Alternative Solution Approaches Research Articles

A Necessity-Based Optimization Approach for Closed-Loop Logistics Considering Carbon Emission Penalties and Rewards under Uncertainty

The recycling of waste products can bring enormous economic and environmental benefits to supply chain participants. Under the government’s reward and punishment system, the manufacturing industry is facing unfolded pressure to minimize carbon emissions. However, various factors related to the design of closed-loop logistics networks are uncertain in nature, including demand, facility capacity, transportation cost per unit of product per kilometer, landfill cost, unit carbon penalty cost, and carbon reward amount. As such, this study proposes a new fuzzy programming model for closed-loop supply chain network design which directly relies on fuzzy methods based on the necessity measure. The objective of the proposed optimization model is to minimize the total cost of the network and the sum of carbon rewards and penalties when selecting facility locations and transportation routes between network nodes. Based on the characteristics of the problem, a genetic algorithm based on variant priority encoding is proposed as a solution. This new solution encoding method can make up for the shortcomings of the four traditional encoding methods (i.e., Prüfer number-based encoding, spanning tree-based encoding, forest data structure-based encoding, and priority-based encoding) to speed up the computational time of the solution algorithm. Several alternative solution approaches were considered to evaluate the proposed algorithm including the precision optimization method (CPLEX) and priority-based encoding genetic algorithm. The results of numerous experiments indicated that even for large-scale numerical examples, the proposed algorithm can create optimal and high-quality solutions within acceptable computational time. The applicability of the model was demonstrated through a sensitivity analysis which was conducted by changing the parameters of the model and providing some important management insights. When external parameters change, the solution of the model maintains a certain level of satisfaction conservatism. At the same time, the changes in the penalty cost and reward amount per unit of carbon emissions have a significant impact on the carbon penalty revenue and total cost. The results of this study are expected to provide scientific support to relevant supply chain enterprises and stakeholders.

Optimal operation scheduling of mobile hydrogen charging stations: A mathematical optimization model and heuristic approach

Demand for hydrogen vehicles is steadily increasing due to sustainable development and strengthening of policies to support the hydrogen industry. However, due to the lack of hydrogen charging infrastructure, continuous operation is limited, which is an obstacle to the expansion of the hydrogen car market. To solve this problem, steady expansion of fixed hydrogen charging stations (HCSs) is underway, but the use of mobile hydrogen charging stations (MHCSs) is also actively considered. MHCSs can compensate for the shortcomings of expanding charging infrastructure due to the establishment cost of fixed HCSs and the selection of sites and contribute to resolving hydrogen charging blind spots. In this study, optimal operation of a number of MHCSs was conducted. To derive the optimal operation schedule, a mathematical optimization model and an alternative solution approach, a Multiple Vehicle and Multiple Trip Routing Algorithm for Selective Use and Split Service (MVMTRA-SUSS) was developed. Case study, sensitivity analysis, and numerical experiments have verified the practical applicability of the proposed model.

Regression-Based Interpretation Method for Confined Aquifer Pumping Tests

The constant-discharge pumping test is a widely used aquifer characterization tool for estimating hydrogeological parameters. Various graphical and numerical solution techniques have been devised for interpretation of pumping test results. This study proposes an alternative regression-based solution approach for analyzing pumping tests conducted in nonleaky, confined aquifers. A regression model was developed by making use of the similarity solution that describes the temporal drawdown behavior at a monitoring well within a pumping period. The field curve obtained from a pumping test (drawdown versus time data) and the theoretical type curve (dimensionless drawdown versus dimensionless time) exhibit identical behavior in logarithmic scale. Correspondingly, based on the equivalence of the area above these two curves, the proposed regression equation establishes a link between a selected drawdown value and its dimensionless counterpart. Once this drawdown value is associated with the corresponding dimensionless drawdown, the explored aquifer transmissivity and storativity can be retrieved easily with the similarity solution. The proposed fit equation enables users to retrieve hydrogeological parameters effortlessly by eradicating the difficulties encountered while implementing conventional graphical or optimization-based methods. The method was tested for a large number of hypothetical noise-free and noise-perturbed time drawdown data sets, each synthesized with different aquifer parameters within a wide range, and in all these attempts the proposed algorithm achieved providing highly accurate parameter estimates. In addition, two published test cases were employed to assess the estimation performance of the method in comparison with the existing techniques. The developed solution scheme was revealed to yield results in very good agreement with those reported in previous works. Considering the accuracy of the method and the ease of its implementation, the proposed approach can be a practical tool for analyzing constant-discharge tests performed in confined aquifers.

Identification of Explainable Structures in Data with a Human-in-the-Loop

Explainable AIs (XAIs) often do not provide relevant or understandable explanations for a domain-specific human-in-the-loop (HIL). In addition, internally used metrics have biases that might not match existing structures in the data. The habilitation thesis presents an alternative solution approach by deriving explanations from high dimensional structures in the data rather than from predetermined classifications. Typically, the detection of such density- or distance-based structures in data has so far entailed the challenges of choosing appropriate algorithms and their parameters, which adds a considerable amount of complex decision-making options for the HIL. Central steps of the solution approach are a parameter-free methodology for the estimation and visualization of probability density functions (PDFs); followed by a hypothesis for selecting an appropriate distance metric independent of the data context in combination with projection-based clustering (PBC). PBC allows for subsequent interactive identification of separable structures in the data. Hence, the HIL does not need deep knowledge of the underlying algorithms to identify structures in data. The complete data-driven XAI approach involving the HIL is based on a decision tree guided by distance-based structures in data (DSD). This data-driven XAI shows initial success in the application to multivariate time series and non-sequential high-dimensional data. It generates meaningful and relevant explanations that are evaluated by Grice’s maxims.

Flare-fork collaborative strategy: expanding design space via opportunistic ideation in engineering product design


 
 
 Restricted exploration of design space is a problem that novice designers face when solving engineering product design problems. Consequences of limited exploration can be the generation of sub-optimal solutions and fixation towards the first solution idea or known solution space. Expert designers sift through their vast repertoire of solution alternatives and choose the appropriate solution for the given design problem. Novices, however, lack this vast repository of alternative solution approaches. Therefore, it is good practice for novices to expand the problem and solution space and explore different aspects of the product design problem before identifying solutions appropriate for the design problem.
 Flare-fork collaborative strategy is a design exploration strategy that enables designers to generate opportunistic ideas related to the design problem and integrate them during the design process thereby expanding problem and solution space. The flare-fork collaborative strategy leverages rapid ideation, and semantic analogy thought transformation strategy to generate new ideas, interlinking ideas in design space map (DSM) for the elaboration of ideas, and thought transformer strategy to manipulate ideas for expanding problem and solution space. This paper describes a study to examine how the operationalization of the flare aspect of flare-fork collaborative strategy as an intervention supports the design process of three teams of students. We found that students frequently traverse between problem and solution space via an intermediate bridge space. Also, regardless of where the students begin, they do a comprehensive exploration of problem and solution space while using flare-fork collaborative strategy. Students’ perception of using flare-fork collaborative strategy to explore engineering product design is predominantly positive, with students identifying several ways in which flare aspect of flare-fork collaborative strategy aided them in their expansion of problem and solution space.
 
 

A Fuzzy Multi-Criteria Decision Making Methodology for Job Evaluation

Aims: In this study, the integrated methods Hesitant Fuzzy Analytic Hierarchy Process (HF-AHP), Fuzzy COmplex Proportional Assessment (F-COPRAS) and Fuzzy Technique for Order Performance to Ideal Solution (F-TOPSIS) were used for job evaluation studies in a food company. Background: There has been a decline in employee performance in the company. Unfair wages and unequal workload were identified as the reasons for the failure. Therefore, it has been observed that the staff turnover rate in the company is quite high. Objective: The objective is to determine a fair wage policy that will increase employee satisfaction by stratifying with job evaluation analysis between positions. Methods: The experts of Human Resources Department determined eight competency evaluation criteria for job evaluation studies in the proposed approach. Based on their judgments on these criteria, the competencies were rated using a linguistic scale and the weighting values were calculated using HF-AHP method. These values are inputs for the next stage. Employees were ranked using F-COPRAS and F-TOPSIS methods. Results: This study showed that the integrated method can be an effective alternative solution approach for calculating the weighting values and ranking of competencies in job evaluation studies. Conclusion: It has been shown that the use of the strata created as a result of this study is a great facilitator in determining employee pay policies.

Pricing and advertising decisions in a direct-sales closed-loop supply chain

Remanufacturing and recycling of end-of-life products have changed the structure of supply chain networks, and the option of closed-loop supply chains gains popularity. Growing strict environmental and social legislations are expected to enhance sustainability of closed-loop supply chains. This study focuses on the pricing and advertising decisions in a closed-loop supply chain network. Although pricing decisions have been well-studied in this area, there is a little attention to advertising decisions. It is well-known that advertising plays a significant role in influencing customer behavior in returning end-of-life products for the closed-loop supply chain. Therefore, this research develops an operational and tactical plan for promoting advertising programs considering different elasticity effects. As such, the proposed optimization plan considers the pricing decisions in a more comprehensive view, where the price of similar products in the market and their substitution degree have a high impact on the profitability of manufacturers in a direct-sales closed-loop supply chain. Hence, the main novelty of this paper is to develop a new optimization model with pricing and advertising decisions in a direct-sales closed-loop supply chain. Since the proposed model is more complex than the majority of existing optimization models in the area of closed-loop supply chains, another novelty of this paper is to propose an improvement to the standard particle swarm optimization algorithm using the crowd-learning theory. The developed algorithm is validated by the exact solver and compared with the state-of-the-art algorithms in this research area. An extensive computational experiment is performed considering a number of comparative metrics. The findings show the superior performance of the proposed metaheuristic against the alternative solution approaches in terms of computational time and solution quality. Moreover, some important insights are obtained from this research, which could provide a basis for configuration of pricing schemes and advertising campaigns to improve the efficiency of closed-loop supply chains.

An efficient semi-implicit solver for solid electrolyte interphase growth in Li-ion batteries

Growth of the Solid Electrolyte Interphase is one of the major degradation processes in Li-ion batteries and yields an increase in cell resistance, as well as a reduction in capacity. In order to facilitate computer-aided design of novel cell concepts and omit costly prototyping, it is crucial to incorporate this mechanism into electrochemical simulations on the microscale and to develop efficient numerical solvers. Electrochemical battery models without degradation are commonly discretized with a fully implicit discretization resulting in a monolithic scheme. Solving the resulting systems with a Newton method allows for quadratic convergence, where the major part of the computational effort is spent on solving the underlying linear systems. Hence, finding a suitable preconditioner for the linear solver is essential for overall solver performance. While an efficient algebraic multigrid preconditioner results in a good performance for the model without degradation, we encounter a noticeable loss in performance of the solver when including the coupled degradation model. We attribute the observed performance issues to the implicitly defined interface currents introduced by the degradation model. By taking into account the slow dynamics of the degradation, we propose an alternative semi-implicit solution approach separating the degradation dynamics and eliminating the implicit interface currents, in order to promote the efficient utilization of the algebraic multigrid preconditioner. The monolithic and semi-implicit solvers are evaluated by performing a series of full cell simulations featuring calendar and cyclic aging scenarios and a complex geometry including the binder domain in each electrode. Based on the results, the semi-implicit solver significantly improves the performance, while maintaining the convergence behaviour.

NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

Network Models for Multiobjective Discrete Optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

Improved penalty algorithm for mixed integer PDE constrained optimization problems

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the branch-and-bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially in a large-scale context, this article investigates penalization techniques. Taking inspiration from a well-known family of existing exact penalty algorithms, a novel improved penalty algorithm is derived, whose key ingredients are a basin hopping strategy and an interior point method, both of which are specialized for the problem class. A thorough numerical investigation is carried out for a standard stationary test problem. Extensions to a convection-diffusion as well as a nonlinear test problem finally demonstrate the versatility of the approach.

Value-driven design for product families: a new approach for estimating value and a novel industry case study

Advanced product platform and product family design methods are needed to define and optimize the value they bring to a company. Maximizing platform commonality and individual product performance often fails to realize the most valuable product family during optimization; however, few examples exist in the literature to explore these trade-offs. This paper introduces a novel industry case study to explore the differences between “traditional” multidisciplinary design optimization (MDO) and value-driven design (VDD) approaches to product family design. The case study involves a family of five commercially-available washing machines and integrates multidisciplinary analyses, simulations, mathematical models, and response surface models to obtain ratings for individual product attributes. These attributes are then aggregated into a value function for the product family using a novel approach to estimate sales volume and a demand sensitivity curve derived from publicly available data. We then formulate and solve a “traditional” MDO product family design problem using a multi-objective genetic algorithm to minimize performance deviation and a product family penalty function. A novel VDD formulation is then introduced and solved to maximize the net present value (NPV) for the firm producing the family of products. Visualization and comparison of the results illustrate that the “traditional” MDO formulation can find several promising solutions for the product family, but it fails to find solutions that maximize the value to the firm. The results also provide a benchmark for researchers to explore alternative value function formulations and solution approaches for product family design using the novel industry case study.

Scheduling Multiple Sports Leagues with Travel Distance Fairness: An Application to Argentinean Youth Football

The first division clubs in Argentinean professional football maintain teams in each of six youth leagues, classed by age as major divisions (Under-20, Under-18, Under-17) and minor divisions (Under-16, Under-15, Under-14). Regular season play in these leagues typically follows a single round-robin format; the minor divisions play the same schedule as the majors but with the home-away status of the matches reversed. This setup can give rise to very significant differences in travel distances between the major and minor division teams of a given club, which is a frustrating situation for club officials, coaches, and players alike but almost impossible to avoid with manual season scheduling techniques. Nor are these methods able to take into account any number of other criteria that go into the design of a satisfactory match calendar. This paper reports on models developed using mathematical programming to simultaneously schedule multiple leagues while also meeting a series of other desirable conditions. The central criterion is a better balance in the travel distances of the various teams, pursued through the application of two alternative solution approaches: one based on regional team clusters and the other on explicit analysis of actual distances between the teams’ home venues. The solutions generated by these approaches have been used by the organizers of the Argentinean youth leagues to draw up their season schedules since 2018, which has resulted in a series of benefits for all stakeholders.

Dynamic production-pricing strategies for multi-generation products under uncertainty

Due to rapid advances in technology and design, firms periodically release new generations of electronic products such as mobile phones and computers. In order to increase product variability, firms may wish to develop a multiple-generation product line rather than replace the older versions with new ones. However, when multiple generations are available in the market, different generations compete with each other as well as other products in the market. Firms need to take joint decisions for the purpose of inventory management and dynamic pricing of multiple generations to tackle impact of uncertain demand and market competition. In this paper, we present a dynamic joint production-pricing decision model to obtain optimal strategies for a firm selling multiple generations of a product. We account for the internal competition among multiple generations by evaluating customer choices. In order to tackle a curse of dimensionality, we introduce a forward dynamic programming approach for approximately solving the joint production-pricing problem. We also propose a two-stage heuristic algorithm as an alternative solution approach. Different pricing rules determined from the abridged model and a price list derived by theoretical bounds are integrated to improve further computational performance of the solution approaches. We design computational experiments to illustrate effectiveness and efficiency of these approximate methods and show the benefit of joint decision-making process in multi-generation product line.

A Green’s Function Iterative Approach for the Solution of a Class of Fractional BVPs Arising in Physical Models

The aim of this study is to present an alternative approach for the numerical solution of a wide class of fractional boundary value problems (FBVPs) that arise in various physical applications. Examples of such FBVP include but not limited to Bagley–Torvik, Riccati, Bratu, and Troesch’s problems that appear in applied mathematics and mechanics. The method is based on first constructing an integral operator that is given in terms of the Green’s function associated with the linear differential term of the fractional differential equation. Fixed point iterative procedures, such as Picard’s and Mann’s, are then applied to the operator to generate an iterative scheme that yields a convergent semi-analytical solution. Numerical examples are reported to confirm the efficiency, reliability, accuracy and fast convergence of the scheme.

A GIS-LP integrated approach for the logistics hub location problem

This study solves the location problem for establishing a logistics hub that serves as a consolidation center to distribute urban freight in the North Western Region of Iran. A novel multi-method approach is developed to implement a two-stage research framework. GIS-embedded multi-criteria decision tools are applied to identify potential regions; a K-means based heuristic approach is developed to select five potential sites; and PROMETHEE, multi-criteria decision-making tool, is implemented to ascertain the best possible site for establishing logistics hub. “Višekriterijumska Optimizacija i kompromisno Rešenje” (VIKOR) method is applied on multiple region-specific criteria to identify potential regions suitable for the logistics hub. A novel clustering Mixed Integer Quadratic constrained Programming (MIQCP) is then applied for clustering the centriods representing the most suitable sites.A K-means heuristic approach is also implemented as an alternative clustering solution approach to improve computational time for data processing. Several criteria such as cost, profit, health effects, political matters and regulations are then used to identify the best site using PROMETHEE method. The outputs of this study may inform evidence based decision-making help to solve highly complex, multi-scaled, and multi-criteria location problems. Municipal authorities, in conjunction with industry, can apply this framework to identify the best compromised site for establishing a regional logistics hub, which in turn help reduce costs, improve logistic efficiency and enhance regional performance.

Backhaul-Aware Optimization of UAV Base Station Location and Bandwidth Allocation for Profit Maximization

Unmanned Aerial Vehicle Base Stations (UAVBSs) are envisioned to be an integral component of the next generation Wireless Communications Networks (WCNs) by dynamically moving the supply towards the demand. A significant drawback of the state-of-the-art have been designing a WCN in which the service-oriented performance measures (e.g., throughput) are optimized without considering different relevant decisions such as determining the location and allocating the resources, jointly. In this study, we address the UAVBS location and bandwidth allocation problems together to optimize the total network profit. In particular, a Mixed-Integer Non-Linear Programming (MINLP) formulation is developed, in which the location of a single UAVBS and bandwidth allocations to users are jointly determined. The objective is to maximize the total profit without exceeding the backhaul and access capacities. The profit gained from a specific user is assumed to be a piecewise-linear function of the provided data rate level, where higher data rate levels would yield higher profit. Due to high complexity of the MINLP, we propose an efficient heuristic algorithm with lower computational complexity. We show that, when the UAVBS location is determined, the resource allocation problem can be reduced to a Multidimensional Binary Knapsack Problem (MBKP), which can be solved in pseudo-polynomial time. To exploit this structure, the optimal bandwidth allocations are determined by solving several MBKPs in a search algorithm. We test the performance of our algorithm with two heuristics and with the MINLP model solved by a commercial solver. Our numerical results show that the proposed algorithm outperforms the alternative solution approaches and would be a promising tool to improve the total network profit.

A case for the adoption of decentralised reinforcement learning for the control of traffic flow on South African highways

As an alternative to capacity expansion, various dynamic highway traffic control measures have been introduced. Ramp metering and variable speed limits are often considered to be effective dynamic highway control measures. Typically, these control measures have been employed in conjunction with either optimal control methods or online feedback control. One shortcoming of feedback control is that it provides no guarantee of optimality with respect to the chosen metering rate or speed limit. Optimal control approaches, on the other hand, are limited in respect of their applicability to large traffic networks due to their significant computational expense. Reinforcement learning is an alternative solution approach, in which an agent learns a near-optimal control strategy in an online manner, with a smaller computational overhead than those of optimal control approaches. In this paper an empirical case is made for the adoption of a decentralised reinforcement learning approach towards solving the control problems posed by both ramp metering and variable speed limits simultaneously, and in an online manner. The effectiveness of this approach is evaluated in the context of a microscopic traffic simulation model of a section of the N1 national highway outbound from Cape Town in South Africa's Western Cape Province.

A fractional 0–1 program for task assignment with respect to preferences

We consider a task assignment problem with respect to preferences. The objective is to maximize total weighted satisfaction while maintaining a fair distribution. The problem’s mathematical model turns out to be a multiple-ratio, constrained, fractional 0–1 program since satisfaction is defined as a ratio of two linear functions. We discuss the computational complexity of the problem, give three equivalent mixed-integer linear formulations, and propose a naive heuristic the usefulness of which is demonstrated by a numeric study. This paper not only provides a new application of fractional 0–1 programming, but it also suggests an alternative solution approach for a similar problem dealt in the literature before with nonlinear nonconvex methods.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.