Solution Approach For Problem Research Articles

A modelling and solution approach for wind-affected drone-truck routing problem under uncertainty

In the field of logistics and transportation, drones and trucks effectively enhance each other’s capabilities by offering complementary benefits in terms of speed, cargo capacity, and charging frequency. Thus, efficient management of their collaboration is an important task. Although there is a vast literature addressing different aspects of drone-truck combined operations (DTCO), only a few studies incorporate the energy consumption of drones into the optimization model, and the existing ones have made simplified assumptions. This paper proposes an optimization model for DTCO by incorporating a comprehensive energy function affected by the drone speed, cargo weight, wind speed, and wind direction, paying attention to environmental viewpoints. Due to this energy function, the problem is formulated as a mixed-integer nonlinear programming (MINLP) model. To enhance tractability and efficiency, we provide a linear approximation for the MINLP model. Given the stochastic nature of wind conditions throughout the day, we extend the deterministic model as a scenario-based stochastic one. Incorporating uncertainty makes the model more complex and hence, we adopt a modified progressive hedging algorithm (PHA) to efficiently solve the model. Computational results over a variety of instances confirm the effectiveness of the proposed approach.

The UPC CoA’s first substantive order—central issues clarified, but on a high level

Abstract In its decision, the UPC Court of Appeal confirms the application of key principles of patent claim interpretation for unitary patents. With regard to the inventive step, a tentative path is chosen that does not clearly follow the problem–solution approach of the European Patent Office and instead, comprehensively takes the state of the art into account at the outset. The standard for the necessary probability of infringement and validity is set at a preponderance of probability (sufficient degree of certainty, ie more likely than not). Furthermore, the temporal and factual necessity of the injunction is also important in determining whether a preliminary injunction should be ordered. Ultimately, the granting of injunctive relief hinges on an overall weighing of the interests.

Consumer service level-oriented resilience optimisation for e-commerce supply chain considering hybrid strategies with blockchain adoption

ABSTRACT The booming development of customised e-commerce makes e-commerce supply chains experience a severe test of consumer service level (CSL). An efficient e-commerce supply chain resilience optimisation method addressing economic performance and service performance is proposed to improve customised services under disruption risks. The proposed method includes a hybrid strategy considering both a resistance strategy with blockchain (BCT) adoption and time-dependent recovery strategies simultaneously. A two-stage multi-period multi-product stochastic programming with BCT adoption is then proposed, which (1) implements BCT as the resistance strategy in the pre-disruption stage; (2) collaborates four recovery strategies in the post-disruption stage; (3) supports the e-tailer in making decisions and optimises his profit and order fulfillment time while taking product priorities into account. Using the actual data of Chinese e-commerce during the public health emergency in 2020, it is demonstrated that (1) the applicability of the model with BCT adoption in both supply chain resilience and CSL improvement; (2) the performance of the hybrid strategy in long-term disruption management; (3) the efficiency and robustness of the proposed solution approach for multi-objective high-dimensional stochastic programming problems. E-tailers can optimise decision-making under long-term disruptions by the proposed methodology in practices.

D3S: Decision support system for sectorization

Sectorization problems refer to dividing a large set, area or network into smaller parts concerning one or more objectives. A decision support system (DSS) is a relevant tool for solving these problems, improving optimisation procedures, and finding feasible solutions more efficiently. This paper presents a new web-based Decision Support System for Sectorization (D3S). D3S is designed to solve sectorization problems in various areas, such as school and health districting,planning sales territories and maintenance operations zones, or political districting. Due to its generic design, D3S bridges the gap between sectorization problems and a state-of-the-art decision support tool. The paper aims to present the generic and technical attributes of D3S by providing detailed information regarding the problem-solution approach (based on Evolutionary Algorithms), objectives (most common in sectorization), constraints, structure and performance.

Approximate inner solvers for block preconditioning of the incompressible Navier–Stokes problems discretized by isogeometric analysis

AbstractWe deal with efficient numerical solution of the steady incompressible Navier–Stokes equations (NSE) using our in‐house solver based on the isogeometric analysis (IgA) approach. We are interested in the solution of the arising saddle‐point linear systems using preconditioned Krylov subspace methods. Based on our comparison of ideal versions of several state‐of‐the‐art block preconditioners for linear systems arising from the IgA discretization of the incompressible NSE, suitable candidates have been selected. In the present paper, we focus on selecting efficient approximate solvers for solving subsystems within these preconditioning methods. We investigate the impact on the convergence of the outer solver and aim to identify an effective combination. For this purpose, we compare convergence properties of the selected solution approaches for problems with different viscosity values, mesh refinement levels and discretization bases.

A new gray optimization model for disposing or re-commercializing unsold goods in reverse logistics networks with a cross-docking center

PurposeThis paper investigates a problem in a reverse logistics (RLs) network to decide whether to dispose of unsold goods in primary stores or re-commercialize them in outlet centers. By deducting the costs associated with each policy from its revenue, this study aims to maximize the profit from managing unsold goods.Design/methodology/approachA new mixed-integer linear programming model has been developed to address the problem, which considers the selling prices of products in primary and secondary stores and the costs of transportation, cross-docking and returning unwanted items. As a result of uncertain nature of the cost and time parameters, gray numbers are used to deal with it. In addition, an innovative uncertain solution approach for gray programming problems is presented that considers objective function satisfaction level as an indicator of optimism.FindingsAccording to the results, higher costs, including transportation, cross-docking and return costs, make sending goods to outlet centers unprofitable and more goods are disposed of in primary stores. Prices in primary and secondary stores heavily influence the number of discarded goods. Higher prices in primary stores result in more disposed of goods, while higher prices in secondary stores result in fewer. As a result of the proposed method, the objective function satisfaction level can be viewed as a measure of optimism.Originality/valueAn integral contribution of this study is developing a new mixed-integer linear programming model for selecting the appropriate goods for re-commercialization and choosing the best outlet center based on the products' price and total profit. Another novelty of the proposed model is considering the matching percentage of boxes with secondary stores’ desired product lists and the probability of returning goods due to non-compliance with delivery dates. Moreover, a new uncertain solution approach is developed to solve mathematical programming problems with gray parameters.

Following the Writer’s Path to the Dynamically Coalescing Reactive Chains Design Pattern

Two recent studies addressed the problem of reducing transitional turbulence in applications developed in C# on .NET. The first study investigated this problem in desktop and Web GUI applications and the second in virtual and augmented reality applications using the Unity3D game engine. The studies used similar solution approaches, but both were somewhat embedded in the details of their applications and implementation platforms. This paper examines these two families of applications and seeks to extract the common aspects of their problem definitions and solution approaches and codify the problem-solution pair as a new software design pattern. To do so, the paper adopts Wellhausen and Fiesser’s writer’s path methodology and follows it systematically to discover and write the pattern, recording the reasoning at each step. To evaluate the pattern, the paper applies it to an arbitrary C#/.NET GUI application. The resulting design pattern is named Dynamically Coalescing Reactive Chains (DCRC). It enables the approach to transitional turbulence reduction to be reused across a range of related applications, languages, and user interface technologies. The detailed example of the writer’s path can assist future pattern writers in navigating through the complications and subtleties of the pattern-writing process.

A novel evolutionary solution approach for many-objective reliability-redundancy allocation problem based on objective prioritization and constraint optimization

The reliability redundancy allocation problem (RRAP) has been mostly solved either as a single or as a multi-objective optimization problem. However, this problem also has numerous important constraints which play prominent roles in meeting the objectives. This paper proposes a novel formulation named ‘prioritized many reliability redundancy allocation problems (PrMaORRAP)’ that optimizes all the problem objectives concurrently, and also preserves the priority among them. Then, we propose a hybrid method which utilizes the features of many-objective optimization as well as priority relations between different objectives. Here, we divide the procedure into two modules: one is the main priority or the leader which will stay at the top level; underneath the first lie the second part in which rest of the objectives are optimized. The solution approach embeds the optimization structure within the evolutionary process making a prioritized many-objective evolutionary algorithms. We formulate various structures such as series, series-parallel, complex bridge and overspeed gas turbine system of RRAP as many-objective optimization problems, and provide detailed experimental demonstration on how our proposed model works for all these structures. We compare the results given by the proposed approach with the results of other approaches available in the literature and establish the superiority of our proposed solution approach.

Legal Research Perspective through Problem Solution Approach

This study aims to find out what is the point of view of legal research with a problem solution approach (dispute resolution) on legal disputes that exist both in court and outside the court in force in Indonesia. This research method uses a qualitative method with a literature study approach where legal materials are obtained from library books, both printed and electronic. The formulation of the problem for this research are: a. how is the settlement of legal disputes that occur in Indonesia?; b. What are the judges' considerations in their decisions regarding the settlement of legal disputes that occurred in Indonesia? The conclusions of this study are 1. Legal research with a dispute resolution approach (problem solution) can be carried out outside the court and in court where both have advantages, disadvantages and procedures that differ from one another; 2. The legal research approach with out-of-court dispute resolution is difficult to obtain legal documents because it is closed (not published) while dispute resolution through the courts can be analyzed in terms of court decisions, judges' legal considerations and legal findings by judges. It is recommended that the results of dispute resolution outside the court can be obtained openly so that decisions and legal considerations can be examined on existing disputes and laws and other regulations so that they are immediately made to strengthen the legal position of the judge's legal findings.

A new solution approach for non-convex combined heat and power economic dispatch problem considering power loss

The combined heat and power economic dispatch (CHPED) problem is a non-convex multivariate global optimization problem. The objective of the problem is to reduce total production costs while imposing a variety of constraints and meeting the demand for power and heat. Three recently presented metaheuristic approaches, Slime Mould Algorithm (SMA), COOT algorithm and Marine Predators Algorithm (MPA), are applied for solving CHPED problem. Studies dealing with the CHPED problem in the literature often do not consider valve points effect, prohibited operation zones for power-only units, feasible region constraints of combined heat and power units, all at once. Furthermore, power losses are neglected especially in large-scale problems. In this study, the CHPED problem is solved by considering all operational constraints including active power transmission losses. Three separate case studies with dimensions of 11 units, 48 units, and 96 units were used in the tests under various limitations. The experimental results revealed that MPA outperformed not only SMA, and COOT but also the algorithms proposed previously in the literature.

A solution approach for sustainable multi-objective multi-item 4D solid transportation problem involving triangular intuitionistic fuzzy parameters

Sustainability pertains to the interplay between environmental, economic, and social systems at varying scales. In transportation systems, vehicles use different fuels to fulfill their energy requirements. However these fuels emit green house gases that pollute the environment. Taking into account this fact, the present paper delves into the investigation of a multi-objective multi-item fixed cost solid transportation problem with various driving styles. Also, three types of fuels are incorporated in the proposed model. The primary focus of this paper is to maximize profit by reducing breakage of the items along with reducing carbon emission and time of transportation. In real-life situations, the parameters of multi-objective multi-item fixed cost solid transportation problem may not be tackled crisply. Hence triangular intuitionistic fuzzy numbers are introduced in the proposed model. The score function is employed to convert intuitionistic fuzzy problem to deterministic one. Thereafter, a methodology is developed to solve the proposed model involving different driving styles and is extended to consider the optimistic, pessimistic, and mixed view of the decision maker. Comparisons are made among the compromise solutions that are derived from different approaches and are shown by various charts and graphs. A case study is included to illustrate the applicability and validity of the proposed methodology.

A Mobile Sensing Framework for Bridge Modal Identification through an Inverse Problem Solution Procedure and Moving-Window Time Series Models.

With the rise and development of smart infrastructures, there has been a great demand for installing automatic monitoring systems on bridges, which are key members of transportation networks. In this regard, utilizing the data collected by the sensors mounted on the vehicles passing over the bridge can reduce the costs of the monitoring systems, compared with the traditional systems where fixed sensors are mounted on the bridge. This paper presents an innovative framework for determining the response and for identifying modal characteristics of the bridge, utilizing only the accelerometer sensors on the moving vehicle passing over it. In the proposed approach, the acceleration and displacement response of some virtual fixed nodes on the bridge is first determined using the acceleration response of the vehicle axles as the input. An inverse problem solution approach based on a linear and a novel cubic spline shape function provides the preliminary estimations of the bridge's displacement and acceleration responses, respectively. Since the inverse solution approach is only capable of determining the response signal of the nodes with high accuracy in the vicinity of the vehicle axles, a new moving-window signal prediction method based on auto-regressive with exogenous time series models (ARX) is proposed to complete the responses in the regions with large errors (invalid regions). The mode shapes and natural frequencies of the bridge are identified using a novel approach that integrates the results of singular value decomposition (SVD) on the predicted displacement responses and frequency domain decomposition (FDD) on the predicted acceleration responses. To evaluate the proposed framework, various numerical but realistic models for a single-span bridge under the effect of a moving mass are considered; the effects of different levels of ambient noise, the number of axles of the passing vehicle, and the effect of its speed on the accuracy of the method are investigated. The results show that the proposed method can identify the characteristics of the three main modes of the bridge with high accuracy.

Small- or Medium-Sized Enterprise Uses Operations Research to Select and Develop its Headquarters Location

Location decisions are strategic and usually multicriteria. In decision making, companies need to anticipate future developments at potential locations. Company-driven and municipal development measures change location conditions over time. For location-seeking companies, the realization of municipal measures is fraught with uncertainty. They are planned by several municipal actors, and their long-term implications are hard to predict. Thus, the early-systematic consideration of company-internal and -external development measures is vital for decision makers (DMs) in a future-oriented location assessment. In our paper, we develop a robust decision support framework for companies to solve the regional facility location and development planning problem (RFLDP). Our framework includes a quantitative planning approach based on established operations research (OR) optimization models and a practical guideline for a structured acquisition of relevant data. The chief executive officer (CEO) (or DM) of a small- or medium-sized enterprise (SME) asked us to solve his acute RFLDP. For this, we proposed a systematic workflow and accompanied the SME’s regional facility location and development planning. In doing so, we structured the CEO’s decision-making process effectively and created an objective-transparent basis for his strategic decisions. The core feature of our work is the inclusion of the human factor of DMs, as we interacted with the CEO along his decision-making process to gradually develop decision recommendations. As a result, the SME benefited from a better-informed and transparent planning process. We recommended a decision option that was structurally superior to other options, which emerged from the CEO’s intuition and conventional facility location problem solution approaches. Other stakeholders also benefited from the results of our work. History: This paper was refereed. Funding: This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [Grant 439640382].

Modeling Minimum Cost Network Flows With Port‐Hamiltonian Systems

AbstractWe give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal control problems constrained by port‐Hamiltonian systems (pHS). The first‐order optimality system for the port‐Hamiltonian system‐constrained optimal control problem is formally derived. Then we propose a gradient‐based algorithm to find optimal controls. The port‐Hamiltonian system formulation naturally conserves flow and supports a wide array of further modeling options as, for example, node reservoirs, flow dependent costs, leaking pipes (dissipation) and coupled sub‐networks (ports). They thus provide a versatile alternative to state‐of‐the art approaches towards dynamic network flow problems, which are often based on computationally costly time‐expanded networks. We argue that this opens the door for a plethora of modeling options and solution approaches for network flow problems.

Investigating the effect of the presence of a pulsating heat pipe on the geometrical parameters of the microchannel heat sink

In this study, the effect of the presence of a pulsating heat pipe on the geometrical parameters of the microchannel heat sink will be investigated. The embedding of a pulsating heat pipe (PHP) in the solid part of the microchannel heat sink (MCHS) increases the cooling performance of the MCHS and reduces the maximum temperature of the electronic piece. A numerical investigation of MCHS equipped with a PHP is investigated and compared with an optimized conventional MCHS without PHP. The inverse problem solution approach is used to optimize the geometric parameters of the MCHS. The geometrical variables in the optimization process are N (number of channels), α (aspect ratio of the channel), and β (width ratio of the channel to pitch). The pumping power is considered a constraint and is tried to reach the minimized objective function (thermal resistance (R)). Results show that the optimal values of geometrical and physical parameters change from N = 100, α = 13.9, β = 0.6, R = 0.0268, in conventional MCHS to N = 120, α = 14.3, β = 0.7, R = 0.0231 in MCHS with PHP. At this point, the system’s thermal performance improved by 16.02% compared to the previous optimal state.

Freight-on-Transit for urban last-mile deliveries: A strategic planning approach

We study a delivery strategy for last-mile deliveries in urban areas which combines freight transportation with mass mobility systems with the goal of creating synergies contrasting negative externalities caused by transportation. The idea is to use the residual capacity on public transport means for moving freight within the city. In particular, the system is such that parcels are first transported from origins (central distribution centers) to drop-in stations, which are stop locations on public vehicle itineraries. Then, they are transported on public vehicles to drop-out stations, from where they are delivered to destination by green vehicles (such as bikes, drones, porters, etc.). The system is known as Freight-On-Transit (FOT). In this paper, we focus on the strategic decisions related to defining the public transportation network that will take part in the delivery system, i.e., which public vehicle lines and stop locations will be included (and thus equipped for the service). We propose different formulations for the problem and effective heuristic solution approaches based on column generation. We perform exhaustive tests aimed at providing managerial insights on the performance and the efficiency of the system.

Branch-and-cut solution approach for multilevel mixed integer linear programming problems

A multilevel programming problem is an optimization problem that involves multiple decision makers, whose decisions are made in a sequential (or hierarchical) order. If all objective functions and constraints are linear and some decision variables in any level are restricted to take on integral or discrete values, then the problem is called a multilevel mixed integer linear programming problem (ML-MILP). Such problems are known to have disconnected feasible regions (called inducible regions), making the task of constructing an optimal solution challenging. Therefore, existing solution approaches are limited to some strict assumptions in the model formulations and lack universality. This paper presents a branch-and-cut (B&C) algorithm for the global solution of such problems with any finite number of hierarchical levels, and containing both continuous and discrete variables at each level of the decision-making hierarchy. Finite convergence of the proposed algorithm to a global solution is established. Numerical examples are used to illustrate the detailed procedure and to demonstrate the performance of the algorithm. Additionally, the computational performance of the proposed method is studied by comparing it with existing method through some selected numerical examples.

Solving large scale industrial production scheduling problems with complex constraints: an overview of the state-of-the-art

Production scheduling is challenging and the body of literature addressing various variants of the problem is large. It can roughly be divided into two streams: The first stream addresses and generalizes established scheduling problems, being general in the sense that they are not only applicable in a particular industry. The second stream works on less generic scheduling approaches for real industry cases by enriching standard models with all the required realistic aspects, such as process overlapping or sequence dependent setup times. Furthermore, different approaches have different limitations in terms of the problem size that they can tackle. The rise of Industry 4.0 has lead to a significant increase in data collection activities and the gathered information is used to build larger and more complex models. Industrial use cases may consist of several thousand operations on a large variety of machines, while classical benchmark instances tend to range up to only a few hundred of operations. It is therefore necessary to identify and highlight approaches, that can meet the challenges of scheduling in the era of Industry 4.0 and are suitable to tackle large scale problems.In this work, we conduct a structured literature review on scheduling problems incorporating several real world aspects among a broad range of use cases. Based on the identified publications we find that advanced solution approaches for large scale scheduling problems usually belong to one out of three categories, namely metaheuristic methods, constraint programming and machine learning. Our review shows that comparably few contributions tackling (very) large scale problems exist, emphasizing the need for additional research in this field. We identify promising approaches for further research, such as powerful metaheuristics combining concepts of tabu search and genetic algorithms. We further discuss the possibility to enhance solution methods by integrating constraint programming concepts and investigating problem decomposition.

An enhanced solution approach for multi-period discrete manufacturing product assembly inventory routing problem with supply failure risks and customer demand uncertainty

PurposeThis study primarily aims to develop and solve an enhanced optimisation model for an assembly product multi-period inbound inventory routing problem (IRP). The many-to-one (inbound) model considers the bill of materials (BOM), supply failure risks (SFR) and customer demand uncertainty. The secondary objective is to study the influence of potential time-dependent model variables on the overall supply network costs based on a full factorial design of experiments (DOE).Design/methodology/approachA five-step solution approach is proposed to derive the optimal inventory levels, best sourcing strategy and vehicle route plans for a multi-period discrete manufacturing product assembly IRP. The proposed approach considers an optimal risk mitigation strategy by considering less risk-prone suppliers to deliver the required components in a specific period. A mixed-integer linear programming formulation was solved to derive the optimal supply network costs.FindingsThe simulation results indicate that lower demand variation, lower component price and higher supply capacity can provide superior cost performance for an inbound supply network. The results also demonstrate that increasing supply capacity does not necessarily decrease product shortages. However, when demand variation is high, product shortages are reduced at the expense of the supply network cost.Research limitations/implicationsA two-echelon supply network for a single assembled discrete product with homogeneous vehicle fleet availability was considered in this study.Originality/valueThe proposed multi-period inbound IRP model considers realistic SFR, customer demand uncertainties and product assembly requirements based on a specific BOM. The mathematical model includes various practical aspects, such as supply capacity constraints, supplier management costs and target service-level requirements. A sensitivity analysis based on a full factorial DOE provides new insights that can aid practitioners in real-life decision-making.

An Ecological Context That Scars: Reflections on Three Nature Documentaries of 2020

An Ecological Context That Scars: Reflections on Three Nature Documentaries of 2020