Barrett W. Thomas

The stochastic p-hub center problem with service-level constraints

Small package delivery companies offer services where packages are guaranteed to be delivered within a given time-frame. With variability in travel time, the configuration on the hub-and-spoke delivery network is vital in ensuring a high probability of meeting the service-level guarantee. We present the stochastic p-hub center problem with chance constraints, which we use to model the service-level guarantees. We discuss analytical results, propose solution heuristics, and present the results from computational experiments.

Anticipatory Route Selection

Mobile communication technologies enable communication between dispatchers and drivers and hence can enable fleet management based on real-time information. We assume that such communication capability exists for a single pickup and delivery vehicle and that we know the likelihood, as a function of time, that each of the vehicles potential customers will make a pickup request. We then model and analyze the problem of constructing a minimum expected total cost route from an origin to a destination that anticipates and then responds to service requests, if they occur, while the vehicle is en route. We model this problem as a Markov decision process and present several structured results associated with the optimal expected cost-to-go function and an optimal policy for route construction. We illustrate the behavior of an optimal policy with several numerical examples and demonstrate the superiority of an optimal anticipatory policy, relative to a route design approach that reflects the reactive nature of current routing procedures for less-than-truckload pickup and delivery.

A Compressed-Annealing Heuristic for the Traveling Salesman Problem with Time Windows

This paper describes a variant of simulated annealing incorporating a variable penalty method to solve the traveling-salesman problem with time windows (TSPTW). Augmenting temperature from traditional simulated annealing with the concept of pressure (analogous to the value of the penalty multiplier), compressed annealing relaxes the time-window constraints by integrating a penalty method within a stochastic search procedure. Computational results validate the value of a variable-penalty method versus a static-penalty approach. Compressed annealing compares favorably with benchmark results in the literature, obtaining best known results for numerous instances.

Probabilistic Traveling Salesman Problem with Deadlines

Time-constrained deliveries are one of the fastest growing segments of the delivery business, and yet there is surprisingly little literature that addresses time constraints in the context of stochastic customer presence. We begin to fill that void by introducing the probabilistic traveling salesman problem with deadlines (PTSPD). The PTSPD is an extension of the well-known probabilistic traveling salesman problem (PTSP) in which, in addition to stochastic presence, customers must also be visited before a known deadline. We present two recourse models and a chance constrained model for the PTSPD. Special cases are discussed for each model, and computational experiments are used to illustrate under what conditions stochastic and deterministic models lead to different solutions.

The orienteering problem with stochastic travel and service times

In this paper, we introduce a variant of the orienteering problem in which travel and service times are stochastic. If a delivery commitment is made to a customer and is completed by the end of the day, a reward is received, but if a commitment is made and not completed, a penalty is incurred. This problem reflects the challenges of a company who, on a given day, may have more customers than it can serve. In this paper, we discuss special cases of the problem that we can solve exactly and heuristics for general problem instances. We present computational results for a variety of parameter settings and discuss characteristics of the solution structure.

Waiting Strategies for Anticipating Service Requests from Known Customer Locations

This paper considers a dynamic and stochastic routing problem in which information about customer locations and probabilistic information about future service requests are used to maximize the expected number of customers served by a single uncapacitated vehicle. The problem is modeled as a Markov decision process, and analytical results on the structure of the optimal policy are derived. For the case of a single dynamic customer, we completely characterize the optimal policy. Using the analytical results, we propose a real-time heuristic and demonstrate its effectiveness compared with a series of other intuitively appealing heuristics. We also use computational tests to determine the heuristic value of knowing both customer locations and probabilistic information about future service requests.

Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand

We examine neighborhood structures for heuristic search applicable to a general class of vehicle routing problems (VRPs). Our methodology utilizes a cyclic-order solution encoding, which maps a permutation of the customer set to a collection of many possible VRP solutions. We identify the best VRP solution in this collection via a polynomial-time algorithm from the literature. We design neighborhoods to search the space of cyclic orders. Utilizing a simulated annealing framework, we demonstrate the potential of cyclic-order neighborhoods to facilitate the discovery of high quality a priori solutions for the vehicle routing problem with stochastic demand (VRPSD). Without tailoring our solution procedure to this specific routing problem, we are able to match 16 of 19 known optimal VRPSD solutions. We also propose an updating procedure to evaluate the neighbors of a current solution and demonstrate its ability to reduce the computational expense of our approach.

The dynamic shortest path problem with anticipation

Mobile communication technologies enable truck drivers to keep abreast of changing traffic conditions in real-time. We assume that such communication capability exists for a single vehicle traveling from a known origin to a known destination where certain arcs en route are congested, perhaps as the result of an accident. Further, we know the likelihood, as a function of congestion duration, that congested arcs will become uncongested and thus less costly to traverse. Using a Markov decision process, we then model and analyze the problem of constructing a minimum expected total cost route from an origin to a destination that anticipates and then responds to changes in congestion, if they occur, while the vehicle is en route. We provide structural results and illustrate the behavior of an optimal policy with several numerical examples and demonstrate the superiority of an optimal anticipatory policy, relative to a route design approach that reflects the reactive nature of current routing procedures.

Rollout Policies for Dynamic Solutions to the Multivehicle Routing Problem with Stochastic Demand and Duration Limits

We develop a family of rollout policies based on fixed routes to obtain dynamic solutions to the vehicle routing problem with stochastic demand and duration limits VRPSDL. In addition to a traditional one-step rollout policy, we leverage the notions of the pre-and post-decision state to distinguish two additional rollout variants. We tailor our rollout policies by developing a dynamic decomposition scheme that achieves high quality solutions to large problem instances with reasonable computational effort. Computational experiments demonstrate that our rollout policies improve upon the performance of a rolling horizon procedure and commonly employed fixed-route policies, with improvement over the latter being more substantial.

Runtime reduction techniques for the probabilistic traveling salesman problem with deadlines

The probabilistic traveling salesman problem with deadlines (PTSPD) is an extension of the well-known probabilistic traveling salesman problem in which, in addition to stochastic presence, customers must also be visited before a known deadline. For realistically sized instances, the problem is impossible to solve exactly, and local-search methods struggle due to the time required to evaluate the objective function. Because computing the deadline violations is the most time consuming part of the objective, we focus on developing approximations for the computation of deadline violations. These approximations can be imbedded in a variety of local-search methods, and we perform experiments comparing their performance using a 1-shift neighborhood. These computational experiments show that the approximation methods lead to significant runtime improvements without loss in quality.