ judgment. S-O then combines the (quantitative) cost-related criteria and considers supply disruptions and uncertain supplier–buyer parameters. By running this approach on data generated based on previous studies, we evaluate the impact of the decision maker’s and the objective’s weight, which are considered important in supplier selection.

The maximal covering bicycle network design problem

Considering the lack of adequate cycling infrastructure networks in many cities, decision makers must face the challenge of designing connected bicycle facility networks to ensure safe and comfortable access to urban opportunities for cyclists and the usability of infrastructure. This paper addresses the maximal covering bicycle network design problem (MCBNDP). MCBNDP involves making investment decisions to build a cycling network that is aimed at maximizing the coverage of cyclists, while maintaining a minimum total network cost at its minimum. The derived network is subject to a budget limit and accounts for the entire connectivity and directness as fundamental bicycle network design criteria. Cyclists who are located at a given origin are considered covered by the network if a connected path of dedicated cycling infrastructure links them to their desired destination, within a maximum travel distance. We propose a mixed-integer linear programming (MILP) formulation, including a two-phase solution approach to solving the MCBNDP. In addition, using a commercial solver, our MILP formulation allows exact solutions to be obtained for large-scale instances with reasonable computing times for these types of problems. This MILP formulation is employed to solve a real instance that is applied to a wide territory of analysis in Medellin city (Colombia). The findings of this paper will contribute to existing literature and support urban policymakers to better spatially allocate the resources and, consequently, maximize the impact of their investments on connected cycling infrastructure networks. Our findings indicate that access to opportunities for cyclists can be easily favored by making small improvements to the existing infrastructure to guarantee safe, direct, and comfortable cycling infrastructure. Because we specify a maximum travel distance rather than a shortest path limitation, our problem ensures that cyclists may have several possibilities for their routes, which may go along the shortest path or any other alternative, however, without exceeding the maximum travel distance. In this direction, our findings confirm that prioritizing coverage, while accounting for full network connectivity, will benefit more cyclists because of the flexible configuration of the new network, which also may ensure its usability.

Correction to: Evaluating the risk exposure of sustainable freight transportation: a two-phase solution approach

Correction to: Evaluating the risk exposure of sustainable freight transportation: a two-phase solution approach

Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition

We solve the type-2 assembly line balancing problem in the presence of sequence-dependent setup times, denoted SUALBP-2. The problem consists of a set of tasks of a product, requiring to be processed in different assembly stations. Each task has a definite processing and setup times. The magnitude of setup times for each task is dependent on the processing sequence within each station. Processing and setup times of tasks assigned to each station constitute the station time. The goal is to minimize the cycle time (the maximum station time) by optimally (i) assigning tasks to assembly stations and (ii) sequencing these tasks within each station. To solve this challenging optimization problem, we first improve upon an existing mixed-integer programming (MIP) model by our proposed lower and upper bounds. These enhancements reduce the MIP model’s (solved CPLEX) average optimality gap from 41.61% to 20.77% on extra-large instances of the problem. To further overcome the intractability of the MIP model, we develop an exact logic-based Benders decomposition (LBBD) algorithm. The LBBD algorithm effectively incorporates a novel two-phase solution approach, the lower and upper bounds, various preprocessing techniques, relaxations, and valid inequalities. Using existing benchmarks in the literature, we demonstrate that our LBBD algorithm finds integer feasible solutions for 100% of all 788 instances (64% for the MIP), verifies optimality for 47% of instances (37% for the MIP), and achieves an average optimality gap of 5.04% (7.72% for the MIP obtained over 64% solved small instances). The LBBD algorithm also significantly reduces the computational time required to solve these benchmarks. Summary of Contribution: Assembly line balancing plays a crucial role in productivity enhancement in manufacturing and service companies. A balanced assembly line ensures higher throughput rate and fairer distribution of workload among assembly stations (workers). Assembly line balancing, in its simplest form, is one of the most challenging combinatorial optimization problems. Its complexity is further intensified when the sequence of executing tasks assigned to each station influences the magnitude of the setup performed between any two successive tasks. In view of such complexity, most assembly line balancing problems have been solved by randomized search techniques that do not provide any guarantee on the quality of solutions found. The mission of this paper is to understand whether there is any special structure within the existing mathematical models in the literature and, if so, exploit them toward developing computationally efficient exact techniques that can provide guarantee on the quality of solutions. Indeed, we demonstrate that such a special mathematical structure exists and we thus develop the first decomposition technique in form of a logic-based Benders decomposition (LBBD) to efficiently solve the type-2 sequence-dependent assembly line balancing problem. Specifically, we show that our LBBD significantly reduces cycle time and the time required for decision making. Our LBBD generalizes the scope of exact techniques for decision-making beyond the assembly line problems and is extendable to many other shop scheduling problems that arrange their stations (machines) serially and there are sequence-dependent setup times among their tasks.

Evaluating the risk exposure of sustainable freight transportation: a two-phase solution approach

A combination of sustainability-related regulations and increased demand from stakeholders has pressed firms to adequately address sustainability-related risks. This issue is particularly important, and challenging, for the freight transportation sector due to its exposure to a large number of inherent sustainability risks. Despite the growing significance of sustainability risks, there is a lack of research related to sustainability risk management, which may be due to the difficulties in identifying and evaluating sustainability risks. We aim to fill this research gap by identifying, measuring and modelling sustainability risks in the context of freight transportation. Our research makes three primary contributions. First, we introduce the concept of a sustainability risk index (SRI) to understand the risk exposure of freight transportation systems (FTSs) in the context of India, an emerging market. The SRI is a mathematical tool used to measure sustainability risks and to quantify a firm’s exposure to sustainability-related risks. Second, we propose an integrated two-phase model based on an interval 2-tuple linguistic model and a digraph matrix approach to calculate the SRI. In contrast to other existing techniques, the proposed approach can effectively deal with uncertain and incomplete linguistic assessments without suffering a loss of information. Third, we propose a framework for calculating both the disruption scores and influencing power of sustainability risks to evaluate the associated criticality and triggering power. For a robustness check, we also conduct a sensitivity analysis of the impact of risk variations on the SRI. Unlike conventional perceptions, our results show that organisational and governmental risks, which are mostly behavioural and skills-induced, are more significant for sustainable FTSs compared to financial risks. Our research helps the managerial community in the freight transportation sector in emerging markets to engage in more informed decision-making to proactively mitigate sustainability risks, which have potentially devastating financial, environmental and societal impacts.

Exact Multiple Sequence Alignment by Synchronized Decision Diagrams

This paper develops an exact solution algorithm for the multiple sequence alignment (MSA) problem. In the first step, we design a dynamic programming model and use it to construct a novel multivalued decision diagram (MDD) representation of all pairwise sequence alignments (PSA). PSA MDDs are then synchronized using side constraints to model the MSA problem as a mixed-integer program (MIP), for the first time, in polynomial space complexity. Two bound-based filtering procedures are developed to reduce the size of the MDDs, and the resulting MIP is solved using logic-based Benders decomposition. For a more effective algorithm, we develop a two-phase solution approach. In the first phase, we use optimistic filtering to quickly obtain a near-optimal bound, which we then use for exact filtering in the second phase to prove or obtain an optimal solution. Numerical results on benchmark instances show that our algorithm solves several instances to optimality for the first time, and, in case optimality cannot be proven, considerably improves upon a state-of-the-art heuristic MSA solver. Comparison with an existing state-of-the-art exact MSA algorithm shows that our approach is more time efficient and yields significantly smaller optimality gaps.

Minimizing late deliveries in a truck loading problem

In this work we address the problem of determining the optimal types of products and their quantities that should be loaded on a fleet of heterogeneous one or two level trucks so that the weighted sum of delivered products is maximized, with the weights being an exponential function of the lateness computed for each unit shipped. We propose a mixed integer linear formulation followed by a two-phase solution approach. During phase one the formulation is solved aiming at maximizing the weighted sum of products delivered, whereas for the second phase, the formulation is solved aiming at minimizing the number of trucks, while ensuring that the objective function attained in phase one is not compromised. A greedy heuristic is also proposed in order to better quantify the advantages of adopting the proposed exact approach with respect to solution quality. To assess the performance of the proposed approach we used two sets of test instances, a large set of randomly generated instances that resemble the practical application that motivated this research, and a small set of real instances provided by the company. The results of our computational experiments suggest that the proposed exact solution approach is very effective in solving realistic sized instances.

A two-phase solution approach for a manufacturing-distribution problem with rework, outsourcing, and multi-shipment policy

In a recent study, a manufacturing batch-size and end-product shipment problem with outsourcing, multi-shipment, and rework was investigated using mathematical modeling and derivatives in its solution procedure. This study demonstrates that a simplified two-phase algebraic approach can also solve the problem and decide the cost-minimization policies for batch-size and end-product shipments. Our proposed straightforward solution approach enables the practitioners in the production planning and controlling filed to comprehend and efficiently solve the best replenishing batch-size and shipment policies of this real problem.

Solving operational problems in outpatient chemotherapy clinics using mathematical programming and simulation

Increasing number of cancer survivors besides effective medications increase the demand for cancer care services. Therefore, managers have to investigate new ways to enhance the operational performance of the outpatient chemotherapy clinics (OCCs). However, the management process is complex due to significant variability in treatment times as a result of the different cancer types and accordingly different chemotherapy protocols and scarce resources such as nurses, chemotherapy chairs/beds, and pharmacists. In this paper, we address two problems in OCCs. First, in the planning problem, the objective is assigning the optimum first day to start the treatment for a set of new patients, and computing the required number of nurses and pharmacists given the limited resources. Second, the operational problem of scheduling the patients’ appointments. In this problem, the objective is to set the best appointment schedules for all patients, new and existing to improve the operational performance of the clinic. As the two problems are highly interrelated, we propose a two-phase solution approach starting by a mixed integer programming model that assigns the starting day of treatment for new patients and finds the optimum number of needed nurses and pharmacists to fulfill two objectives. Then, in the second phase, a discrete event simulation model is used to generate patient appointment schedules that minimise the treatment delay for patients and the total completion times of treatments in each day under resources availability constraints, including two new constraints covering the drug availability and pharmacists working-hours. Finally, the proposed simulation model is applied for evaluating the operations performance of a current case study and finding the best scheduling rule for patient appointment times to achieve a minimum wait time in the OCC.

Content-Based Conference Scheduling Optimization

A scientific conference is an activity organized by a community of researchers aimed at offering a platform for knowledge sharing and scientific exchange. The planning of a conference includes the creation of the program schedule where decisions about track composition, in terms of talks, and the temporal allocation of those tracks need to be considered. Designing such a schedule represents a difficult task in which aspects as content similarity and the overlapping of similar tracks should be taken into account. In this paper a two-phase solution approach is proposed for helping planners designing schedules. In first place, talks are grouped into tracks upon the basis of talks content. Then, a timetable for the tracks is created by group them over the basis of content similarity, avoiding those with similar content to be scheduled in parallel. Both problems demonstrate to require a considerably computational effort; consequently, advanced algorithmic approaches as column generation and GRASP are exploited with the purpose of finding near-optimal solutions in a short computational time.

A Two-Phase Solution Approach for a Real-Life Examination Timetabling Problem

A Two-Phase Solution Approach for a Real-Life Examination Timetabling Problem

A Decision Support System for Managing the Water Space

A novel decision support system comprising of several interference identification algorithms for the detection of hazardous (i.e., risk to life, assets, and/or mission) voyages and water space allocations in maritime operations is proposed. Given a specified spatio-temporal region for each polygonal or ellipsoidal object, the objective is to identify interference, defined as overlap, among the assigned regions. The challenge is to fuse information on bathymetry, obstacles, and planned spatial assignments to identify conflicts among any combination of polygons or ellipses. We briefly review data structures for the representation of spatio-temporal regions computationally, and efficient algorithms for collision detection. Specifically, we propose a two-phase solution approach to interference identification using time-parameterized R-trees, linear programming, and quadratic programming. The proposed interference detection algorithms can detect overlaps among thousands of polygons and elliptic regions. The resulting decision support tool, conflict identification, is part of a larger system for water space planning.

A path-based solution approach for the Green Vehicle Routing Problem

The Green Vehicle Routing Problem concerns routing alternative fuel vehicles, based at a single depot, to handle a subset of customers while minimizing the total travel distance. Due to limited fuel autonomy, each vehicle may need to stop at Alternative Fuel Stations (AFSs) during its trip. We propose a two-phase solution approach in which a route is seen as the composition of paths, each one handling a subset of customers without intermediate stops at AFSs. In the first phase, all feasible paths are generated limiting their number through dominance rules. In the second phase, the paths are selected and properly combined to generate the routes via Mixed Integer Linear Programming. Our approach, tested on small- to medium-sized benchmark instances, outperforms the existing exact methods obtaining always the optimal solution in a smaller average computational time. Furthermore, the approach was converted into a heuristic one considering in the first phase only a subset of feasible non-dominated paths. In this way, we can also address larger- sized instances outperforming, in terms of solution quality, the best heuristic approach in the literature.

Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model

This article introduces a sustainable integrated bi-objective location-routing model, its two-phase solution approach and an analysis procedure for the distribution side of three-echelon logistics networks. The mixed-integer programming model captures several real-world factors by introducing an additional objective function and a set of new constraints in the model that outbound logistics channels find difficult to reconcile. The sustainable model minimises CO2 emissions from transportation and total costs incurred in facilities and the transportation channels. Design of Experiment (DoE) is integrated to the meta-heuristic based optimiser to solve the model in two phases. The DoE-guided solution approach enables the optimiser to offer the best stable solution space by taking out solutions with poor design features from the space and refining the feasible solutions using a convergence algorithm thereby selecting the realistic results. Several alternative solution scenarios are obtained by prioritising and ranking the realistic solution sets through a multi-attribute decision analysis tool, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The robust model provides the decision maker the ability to take decisions on sustainable open alternative optimal routes. The outcomes of this research provide theoretical and methodological contributions, in terms of integrated bi-objective location-routing model and its two-phase DoE-guided meta-heuristic solution approach, for the distribution side of three-echelon logistics networks.

Optimal fleet composition and mix periodic location-routing problem with time windows in an offshore oil and gas industry: A case study of National Iranian Oil Company

This paper presents a new Mixed-Integer Non-Linear Programming (MINLP) model for a Supply Vessel Planning (SVP) problem. The traditional SVP, which is a maritime transportation problem, is developed to a Maritime Fleet Sizing Mix Periodic Location-Routing Problem with Time Windows (MFSMPLRPTW) by considering suppliers, location of onshore-base(s) and some real life aspects. The objective of this model is to decide the composition of fleets, optimal voyages, schedules and also the optimal location(s) for onshore-base(s) in such a way that the total cost is minimized and the needs of operation regions are fulfilled. The MFSMPLPRTW model is solved by an exact two-phase solution approach for both small and medium cases. Also, two meta-heuristic algorithms are used to solve the large-sized instances. In order to justify and show how the model and solution can lead to significant economic improvements for real life instances, a case study by the IOOC is considered, which is the only offshore oil and gas producer in Iran that has lots of installations and operation regions in the Persian Gulf and the Sea of Oman.

A two-phase optimization method for a multiobjective vehicle relocation problem in electric carsharing systems

The paper focuses on one-way electric carsharing systems, where the fleet of cars is made up of Electric Vehicles (EVs) and the users can pick-up the EV at a station and return it to a different one. Such systems require efficient vehicle relocation for constantly balancing the availability of EVs among stations. In this work, the EVs are relocated by workers, and the issue of finding a trade-off among the customers’ satisfaction, the workers’ workload balance and the carsharing provider’s objective is addressed. This leads to a three-objective optimization problem for which a two-phase solution approach is proposed. In the first phase, feasible routes and schedules for relocating EVs are generated by different randomized search heuristics; in the second phase, non-dominated solutions are found through epsilon-constraint programming. Computational results are performed on benchmark instances and new large size instances based on the city of Milan.