Ahmad I. Jarrah

A Decision Support Framework for Airline Flight Cancellations and Delays

Aircraft shortages occasionally occur during day-to-day airline operation due to factors such as unfavorable weather conditions, mechanical problems, and delays in the schedule of incoming flights. Flight controllers need to respond to such shortages on a real-time basis by delaying or cancelling flights, swapping aircraft among scheduled flights, or requesting the usage of surplus aircraft. The choices undertaken aim at minimizing the losses incurred while retaining an operable flight schedule. In this paper, we represent two network models for aiding flight controllers in this complex decision environment. The models represent an attempt at conceptualizing this important and relatively unstudied problem, and form the basis for an evolving decision support system at United Airlines.

Airline Fleet Assignment with Time Windows

Recognizing that allowing variability in scheduled flight departure times can result in improved flight connection opportunities and a more cost effective fleet assignment, we present a generalized fleet assignment model for simultaneously assigning aircraft types to flights and scheduling flight departures. Our model, a simple variant of basic fleet assignment models, assigns a time window to each flight and then discretizes each window, allowing flight departure times to be optimized. Because problem size can become formidable, much larger than basic fleet assignment models, we develop two algorithmic approaches for solving the model. Our direct solution approach is good for speed and simplicity, whereas our iterative technique minimizes memory usage. Using data from a major U.S. airline, we show that our model can solve real, large-scale problems, and we evaluate the effects of schedule flexibility. In every test scenario, the model produces a fleet assignment with significantly lower costs than the basic model, and, in a separate analysis, the model is used to tighten the schedule, potentially saving aircraft.

Large-Scale, Less-than-Truckload Service Network Design

We present a novel formulation for the service network design problem in the context of large-scale, less-than-truckload (LTL) freight operations. The formulation captures the basic network design constraints; the load-planning requirement that all freight at a location, irrespective of the freights origin, loads to the same next terminal; and other important LTL-specific requirements. Our modeling scheme fragments the underlying massive network design model with up to 1.3 million 0--1 variables and 1.3 million rows into a separate and efficient integer programming (IP) problem for each destination terminal along with a coordinating master network design problem. We produce high-quality solutions in very reasonable CPU times (∼2 hours) using slope scaling and load-planning tree generation with corresponding potential annual savings of

The therapist routing and scheduling problem

20--25 million dollars for the target company for which the research was conducted.

The traveling therapist scheduling problem

In a majority of settings, rehabilitative services are provided at healthcare facilities by skilled therapists who work as independent contractors. Facilities include hospitals, nursing homes, clinics, and assisted living centers and may be located throughout a wide geographic area. To date, the problem of constructing weekly schedules for the therapists has yet to be fully investigated. This article presents the first algorithm for supporting weekly planning at the agencies that do the contracting. The goal is to better match patient demand with therapist skills while minimizing treatment, travel, administrative and mileage reimbursement costs. The problem was modeled as a mixed-integer program but has several complicating components, including different patient classes, optional weekly treatment patterns and a complex payment structure that frustrated the use of exact methods. Alternatively, a parallel (two-phase) greedy randomized adaptive search procedure was developed that relies on an innovative decomposition scheme and a number of benefit measures that explicitly address the trade-off between feasibility and solution quality. In Phase I, daily routes are constructed for the therapists in parallel and then combined to form weekly schedules. In Phase II, a high-level neighborhood search is executed to converge towards a local optimum. This is facilitated by solving a series of newly formulated traveling salesman problems with side constraints. Extensive testing with both real data provided by a U.S. rehabilitation agency and associated random instances demonstrates the effectiveness of the purposed procedure.

Large-scale pickup and delivery work area design

This article presents a new model for constructing weekly schedules for therapists who treat patients with fixed appointment times at various healthcare facilities throughout a large geographic area. The objective is to satisfy the demand for service over a 5-day planning horizon at minimum cost subject to a variety of constraints related to time windows, overtime rules, and breaks. Each therapist works under an individually negotiated contract and may be full-time or part-time. Patient preferences for specific therapists and therapist preferences for assignments at specific facilities are also taken into account when they do not jeopardize feasibility. To gain an understanding of the computational issues, the complexity of various relaxations is examined and characterized. The results indicated that even simple versions of the problem are NP-hard. The model takes the form of a large-scale mixed-integer program but was not solvable with CPLEX for instances of realistic size. Subsequently, a branch-and-price-and-cut algorithm was developed and proved capable of finding near-optimal solutions within 50 minutes for small instances. High-quality solutions were ultimately found with a rolling horizon algorithm in a fraction of that time. The work was performed in conjunction with Key Rehab, a company that provides physical, occupational, and speech therapy services throughout the U.S. Midwest. The policies, practices, compensation rules, and legal restrictions under which Key operates are reflected in the model formulation.

A heuristic for machine scheduling at general mail facilities

This paper presents a new approach to rationalizing the design of work areas for drivers who pickup and deliver hundreds of packages a day. Taking into account the random nature of demand, visit frequency, and service time, the objective is to partition the customers into the minimum number of convex, continuous clusters such that each can be serviced by a single vehicle within the time available in a day. An additional requirement is that the aspect ratio of a work area must satisfy certain geometric conditions. The problem is formulated as a generic capacitated clustering problem with side constraints and solved with a combination of aggregation to achieve analytic tractability, column generation to determine good clusters, regeneration to diversify the exploration of the feasible region, and heuristic variable fixing to find good feasible solutions. A novel set of geometric constraints allows for the implicit generation of clusters, and several valid inequalities are introduced to strengthen the pricing subproblem formulation. In addition, ideas from tabu search are adopted to limit the number of subproblems that are solved at each iteration. This greatly improved the efficiency of the column generation algorithm without sacrificing quality. The methodology was tested with data provided by a leading carrier. Six data sets were examined, ranging in size from roughly 6000 to 45,000 customers. The results showed that much more compact work areas could be obtained than currently exist, and that the number of drivers could be reduced by an average of 7.6%. This translates into millions of dollars in annual saving when all service areas across the U.S. are taken into account.

Validating vehicle routing zone construction using Monte Carlo simulation

Abstract In most major population centers mail collected during the day and mail arriving from outside the area are centrally processed at a general mail facility (GMF). This paper addresses the problem faced by the four supervisor who must schedule machines at a GMF to handle the hourly fluctuations in workload without violating critical dispatch times and service standards. The problem is complicated by the fact that decisions made upstream often have unpredictable consequences on downstream operations and inter-process storage. Machine scheduling in GMFs involves managing up to 200 different mail streams over a 24-hour period. Arriving mail must be separated according to major categories, stored, and assembled into suitable batches prior to sorting. During the distribution operations, a given mail piece may follow any one of a dozen routes through the system. The purpose of this paper is to present an efficient heuristic for generating operational machine schedules that are both smooth with respect to their utilization profiles, and consistent with the goal of batch processing. An example, based on data obtained from the Northern Virginia GMF, is given to demonstrate the computations.

Pickup and delivery network segmentation using contiguous geographic clustering

The primary purpose of this paper is to validate a clustering procedure used to construct contiguous vehicle routing zones (VRZs) in metropolitan regions. Given a set of customers with random demand for pickups and deliveries over the day, the goal of the design problem is to cluster the customers into zones that can be serviced by a single vehicle. Monte Carlo simulation is used to determine the feasibility of the zones with respect to package count and tour time. For each replication, a separate probabilistic traveling salesman problem (TSP) is solved for each zone. For the case where deliveries must precede pickups, a heuristic approach to the TSP is developed and evaluated, also using Monte Carlo simulation. In the testing, performance is measured by overall travel costs and the probability of constraint violations. Gaps in tour length, tour time and tour cost are the measure used when comparing exact and heuristic TSP solutions. To test the methodology, a series of experiments were conducted using data provided by a leading shipping carrier for the Pittsburgh area. Currently, the region is divided into 73 VRZs, compared to 64 indicated by the clustering procedure. The simulation results showed that a redesign would yield approximately

The Destination-Loader-Door Assignment Problem for Automated Package Sorting Centers

334,360 in annual savings without any noticeable deterioration in service. In addition, when the heuristic TSP model was solved in place of the exact model, the average gap in tour duration increased by only 0.16Â hours and 0.2Â hours for the cases of 73 clusters and 64 clusters, respectively, indicating a small upward bias. However, runtimes decreased by almost 70%.