Alan L. Erera

Optimization for Dynamic Ride-Sharing: A Review

Dynamic ride-share systems aim to bring together travelers with similar itineraries and time schedules on short-notice. These systems may provide significant societal and environmental benefits by reducing the number of cars used for personal travel and improving the utilization of available seat capacity. Effective and efficient optimization technology that matches drivers and riders in real-time is one of the necessary components for a successful dynamic ride-share system. We systematically outline the optimization challenges that arise when developing technology to support ride-sharing and survey the related operations research models in the academic literature. We hope that this paper will encourage more research by the transportation science and logistics community in this exciting, emerging area of public transportation.

Robust Optimization for Empty Repositioning Problems

We develop a robust optimization framework for dynamic empty repositioning problems modeled using time-space networks. In such problems, uncertainty arises primarily from forecasts of future supplies and demands for assets at different time epochs. The proposed approach models such uncertainty using intervals about nominal forecast values and a limit on the systemwide scaled deviation from the nominal forecast values. A robust repositioning plan is defined as one in which the typical flow balance constraints and flow bounds are satisfied for the nominal forecast values, and the plan is recoverable under a limited set of recovery actions. A plan is recoverable when feasibility can be reestablished for any outcome in a defined uncertainty set. We develop necessary and sufficient conditions for flows to be robust under this definition for three types of allowable recovery actions. When recovery actions allow only flow changes on inventory arcs, we show that the resulting problem is polynomially solvable. When recovery actions allow limited reactive repositioning flows, we develop feasibility conditions that are independent of the size of the uncertainty set. A computational study establishes the practical viability of the proposed framework.

A Paired-Vehicle Recourse Strategy for the Vehicle-Routing Problem with Stochastic Demands

This paper presents a paired-vehicle recourse strategy for the vehicle routing problem with stochastic demands (VRPSD). In the VRPSD, a fleet of homogeneous capacitated vehicles is dispatched from a terminal to serve single-period customer demands, which are known in distribution when planning, but only revealed with certainty upon vehicle arrival. While most existing research for this problem focuses on recourse strategies where each vehicle operates independently, this paper alternatively considers a strategy in which vehicles may be coordinated in pairs. A tabu search heuristic is developed to find good solutions to VRPSD instances with homogeneous customer demand distributions given this alternative recourse strategy. Finally, a computational study on a set of test problems with a variety of demand distributions reveals that the paired-recourse strategy may lead to expected travel cost savings of 3% to 25% on problems with 50 or more customers.

The Vehicle Routing Problem with Stochastic Demand and Duration Constraints

Time considerations have been largely ignored in the study of vehicle routing problems with stochastic demands, even though they are crucial in practice. We show that tour duration limits can effectively and efficiently be incorporated in solution approaches that build fixed, or a priori, tours for such problems. We do so by assuming that each tour must be duration feasible for all demand realizations, and determine the maximum duration of a given delivery tour by solving the optimization problem of an adversary. A computational study demonstrates the approach, and shows that enforcing tour duration limits impacts the structure of nearly-best solutions and may create the need for additional tours. However, for the instances considered, the price paid for robustness is small as the increase in total expected tour duration is modest.

A heuristic for the quay crane scheduling problem based on contiguous bay crane operations

Quay cranes (QC) are key resources at container terminals, and the efficiency of QC operations is vital for terminal productivity. The Quay Crane Scheduling Problem (QCSP) is to schedule the work activities for a set of cranes assigned to a single berthed vessel with the objective of minimizing the completion time of all container handling tasks. The problem is complicated by special characteristics of QC operations. Considering QC moving time and interference constraints, the concept of contiguous bay operations is proposed and a heuristic is developed to generate QC schedules with this feature. The heuristic is efficient and effective: it has polynomial computational complexity, and it produces schedules with a completion time objective bounded above by a small increment over the optimal completion time. Importantly, the heuristic guarantees that no quay cranes are idle due to interference. Numerical experiments demonstrate that the optimality gap is small for practical instances.

Dynamic periodic fixed appointment scheduling for home health

This paper defines the Home Health Nurse Routing and Scheduling (HHNRS) problem and presents a rolling horizon approach for its solution. The HHNRS is a dynamic periodic fixed appointment time routing problem with visit time consistency constraints. A set of patients, revealed dynamically, must be visited according to a prescribed weekly frequency over a prescribed number of weeks, where each visit must be assigned a precise appointment time chosen from a fixed menu of allowable appointments. Furthermore, weekly visits must repeat on the same days and times throughout a patients service duration, and should occur according to an allowable visit day combination for the patient. The objective is to maximize the number of patients served per nurse per unit time. We develop a rolling horizon myopic planning approach for the single nurse HHNRS variant that uses a new capacity-based insertion heuristic to explicitly consider remaining available time in the nurses schedule when inserting current patient requests. A computational study reveals that the heuristic produces schedules which accept 4% more patients and perform 4% more visits per day than a traditional distance-based insertion heuristic, while requiring an average of 8.7% additional minutes of travel per visit.

Improved Load Plan Design Through Integer Programming Based Local Search

We present integer programming models of the service network design problem faced by less-than-truckload LTL freight transportation carriers and a solution approach for the large-scale instances that result in practical applications. To accurately represent freight consolidation opportunities, the models use a fine discretization of time. Furthermore, the models simultaneously route freight and empty trailers and thus explicitly recognize the efficiencies presented by backhaul lanes. The solution approach can generate the traditional service network designs commonly used by LTL carriers but also enables the construction of designs that allow more flexibility, e.g., that allow freight routes to vary by day of week. An iterative improvement scheme is employed that searches a large neighborhood, each iteration using an integer program. Computational experiments using data from a large U.S. carrier demonstrate that the proposed modeling and solution approach has the potential to generate significant cost savings.

On Planning and Design of Logistics Systems for Uncertain Environments

This paper addresses some issues that arise in the planning and design of logistics systems when the environment in which they are to be operated cannot be modeled accurately with certainty. The paper describes the analytical difficulties introduced by explicitly considering uncertainty, and suggests possible modeling steps that may result in more efficient, uncertainty-friendly plans.

A dynamic driver management scheme for less-than-truckload carriers

This paper describes a scheme for the dynamic management of linehaul drivers developed for a large US less-than-truckload (LTL) carrier. Virtually all scheduling problems faced by transportation service providers are complicated by time-constrained vehicle operators that can be renewed only after resting. LTL driver scheduling is further complicated by the fact that trucking moves, unlike passenger airline flights or train dispatches, are not pre-scheduled. The technology developed in this paper combines greedy search with enumeration of time-feasible driver duties, and is capable of generating in a matter of minutes cost-effective driver schedules covering 15,000-20,000 loads and satisfying a variety of real-life driver constraints. Computational results justify the algorithmic design choices made in the development of the scheme, and a comparison with real-world dispatch data indicates that the technology produces driver schedules of very high quality.

Managing Inventory in Global Supply Chains Facing Port-of-Entry Disruption Risks

Ports-of-entry are critical components of the modern international supply chain infrastructure, particularly container seaports and airfreight hubs. The potential operational and economic impact resulting from their temporary closure is unknown but is widely believed to be very significant. This paper investigates one aspect of this potential impact, focusing specifically on the use of supply chain inventory as a risk mitigation strategy for a one supplier, one customer system in which goods are transported through a port-of-entry subject to temporary closures. Closure likelihood and duration are modeled using a completely observed, exogenous Markov chain. Order lead times are dependent on the status of the port-of-entry, including potential congestion backlogs of unprocessed work. An infinite-horizon, periodic-review inventory control model is developed to determine the optimal average cost ordering policies under linear ordering costs with backlogged demand. When congestion is negligible, the optimal policy is state invariant. In the more complex case of nonnegligible congestion, this result no longer holds. For studied scenarios, numerical results indicate that operating margins may decrease 10% for reasonable-length port-of-entry closures, that margins may be eliminated completely without contingency plans, and that expected holding and penalty costs may increase 20% for anticipated increases in port-of-entry utilization.