Three-stage Stochastic Model Research Articles

STUDYING THE AGE OF ONSET AND DETECTION OF CHRONIC MYELOID LEUKEMIA USING A THREE-STAGE STOCHASTIC MODEL

Chronic Myeloid Leukemia (CML) is a biphasic malignant clonal disorder that progresses, first with a chronic phase, where the cells have enhanced proliferation only, and then to a blast phase, where the cells have the ability of self-renewal. It is well recognized that the Philadelphia chromosome (which contains the BCR-ABL fusion gene) is the “hallmark of CML”. However, empirical studies have shown that the mere presence of BCR-ABL may not be a sufficient condition for the development of CML, and further modifications related to tumor suppressors may be necessary. Accordingly, we develop a three-mutation stochastic model of CML progression, with the three stages corresponding to the non-malignant cells with BCR-ABL presence, the malignant cells in the chronic phase, and the malignant cells in the blast phase. We demonstrate that the model predictions agree with age incidence data from the United States. Finally, we develop a framework for the retrospective estimation of the time of onset of malignancy, from the time of detection of the cancer.

A Three-Stage Stochastic Model to Improve Resilience with Lateral Transshipment in Multi-Period Emergency Logistics

Driven by the growing threat of natural disasters caused by climate change, there is an urgent need to strengthen the emergency rescue logistics network. However, insufficient research has been conducted on optimizing both pre-disaster preparation and post-disaster response, resulting in lower resilience and inefficiency of emergency logistics management. To this end, this study explores the optimization of emergency rescue resource allocation and transportation network design, considering the uncertainty and multi-period nature of natural disaster rescue. By employing a lateral transshipment strategy, a three-stage stochastic programming model is established, which aims to balance economic benefits with the need for devastations, thereby enhancing the resilience of the logistics network. Numerical experiments verify the effectiveness of the proposed model with different instances and the performance of the lateral transshipment strategy by comparing it with a two-stage stochastic programming model. Sensitivity analysis is performed on the costs of constructing a depot and the penalties for unmet needs. The analysis yielded valuable insights that can be used to enhance emergency rescue operations, supply chain network design, and logistics network design. The research outcome can benefit emergency responders and logistics professionals in optimizing their operations.

Investigating alternative power supply solutions under long term uncertainty for offgrid-offshore fish farm: The case of Hinnøya island, Norway

The aim of this paper is to explore potential least-cost decarbonisation solutions for an off-grid and offshore fish farm power supply system under long term uncertainty. The Hinnøya island in Norway is used as a use case. Three distinctive off-grid and grid-based alternative power supply solutions were proposed and studied as a replacement to the existing diesel power solution in a three-stage stochastic model and under two critical long-term uncertainties: (1) access to strong grid and (2) storage battery cost. The TIMES modelling framework is applied. The stochastic model results reveal that grid integrated storage is an optimal near-term investment for a storage battery cost of 295 €/kWh and less by 2025. In scenarios with no access to strong grid, grid integrated storage continues to be a least-cost solution in the long-term as well, whereas in those scenarios with strong grid access, new investment in storage is not required after 2030. Contrary to the stochastic model runs, the equivalent deterministic model runs showed that a hybrid wind and diesel solution is an optimal near-term investment. From 2030, however, a similar technology pattern in both stochastic and deterministic model runs are observed. Nevertheless, the results are very sensitive to the assumed storage battery costs. Higher storage costs (as high as 704 €/kWh by 2025) would make the hybrid wind and diesel solution an optimal solution instead of the grid integrated storage solution in near-term investment in both stochastic and deterministic model runs.

A three-stage stochastic model for emergency relief planning considering secondary disasters

ABSTRACT In the real world, secondary disasters occur frequently after primary disasters, and their diverse and uncertain nature along with the destruction may make the emergency relief operations more challenging. A scenario-based three-stage stochastic programming model is proposed considering the correlation between primary and secondary disasters under uncertain conditions. In order to enhance the computational tractability of the model, an accelerated Benders decomposition algorithm is formulated. In addition, to tackle large-scale cases, an approximation method employing the worst-case scenario in the third stage is established to improve the computational tractability. A computational study is performed to highlight the significance of the model and the efficiency of the proposed solution strategy. The results indicate that, by considering secondary disasters, demand satisfaction can be considerably improved compared with considering only primary disasters.

Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times

We propose a three-stage stochastic programming model which determines flight timing, fleeting and routing decisions while considering the randomness of demand and non-cruise times. Our model differs from the existing two-stage stochastic models by considering not only flight timing and potential passenger demand, but also expected operational expenses, such as fuel burn and carbon emission costs. We include aircraft cruise speed decisions to compensate for non-cruise time variability so as to satisfy the time requirements of the passenger connections. We handle nonlinear functions of fuel and emission costs associated with cruise speed adjustments by utilizing mixed integer second order cone programming. Because the three-stage stochastic model leads to a large decision tree and can be very time-consuming to solve optimally, we suggest a scenario group-wise decomposition algorithm to obtain lower and upper bounds for the optimal value of the proposed model. The lower and upper bounds are obtained by solving a number of group subproblems, which are similar to proposed multi-stage stochastic model defined over a reduced number of scenarios. We suggest a cutting plane algorithm, along with improvements, to efficiently solve each group subproblem. In the numerical experiments, we provide a significant cost savings over two-stage stochastic programming and deterministic approaches.

The age incidence of female breast cancer— simple models and analysis of epidemiological patterns

We show that a three-stage stochastic model of carcinogenesis with a discretized transition probability from the intermediate (hyperplastic) stage to the final (clinically malignant) stage leads to an equation which can be fitted to a wide variety of age-incidence curves for female breast cancer. This includes the inflected (so-called biphasic) incidences observed in many Western countries, as well as the peaked profiles observed in the Orient. Unlike previous mathematical theories which attribute biphasic incidence to a superposition of profiles for two etiologically distinct diseases, the theory presented here hypothesizes its biologic basis as change in ovarian functions accompanying menopause. This leads to an equation which fits the data equally well, though with fewer adjustable parameters. The extent to which the theory simulates the effect of various risk factors, including age at menarche, menopause and first birth, is briefly discussed.