This paper proposes an improved cellular automaton traffic flow model based
on the brake light model, which takes into account that the desired time gap of
vehicles is remarkably larger than one second. Although the hypothetical steady
state of vehicles in the deterministic limit corresponds to a unique
relationship between speeds and gaps in the proposed model, the traffic states
of vehicles dynamically span a two-dimensional region in the plane of speed
versus gap, due to the various randomizations. It is shown that the model is
able to well reproduce (i) the free flow, synchronized flow, jam as well as the
transitions among the three phases; (ii) the evolution features of disturbances
and the spatiotemporal patterns in a car-following platoon; (iii) the empirical
time series of traffic speed obtained from NGSIM data. Therefore, we argue that
a model can potentially reproduce the empirical and experimental features of
traffic flow, provided that the traffic states are able to dynamically span a
2D speed-gap region.
This paper proposes an algorithm that automatically translates the "continuum approximation" (CA) recipes for location problems into discrete designs. It is applied to terminal systems but can also be used for other logistics problems. The study also systematically compares the logistics costs predicted by the CA approach with the actual costs for discrete designs obtained with the automated procedure. Results show that the algorithm systematically finds a practical set of discrete terminal locations with a cost very close to that predicted. The paper also gives conditions under which the CA cost formulae are a tight lower bound for the exact minimal costs.
Diverging junctions are important network bottlenecks, and a better understanding of diverging traffic dynamics has both theoretical and practical implications. In this paper, we first introduce a continuous multi-commodity kinematic wave model of diverging traffic and then present a new framework for constructing kinematic wave solutions to its Riemann problem with jump initial conditions. In supply-demand space, the solutions on a link consist of an interior state and a stationary state, subject to admissible conditions such that there are no positive and negative kinematic waves on the upstream and downstream links respectively. In addition, the solutions have to satisfy entropy conditions consistent with various discrete diverge models. In the proposed analytical framework, kinematic waves on each link can be uniquely determined by the stationary and initial conditions, and we prove that the stationary states and boundary fluxes exist and are unique for the Riemann problem of diverge models when all or partial of vehicles have predefined routes. We show that the two diverge models by Lebacque and Daganzo are asymptotically equivalent. We also prove that the supply-proportional and priority-based diverge models are locally optimal evacuation strategies. With numerical examples, we demonstrate the validity of the analytical solutions of interior states, stationary states, and corresponding kinematic waves. This study presents a unified framework for analyzing traffic dynamics arising in diverging traffic and could be helpful for developing emergency evacuation strategies. Comment: 48 pages, 14 figures
This paper develops a dynamic model of peak period traffic congestion that considers a limited number of bottlenecks. The model predicts the temporal distribution of traffic volumes with an elastic demand model. The choice of route and mode are dependent on travel times and costs. The choice of departure time is based on the tradeoff between travel time and schedule delay. Delays at bottlenecks are modelled with a deterministic queueing model that determines waiting times. This model is used to perform simulation experiments to analyze the impacts of alternative pricing policies and preferential treatment of High Occupancy Vehicles.
We formulate the choice of a best path for a commuter leaving his/her home at a given time and willing to arrive at his/her destination within a given time interval. The objective function integrates constant costs for use of arcs, travel times and schedule delay. The travel times along arcs, which depend on exogenous congestion, are represented by functions of the arrival time at the origin node of the arc. The schedule delay is taken into consideration by penalizing arrival time at the destination outside the desired time interval. The problem is shown to be NP-hard, polynomial subcases are determined and a pseudo-polynomial algorithm is provided for the general case.
Many e-tailers providing attended home delivery, especially e-grocers, offer narrow delivery time slots to ensure satisfactory customer service. The choice of delivery time slots has to balance marketing and operational considerations, which results in a complex planning problem. We study the problem of selecting the set of time slots to offer in each of the zip codes in a service region. The selection needs to facilitate cost-effective delivery routes, but also needs to ensure an acceptable level of service to the customer. We present two fully-automated approaches that are capable of producing high-quality delivery time slot offerings in a reasonable amount of time. Computational experiments reveal the value of these approaches and the impact of the environment on the underlying trade-offs.
Observations of freeway traffic flow are usually quite scattered about an underlying curve when plotted versus density or occupancy. Although increasing the sampling intervals can reduce the scatter, whenever an experiment encompasses a rush hour with transitions in and out of congestion, some outlying data stubbornly remain beneath the "equilibrium" curve. The existence of these non-equilibrium points is an ill-understood phenomenon that appears to contradict the simple kinematic wave (KW) model of traffic flow. This paper provides a tentative explanation of the phenomenon, based on experimental evidence. The evidence was a queue that grew and receded over two detector stations, generating typical flow-density scatter-plots at both locations. The locations were far from other interacting traffic streams. The data revealed that a transition zone where vehicles decelerated gradually existed immediately behind the queue. The transition zone was quite wide (about 1 km at both locations), moved slowly (approximately with the "shock" velocityof KW theory) and spent many minutes over each detector station. Disequilibrium flow-density points arose only when the transition zone was over the detectors, suggesting that the transition zone explains their occurrence. The disequilibrium points drifted gradually from one branch of the curve to the other, as KW theory would have predicted if "shocks" had a characteristic width equal to the dimension of the transition zone. Nothing was found in the data to contradict this view. The paper also shows that if one neglects the shocks' physical dimension, the resulting errors are unimportant for practical purposes. Thus, it appears that KW theory can predict traffic behavior at the back of queues when the lanes at the back of the queue are equally attractive to all drivers.
D. Braess and others have shown that creating a new link in a congested network, or adding capacity to an existing link, can raise total travel costs if drivers switch routes. Here we show that a paradox can also result when routes are fixed, but users choose when to travel. As is true of the Braess paradox, the paradox here arises when the inefficiency due to underpricing of congestion increases by more than the direct benefit of the new capacity. For a corridor with two groups of drivers, we show that expanding capacity of an upstream bottleneck raises travel costs when the reduction in congestion upstream is more than offset by increased congestion downstream. Metering can thus improve efficiency. Optimal capacity for an upstream bottleneck is equal to, or smaller than, optimal capacity downstream. Total construction costs equal total variable travel costs when capacities are optimal and construction costs are independent of scale.
This paper addresses a new vehicle routing problem that simultaneously
involves time windows, split collection and linear weight-related cost, which
is a generalization of the split delivery vehicle routing problem with time
windows (SDVRPTW). This problem consists of determining least-cost vehicle
routes to serve a set of customers while respecting the restrictions of vehicle
capacity and time windows. The travel cost per unit distance is a linear
function of the vehicle weight and the customer demand can be fulfilled by
multiple vehicles. To solve this problem, we propose a exact
branch-and-price-and-cut algorithm, where the pricing subproblem is a
resource-constrained elementary least-cost path problem. We first prove that at
least an optimal solution to the pricing subproblem is associated with an
extreme collection pattern, and then design a tailored and novel label-setting
algorithm to solve it. Computational results show that our proposed algorithm
can handle both the SDVRPTW and our problem effectively.
Smeed (1967) derived conditions under which it is possible for a driver to depart later and arrive earlier at a destination. In this note we replicate Smeed's argument and modify one of the postulates that under realistic traffic assumptions this phenomenon cannot occur.
This paper discusses uniqueness and efficiency of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983, Transportation Science) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths but identical disutility functions from time costs. We first show, by example, that his result may not apply in general networks if disutility functions are allowed to differ. However, for "simple" transportation networks, we can show that user equilibrium is always unique and weakly Pareto efficient (cf. the Braess example) for a general class of utility functions. We investigate if this result applies to more general networks. We also show that user equilibrium is unique in a dynamic bottleneck model with a simple network. We discuss an interesting relationship between the following two problems: the existence of user equilibrium in a finite model and the uniqueness of user equilibrium in a continuum model. In the appendix, we also provide a proof of a slightly generalized version of Daganzo's theorem.
We study “positive network externalities” in a horizontally differentiated industry. We show that a symmetric Nash equilibrium in prices exists if and only if the degree of product differentiation is sufficiently large. We also study the impact of larger or lower compatibility on equilibrium prices.
In this paper, the sequel to 'A Family of Methods for Preliminary Highway Alignment', we apply results from the latter, in addition to some network design models which include locating road junctions ('Generalized Steiner Points') to the design of complete highway networks connecting n given points on any given terrain. The objective is to satisfy given bilateral transportation demands at minimal total cost - including construction and users' costs. The general problem is as follows: for n given nodes (points, city centers, etc. ), upon a not necessarily planar terrain, construct a highway network capable of satisfying all the bilateral transportation demands in such a manner that the construction costs (including earth moving, paving, right-of-way, ecological or social penalty costs, etc. ), together with the projected capitalized users' costs (such as fuel, time value, accidents, mechanical wear and tear, etc. ) and the capitalized projected maintenance costs, will be minimized. Extra nodes, i. e. , road junctions, are to be located as beneficially as possible to that end.
We investigate characteristic properties of the congested traffic states on a 30 km long stretch of the German freeway A5 north of Frankfurt/Main. Among the approximately 245 breakdowns of traffic flow in 165 days, we have identified five different kinds of spatio-temporal congestion patterns and their combinations. Based on an "adaptive smoothing method" for the visualization of detector data, we also discuss particular features of breakdowns such as the "boomerang effect" which is a sign of linearly unstable traffic flow. Controversial issues such as "synchronized flow" or stop-and-go waves are addressed as well. Finally, our empirical results are compared with different theoretical concepts and interpretations of congestion patterns, in particular first- and second-order macroscopic traffic models.
We consider several Vehicle Routing Problems (VRP) with profits, which seek
to select a subset of customers, each one being associated with a profit, and
to design service itineraries. When the sum of profits is maximized under
distance constraints, the problem is usually called team orienteering problem.
The capacitated profitable tour problem seeks to maximize profits minus travel
costs under capacity constraints. Finally, in the VRP with private fleet and
common carrier, some customers can be delegated to an external carrier subject
to a cost. Three families of combined decisions must be taken: customers
selection, assignment to vehicles, and sequencing of deliveries for each route.
We propose a new neighborhood search for these problems, which explores an
exponential number of solutions in pseudo-polynomial time. The search is
conducted on "exhaustive" solutions visiting all customers, while an efficient
"Select" algorithm, based on resource-constrained shortest paths, is repeatedly
used to select customers and to evaluate routes. Speed-up techniques are
introduced to solve more efficiently the shortest paths and prune unpromising
moves. The remarkable performance of these neighborhood structures is
demonstrated by extensive computational experiments with a local search, an
iterated local search and a hybrid genetic algorithm. Intriguingly, even a
local-improvement method to the first local optimum of this neighborhood
achieves an average gap of 0.09% on classic team orienteering problem
instances, rivaling with the current state-of-the-art metaheuristics. For all
three problems, the proposed methodology leads to solutions of higher quality
than previous algorithms in similar CPU time. Promising research avenues on
hybridizations with standard routing neighborhoods are also open.
The question of delay management is whether trains should wait for a delayed feeder train or should depart on time. In classical delay management models passengers always take their originally planned route. In this paper, we propose a model where re-routing of passengers is incorporated. To describe the problem we represent it as an event-activity network similar to the one used in classical delay management, with some additional events to incorporate origin and destination of the passengers. We present an integer programming formulation of this problem. Furthermore, we discuss the variant in which we assume fixed costs for maintaining connections and we present a polynomial algorithm for the special case of only one origin-destination pair. Finally, computational experiments based on real-world data from Netherlands Railways show that significant improvements can be obtained by taking the re-routing of passengers into account in the model.
Transshipment yards, where gantry cranes allow for an effcient transshipment of containers between different freight trains, are important entities in modern railway systems and facilitate the general shift from point-to-point transport to hub-and-spoke railway systems. Modern rail-rail transshipment yards accelerate container handling, so that multiple smaller trains with equal destination can be consolidated to a reduced number of trains without jeopardizing on time deliveries. An important problem continuously arising during the daily operations of a transshipment yard is the train scheduling problem, which decides on the succession of trains at the parallel railway tracks. This problem with a special focus on resolving deadlocks and avoiding multiple crane picks per container move is investigated within the paper on hand. A mathematical program along with a complexity proof is provided and exact (Dynamic Programming) and heuristic (Beam Search) procedures are described.
The objective of this paper is to develop a throughput model of a multiple- lane Automated Highway System (AHS) with lane changes. The paper uses deterministic approximations to model highway throughput, accounting for both longitudinal and lateral requirements. The model is designed to account for trip-length distributions, and the effect of these distributions on the rate of lane changes between each pair of adjacent lanes. To illustrate fundamental principles, the model is applied to an idealized highway operating under sanitary conditions, both in time and space. Parametric analysis is used to study the effects of design parameters, pertaining to the execution of lane change maneuvers, on capacity.
Fundamental to many transportation network studies, traffic flow models can
be used to describe traffic dynamics determined by drivers' car-following,
lane-changing, merging, and diverging behaviors. In this study, we develop a
deterministic queueing model of network traffic flow, in which traffic on each
link is considered as a queue. In the link queue model, the demand and supply
of a queue are defined based on the link's fundamental diagram, and its in- and
out-fluxes are computed from junction flux functions corresponding to
macroscopic merging and diverging rules. We demonstrate that the model is well
defined and can be considered as a continuous approximation to the kinematic
wave model on a road network. From careful analytical and numerical studies, we
conclude that the model is physically meaningful, computationally efficient,
always stable, and mathematically tractable for network traffic flow. As an
addition to the multiscale modeling framework of network traffic flow, the
model strikes a balance between mathematical tractability and physical realism
and can be used for analyzing traffic dynamics, developing traffic operation
strategies, and studying drivers' route choice and other behaviors in
large-scale road networks.
The locomotive scheduling problem (or the locomotive assignment problem) is to assign a consist (a set of locomotives) to each train in a pre-planned train schedule so as to provide them sufficient power to pull them from their origins to their destinations. Locomotive scheduling problems are among the most important problems in railroad scheduling. In this paper, we report the results of a study of the locomotive scheduling problem faced by CSX Transportation, a major US railroad company. We consider the planning version of the locomotive scheduling model (LSM), where there are multiple types of locomotives and we need to decide the set of locomotives to be assigned to each train. We present an integrated model that determines the set of active and deadheaded locomotives for each train, light traveling locomotives from power sources to power sinks, and train-to-train connections (specifying which inbound train and outbound trains can directly connect). An important feature of our model is that we explicitly consider consist-bustings and consistency. A consist is said to be busted when the set of locomotives coming on an inbound train is broken into subsets to be reassigned to two or more outbound trains. A solution is said to be consistent over a week with respect to a train, if the train gets the same locomotive assignment each day it runs. We give a mixed integer programming (MIP) formulation of the problem that contains about 197 thousand integer variables and 67 thousand constraints. An MIP of this size cannot be solved to optimality or near-optimality in acceptable running times using commercially available software. Using problem decomposition, integer programming, and very large-scale neighborhood search, we developed a solution technique to solve this problem within 30 minutes of computation time on a Pentium III computer. When we compared our solution with the solution obtained by the software in-house developed by CSX, we obtained a savings of over 400 l
En la UE se ha estimado que los costes de la congesti�n representan el 2% de su PIB y que el coste de la poluci�n del aire y ruido supera el 0,6% del PIB, siendo alrededor del 90% de los mismos ocasionados por el transporte terrestre. Ante este hecho y el continuo aumento de la demanda del transporte privado frente al p�blico para los desplazamientos, muchos abogan por una conjunci�n de medidas tanto restrictivas como alternativas al uso del coche. Dentro de las primeras se encuentra el establecimiento de un peaje o una tarifa por el uso de las carreteras, medida que aunque desde el punto de vista de la Teor�a Econ�mica es la manera m�s eficiente para corregir el fallo de mercado que supone la congesti�n, desde la visi�n de pol�ticos y del p�blico no goza de gran aceptaci�n. En este trabajo se pretende hacer una simulaci�n de los efectos que tendr�a sobre el bienestar social de la implantaci�n de una medida de este tipo en la Bah�a de C�diz. In the European Union it has been estimated that the congestion cost are the 2% of the gross domestic product and the cost of pollution and noise is over 0,6%, olso it is known that the 90% of this cost are caused by overland transport. For this reason and for the always increasing demand of private transport, there are professionals who thinks that the solution have to be restrictive measures added to alternatives to the car. road pricing is a restrictive measures that for the economic theory is the most efficient way to solve congestion cost but for politicians and user of transport is not always accepted. In this study we are going to simulate road pricing for commuters in the Bah�a of C�diz and then it will be estimated welfare effects.
A dynamic and stochastic distribution problem with a number of terminals and a fleet of vehicles is analyzed. Customers request the transportation of batches of loads between different origins and destinations. A request can be accepted or rejected; if the request is accepted, a reward is received. Holding costs for vehicles and loads at terminals as well as transportation costs are included in the model. The objective is to determine a policy for accepting transportation requests and for dispatching vehicles that maximizes the expected value (rewards minus costs) of operating the distribution system. A Markov decision process model is developed, optimal policies are characterized, and algorithms that exploit the structure of the problem are developed. This research was supported in part by the National Science Foundation under grant DDM-9309579. In this paper a model is formulated and studied of the operations of a less-than-vehicle-load (e.g. less-thantruckload (LTL) or less-than...
We consider the problem of dynamically routing a driver to cover a sequence of tasks #with no consolidation#, using a complex set of driver attributes and operational rules. Our motivating application is dynamic routing and scheduling problems, which require fast response times, the ability to handle a wide range of operational concerns, and the ability to output multiple recommendations for a particular driver. A mathematical formulation is introduced that easily handles real#world operational complexities. Two new algorithms are described, one giving faster performance and the second providing somewhat higher solution quality. Comparisons to optimal solutions are provided, which measures the quality of the solutions that our algorithms provide. Experimental tests show that our algorithms provide high quality solutions, and are fast enough to be run in real#time applications. We consider the problem of routing and scheduling a heterogeneous set of drivers to cover a known set of task...
Dynamic #eet management problems #with a homogeneous #eet# are classically formulated as dynamic networks, or linear programs with side constraints. Recently, a new dynamic control approach was introduced called a logistics queueing network. Instead of a large linear program, the problem is decomposed into small subproblems, that are guided bytwo control variables that push these local problems to produce a solution that is close to a global optimum. In prior work, these control variables were updated using a subgradient approximation. In this paper, we propose a multiplier adjustment method for solving the same problem. Numerical experiments show that this method produces better solutions with greater stability. The new method is somewhat slower, and is more di#cult to implement. We believe that both methods will represent reasonable choices for solving the problem. 1 5 6 4 2 3 7 Vehicle Load Link Terminal Figure 1: Network of transportation services. Resource allocation problems c...
Recently, airlines and aircraft manufacturers have realized the benefits of the emerging concept of dynamic capacity allocation, and have initiated advanced decision support systems to assist them in this respect. Strategic airline fleet planning is one of the major issues addressed through such systems. We present background research connected with the dynamic allocation concept, which accounts explicitly for the stochastic nature of passenger demand in the fleet composition problem. We address this problem through a scenario aggregation-based approach and present results on representative case studies based on realistic data. Our investigations establish clear benefits of a stochastic approach as compared with deterministic formulations, as well as its implementation feasibility using state-of-the-art optimization software.
Motivated by a real application, we consider the following aircraft scheduling problem. At any time, the aircraft are at different locations or are serving a customer and new customer requests arrive, each consisting of a departure location, departure time and destination. Additionally, if a customer request consists of more than one trip, there may be an exclusive use of the aircraft between these trips. Our objective is to satisfy these requests (by subcontracting extra aircraft if necessary) at minimum cost under additional constraints of maintenance requirements and previously scheduled trips. We formulate the problem as a 0-1 integer program, show its complexity and find that many instances of small and medium size problems can be solved by Cplex. For larger problems and for `bad' instances, we provide a very fast heuristic with good performance. Key Words: Vehicle routing; Multiple depot vehicle scheduling; Heuristics; Complexity. A growing number of executives these d...
This paper develops and analyzes a finite horizon Markov decision process model for the airline meal provisioning activity focusing explicitly on developing policies for determining and revising the number of meals to upload. Using annual daily data from over 40 flights, the paper shows that the optimal policies can result in both improved customer service and significant dollar savings, especially in long haul flights. It also applies the model to investigate tradeoffs between having too few and two many meals on a flight.
Airline crew scheduling algorithms widely used in practice assume no disruptions. Since disruptions often occur, the actual cost of the resulting crew schedules is often significantly greater. We consider algorithms for finding crew schedules that perform well in practice. The deterministic crew scheduling model is an approximation of crew scheduling under uncertainty under the assumption that all pairings will operate as planned. We seek better approximate solution methods for crew scheduling under un- # Corresponding author. firstname.lastname@example.org 1 certainty that still remain tractable. We give computational results from three fleets that indicate that the crew schedules obtained from our methodology perform better in operations than the crew schedules found via state-of-the-art methods. We provide a lower bound on the cost of an optimal crew schedule in operations, and demonstrate that some of the crew schedules found using our methodology perform very well relative to this lower bound. For major domes(' carriers crew cos ts ares econd only to fuel cosI$ and can exceed a billion dollars annually. Therefore, airlines devote great e#ort to planning good crew shedules But the planning problem can be very di#cult tosI8 e becaus there are many governmental and contractual regulations concerning pilots and problems found in practice often have billions of pos$('4 s olutions There is currently a great deal of concern about air tra#c conges ion. In June 2000, flight delays were up over 16% from June 1999Phillips and Irwin, 2000. Moreover, air tra#c in America and Europe is expected to double in the next 10-15 year s If airport capacity remains cons$ nt, itis es$fifi ted that each 1% increas e in airport tra#c will bring about a 5% increas in delays Anonymous , 2000. Di...
We consider the problem of distributing goods from one or more plants through a set of warehouses in anticipation of forecasted customer demands. Two results are provided in this paper. First, we present a methodology for approximating stochastic distribution problems that are computationally tractable for problems of realistic size. Comparisons are made to standard deterministic formulations and shown to give superior results. Then, we compare logistics networks with varying degrees of redundancy represented by the number of warehouses which serve each customer. Overlapping service regions for warehouses provides additional #exibility to handle real-time demands. We quantify the expected savings that might result from such strategies. 1 Introduction Distribution problems involve the allocation of goods or resources to storage areas in anticipation of forecasted market demands. A classic example is the movementofinventory from plant to warehouse in anticipation of future customer dem...
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. Keywords: delivery cost approximations, inventory routing problem, stochastic demand, rolling horizon # MSIS Department and Civil Engineering Department, The University of Texas at Austin, Austin, TX 78712, USA, and Mathematics Department, ENPC, 75343 Paris ...
The class of simplicial decomposition (SD) schemes have shown to provide efficient tools for nonlinear network flows. When applied to the traffic assignment problem, shortest route subproblems are solved in order to generate extreme points of the polyhedron of feasible flows, and, alternately, master problems are solved over the convex hull of the generated extreme points. We review the development of simplicial decomposition and the closely related column generation methods for the traffic assignment problem; we then present a modified, disaggregated, representation of feasible solutions in SD algorithms for convex problems over Cartesian product sets, with application to the symmetric traffic assignment problem. The new algorithm, which is referred to as disaggregate simplicial decomposition (DSD), is given along with a specialized solution method for the disaggregate master problem. Numerical results for several well known test problems and a new one are presented. These experimenta...
partial loads 2.1.2 Vehicles 1. Travel time is a deterministic function of the source and destination region, independent of whether a load is being carried 2. The number of vehicles is known and fixed; vehicles are homogeneous and characterized only by their current location or, if in transit, by their destination region and the time at which they will arrive 3. Vehicles can carry (at most) one load at a time 2.1.3 Costs 1. Cost of moving a vehicle empty between a given source and destination region is fixed and deterministic, as are costs for moving a vehicle with a load; there may also be a cost for "holding" a vehicle in a region 2. Each load has an associated reward for delivery 3. There may be a "rejection" cost for failing to pick up a load for transport at its specified pickup time At each time step, all vehicles not currently transporting a load must be assigned to either begin transportation of an available load whose source region match
This research shows that certain time-dependent congestion reduction schemes involving tolls have the potential for benefiting every driver even if the collected revenues are not returned to the payers. The paper considers a population of commuters who use a single bottleneck during the morning rush hour and try to arrive at work on time. It is assumed that the number of commuters is fixed (independent of the control strategy) and that each commuter wishes to pass through the bottleneck at a given time, which may differ across commuters. Commuters are otherwise identical. Each of them chooses his/her arrival time at the bottleneck so as to minimize a linear combination of monetary cost (tolls), queuing time and deviation from the desired passage time. A time-dependent toll is applied during a time window, but some commuters are exempted from paying it. Every day each commuter is classified as either "free" or "paying." The classification method is such that: (i) in the long-run the fra...
This paper presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branchand -bound optimization algorithm without any restrictive assumption on the time windows. Unlike dynamic programming approaches whose performance relies heavily on the degree of discretization applied to the data, our algorithm does not suffer from such space-complexity issues. The data-driven mechanism at its core more fully exploits pruning rules developed in operations research by using them not only a priori but also dynamically during the search. Computational results are reported and comparisons are made with both exact and heuristic algorithms. On Solomon's well-known test bed, our algorithm is instrumental in achieving new best solutions for some of the problems in set RC2 and strengthens the presumption of optimality for the best known solutions to the problems in set C2. Introduction In the last few years, constraint programming (cp) has b...
We propose a dynamic model for optimizing the #ows of #atcars that considers explicitly the broad range of complex constraints that govern the assignment of trailers and containers to a #atcar. The problem is formulated as a logistics queueing network which can handle a wide range of equipmenttypes and complex operating rules. The complexity of the problem prevents a practical implementation of a global network optimization model. Instead, we formulate a global model with the speci#c goal of providing network information to local decision makers, regardless of whether they are using optimization models at the yard level. Thus, our approach should be relatively easy to implement given current rail operations. Initial experiments suggest that a #atcar #eet that is managed locally, without the bene#t of our network information, can achieve the same demand coverage as a #eet that is 10 percent smaller, but which is managed locally with our network information. We consider the problem of m...
Vendor managedi nventory repleni shmenti s a busi ness practi cei n whi ch vendors moni tor thei r customers 'i nventori es, and deci de when and how muchi nventory should be repleni shed. Thei nventory rout i g problem addresses the coordi nati on of i ventory management and transportat ix . The abiS9 y to solve the i ventory routi ng problem contr i utes to the reali(S il of the potentiS sav i gs i i ventory and transportat ix costs brought about by vendor managedi nventory replen ix ment. Thei nventory routi ng problemi s hard, especi allyi f a large number of customersi si nvolved. We formulate thei nventory routi ng problem as a Markov deci si on process, and we propose approxi mati on methods to find good soluti ons wi th reasonable computati onal e#ort. Computati onal results are presented for thei nventory routi ng problem wi thdi rect deli veri es. # Supported by the National Science Foundation under grant DMI-9875400. The inventory routing problem (IRP) is one of the core problems that has to besUW ed when implementing the emergingbus#1HH practice called vendor managed inventory replenishment (VMI). VMI refers to the s tuation where the replenis ment of inventory at a number of locations is controlled by a central decis on maker (vendor). The centraldecisH n maker can be thes upplier and the inventory can be kept at independent cusU4#U, or the centraldecis5# maker can be a manager res ons41# for inventoryreplenis,fi3 t at a number of warehous es or retail outlets of thesW e company. Often the central decis on maker manages a fleet of vehicles that make the deliveries Inthis paper the centraldecisH3 maker is called thes,UD4HD and the inventory locations are referred to as the cus omers VMI di#ers from conventional inventory management in the following way. I...
We consider a pickup and delivery vehicle routing problem commonly encountered in real-world logistics operations. The problem involves a set of practical complications that have received little attention in the vehicle routing literature. In this problem, there are multiple carriers and multiple vehicle types available to cover a set of pickup and delivery orders, each of which has multiple pickup time windows and multiple delivery time windows. Orders and carrier/vehicle types must satisfy a set of compatibility constraints that specify which orders cannot be covered by which carrier/vehicle types and which orders cannot be shipped together. Order loading and unloading sequence must satisfy the nested precedence constraint that requires that an order cannot be unloaded until all the orders loaded into the truck later than this order are unloaded. Each vehicle trip must satisfy the driver's work rules prescribed by the Department of Transportation which specify legal working hours of ...
This paper is concerned with the existence of solutions to a dynamic network equilibrium problem modelled as an infinite dimensional variational inequality. Our results are based on properties of operators that map path flow departure rates to consistent time-dependent path flows and other link performance functions. The existence result requires the introduction of a novel concept that strengthens the familiar concept of FIFO (`First-In-First-Out'). Following Ben-Akiva , one can identify four main elements in any dynamic network equilibrium model (DNEP): arc performance functions, path choice criterion, a demand model, flow conservation relationships at the nodes of the network. According to this author, the extension of a static to a dynamic setting requires the determination of time-dependent arc performance functions, temporal origin-destination demand, and the assessment of queueing effects on time-varying arrival rates. In general, these relationships are not available in clos...
The most common approach for modeling and solving routing and scheduling problems in a dynamic setting is to solve, as close to optimal as possible, a series of deterministic, myopic models. The argument is most often made that if the data changes, then we should simply reoptimize. We use the setting of the load matching problem that arises in truckload trucking to compare the value of optimal myopic solutions versus varying degrees of greedy, suboptimal myopic solutions in the presence of three forms of uncertainty: customer demands, travel times, and, of particular interest, user noncompliance. A simulation environment is used to test di#erent dispatching strategies under varying levels of system dynamism. An important issue we consider is that of user noncompliance, which is the e#ect of optimizing when users do not adopt all of the recommendations of the model. Our results show that #myopic# optimal solutions only slightly outperform greedy solutions under relatively high levels of...
Dynamic #eet management problems are normally formulated as networks over dynamic networks. Additional realism usually implies the inclusion of complicating constraints, typically producing exceptionally large integer programs. In this paper, we present for the #rst time the formulation of dynamic #eet management problems in an optimal control setting, using a novel formulation called a Logistics Queueing Network #LQN#. This formulation replaces a single, large optimization problem with a series of very small problems that involve little more than solving a single sort at each point in space and time. We show that this approach can produce solutions that are within a few percent of a global optimum, but providing for considerably more #exibility than standard linear programs. We consider the problem of managing a homogeneous #eet of vehicles over time to serve a set of loads, each with a known origin and destination, and a speci#ed time window in which they must be served. The proble...
. We present two formulations of a model for finding equilibrium passengers and operators flows in a partially regulated transit system where bus operators are free to choose the routes where they offer public transport services. The transit fares are assumed fixed and known. The model offers a detailed representation of the transit system network and of the transit users behavior. Congestion effects are also considered as a consequence of cars and buses operation over a common road network. Two algorithmic solution approaches are investigated. Key words: equilibrium, transit networks, bus operators, regulation. Introduction. In this paper we consider an urban public transport system served by buses that are individually owned and operated by small entrepreneurs under partially unregulated conditions. Given a set of lines where public transport can be offered, private operators freely decide on which of these lines to run their buses such that their individual net benefit be maximi...
. We develop a new local search approach based on a network flow model that is used to simultaneously evaluate several customer ejection and insertion moves. We use this approach and a direct customer swap procedure to solve the well-known Vehicle Routing Problem. The capacity constraints are relaxed using penalty terms whose parameter values are adjusted according to time and search feedback. Tabu Search is incorporated into the procedure to overcome local optimality. More advanced issues such as intensification and diversification strategies are developed to provide effective enhancements to the basic tabu search algorithm. Computational experience on standard test problems is discussed and comparisons with best-known solutions are provided. Key words. Vehicle Routing Problem, Network Flow Model, Local Search Heuristic, Tabu Search. 2 Jiefeng Xu and James P. Kelly Introduction The Vehicle Routing Problem (VRP) is an important management problem in the field of physical distributi...
The vehicle routing problem with time windows is a hard combinatorial optimization problem which has received considerable attention in the last decades. This paper proposes a two-stage hybrid algorithm for this transportation problem. The algorithm rst minimizes the number of vehicles using simulated annealing. It then minimizes travel cost using a large neighborhood search which may relocate a large number of customers. Experimental results demonstrate the eectiveness of the algorithm which has improved 13 (23%) of the 58 best published solutions to the Solomon benchmarks, while matching or improving the best solutions in 47 problems (84%). More important perhaps, the algorithm is shown to be very robust. With a xed conguration of its parameters, it returns either the best published solutions (or improvements thereof) or solutions very close in quality on all Solomon benchmarks. Results on the extended Solomon benchmarks are also given. 1
In this paper, M/G/C/C state dependent queueing models are proposed for modeling and analyzing vehicular traffic flows. Congestion aspects of traffic flow are represented by introducing state dependent service rates as a function of number of vehicles on each road link. Analytical models for unidirectional and multi-source flows are presented. Finally, queueing models to analytically determine the optimal capacity and performance measures of the road links are incorporated into a series of software programs available from the authors. Keywords: Vehicular Traffic Flow, M/G/C/C State Dependent Queues Department of Mechanical and Industrial Engineering, University of Massachusetts Amherst Massachusetts 01003 1 . 0. 0. 0 MGCC State Dependent Jain & Smith
In this paper we introduce the problem of shunting passenger train units in a railway station. Shunting occurs whenever train units are temporarily not necessary to operate a given timetable. We discuss several aspects of this problem and focus on two subproblems. We propose mathematical models for these subproblems together with a solution method based on column generation. Furthermore, a new efficient and speedy solution technique for pricing problems in column generation algorithms is introduced. Finally, we present computational results based on real life instances from Netherlands Railways.
We investigate dynamic policies for allocating scarce inventory to stochastic demand for multiple fare classes, in a network environment so as to maximize total expected revenues. Typical applications include sequential reservations for an airline network, ...