arXiv subjects

Md. Noor-E-Alam

Publications and source records attributed to Md. Noor-E-Alam.

24 records · Page 2Linked to original sources

arXiv2019

Generalized Affine Scaling Algorithms for Linear Programming Problems

Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we integrate Nesterov's restarting strategy in the primal affine scaling method with an extra parameter, which in turn generalizes the original primal affine scaling method. We provide the proof of convergence for the proposed generalized algorithm considering long step size. We also provide the proof of convergence for the primal and dual sequence without the degeneracy assumption. This convergence result generalizes the original convergence result for the affine scaling methods and it gives us hints about the existence of a new family of methods. Then, we introduce a second algorithm to accelerate the convergence rate of the generalized algorithm by integrating a non-linear series transformation technique. Our numerical results show that the proposed algorithms outperform the original primal affine scaling method.

math.OC↗

arXiv2019

Resilient Supplier Selection in Logistics 4.0 with Heterogeneous Information

Supplier selection problem has gained extensive attention in the prior studies. However, research based on Fuzzy Multi-Attribute Decision Making (F-MADM) approach in ranking resilient suppliers in logistic 4 is still in its infancy. Traditional MADM approach fails to address the resilient supplier selection problem in logistic 4 primarily because of the large amount of data concerning some attributes that are quantitative, yet difficult to process while making decisions. Besides, some qualitative attributes prevalent in logistic 4 entail imprecise perceptual or judgmental decision relevant information, and are substantially different than those considered in traditional suppler selection problems. This study develops a Decision Support System (DSS) that will help the decision maker to incorporate and process such imprecise heterogeneous data in a unified framework to rank a set of resilient suppliers in the logistic 4 environment. The proposed framework induces a triangular fuzzy number from large-scale temporal data using probability-possibility consistency principle. Large number of non-temporal data presented graphically are computed by extracting granular information that are imprecise in nature. Fuzzy linguistic variables are used to map the qualitative attributes. Finally, fuzzy based TOPSIS method is adopted to generate the ranking score of alternative suppliers. These ranking scores are used as input in a Multi-Choice Goal Programming (MCGP) model to determine optimal order allocation for respective suppliers. Finally, a sensitivity analysis assesses how the Suppliers Cost versus Resilience Index (SCRI) changes when differential priorities are set for respective cost and resilience attributes.

cs.AI↗

arXiv2019

A Possibility Distribution Based Multi-Criteria Decision Algorithm for Resilient Supplier Selection Problems

Thus far, limited research has been performed on resilient supplier selection - a problem that requires simultaneous consideration of a set of numerical and linguistic evaluation criteria, which are substantially different from traditional supplier selection problem. Essentially, resilient supplier selection entails key sourcing decision for an organization to gain competitive advantage. In the presence of multiple conflicting evaluation criteria, contradicting decision makers, and imprecise decision relevant information (DRI), this problem becomes even more difficult to solve with the classical optimization approaches. However, prior research focusing on MCDA based supplier selection problem has been lacking in the ability to provide a seamless integration of numerical and linguistic evaluation criteria along with the consideration of multiple decision makers. To address these challenges, we present a comprehensive decision-making framework for ranking a set of suppliers from resiliency perspective. The proposed algorithm is capable of leveraging imprecise and aggregated DRI obtained from crisp numerical assessments and reliability adjusted linguistic appraisals from a group of decision makers. We adapt two popular tools - Single Valued Neutrosophic Sets (SVNS) and Interval-valued fuzzy sets (IVFS), and for the first time extend them to incorporate both crisp and linguistic evaluations in a group decision making platform to obtain aggregated SVNS and IVFS decision matrix. This information is then used to rank the resilient suppliers by using TOPSIS method. We present a case study to illustrate the mechanism of the proposed algorithm.

cs.AI↗

arXiv2019

Robust policy evaluation from large-scale observational studies

Under current policy decision making paradigm, we make or evaluate a policy decision by intervening different socio-economic parameters and analyzing the impact of those interventions. This process involves identifying the causal relation between interventions and outcomes. Matching method is one of the popular techniques to identify such causal relations. However, in one-to-one matching, when a treatment or control unit has multiple pair assignment options with similar match quality, different matching algorithms often assign different pairs. Since, all the matching algorithms assign pair without considering the outcomes, it is possible that with same data and same hypothesis, different experimenters can make different conclusions. This problem becomes more prominent in case of large-scale observational studies. Recently, a robust approach is proposed to tackle the uncertainty which uses discrete optimization techniques to explore all possible assignments. Though optimization techniques are very efficient in its own way, they are not scalable to big data. In this work, we consider causal inference testing with binary outcomes and propose computationally efficient algorithms that are scalable to large-scale observational studies. By leveraging the structure of the optimization model, we propose a robustness condition which further reduces the computational burden. We validate the efficiency of the proposed algorithms by testing the causal relation between Hospital Readmission Reduction Program (HRRP) and readmission to different hospital (non-index readmission) on the State of California Patient Discharge Database from 2010 to 2014. Our result shows that HRRP has a causal relation with the increase in non-index readmission and the proposed algorithms proved to be highly scalable in testing causal relations from large-scale observational studies.

stat.ME↗

arXiv2018

A Column Generation Algorithm for Vehicle Scheduling and Routing Problems

During natural or anthropogenic disasters, humanitarian organizations face a series of time-sensitive tasks. One of the tasks involves picking up critical resources (e.g., first aid kits, blankets, water) from warehouses and delivering them to the affected people. To successfully deliver these items to the people in need, the organization needs to make decisions that range from the quick acquisition of vehicles from the local market, to the preparation of pickup and delivery schedules and vehicle routes. During crises, the supply of vehicles is often limited, their acquisition cost is steep, and special rental periods are imposed. At the same time, the affected area needs the aid materials as fast as possible, and deliveries must be made within due time. Therefore, it is imperative that the decisions of acquiring, scheduling, and routing of vehicles are made optimally and quickly. In this paper, we consider a variant of a truckload open vehicle routing problem with time windows, which is suitable for modeling vehicle routing operations during a humanitarian crisis. We present two integer linear programming models to formulate the problem, with the first one being an arc-based mixed integer linear programming model. The second model is a path-based integer linear programming model, for which we design two fast path generation algorithms. The first model is solved exactly using the commercial solver, while we propose to solve the second model within a column generation framework. Finally, we perform numerical experiments and compare the results obtained from the two models. We show that the path-based model, when solved with our column generation algorithm, outperforms the arc-based model in terms of solution time without sacrificing the solution quality.

math.OC↗

arXiv2018

A Distance Measuring Algorithm for Location Analysis

Approximating distance is one of the key challenge in a facility location problem. Several algorithms have been proposed, however, none of them focused on estimating distance between two concave regions. In this work, we present an algorithm to estimate the distance between two irregular regions of a facility location problem. The proposed algorithm can identify the distance between concave shape regions. We also discuss some relevant properties of the proposed algorithm. A distance-sensitive capacity location model is introduced to test the algorithm. Moreover, sSeveral special geometric cases are discussed to show the advantages and insights of the algorithm.

math.OC↗