Minnie H. Patel

OPTIMAL ROUTING OF HAZARDOUS MATERIALS CONSIDERING RISK OF SPILL

The diffusion of gases over wide areas from possible spills during transport of hazardous materials is considered when determining the least risk path through a network. Spills could occur through improper operation of vehicle or container or through a collision. Relationships for minimum risk paths are developed for these cases: specific wind directions, uniform average wind direction, maximum concentration wind directions, wind-rose averaged wind directions and speeds, and multiday routing with uncertain weather conditions. The relationships are illustrated for a full-sized urban network. This paper illustrates, how a Geographical Information System approach coupled with elementary principles of optimization theory can be used to solve such complex routing problems. The mathematics developed also reveals some consistent properties of all routing problems that are generalizable. For short trips the least risk path is invariant with the assumed wind speed, the size of spill, and the toxicity of the material. It is also invariant with the selection between uniform average wind direction and maximum risk direction criteria. A hybrid between numerical and analytical methods was adopted to reduce computation requirements which are still large but acceptable.

THROUGH-TRIP TABLES FOR SMALL URBAN AREAS: A METHOD FOR QUICK-RESPONSE TRAVEL FORECASTING

Regionwide travel forecasts in small urban areas require good knowledge of through-trip tables for each of several vehicle classes. Survey data are often unavailable or incomplete, so planners would benefit from a means of estimating through-trips from readily available information. A model for a through-trip table from trip-distribution theory and elementary geographical principles is postulated and tested. The model considers the level of through-traffic at external stations, the shape of urban areas, and the necessity that trips between any two external points pass through the region because of barriers that impede travel. Separate model variations are developed for a region of arbitrary shape and for a region of circular shape. To ascertain the validity of the approximations, the model is applied to two cities: Oshkosh, Wisconsin, and Tallahassee, Florida. The model for circular-shaped urban areas has produced excellent results for both cities, each of which previously had prepared external-to-external trip tables by sampling actual traffic. Oshkosh’s geography is particularly interesting because of two large neighboring lakes that constitute barriers to travel. The model explains almost 96 percent of the variation in the trip table in Oshkosh and almost 100 percent of the variation in Tallahassee. These values exceed goodness-of-fit measures that are reported for other models that are described in the literature. Errors in through-trip flows on individual links that potentially serve through-trips are estimated at only about 10 percent in Oshkosh and 14 percent in Tallahassee.

A simulation study of the productivity of large trucks with shorter trailers

The need for improving the productivity in freight transportation has become urgent in recent years due to rising fuel cost, labour shortage, healthcare cost for its labour force, and congestion on the roadways. This paper presents a productivity study about using three shorter, lighter trailers for moving household goods versus using one long, heavy trailer as commonly practised in the van-line industry. The conventional operations necessitate long delays due to loading and unloading. A goal of the proposed Shorter Trailer Combination Vehicles (STCV) operations is to maximise the operational efficiencies of long-haul trucks and the industry by dedicating such trucks to what they do best: moving, not waiting. A simulation approach is used to compare the performance of the conventional and STCV operations with respect to a stochastic Multi-Vehicle Pickup and Delivery Problem (MVPDP) in which the demand is random with random delivery due dates. The objective of the simulation is to determine the number of trucks and trailers, the pickup-and-delivery dispatch rule, and the type of transportation operations (conventional vs. STCV) that optimise various performance measures.

A linear program to detect extrapolation in predicting new responses of a multiple linear regression model

A region of interpolation is defined as the smallest convex set containing all original n data points used to build a regression model. In this paper, we present a linear program with n variables and (k + 1) constraints whose feasibility exactly determines whether or not a given new point, at which a response is predicted, is an extrapolation. Here k is the number of regressor variables used to build the regression model. This method has an advantage over the other methods used in the literature for the determination of extrapolation, in that, whenever a new point is indeed an extrapolation point, the developed method identifies it as an extrapolation, while the other methods may fail to identify it as an extrapolation point.

Air cargo pickup schedule for single delivery location

In this paper, various deterministic models for determining optimal pickup times for air cargo from an airport and delivering it to a local distribution center for a global manufacturer are presented. The arrival times of the flights that can potentially bring air cargo are assumed to be deterministic and known. In addition, the custom clearance time for the air cargo and the traveling time from the airport to the local distribution center are assumed to be deterministic and known. These models are formulated mathematically as linear binary integer programming models without air cargo weight considerations. Deterministic formulations without air cargo weight information are shown to be related to the p-Median problem. The deterministic formulation of air cargo pickup times with air cargo weight consideration is shown to be a nonlinear binary integer programming model. The solutions of these models serve as an initial starting point to solve the stochastic problem with random arrival times of the flights and random custom clearance times and travel times.

Spherical minimax location problem using the euclidean norm: formulation and optimization

The minimax spherical location problem is formulated in the Cartesian coordinate system using the Euclidean norm, instead of the spherical coordinate system using spherical arc distance measures. It is shown that minimizing the maximum of the spherical arc distances between the facility point and the demand points on a sphere is equivalent to minimizing the maximum of the corresponding Euclidean distances. The problem formulation in this manner helps to reduce Karush-Kuhn-Tucker necessary optimality conditions into the form of a set of coupled nonlinear equations, which is solved numerically by using a method of factored secant update with a finite difference approximation to the Jacobian. For a special case when the set of demand points is on a hemisphere and one or more point-antipodal point pair(s) are included in the demand points, a simplified approach gives a minimax point in a closed form.

The effect of space-time demand processes on the solution of transportation problems

Abstract Using a formulation of the transportation problem with a stochastic demand represented by a space-time autoregressive moving average (STARMA) model, a simulation study is presented whereby the consequences of ignoring space and/or time dependencies in the demand process are evaluated. It is found that the percentage change in total deliveries, x PCT , when space-time dependency is ignored varies linearly with space-time autoregressive (STAR) parameters. Furthermore, x PCT is larger when we ignore spatial dependency than temporal dependency. When both dependencies are ignored, x PCT may be larger than that for both spatial and temporal cases depending upon the signs of STAR parameters. Results for space-time moving average (STMA) are similar to that of STAR. However, for STARMA, when both the temporal and spatial dependencies in demand are ignored, x PCT is piecewise linear. The improvement in percentage change in total cost, PCT, is found to vary between 1–55% as the ratio of unit holding cost to unit product cost, H/P, varies from its minimum to its maximum, and 1–95% for the ratio of unit shortage cost to unit product cost, SH/P, when space-time dependencies are taken into account, depending upon the values of various parameters.

A two-stage stochastic programming model for integrated airport surface operations under uncertainties

In this research, we have built a scenario tree-based two-stage stochastic programming model to optimise airport surface operations as an integrated system by taking into consideration uncertainties. We consider the uncertainties in aircraft readiness time for pushback and taxi speed due to weather conditions, which occur commonly in reality. The model assumptions and implications are consistent with practice. Our mathematical models, implemented in OPL-CPLEX, are applied to an airport with two runways and a taxiway network of 41 nodes and 70 links. The solution results are consistent with our expectations. We also quantify the benefit of the stochastic-programming approach through comparison with the deterministic models.