Knapsack problem in fuzzy nature: Different models based on credibility ranking method

This paper deals with knapsack problem in fuzzy nature, where both the objective function and constraints are considered to be fuzzy. Three different models for fuzzy knapsack problem are proposed including, expected value model, chance-constrained model, and dependent-chance model. Credibility ranking method is applied to convert the fuzzy models into a crisp equivalent linear one considering triangular and trapezoidal fuzzy numbers. The solution of the fuzzy problem is obtained with respect to different satisfaction degrees in the objective function and constraints. Several numerical examples are given to demonstrate different models and concepts. The proposed approaches are applied to model and to solve a fuzzy pre-disaster investment decision problem.

Reverse Logistics Network Construction of Waste Electronic Products

The acceleration of the updating and iteration of electronic products leads to the increasing types and quantity of waste electronic products, which poses a great threat to environmental protection and social development. The problem of reverse logistics of waste electronic products has gradually become the focus of social attention. This paper constructed the expected value model of the reverse logistics of waste electronic products based on the open loop supply chain, and made the implementation plan of the reverse logistics through the empirical analysis of the electronic and electrical appliances market in H city.

Uncertain Single-Machine Scheduling with Deterioration and Learning Effect

A single-machine scheduling problem with deterioration and learning effect is studied in the present paper. The processing time and due date are considered uncertain variables due to lack of historical data. The aim is to minimize the makespan, total completion time, total weight completion time, and maximum lateness under an uncertain environment. To address the problem in an uncertain environment, the expected value model and pessimistic value model are developed. These models can be converted into equivalent models based on the inverse distribution method. It is proved that the corresponding dispatching rules can solve the problem optimally under different objective criteria. Finally, sensitivity analysis is used to illustrate the effectiveness of these rules.

Predicting Minimal Residual Disease in Acute Myeloid Leukemia through Stochastic Modeling of Clonality

Background. Relapse affects about 50% of AML patients who achieved remission after treatment, and the prognosis of relapsed AML is poor. Current evidence has shown that in many patients, mutations giving rise to relapse are already present at diagnosis and remain in small numbers in remission, defined as the minimal residual disease (MRD) [1]. Chemoresistant clones contributing to relapse of the disease arise from minimal residual disease (MRD) rather than resulting from newly acquired mutations during or after chemotherapy. MRD is the presence of measurable leukemic cells using non-morphologic assays. It is considered a strong predictor of relapse. The dynamics of clones comprising MRD is poorly understood and is considered influenced by a form of Darwinian selection.Methods. We propose a stochastic model based on a multitype (multi-clone) age-dependent Markov branching process to study how random events in MRD contribute to the heterogeneity in response to treatment in a cohort of six patients from The Cancer Genome Atlas database with whole genome sequencing data at two time points. Because human bone marrow cell counts are too large for direct stochastic simulation methods to be effective, we developed a hybrid numerical algorithm combining stochastic Gillespie-type and tau-leaping algorithms, and a deterministic differential equation solver, which uses much less computer time than a "straight Gillespie algorithm". Results. We developed a stochastic model of clonal evolution based on a multitype (multi-clone) age-dependent Markov branching process model of cell proliferation. In brief, we consider the critical time interval between diagnosis and initial relapse of AML that includes cytotoxic chemotherapy, chemotherapy-induced myelosuppression and decrease in leukemic cells, non-leukemic marrow recovery, and growth of the leukemic clones due to refractory or relapsed disease. Underlying our model are assumptions regarding the structure of growth, differentiation, and competition of the normal and leukemic clones. Our model reflects the stochasticity inherent when leukemic clones are near depletion after chemotherapy, which we hypothesize strongly contributes to the interpatient heterogeneity in treatment response. The parameters are estimated by fitting the expected-value model to the patient's clinical data. The available data at diagnosis includes patient's weight, percent cellularity, white blood cell count, percentage of blasts in both peripheral blood and bone marrow, and percentage of normal neutrophils in the peripheral blood. Importantly, the time to relapse and percentage of blasts in bone marrow at relapse are available. The parameters fitted to the expected-value model offer an explanation of how a leukemic clone can escape chemotherapy and promote relapse. These clones have either high proliferation rates or high self-renewal rates. As a result, there is a range of different parameter combinations that can explain their ability to succeed. On the other hand, we also study the clones that have been eradicated by the time of relapse and conclude that these clones might be eliminated either because they are not competitive and therefore surrender to other clones, or they are simply killed by chemotherapy. Also, we checked if the parameters are biologically relevant by using the model to compute the corresponding clonal growth rates for each patient. That these values fit in the clinically observed range independently found in for patients with the NPM1 mutations [1], suggests that the model is consistent with clinical data. Conclusions. Our model offers a more accurate understanding of how relapse arises and which properties allow a leukemic clone to thrive in the Darwinian competition among leukemic and normal hematopoietic clones. The model suggests a quantitative relationship between MRD and time to relapse and therefore may aid clinicians in determining when and how to implement treatment changes to postpone or prevent the time to relapse. [1]Assessment of Minimal Residual Disease in Standard-Risk AML. N Engl J Med. 2016;374:422. Relationship between MRD and time to relapse for all patients. Estimates of MRD and time to relapse are mean values from 1000 stochastic simulations. Each color corresponds to a single patient; left triangles, circles, and right triangles correspond to three parameter sets. Simulated points are fitted with a sigmoidal Hill function. Figure Disclosures No relevant conflicts of interest to declare.

A Stochastic Optimization Method for Energy Storage Sizing Based on an Expected Value Model

Energy storage technologies have been rapidly evolving in recent years. Energy storage plays different roles in various scenarios. For electricity consumers, they are concerned with how to use the energy storage system (ESS) to reduce their costs of electricity or increase their profits. In this paper, a stochastic optimization method for energy storage sizing based on an expected value model for consumers with Photovoltaic Generation (PV) is proposed. Firstly, the Gaussian mixture model clustering method is used to cluster the historical load and PV data and calculate the probability of each cluster. Secondly, the optimal model of total system profit is established. Finally, according to the expected value model, the optimal ESS power and capacity are determined. Two case studies are used to demonstrate the calculation of optimal ESS capacity. The results obtained by the method proposed in this paper are compared with the results produced by the deterministic method. Through the analysis and comparison, the validity and superiority of the method proposed in this paper are verified. The profits obtained by the method proposed in this paper are 0.87% to 127.16% more than the deterministic method.

Handling Optimization Under Uncertainty Using Intuitionistic Fuzzy-Logic-Based Expected Value Model

Uncertainty in parameters during deterministic optimization studies can have large impact on the outcome of the optimization result. It is pragmatic that these parameters are uncertain as they have direct link with real life scenarios, e.g. fuel price appearing as a parameter in objective function or constraints. However, their variability is ignored while solving the problem in a deterministic optimization framework. While mitigating the above mentioned scenario, it is, therefore, necessary to investigate the development of uncertainty handling techniques for a realistic optimization problem. In this work, we propose intuitionistic fuzzy expected value model (IFEVM), which assumes uncertain parameters as intuitionistic fuzzy variables and derives the solution out of an equivalent transformed deterministic formulation while defining the expected values of the objective functions and constraints. Intuitionistic fuzzy parameters can be regarded as a superset of the conventional fuzzy set where the aspect of non-determinacy of a fuzzy member to a set is additionally taken into account. The proposed IFEVM technique has been applied on two examples: first, with the Binh-korn's multi-objective test function where uncertain parameters are linearly related and next with a real life case study of industrial grinding operation having multiple numbers of non-linearly related uncertain parameters. The technique has been further applied to these case studies considering three different levels of risk scenarios e.g. optimistic, pessimistic and intermediate approaches. The IFEVM technique is fairly generic and advantageous, can be applied to any kind of system for handling uncertainty in parameters.

Solving a Two-Stage Stochastic Capacitated Location-Allocation Problem with an Improved PSO in Emergency Logistics

A stochastic expected value model and its deterministic conversion are developed to formulate a two-stage stochastic capacitated location-allocation (LA) problem in emergency logistics; that is, the number and capacities of supply centers are both decision variables. To solve these models, an improved particle swarm optimization algorithm with the Gaussian cloud operator, the Restart strategy, and the adaptive parameter strategy is developed. The algorithm is integrated with the interior point method to solve the second-stage model. The numerical example proves the effectiveness and efficiency of the conversion method for the stochastic model and the proposed strategies that improve the algorithm.