Maged Dessouky

A modeling framework for facility location of medical services for large-scale emergencies

Research on facility location is abundant. However, this research does not typically address the particular conditions that arise when locating facilities to service large-scale emergencies, such as earthquakes, terrorist attacks, etc. In this work we first survey general facility location problems and identify models used to address common emergency situations, such as house fires and regular health care needs. We then analyze the characteristics of large-scale emergencies and propose a general facility location model that is suited for large-scale emergencies. This general facility location model can be cast as a covering model, a P-median model or a P-center model, each suited for different needs in a large-scale emergency. Illustrative examples are given to show how the proposed model can be used to optimize the locations of facilities for medical supplies to address large-scale emergencies in the Los Angeles area. Furthermore, comparison of the solutions obtained by respectively using the proposed model and the traditional model is given to show the benefits of the proposed model in reducing loss of life and economic losses.

Solution approaches for facility location of medical supplies for large-scale emergencies

In this paper, we propose models and solution approaches for determining the facility locations of medical supplies in response to large-scale emergencies. We address the demand uncertainty and medical supply insufficiency by providing each demand point with services from a multiple quantity of facilities that are located at different quality levels (distances). The problem is formulated as a maximal covering problem with multiple facility quantity-of-coverage and quality-of-coverage requirements. Three heuristics are developed to solve the location problem: a genetic algorithm heuristic, a locate-allocate heuristic, and a Lagrangean relaxation heuristic. We evaluate the performance of the model and the heuristics by using illustrative emergency examples. We show that the model provides an effective method to address uncertainties with little added cost in demand point coverage. We also show that the heuristics are able to generate good facility location solutions in an efficient manner. Moreover, we give suggestions on how to select the most appropriate heuristic to solve different location problem instances.

A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller–Tucker–Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.

BUS DISPATCHING AT TIMED TRANSFER TRANSIT STATIONS USING BUS TRACKING TECHNOLOGY

A timed transfer terminal synchronizes the arrival of incoming vehicles with the departure of outgoing vehicles so as to minimize transfer delays. Most bus timed transfer terminals follow fixed schedules, and do not utilize intelligent transportation systems for vehicle tracking and control. This paper reviews technologies that enable real-time control of timed transfer. We evaluate the benefits of tracking bus locations and executing dynamic schedule control through the simulation of a generic timed transfer terminal under a range of conditions. Based on empirical data collected by the Los Angeles County/Metropolitan Transit Agency, we found delay over segments of long-headway bus lines to be negatively correlated with lateness at the start of the segment, indicating that buses have a tendency to catch up when they fall behind schedule. The simulation analysis showed that the benefit of bus tracking is most significant when one of the buses experiences a major delay, especially when there is a small number of connecting buses.

An Exact Algorithm for the Multiple Vehicle Pickup and Delivery Problem

We consider the multiple vehicle pickup and delivery problem (MVPDP) with the objective of minimizing the total travel cost and the fixed vehicle cost. Most of the optimization-based approaches for solving the MVPDP are developed for a restrictive hard time window or tight capacity environment that depend significantly on the reduction of the feasible solution space. We develop an alternative optimization solution approach for the MVPDP that does not require these constraints to be tight. The problem is formulated as a 0-1 integer-programming problem. A branch-and-cut algorithm is developed to optimally solve the problem. Four classes of valid inequalities for the MVPDP are proposed. By using the proposed solution approach, we were able to optimally solve problem instances of up to 5 vehicles and 17 customers on problems without clusters and up to 5 vehicles and 25 customers on problems with clusters within a stopping criterion of three CPU hours on a SUN Fire 4800 server.

A new insertion-based construction heuristic for solving the pickup and delivery problem with time windows

Abstract In this paper we present a new insertion-based construction heuristic to solve the multi-vehicle pickup and delivery problem with time windows. The new heuristic does not only consider the classical incremental distance measure in the insertion evaluation criteria but also the cost of reducing the time window slack due to the insertion. We also present a non-standard measure, crossing length percentage , in the insertion evaluation criteria to quantify the visual attractiveness of the solution. We compared our heuristic with a sequential and a parallel insertion heuristic on different benchmarking problems, and the computational results show that the proposed heuristic performs better with respect to both the standard and non-standard measures.

A genetic algorithm approach to the integrated inventory-distribution problem

We introduce a new genetic algorithm (GA) approach for the integrated inventory distribution problem (IIDP). We present the developed genetic representation and use a randomized version of a previously developed construction heuristic to generate the initial random population. We design suitable crossover and mutation operators for the GA improvement phase. The comparison of results shows the significance of the designed GA over the construction heuristic and demonstrates the capability of reaching solutions within 20% of the optimum on sets of randomly generated test problems.

Waiting Strategies for Dynamic Vehicle Routing

Many real-world vehicle routing problems are dynamic optimization problems, with customer requests arriving over time, requiring a repeated reoptimization. In this paper, we consider a dynamic vehicle routing problem where one additional customer arrives at a beforehand unknown location when the vehicles are already under way. Our objective is to maximize the probability that the additional customer can be integrated into one of the otherwise fixed tours without violating time constraints. This is achieved by letting the vehicles wait at suitable locations during their tours, thus influencing the position of the vehicles at the time when the new customer arrives. For the cases of one and two vehicles, we derive theoretical results about the best waiting strategies. The general problem is shown to be NP-complete. Several deterministic waiting strategies and an evolutionary algorithm to optimize the waiting strategy are proposed and compared empirically. It is demonstrated that a proper waiting strategy can significantly increase the probability of being able to service the additional customer, at the same time reducing the average detour to serve that customer.

REAL-TIME CONTROL OF BUSES FOR SCHEDULE COORDINATION AT A TERMINAL

Recently, bus transit operators have begun to adopt technologies that enable bus locations to be tracked from a central location in real-time. Combined with other technologies, such as automated passenger counting and wireless communication, it is now feasible for these operators to execute a variety of real-time strategies for coordinating the movement of buses along their routes. This paper compares control strategies that depend on technologies for communication, tracking and passenger counting, to those that depend solely on local information (e.g., time that a bus arrived at a stop, and whether other connecting buses have also arrived). We also develop methods to forecast bus arrival times, which are most accurate for lines with long headways, as is usually the case in timed transfer systems. These methods are tested in simulations, which demonstrate that technology is most advantageous when the schedule slack is close to zero, when the headway is large, and when there are many connecting buses.

Hybrid scheduling methods for paratransit operations

We study an extension to the general routing problem, which deals with integrating fixed route service with the general pickup and delivery problem to create a hybrid routing problem. The primary application for such a service is a dial-a-ride system used by transit agencies to transport disabled or elderly individuals. The main aim of the integration is to reduce the vehicle miles of the on-demand vehicles while not significantly reducing the customer service level. Due to the combinatorial nature of the problem, we propose a heuristic algorithm that provides an approximate solution, which is computationally efficient for solving large sized problems. The proposed heuristic is tested using real data from a transit agency.