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In unsplittable network flow problems, certain nodes must satisfy a combinatorial requirement that the incoming arc flows cannot be split or merged when routed through outgoing arcs. This so-called no-split no-merge requirement arises in unit train scheduling where train consists should remain intact at stations that lack necessary equipment and manpower to attach/detach them. Solving the unsplittable network flow problems with standard mixed-integer programming formulations is computationally difficult due to the large number of binary variables needed to determine matching pairs between incoming and outgoing arcs of nodes with no-split no-merge constraint. In this paper, we study a stochastic variant of the unit train scheduling problem where the demand is uncertain. We develop a novel decision diagram (DD)-based framework that decomposes the underlying two-stage formulation into a master problem that contains the combinatorial requirements and a subproblem that models a continuous network flow problem. The master problem is modeled by a DD in a transformed space of variables with a smaller dimension, leading to a substantial improvement in solution time. Similar to the Benders decomposition technique, the subproblems output cutting planes that are used to refine the master DD. Computational experiments show a significant improvement in solution time of the DD framework compared with that of standard methods. History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics. Funding: This work was supported by the Iowa Energy Center [Grant 20IEC005]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1194. [ABSTRACT FROM AUTHOR]

This paper proposes a new mixed integer programming formulation and branch and cut (BC) algorithm to solve the dial-a-ride problem (DARP). The DARP is a route-planning problem where several vehicles must serve a set of customers, each of which has a pickup and delivery location, and includes time window and ride time constraints. We develop "restricted fragments," which are select segments of routes that can represent any DARP route. We show how to enumerate these restricted fragments and prove results on domination between them. The formulation we propose is solved with a BC algorithm, which includes new valid inequalities specific to our restricted fragment formulation. The algorithm is benchmarked on existing and new instances, solving nine existing instances to optimality for the first time. In comparison with current state-of-the-art methods, run times are reduced between one and two orders of magnitude on large instances. [ABSTRACT FROM AUTHOR]

There is a vivid debate in cities all over the world on how to distribute the restricted space in urban areas among stakeholders. Urban design movements such as new pedestrianism or Copenhagenization advocate that too much space is attributed to cars. In this context, our research investigates the optimization of parking lots with the help of mathematical programming. For the given ground plot of a parking lot, we maximize the number of parking spaces each reachable via a driving lane, so that the urban space attributed to the parking of cars is efficiently used. Based on a grid of squares in which we rasterize the ground plot, this paper presents mixed-integer programs based on three different resolutions for orthogonal parking. Our computational study explores the tradeoff between the additional parking spaces promised by a higher resolution and the increased computational effort because of the larger solution space (and vice versa). We compare our optimization approaches with a sample of 177 real-world parking lots and show that optimization can be a serviceable car park design tool with the help of a case study. [ABSTRACT FROM AUTHOR]

This paper extends the dynamically formulated hidden Markov models to a high-order hidden Markov model (HO-HMM) formulation. In the HO-HMM, the Markovian assumption that the future states (interpreted as the states of preferences or attitudes) depend only on the current state has been relaxed. Instead, the HO-HMM generalizes that the future states will depend on a number of states occurring beforehand. This paper develops the theoretical formulation of a HO-HMM framework. A recursive algorithm of likelihood computation is derived for model estimation. The algorithm significantly reduces the complexity of estimation and ensures the applicability of high-order hidden Markov modeling. The proposed methodology is further demonstrated on a vehicle ownership choice application using Puget Sound Transportation Panel data coupled with a few supplementary data sources. Long-term life-cycle stage changes in households are used as proxies for the high-order Markov transitions in car ownership hidden states. Results indicate that the HO-HMM has superior explanatory power in fitting longitudinal data. [ABSTRACT FROM AUTHOR]

A novel analysis framework for the spatial aspects of car travel, measured by vehicle miles traveled (VMT), is introduced in this paper. The specification of a dynamic spatial Durbin model enables the analysis of VMT spatial spillovers and diffusion between neighboring areas in the short and long run. The framework is further developed to capture and introduce to a spatial setting potential asymmetry and hysteresis that can reflect reference dependence and habits. A panel data set is compiled at the subregional level, based on official car mileage recordings in England and Wales. In addition to the inelastic long-run responses of VMT to fuel price (-0:124) and income (0.116) changes, the results illustrate asymmetries and hysteresis in price elasticities with a significant spatial component. The impact magnitude on VMT from a number of factors, such as alternative fuel use, fuel deserts in rural areas, and road network and car fleet characteristics, is also estimated. The results are consistent with the car use saturation hypothesis through the positive impact of motorization rate to VMT. The negative effect of public transport infrastructure on car travel is only significant in the spatial models. The paper demonstrates the applicability and importance of spatial econometrics in transport research. [ABSTRACT FROM AUTHOR]

Logistics is a cost sensitive industry with large and fast growing routing networks. In this paper we devise a computational, robust optimization method for the strategic routing decisions of a logistics' customer, i.e., a company that uses the services of different freight forwarders to meet its transportation demands between several sources, sinks, and hubs. The costs of such transports are determined by tariff systems that typically show economies of scale and reward the consolidation of goods that complement each other in properties relevant for transport, such as weight and volume. In the strategic planning phase, routes and hubs have to be chosen roughly one year ahead, in particular, before the actual demand is known. Our method anticipates the fluctuation of demands by minimizing the worst-case cost over a restricted scenario set. The combination of a realistic cost function, a robust modeling of uncertainty, and large-scale networks leads to highly intractable models. We show that the corresponding adversary problem is NP-hard. To nevertheless find solutions for real instances with very good worst-case cost we derive a carefully relaxed and simplified mixed-integer linear program that solves well for large instances because of its powerful linear programming relaxation. We test the method for real-world instances. The results show that robust optimization can significantly reduce worst-case cost. Furthermore, we derive from our method two heuristic techniques to solve even larger networks and report on the corresponding computational results. Neglecting the typical uncertainty about demand values can cause significant cost in logistic routing problems. This paper provides for a practical method to avoid such costs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the vehicle routing problem (VRP) with fractional objective function. We investigate how the principal techniques used either in the context of fractional programming or in the context of vehicle routing problems interact. We present new dual and primal bounding procedures that have been incorporated in an exact method. The method proposed allows extending specific variants of the VRP to their counterpart with a fractional objective function. Extensive numerical experiments prove the validity of our approach. [ABSTRACT FROM AUTHOR]

We consider a road-ban problem in hazardous material (hazmat) transportation. We formulate the problem as a network design problem to select a set of closed road segments for hazmat traffic and obtain a bilevel optimization problem. While modeling probabilistic route choices of hazmat carriers by the random utility model (RUM) in the lower level, we consider a risk-averse measure called conditional value at risk (CVaR) in the upper level, instead of the widely used expected risk measure. Using the RUM and CVaR, we quantify the risk of having hazmat accidents and large consequences and design the network policy for road bans accordingly. Although CVaR has been used in hazmat routing problems, this paper is the first attempt to apply CVaR in risk averse hazmat network design problems considering stochastic route choices of hazmat carriers. The resulting problem is a mixed integer nonlinear programming problem, for which we devise a line search approach combined with Benders decomposition. We demonstrate the efficiency of the proposed computational method with case studies. The average computation time for a network with 105 nodes and 268 arcs is three hours. By applying CVaR to the route-choice behavior of hazmat carriers, we protect the road network from undesirable route choices that may lead to severe consequences. We define the value of RUM-CVaR solutions (VRCS) over the deterministic model based on shortest-path problems and the expected risk measure. Our case study shows that the VRCS can range from 4.9% to 64.1% depending on the probability threshold used in the CVaR measure. [ABSTRACT FROM AUTHOR]

Public transportation systems in metropolitan areas carry a high density of daily traffic, heterogeneously distributed, and exposed to the negative consequences derived from service disruptions. Breakdowns, accidents, strikes, etc., require on-line operation adjustments to address these incidents and thus reduce their side effects, such as passenger extra-waiting times, complaints, potential operational dangers, etc. The Vehicle Rescheduling Problem consists of defining a new schedule for a set of previously scheduled trips, given that one/several trips cannot be carried out. This paper addresses the rescheduling problem in a transit line that has suffered a fleet size reduction (also denoted as Reduced Fleet Rescheduling Problem). We present different modeling possibilities depending on the assumptions that must be included in the modelization and we show that the problem can be rapidly solved using a reformulation that will be proven to have the integrality property. We test our results in a testbed of random instances outperforming previous results in the literature. We also include a real-world case of the commuter trains of Madrid, Spain to illustrate our solutions. [ABSTRACT FROM AUTHOR]

The Pickup and Delivery Problem with Time Windows and Scheduled Lines (PDPTW-SL) consists of routing and scheduling a set of vehicles, by integrating them with scheduled public transportation lines, to serve a set of freight requests within their time windows. This paper presents an exact solution approach based on a branch-and-price algorithm. A path-based set partitioning formulation is used as the master problem, and a variant of the elementary shortest path problem with resource constraints is solved as the pricing problem. In addition, the proposed algorithm can also be used to solve the PDPTW with transfers (PDPTW-T) as a special case. Results of extensive computational experiments confirm the efficiency of the algorithm: it is able to solve small- and medium-size instances to optimality within reasonable execution time. More specifically, our algorithm solves the PDPTW-SL with up to 50 requests and the PDPTW-T with up to 40 requests on the considered instances. The online appendix is available at https://doi.org/10.1287/trsc.2017.0798. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of routing in-house transport vehicles that feed parts to workstations in assembly plants or workshops just in time. The capacitated vehicles, typically so-called tow trains, perform their assigned route cyclically without break and provide each station with the exact quantity of parts required until the next arrival of the vehicle. Hence, the demand of each station depends on the duration of the route serving the station: The longer the route duration, the less frequently the station is visited and the higher its demand. The goal is to minimize first the number of vehicles and second the total route duration, while respecting given minimum service frequencies at the stations. We provide a mathematical formulation of this novel problem and address it by means of a large neighborhood search. The algorithm is able to solve realistic instances in acceptable time and vastly outperforms a default solver. We discuss two variants of the problem, one in which split deliveries to stations are allowed and another assuming that all stations lie on a straight line. Finally, we investigate the extent to which assuming constant demand rates may lead to problems during the day-to-day operations of the part-feeding system, where demands are not necessarily constant. [ABSTRACT FROM AUTHOR]

We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely influenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set. In the recourse model, the routing, the order of port visits, and the quantities to load and unload are fixed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances. [ABSTRACT FROM AUTHOR]

The dynamic traffic equilibrium problem has been a pivotal area of research in transportation for a few decades. The current state-of-the-art research in this area generally considers simultaneous departure time and route choice. In this paper, we theoretically prove that, in the simplest standard bottleneck model with a sufficient number of commuters, a dynamic user equilibrium (DUE) cannot be reached through a day-to-day evolution process of travelers' departure rate--a central idea behind the iterative dynamic traffic equilibrium algorithms prevalent in the literature. We carry out our exploration with the proportional swap system and then extend our analysis to other typical dynamic equilibrium algorithms such as the network tatonnement process, the simplex gravity flow dynamics, the projected dynamical system, and the evolutionary traffic dynamics. Our investigation indicates that any algorithm analogous to the five categories of systems must be cautious in terms of convergence when it is applied to solve the DUE problem with a departure time choice, and hence puts forward a general question: Are we really solving the DUE problem with a departure time choice? [ABSTRACT FROM AUTHOR]

This paper addresses the problem of finding the optimal routing policies with only trajectory information in a stochastic time-dependent network where all link travel times are temporally and spatially correlated. Two equivalent definitions are given for trajectory-adaptive routing policy. The first definition follows the mapping definition in a series of previous studies, where the trajectory information is included in the state variable. With that definition, any subpolicy of an optimal routing policy must also be optimal, and the algorithm developed in previous studies could serve as an exact solution, but the nature of the definition that trajectory information is included in the state variable determines that the number of states is prohibitively huge. Therefore, a second definition is given as a recursive definition, where the trajectory information is not included in the state variable. It is shown that, with the second definition, a subpolicy of an optimal/nondominated routing policy is not necessarily optimal/nondominated, but any subpolicy of a pure routing policy must also be pure which is a new property defined based on nondominance. An exact algorithm is designed to find optimal trajectory-adaptive routing policies based on the aforementioned property of pure routing policy. A comparison is made between the optimal trajectory-adaptive routing policies and the optimal paths in the same test networks to investigate the benefit of being adaptive. The results show that the benefit of being adaptive to trajectory information is more significant with a higher risk aversion, a higher correlation, and/or a larger network. [ABSTRACT FROM AUTHOR]

This paper presents the development of a macroscopic dynamic traffic assignment model for continuum transportation systems with elastic demand. A reactive dynamic user equilibrium model is extended to simulate network equilibrium problems for an urban area with multiple central business districts (CBDs). Each copy of traffic flow reactively makes route choice decisions to minimize the total travel cost from origin to destination, based on instantaneous traffic information from a radio broadcasting service or route guidance system. The elastic demand function for each copy of flow is associated with its total instantaneous travel cost. The model is solved by a cell-centered finite volume method for conservation law equations and a fast sweeping method for Eikonal-type equations on unstructured grids. Numerical experiments for an urban traffic network with two CBDs are presented to verify the rationality of the model and the validity of the numerical method. The numerical results indicate that the model captures some macroscopic characteristics of two copies of flow interacting in time-varying urban transportation systems, e.g., the spatial distributions of the flow density and flux and the path choice behavior in response to elastic demand, and can describe traffic equilibrium phenomena, such as self-organization and traffic congestion build-up and dissipation. [ABSTRACT FROM AUTHOR]

The importance of historical travel demand has been well recognized by transportation researchers and practitioners. This paper presents a new nonlinear demand estimator that can be applied in both ground and air transportation. The estimator is formulated such that the distribution of the estimated demand follows a nested logit model. To solve the demand estimator, we develop an exact solution algorithm, which maximizes its dual problem sequentially along unit directions and keeps some of the first-order optimality conditions satisfied for the estimator. We investigate the convergence of the algorithm. We prove that all of the accumulation points produced by the solution algorithm satisfy some optimality conditions. A large example (a real U.S. network), which contains 66,767 origin-destination pairs, is presented. [ABSTRACT FROM AUTHOR]

In the paper by Cominetti and Correa (2001) [Common-lines and passenger assignment in congested transit I networks. Transportation Sci. 35(3):250-267], an extension to the common-lines problem for general multidestination networks under congestion is analyzed. Their transit equilibrium assignment model allows for a full representation of congestion effects caused by the variation of effective frequencies experienced by passengers at transit stops. This model is the ?rst to address these characteristics consistently with the concept of strategies. In a subsequent paper by Cepeda, Cominetti, and Florian (2006) [A frequency-based assignment model for congested transit networks with strict capacity constraints: Characterization and computation of equilibria. Transportation Res. 40B(6):437-459], the computation of equilibrium is performed heuristically by the minimization of a gap function, using the method of successive averages. In this paper, a reformulation of this congested transit equilibrium assignment model is performed, demonstrating that the problem can be expressed as an equivalent variational inequality. The case of strictly capacitated transit networks is explored under the scope of this new reformulation, and new, broader conditions for the existence of solutions to this congested transit assignment model are determined. [ABSTRACT FROM AUTHOR]

This paper introduces the multiconstraint team orienteering problem with multiple time windows (MC-TOP-MTW). In the MC-TOP-MTW, a set of vertices is given, each with a service time, one or more time windows, and a score. The goal is to maximize the sum of the collected scores, by a fixed number of tours. The tours are limited in length and restricted by the time windows and additional constraints. Next to a mathematical formulation of the MC-TOP-MTW, the main contribution of this paper is a fast and effective algorithm for tackling this problem, by hybridizing iterated local search with a greedy randomized adaptive search procedure. On a large test set, an average run has a score gap of only 5.19% with known high quality solutions, using 1.5 seconds of computational time. For 32% of the test instances, the known high quality solution was found or improved. This solution method also performs well on test instances of the TOPTW, the selective vehicle routing problem with time windows, and the MC-TOP-TW. A sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in the parameter settings. [ABSTRACT FROM AUTHOR]

Transportation agencies often resort to the use of traffic simulation models to evaluate the impacts of changes in network design or network operations. They often have multiple traffic simulation tools that cover the network area where changes are to be made. These multiple simulators may differ in their modeling assumptions (e.g., macroscopic versus microscopic), in their reliability (e.g., quality of their calibration), as well as in their modeling scale (e.g., city-scale versus regional-scale). The choice of which simulation model to rely on, let alone of how to combine their use, is intricate. A larger-scale model may, for instance, capture more accurately the local-global interactions; yet may do so at a greater computational cost. This paper proposes an optimization framework that enables multiple simulation models to be jointly and efficiently used to address continuous urban transportation optimization problems. We propose a simulation-based optimization algorithm that embeds information from both a high-accuracy low-efficiency simulator and a low-accuracy high-efficiency simulator. At every iteration, the algorithm decides which simulator to evaluate. This decision is based on an analytical approximation of the accuracy loss as a result of running the lower-accuracy model. We formulate an analytical expression that is based on a differentiable and computationally efficient to evaluate traffic assignment model. We evaluate the performance of the algorithm with a traffic signal control problem on both a small network and a city network. We show that the proposed algorithm identifies signal plans with excellent performance, and can do so at a significantly lower computational cost than when systematically running the high-accuracy simulator. The proposed methodology contributes to enable large-scale high-resolution traffic simulation models to be used efficiently for simulation-based optimization. More broadly, it enables the use of multiple simulation models that may differ, for instance, in their scale, their resolution, or their computational costs, to be used jointly for optimization. [ABSTRACT FROM AUTHOR]

Aerodynamic efficiency of intermodal freight trains can be significantly improved by minimizing the adjusted gap lengths between adjacent loads. This paper first develops a static model to optimize load placement on a sequence of intermodal trains that have scheduled departure times. This model applies when full information on all trains and loads is available. Then, we develop a dynamic model to account for the more realistic situation in which there is incomplete or uncertain information on future trains and incoming loads. This paper develops methodology to balance between (i) the advantage from optimizing multiple trains together and (ii) the risk of making suboptimal decisions due to incomplete future information. We propose a rolling horizon scheme to address this challenge, where exponentially decreasing weights are assigned to the objective functions of future trains. Numerical results based on empirical data show significant aerodynamic efficiency benefits from these optimization models. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of convergence to equilibrium in dynamic traffic assignment. Within-day time is considered to be a continuous variable, so that traffic flows and costs are functions of within-day time. Flow propagates along routes connecting origin-destination (OD) pairs with the demand for travel between each OD pair considered to be rigid (fixed from day to day although it can vary within day). Day-to-day time is also modelled as continuous with the day-to-day dynamical system derived naturally from the usual dynamical user equilibrium (DUE) condition. This paper focuses on the bottleneck model, which has deterministic vertical queueing at bottleneck link exits when flow exceeds capacity. A new property called decay monotonicity is introduced. The link delay (and hence link cost) function is shown to be a decay monotone function of link flow provided that the link capacity is continuously differentiable and positive. In a restricted version of the single bottleneck per route case, it is shown that link cost decay monotonicity implies route cost decay monotonicity. Decay monotonicity of the route cost function is shown to be sufficient for convergence to equilibrium of the dynamical system. [ABSTRACT FROM AUTHOR]

The principal focus of this paper is to study carrier pricing decisions for a type of vehicle routing problems defined in a competitive and dynamic environment. This paper introduces the vehicle routing problem in a competitive environment (VRPCE) as an extension of the traveling-salesman problem with profits (TSPP) to a dynamic competitive auction environment. In the VRPCE, the carrier must estimate the incremental cost of servicing new service requests as they arrive dynamically. The paper presents a rigorous and precise treatment of the sequential pricing and costing problem that a carrier faces in such an environment. The sequential pricing problem presented here is an intrinsic feature of a sequential auction problem. In addition to introducing the formulation of this class of problems and discussing the main sources of difficulty in devising a solution, a simple example is constructed to show that carriers' prices under first-price auction payment rules do not necessarily reflect the cost of servicing transportation requests. An approximate solution approach with a finite rolling horizon is presented and illustrated through numerical experiments, in competition with a static approach with no look-ahead. [ABSTRACT FROM AUTHOR]

Railway rolling stock is one of the most significant cost components for operators of passenger trains. The efficient circulation of rolling stock is therefore one of the main objectives pursued in practice. This paper focuses on the determination of appropriate numbers of train units of different types together with their efficient circulation on a single line. To utilize the train units on this line in an efficient way, they are coupled to or uncoupled from the trains in certain stations according to the passengers' seat demand in peak and off-peak hours. Because coupling and uncoupling train units must respect specific rules related to the shunting possibilities in the stations, it is important to take into account the order of the train units in the trains. This aspect strongly increases the complexity of the rolling stock circulation problem. This paper presents a solution approach based on an integer multicommodity flow model with several additional constraints related to the shunting processes at the stations. The approach is applied to a real-life case study based on the timetable of NS Reizigers, the main Dutch operator of passenger trains. [ABSTRACT FROM AUTHOR]

With the increasing availability of real-time information and communication systems in logistics, the need for appropriate planning algorithms, which make use of this technology, arises. Customers in transport markets increasingly expect quicker and more flexible fulfillment of their orders, especially in the electronic marketplace. This paper considers a dynamic routing system that dispatches a fleet of vehicles according to customer orders arriving at random during the planning period. Each customer order requires a transport from a pickup location to a delivery location in a given time window. The system disposes of online communication with all drivers and customers and, in addition, disposes of online information on travel times from a traffic management center. This paper presents a planning framework for this situation which, to our knowledge, has not yet been addressed in the literature. It then describes three routing procedures for event-based dispatching, which differ in the length of the planning horizon per event. We focus on the use of dynamic travel time information, which requires dynamic shortest path calculations. The procedures are tested and compared using real-life data of an urban traffic management center and a logistics service provider. [ABSTRACT FROM AUTHOR]

In this paper, we consider empty freight car distribution in a scheduled railway system. We analyze the cost structure for the repositioning of empty cars, and conclude that the distribution cost shows an economy-of-scale behavior. In addition to the cost proportional to the number of cars sent from origin to destination, there is a cost related to car-handling operations at yards, which depends on the number of car groups that are handled. Thus, if we can find a transportation pattern in which fewer but larger groups of cars are built, the total distribution cost can be decreased. The objective of the paper is to propose an optimization model that explicitly takes this economy-of-scale effect into account. We use a time-dependent network to describe the possible car movements in time and space, and show how this network can be transformed into a network with fixed costs on links representing movements of cars with identical origin and destination terminals. The resulting optimization model is a capacitated network design model, where each capacity constraint limits the flow on several arcs. We describe a tabu heuristic for solving the model, and present computational results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to review the current status of ship routing and scheduling. We focus on literature published during the last decade. Because routing and scheduling problems are closely related to many other fleet planning problems, we have divided this review into several parts. We start at the strategic fleet planning level and discuss the design of fleets and sea transport systems. We continue with the tactical and operational fleet planning level and consider problems that comprise various ship routing and scheduling aspects. Here, we separately discuss the different modes of operations: industrial, tramp, and liner shipping. Finally, we take a glimpse at naval applications and other related problems that do not naturally fall into these categories. The paper also presents some perspectives regarding future developments and use of optimization-based decision-support systems for ship routing and scheduling. Several of the trends indicate both accelerating needs for and benefits from such systems and, hopefully, this paper will stimulate further research in this area. [ABSTRACT FROM AUTHOR]

This paper presents an overview of several important areas of operations research applications in the air transport industry. Specific areas covered are: the various stages of aircraft and crew schedule planning; revenue management, including overbooking and leg-based and network-based seat inventory management; and the planning and operations of aviation infrastructure (airports and air traffic management). For each of these areas, the paper provides a historical perspective on OR contributions, as well as a brief summary of the state of the art. It also identifies some of the main challenges for future research. [ABSTRACT FROM AUTHOR]

The inventory routing problem considered in this paper is concerned with the repeated distribution of a commodity, such as heating oil, over a long period of time to a large number of customers. The problem involves a central depot as well as various satellite facilities which the drivers can visit during their shift to refill their vehicles. The customers maintain a local inventory of the commodity. Their consumption varies daily and cannot be predicted deterministically. In case of a stockout, a direct delivery is made and a penalty cost is incurred. In this paper, we present incremental cost approximations to be used in a rolling horizon framework for the problem of minimizing the total expected annual delivery costs. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of finding the minimum number of vehicles required to visit a set of nodes subject to time window and capacity constraints. The fleet is homogeneous and is located at a common depot. Each node requires the same type of service. An exact method is introduced based on branch and cut. In the computations, ever increasing lower bounds on the optimal solution are obtained by solving a series of relaxed problems that incorporate newly found valid inequalities. Feasible solutions or upper bounds are obtained with the help of greedy randomized adaptive search procedure (GRASP). A wide variety of cuts is introduced to tighten the linear programming (LP) relaxation of the original mixed-integer program. To find violated cuts, it is necessary to solve a separation problem. A substantial portion of the paper is aimed at describing the heuristics developed for this purpose. A new approach for obtaining feasible solutions from the LP relaxation is also discussed. Numerical results for standard 50- and 100-node benchmark problems are reported. [ABSTRACT FROM AUTHOR]

Existing models of stochastic network equilibrium route choice in transport networks are able to represent exogenously specified variations in drivers' actual or perceived travel costs, but assume throughout that flows are deterministic. In this paper, a new notion of equilibrium is presented based on stochastic flow variables, in which the impact of variable flows on the variability in travel costs is endogenously handled. Firstly, a very general notion of equilibrium is deduced as a fixed point condition on the joint probability distribution of network flows. Then, an approximation to this condition is derived, which operates by equilibrating moments of order n and below of the joint flow probability distribution, and is termed a Generalized Stochastic User Equilibrium of order n, being denoted GSUE(n). The GSUE(1) model is seen to be a conventional Stochastic User Equilibrium. The paper goes on to focus on the second order model, GSUE(2). Conditions are presented to guarantee the existence of GSUE(2) solutions. Conditions are deduced to guarantee (a) uniqueness of solutions in networks with a single interzonal movement, and (b) proximity of solutions in networks with multiple interzonal movements. Finally, a simple example is presented. [ABSTRACT FROM AUTHOR]

In a companion paper (Godfrey and Powell 2002) we introduced an adaptive dynamic programming algorithm for stochastic dynamic resource allocation problems, which arise in the context of logistics and distribution, fleet management, and other allocation problems. The method depends on estimating separable nonlinear approximations of value functions, using a dynamic programming framework. That paper considered only the case in which the time to complete an action was always a single time period. Experiments with this technique quickly showed that when the basic algorithm was applied to problems with multiperiod travel times, the results were very poor. In this paper, we illustrate why this behavior arose, and propose a modified algorithm that addresses the issue. Experimental work demonstrates that the modified algorithm works on problems with multiperiod travel times, with results that are almost as good as the original algorithm applied to single period travel times. [ABSTRACT FROM AUTHOR]

In this paper, we undertake a detailed study of the bus stop problem in congested transit networks. In the first part of the paper, we present and discuss the bus stop models existing in the literature. In the second part, we propose a new general model for which we prove a number of good properties and we give equivalent formulations. Then, we examine two special cases of the general model. In the first case, the line capacities are considered limited and therefore they can not be exceeded by the on-board passenger flows. In the second case, the strict capacity constraints are relaxed in order to obtain a stop model that can be easily integrated into an assignment model to predict the global passenger behavior in transit networks. [ABSTRACT FROM AUTHOR]

This paper describes an analytic model that determines the optimal vehicle holding time at a control stop along a transit route. This model is based on a stochastic transit service model presented by Andersson and Scalia-Tomba (1981) and enhanced by Marguier (1985). The use of a stochastic service model allows greater realism in the analytic modeling. Making use of these results, the paper presents an analytic model that may be used to determine the optimal holding time for a vehicle at a control stop. As it is formulated, the single vehicle holding problem is a convex quadratic program in a single variable, and is easily solved using gradient or line search techniques. The analytic holding model overcomes two noted problems in the literature: it includes stochastic service attributes of vehicle running times and passenger boarding and alighting processes, and the model may be used for real-time control purposes. The use and potential benefits of the model are illustrated in a simple example. This model may be useful in developing a computerized decision support system to enhance the effectiveness of transit operational decision-making. [ABSTRACT FROM AUTHOR]

Vehicle scheduling is the process of assigning vehicles to a set of predetermined trips with fixed starting and ending times, while minimizing capital and operating costs. This paper considers modeling, algorithmic, and computational aspects of the polynomially solvable case in which there is a single depot and vehicles are identical. A quasiassignment formulation is reviewed and an alternative asymmetric assignment formulation is given. The main contributions of the paper area new two-phase approach which is valid in the case of a special cost structure, an auction algorithm for the quasiassignment problem, a core-oriented approach, and an extensive computational study. New algorithms are compared with the most successful algorithms for the vehicle-scheduling problem, using both randomly generated and real-life data. The new algorithms show a significant performance improvement with respect to computation time. Such improvement can, for example, be very important when this particular vehicle-scheduling problem appears as a subproblem in more complex vehicle- and crew-scheduling problems. [ABSTRACT FROM AUTHOR]

This paper proposes a methodological framework to analyze the activity and travel pattern of workers during the evening commute. The framework uses a discrete-continuous econometric system to model jointly the decision to participate in an activity during the evening commute and the following attributes of the participation: activity type, activity duration, and travel time deviation to the activity location relative to the direct travel time from work to home. The model parameters are estimated using a sample of workers from the 1991 Boston Household Activity Survey. The paper also presents mathematical expressions to evaluate the effect of changes in sociodemographic variables and policy-relevant exogenous variables on the temporal pattern of trips and cold starts attributable to commute stops. The application of the model indicates that failure to accommodate the joint nature of the activity decisions during the evening commute can lead to misdirected policy actions for traffic congestion alleviation and for mobile-source emissions reduction. [ABSTRACT FROM AUTHOR]

In this paper we study a vehicle routing problem where customers request multiple commodities. We study the impact on transportation cost from using vehicles dedicated to a single commodity compared with using flexible vehicles capable of carrying any set of commodities. With vehicles that carry multiple commodities, we consider when the delivery to a customer can be made by more than one vehicle. If multiple vehicles can be used, we examine when deliveries of individual commodities may be split and when they may not be split. The latter problem has not previously been studied, and we present a mathematical programming model for it. We use worst case and computational analysis to compare these different models. [ABSTRACT FROM AUTHOR]

Today many web-based logistics platforms exist, enabling logistics agents worldwide to interact and form collaborations in an effective manner. In particular, some advanced e-platforms support online bidding of shipments. This paper integrates shipment bidding with logistics decisions. First, we formulate the shipment bidding and logistics planning model as a 0-1 mixed integer program, which addresses only buyout bids. Based on the properties of the model, we design a two-echelon solution procedure to search for the optimal shipment portfolio and the corresponding logistics requirements. We then extend the model to include placing either a buyout bid or an alternative bid for a new shipment with an estimated probability of success. The general model is formulated as a two-stage mixed 0-1 stochastic integer program, which allows forwarders to acquire some new jobs right away while placing alternative bids on others. The model is solved by modifying the two-echelon procedure. An illustrative example is included to highlight the significance of integrating shipment bidding with shipment logistics planning. Managerial issues are explored based on this example. [ABSTRACT FROM AUTHOR]

This paper derives six objectives for routing hazardous material by viewing shipments as a sequence of independent Bernoulli trials. An example that compares these objectives is presented. Suitable approximations toward the use of these objectives in an optimization framework are provided. The paper also discusses the objectives from the viewpoint of their use to make actual hazardous material routing decisions. [ABSTRACT FROM AUTHOR]

To achieve high productivity in manufacturing plants and warehouses, an orderly and flexible flow of materials is essential. The interaction between the manufacturing plants and warehouses and issues related to distribution of multiple commodities to customers from warehouses represents a crucial step toward an integrated and systematic facilities' design. In this paper we develop a mixed integer programming model for the plant and warehouse location problem where the objective is to minimize the total transportation and distribution costs and the fixed costs for opening and operating plants and warehouses. We employ Lagrangian relaxation to the model, and also present a heuristic to produce an effective feasible solution for the problem. This problem has resulted from a study conducted by the authors for a large company manufacturing health-care products. The paper reports on the development of a model structure that can be used to predict the performance of the company. [ABSTRACT FROM AUTHOR]

In this paper a form of the stochastic shortest path problem is considered where the optimal path is one that maximizes the expected utility which is concave and quadratic. The principal contribution of this paper is the development of a relaxation based pruning technique which is incorporated into a label setting procedure. The basic label setting procedure solves the problem by generating all Pareto-optimal paths. However, the number of such paths can grow exponentially with the size of the problem. The relaxation based pruning technique developed here is able to recognize and discard most of the Pareto-optimal paths that do not contribute to the optimal path. Our computational results show that the label setting procedure that incorporates the pruning technique consistently outperforms the basic label setting procedure, and is able to solve large problems very quickly. [ABSTRACT FROM AUTHOR]

Dynamic models of the behavior of automobile drivers in choosing routes through urban transportation networks are required for the design and operation of intelligent transportation systems generally, and traveler information systems in particular. In this paper, drivers' route choice behavior based on current, or instantaneous, information on network conditions is described using an optimal control theory formulation. The time-dependent origin-destination vehicle trip pattern is assumed to be known. The instantaneous dynamic user-optimal route choice problem is to allocate vehicle flows to the current minimal-cost routes, defined as the routes that minimize the route travel cost between each decision node (any node on the route including the origin) and the destination node based on the currently prevailing travel times. The continuous time formulation of the problem is transformed into a discrete time nonlinear programming (NLP) formulation. Each of a sequence of NLPs is then solved by an algorithm based on the Frank-Wolfe technique. In this sequence, approximate link travel times are updated iteratively in order to represent flow propagation over routes. Computational results from applying the algorithm to two test networks conclude the paper. [ABSTRACT FROM AUTHOR]

This paper examines a routing problem in which vehicles from a single depot cover a large area, where randomly located customers request pickup and delivery service. The paper assumes that each vehicle must serve its deliveries before it collects any pickups, that vehicles do not need to return to the depot between delivery and collection, and that each vehicle can serve at most C deliveries, but an unlimited number of pickups. This paper does not propose a detailed algorithm; rather, it discusses the pros and cons of various broad routing schemes, and quantifies their performance with simple distance formulas. The broad schemes describe implementable solutions, which can in turn be used to initialize fine-tuning algorithms. The choice of a routing scheme only depends on two dimensionless parameters: the size of the service area, relative to the area covered by one delivery route; and the ratio of the number of pickup customers to the number of deliveries. The clusters of deliveries and pickups served by a vehicle should often be radically different; unlike deliveries, pickups should be clustered in zones that have been elongated as much as possible, reaching all the way to the depot if it is internally located. It also appears that in a majority of cases not much is lost by routing for deliveries first (ignoring pickups) and for pickups second. Instances where they should be considered jointly are identified. [ABSTRACT FROM AUTHOR]

This paper presents a theory of traffic equilibrium which involves responsive signal control policies; in this theory drivers' route choices and the control policy's choice of green times are treated in a symmetrical manner. The central theme of the paper is the iterative optimization assignment algorithm. This algorithm may be considered as a means of calculating equilibria which are consistent with a given responsive control policy. But it may also be regarded as a highly idealized model of the day to day dynamics of drivers' route choices when a responsive signal setting policy is employed; on "day" 1 the signals are held fixed and drivers settle down to an equilibrium flow pattern, on "day 2" the flow pattern is held fixed and the signals are updated according to the control policy for the fixed flow pattern, on "day" 3 the signals are held fixed and drivers settle down to an equilibrium flow pattern.... We state natural but strong conditions on the responsive control policy which guarantee that this algorithm is bound to converge to a convex set of (flow, control) pairs such that (i) the flow is a user equilibrium and (ii) the control parameters satisfy the responsive control policy; and we give a proof of convergence under these conditions--we do not seek to minimize total travel cost. Our conditions involve the delay or cost formula used; with the BPR cost formula, modified in a natural way to allow for green times, the traditional policy of choosing control parameters which minimize delay for the observed traffic pattern does satisfy these conditions in full. However, with Webster's delay formula traditional control policies are a long way... [ABSTRACT FROM AUTHOR]

A pavement deterioration model predicts the performance of a pavement over time as a function of traffic, pavement characteristics and environmental factors. The most important performance characteristics of a pavement are its ability to bear traffic loads and its ability to provide a smooth ride. However, there is no unambiguous approach to directly measure these performance characteristics. Therefore, we consider pavement performance to be unobservable. The problem of designing pavement deterioration models is the problem of defining the above unobservable characteristics in terms of what is observed, i.e., in terms of measured extents and severities of different damage components. The methodology presented in this paper describes a statistical technique to estimate latent pavement performance from observed pavement damage. No constraints are placed on the number or type of measurements required, so the methodology is flexible enough to include different measurement techniques and data collection strategies. The estimation procedure simultaneously fits a deterioration model and a performance index calibration model to data, thereby producing much better fits to data than traditional deterioration models. The methodology presented in this paper will be useful for deriving more realistic predictive models of pavement deterioration and for defining better data collection strategies. [ABSTRACT FROM AUTHOR]

The study of stochastic networks of queues in transportation has been confined to the use of highly simplified analytical models or the development of large, computationally expensive Monte Carlo simulations. We introduce a discrete-time approach for simulating stochastic, transient networks of bulk queues that often arise in consolidation networks. This paper presents the state variables and equations required to model the problem, and introduces a set of approximations to produce a computationally tractable algorithm. A companion paper describes the results of extensive numerical experiments which test the accuracy of the approximations and the overall efficiency of the procedure. [ABSTRACT FROM AUTHOR]

In this paper we discuss three mean-variance location problems. Two of them are constrained problems where one performance measure--mean of the weighted distance, or variance, is minimized subject to an upper bound constraint on the value of the other. In the third problem the objective function minimized is given by the mean plus a constant times the variance. The paper includes polynomial time algorithms to solve the three problems. The solutions produced by these algorithms are Pareto optimum solutions (solutions that are strictly better than any other solution in at least one of the two measures: mean and variance). [ABSTRACT FROM AUTHOR]

This paper examines a relaxed version of the generic vehicle routing problem. In this version, a delivery to a demand point can be split between any number of vehicles. In spite of this relaxation the problem remains computationally hard. The main contribution of this paper is in demonstrating the potential for cost savings through split deliveries. The solution scheme allowing for split deliveries is compared with a solution in which no split deliveries are allowed on a large set of 540 problems. Significant cost savings are realized both in terms of the total distance and the number of vehicles required. The. vehicle routes constructed by our procedure, tend to cover cohesive geographical. zones and retain some properties of optimal solutions. [ABSTRACT FROM AUTHOR]

The objective of the ‘transportation problem’ is to minimize the cost of satisfying customer product requirements without exceeding supplier capacities. This paper examines the transportation problem with the purpose of ascribing graphical meaning to the solution. The paper summarizes prior results as well as provides new results relative to supplier lattice structures and nonlinear costs. [ABSTRACT FROM AUTHOR]

Modeling of transportation systems must invariably balance behavioral richness and computational tractability. In this paper, we develop a transportation equilibrium model and an algorithm for the simultaneous prediction of trip generation, trip distribution, modal split, and trip assignment on large-scale networks. The model achieves a practical compromise between behavioral and computational aspects of modeling the problem. It is formulated as an equivalent convex optimization problem, yet it is behaviorally richer than other models that can be cast as equivalent convex programs. Although the model is not as behaviorally rich as the most general equilibrium models, it has computational advantages. The applications reported in this paper of the model to real systems, i.e., the intercity transport network of Egypt and the urban transportation network of Austin, Texas, illustrate the computational attractiveness of the approach. These results indicate that equivalent optimization formulations are not as restrictive as previously thought, and hence, the equivalent convex programming approach for modeling and predicting equilibrium on transportation systems remains a viable and fruitful avenue for future consideration. [ABSTRACT FROM AUTHOR]

This paper extends the results of a previous study concerning distribution with time windows. It is recognized that customers who do not need to be allocated to a time window should receive different service than the rest. Three strategies were studied to accomplish that: stratified service, discriminating service, and staggered and discriminating service. Of these, the last strategy yields the lowest local distribution distance per customer, a distance which can be less than hall that for the strategy explained in the previous paper (joint service). Stratified service, however, can yield a lower line-haul distance per customer than staggered and discriminating service. In a specific case, a numerical comparison between stratified service and staggered and discriminating service should determine the overall best choice. This choice notwithstanding, the best strategy involves overlapping vehicle tours. The conventional wisdom of dividing customers into non-overlapping clusters for vehicle muting does not seem attractive for distribution problems with time windows. [ABSTRACT FROM AUTHOR]