Applied & Industrial Mathematics
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Browsing Applied & Industrial Mathematics by Subject "Applied mathematics"
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Item Open Access A Branch-and-Price Algorithm for Bin Packing Problem(2015-12-16) Ataei, Masoud; Chen, MichaelBin Packing Problem examines the minimum number of identical bins needed to pack a set of items of various sizes. Employing branch-and-bound and column generation usually requires designation of the problem-specific branching rules compatible with the nature of the pricing sub-problem of column generation, or alternatively it requires determination of the k-best solutions of knapsack problem at level kth of the tree. Instead, we present a new approach to deal with the pricing sub-problem of column generation which handles two-dimensional knapsack problems. Furthermore, a set of new upper bounds for Bin Packing Problem is introduced in this work which employs solutions of the continuous relaxation of the set-covering formulation of Bin Packing Problem. These high quality upper bounds are computed inexpensively and dominate the ones generated by state-of-the-art methods.Item Open Access The Effects of Pre-Movement on Large Building Evacuations(2015-12-16) Farnell, Lisa Carroll Ruth; Madras, Neal; Chen, Shengyuan MichaelEvacuation times for buildings with a range of heights and occupant loads were generated by a computer simulation algorithm, assuming simultaneous start. Additional evacuation times were generated for the same buildings with pre-movement times assigned to building occupants. Pre-movement times were assigned based on uniform and gamma distributions. Building evacuation times with pre-movement were compared to those without, to determine the quantitative effects of pre-movement. Using regression analysis, equations were generated to predict the effects of pre-movement for given building heights and occupant loads. Regression equations were shown to reasonably predict the effects of pre-movement for the building cases used for the regression analysis. Additional simulations were performed with and without pre-movement for buildings with alternative heights and occupant loads. The regression function was applied to these additional simulations, and found to predict the effects of pre-movement in these building cases with some accuracy.Item Open Access The Impact of Population Heterogeneities and Disease Interventions on Herd Immunity: A Case Study of the COVID-19 Pandemic in Ontario(2023-03-28) Liwag, Maria Geneva Roselle Marino; Moghadas, SeyedIn epidemiology, herd immunity refers to the population level of immunity required to prevent or extinguish a large disease outbreak. In models with homogeneously mixing assumptions and without demographic structures, the herd immunity level may be different from that in heterogeneous models. With the COVID-19 pandemic in Ontario as a case study, a comprehensive deterministic mathematical model of disease spread with age and contact pattern variations was developed to examine the required herd immunity for different variants and compare with theoretical values obtained using homogeneous assumptions. The effects of non-pharmaceutical (testing/isolation of silent infections) interventions and vaccination on epidemic progression and herd immunity were investigated. With the inclusion of age and contact pattern structures, the resulting herd immunity level required to end an epidemic under the assumptions of long-term protection (without re-infection) is lower than theoretical values, even for more transmissible variants. While waning immunity and re-infection results in an oscillation in herd immunity levels in the population, subsequent epidemic peaks are less amplified, suggesting that even with increased variant transmissibility, infections of any variant allow for population immunity to rise, leading to an endemic state.