Minisum and minimax transfer point location problem with random demands points

This paper is concerned with analyzing some models of the weighted transfer point location problem under the minisum and minimax criterions when demand points are randomly distributed over regions of the plane and the location of the service facility is known. In case of minisum objective with rectilinear distance, an iterative procedure was constructed for estimating the optimal transfer point location using the hyperbolic application procedure. Exact analytic solution was obtained when the random demand points follow uniform distributions. A unified analytic optimal solution was provided for all types of probability distributions of the random demand points when the distance is the squared Euclidean distance. For minimax objective with squared Euclidean distance, an iterative procedure based on Karush-Kuhn-Tucker conditions was developed to produce an approximate solution to the optimal solution. Illustrative numerical examples were provided

Theory and computation of optimal low- and medium-thrust transfers

This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points

A Homotopy-Based Method for Optimization of Hybrid High-Low Thrust Trajectories

Space missions require increasingly more efficient trajectories to provide payload transport and mission goals by means of lowest fuel consumption, a strategic mission design key-point. Recent works demonstrated that the combined (or hybrid) use of chemical and electrical propulsion can give important advantages in terms of fuel consumption, without losing the ability to reach other mission objectives: as an example the Hohmann Spiral Transfer, applied in the case of a transfer to GEO orbit, demonstrated a fuel mass saving between 5-10% of the spacecraft wet mass, whilst satisfying a pre-set boundary constraint for the time of flight. Nevertheless, methods specifically developed for optimizing space trajectories considering the use of hybrid high-low thrust propulsion systems have not been extensively developed, basically because of the intrinsic complexity in the solution of optimal problem equations with existent numerical methods. The study undertaken and presented in this paper develops a numerical strategy for the optimization of hybrid high-low thrust space trajectories. An indirect optimization method has been developed, which makes use of a homotopic approach for numerical convergence improvement. The adoption of a homotopic approach provides a relaxation to the optimal problem, transforming it into a simplest problem to solve in which the optimal problem presents smoother equations and the shooting function acquires an increased convergence radius: the original optimal problem is then reached through a homotopy parameter continuation. Moreover, the use of homotopy can make possible to include a high thrust impulse (treated as velocity discontinuity) to the low thrust optimal control obtained from the indirect method. The impulse magnitude, location and direction are obtained following from a numerical continuation in order to minimize the problem cost function. The initial study carried out in this paper is finally correlated with particular test cases, in order to validate the work developed and to start investigating in which cases the effectiveness of hybrid-thrust propulsion subsists

Feasibility algorithms for two pickup and delivery problems with transfers

International audienceThis presentation follows the PhD thesis of Renaud Masson [1] on the Pickup and Delivery Problem with Transfers (PDPT). The motivating application is a dial-a-ride problem in which a passenger may be transferred from the vehicle that picked him/her up to another vehicle at some predetermined location, called transfer point. Both the PDPT and the Dial-A-Ride Problem with Transfers (DARPT) were investigated. An adaptive large neighborhood search has been developed to solve the PDPT [2] and also adapted to the DARPT [3]. In both algorithms, multiple insertions of requests in routes are tested. E ciently evaluating their feasibility with respect to the temporal constraints of the problem is a key issue

Biomechanical evaluation of patient transfers

The purpose of this study is to identify the problem encountered when a patient with limited strength and mobility needs assistance in transferring from a wheelchair to another location. This study took advantage of ergonomic techniques to isolate the source of stress, and limited these stresses according to the standards of the National Institute of Safety and Health Administration. A device was developed whereby the stresses of a patient transfer were eliminated. By using a conventional wheelchair and a recliner as a starting point, effectively combining these components into a single multifunctional unit the goal of reducing stress was achieved. The design allowed people with limited strength and mobility to transfer more independently, reducing the amount of assistance necessary from a caregiver. This design means a safer transfer for patient and caregiver

Patch contribution to near-field radiative energy transfer and van derWaals pressure between two half-spaces

Near-field effects in fluctuational electrodynamics leads to enhancement of radiative energy transfer as well as the emergence of van der Waals and/or Casimir pressure. While much has been learned from the analysis of near-field interactions between two half-spaces separated by a vacuum gap, we shed new light on the problem by finding how much of a surface patch on one of the half-spaces contributes to the energy transfer or van der Waals pressure at any location within the vacuum gap. We show that energy transfer and fluctuation-induced van der Waals pressure at any point on the surface of one half-space are qualitatively and quantitatively different due to the dissimilar zones of influence of interactions. We also show that the contributions from different surface patches are qualitatively similar for half-spaces with dielectric materials (silica, silicon carbide) and half-spaces with metals (gold)

Transonic Flows with Shocks Past Curved Wedges for the Full Euler Equations

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock past a curved wedge for the steady full Euler equations in an important physical regime, which form a nonlinear system of mixed-composite hyperbolic-elliptic type. To achieve this, we first employ the coordinate transformation of Euler-Lagrange type and then exploit one of the new equations to identify a potential function in Lagrangian coordinates. By capturing the conservation properties of the Euler system, we derive a single second-order nonlinear elliptic equation for the potential function in the subsonic region so that the transonic shock problem is reformulated as a one-phase free boundary problem for a second-order nonlinear elliptic equation with the shock-front as a free boundary. One of the advantages of this approach is that, given the shock location or quivalently the entropy function along the shock-front downstream, all the physical variables can expressed as functions of the gradient of the potential function, and the downstream asymptotic behavior of the potential function at the infinite exit can be uniquely determined with uniform decay rate. To solve the free boundary problem, we employ the hodograph transformation to transfer the free boundary to a fixed boundary, while keeping the ellipticity of the second-order equations, and then update the entropy function to prove that it has a fixed point. Another advantage in our analysis here is in the context of the real full Euler equations so that the solutions do not necessarily obey Bernoulli's law with a uniform Bernoulli constant, that is, the Bernoulli constant is allowed to change for different fluid trajectories.Comment: 35 pages, 2 figures in Discrete and Continuous Dynamical Systems, 36 (2016

Penerapan Konsep Vehicle Routing Problem Dalam Kasus Pengangkutan Sampah Di Perkotaan

. Cities in developing countries still operate a traditional waste transport and handling where rubbish were collected at regular intervals by specialized trucks from curb-side collection or transfer point prior to transport them to a final dump site. The problem are worsening as some cities experience exhausted waste collection services because the system is inadequately managed, fiscal capacity to invest in adequate vehicle fleets is lacking and also due to uncontrolled dumpsites location. In this paper problem of waste collection and handling is formulated based on Capacitated Vehicle Routing Problem Time Window Multiple Depo Intermediete Facility (CVRPTWMDIF). Each vehicle was assigned to visit several intermediate transfer points, until the truck loading or volume capacity reached then waste are transported to final landfill or dump site. Finally all trucks will return to a depot at the end of daily operation. Initially the solution of CVRPTWMDIF problem was tested on a simple hypothetical waste handling before being implemented into a real case problem. Solutions found using CVRPTWMDIF compared with the practice of waste transport and handling in the city of Bandung. Based on a common hours of operation and the same number of transport fleets, it was found that CVRPTWMDIF can reduce the volume of waste that is not transported by almost half by the end of the daily operations

Знаходження невідомих параметрів джерела забруднення в одновимірних нестаціонарних задачах масопереносу

У результаті проведеного математичного моделювання процесу масопереносу забруднень від миттєвого точкового джерела в одновимірному нестаціонарному випадку на відрізку, знайдено невідому координату його місцеположення на основі інформації про необхідну кількість замірів концентрації в заданих точках. Розв’язок оберненої крайової задачі знайдено декількома методами. Наведено результати числових експериментів та їх аналіз.As a result of the mathematical modeling of the mass transfer process from a point source of pollution in the one dimensional case on the transient segment an unknown coordinate of its location was found on the basis of identification of the required number measurements of the concentration in the given points. Solution of the inverse boundary value problem was found by several methods. Numerical results were presented and analyzed