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This paper introduces a dynamic spatial price equilibrium model that estimates urban freight-related flows for integrated producer-carrier operations that compete in a market where a generic commodity is traded. The model is applicable to cases where suppliers compete in a market by producing a commodity that is delivered to customers by means of delivery tours. The model obtains the patterns of commodity flows, production levels, and delivery tours that maximize economic welfare. The model is then reinterpreted as a Nash equilibrium model, where a set of suppliers deploys strategies involving production and delivery decisions to maximize profits, that is then solved with a heuristic approach that decomposes the interrelated decisions into how much to produce, how best to deliver to customers, and how much to charge for the cargo. Once the suppliers make these decisions, a market-clearing mechanism determines the amount of supplies that the various consumer nodes purchase from the suppliers. At this stage, the suppliers readjust their market strategies in anticipation of the next time period. The process ends when equilibrium is reached. Three different dynamics of the suppliers' decisions on production levels are tested to gain insight into how efficiently each helps to reach the equilibrium solutions. By developing a model that explicitly considers delivery tours, the paper makes a significant contribution to the fields of spatial price equilibrium and freight demand modeling. [ABSTRACT FROM AUTHOR]

This work addresses a soft-clustered vehicle routing problem that extends the classical capacitated vehicle routing problem with one additional constraint, that is, customers are partitioned into clusters and all customers of the same cluster must be served by the same vehicle. Its potential applications include parcel delivery in courier companies and freight transportation. Due to its NP-hard nature, solving it is computationally challenging. This paper presents an efficient bilevel memetic search method to do so, which explores search space at both cluster and customer levels. It integrates three distinct modules: a group matching-based crossover (to generate promising offspring solutions), a bilevel hybrid neighborhood search (to perform local optimization), and a tabu-driven population reconstruction strategy (to help the search escape from local optima). Extensive experiments on three sets of 390 widely used public benchmark instances are conducted. The results convincingly demonstrate that the proposed method achieves much better overall performance than state-of-the-art algorithms in terms of both solution quality and computation time. In particular, it is able to find 20 new upper bounds for large-scale instances while matching the best-known upper bounds for all but four of the remaining instances. Ablation studies on three key algorithm modules are also performed to demonstrate the novelty and effectiveness of the proposed ideas and strategies. Funding: This work was supported by the Macau Young Scholars Program [Grant AM2020011], Fundo para o Desenvolvimento das Cienciase da Tecnologia (FDCT) [Grant 0047/2021/A1], the National Natural Science Foundation of China [Grants 61903144, 71871142, and 71931007], and the Open Project of the Shenzhen Institute of Artificial Intelligence and Robotics for Society [Grant AC01202005002]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1186. [ABSTRACT FROM AUTHOR]

Deterring the smuggling of nuclear weapons in container freight is critical. Previous work has suggested that such deterrence could be achieved by retaliation threats and partial inspection. However, pre-event declared retaliation threats may not be credible, causing the desired deterrence not to be achieved. In this paper, we extend and complement the work of Haphuriwat et al. (2011) to model credible retaliation threats in a three-stage game, by introducing two additional decision variables and five additional parameters. Our results suggest that noncredible retaliation could be at equilibrium when the reputation loss is low, the reward from the public for retaliation is low, or the costs of retaliation are high. When the declared retaliations are noncredible, we quantitatively show that a higher inspection level would be required to deter nuclear smuggling than would be needed if retaliation threats are always credible. This paper provides additional quantitative insights on the decision-making process for container screening to deter nuclear smuggling. [ABSTRACT FROM AUTHOR]

The article offers information on International Workshop on Freight Transportation and Logistics that was held in Mykonos, Greece on May 2012. Topics discussed include contributions through methodological developments and innovative applications, passenger-oriented transportation systems and revenue management for freight transportation, and integer programming formulation and a heuristic approach method.

This paper addresses the solution of large, complex resource allocation problems, examples of which include large freight transportation companies and supply chain management. Some instances of these problems involve millions of constraints and tens of millions of variables. Classical formulations focus on modeling the physical problem alone. In this paper, we focus on modeling the organization of information and decisions, producing a natural decomposition based on how decisions are actually made. Restricting the size of a subproblem to the sizes of problems actually solved by real decision makers, we avoid the computational demands posed by large problems. The algorithmic challenge is producing high quality solutions that reflect the interaction between subproblems. Linear approximations have been a widely used tool for decomposition, but these can produce unstable solutions of only moderate quality. We introduce the concept of using nonlinear approximations, which creates special technical problems but also produces solutions of very high quality. The strategy is simulated on two problem classes (fleet management and supply chains) and compared against standard modeling strategies. Synchronous and asynchronous strategies are also compared. [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]

In this paper we consider the problem of distributing empty freight cars in a railway company. We describe and analyze the current planning process, identify the shortcomings of the process, and stress the importance of a reliable distribution process for satisfying customer demand and reducing capital costs. We show how the process can be improved using an optimization model which includes capacity constraints on the trains and adheres explicitly to the arrival and departure times of the trains. The optimization model can be characterized as a multicommodity network flow model with integer requirements. Computational tests show that the model can be solved in acceptable time for real size problems, and indicate that the model generates distribution plans that can improve the quality of the planning process. In this paper we consider the problem of distributing empty freight cars in a railway company. We describe and analyze the current planning process, identify the shortcomings of the process, and stress the importance of a reliable distribution process for satisfying customer demand and reducing capital costs. We show how the process can be improved using an optimization model which includes capacity constraints on the trains and adheres explicitly to the arrival and departure times of the trains. The optimization model can be characterized as a multicommodity network flow model with integer requirements. Computational tests show that the model can be solved in acceptable time for real size problems, and indicate that the model generates distribution plans that can improve the quality of the planning process. [ABSTRACT FROM AUTHOR]

This paper addresses the dispatching problem faced by an urban consolidation center. The center receives orders according to a stochastic arrival process and dispatches them in batches for the last-mile distribution. The operator of the center aims to find the cost-minimizing consolidation policy, depending on the orders at hand, preannounced orders, and stochastic arrivals. We present this problem as a variant of the delivery dispatching problem that includes dispatch windows and define a corresponding Markov decision model. Larger instances of the problem suffer from intractably large state-, outcome-, and action spaces. We propose an approximate dynamic programming (ADP) algorithm that can handle such instances, using a linear value function approximation to estimate the downstream costs. To design the value function approximation, we construct various sets of basis functions, numerically evaluate their suitability, and discuss the properties of good basis functions for the dispatching problem. Numerical experiments on toy-sized instances show that the best set of basis functions approximates the optimal values with an error of less than 3%. To cope with large action spaces, we formulate an integer linear program to be used within our ADP algorithm. We evaluate the performance of ADP policies against four benchmark policies: two heuristic policies, a direct cost minimization policy, and a post-decision rollout policy. We test the performance of ADP on a variety of networks. ADP consistently outperforms the benchmark policies, performing particularly well when there is sufficient flexibility in dispatch times. The online appendix is available at https://doi.org/10.1287/trsc.2017.0773. [ABSTRACT FROM AUTHOR]

Planning the transport of maritime containers from the seaport to final inland destinations is challenged by uncertainties regarding the time the container is released for further transport and the transit time from the port to its final destination. This paper assesses the value of information in container transport in terms of efficiency and reliability. The analysis uses a stylized single period model where a decision maker allocates released containers to two transport modes (slow, low price, no flexible departure times versus fast, high price, flexible departure times) and plans the departure time of the inflexible mode. We construct Pareto frontiers and the corresponding Pareto optimal decisions under various information scenarios and show that the Pareto frontiers move in a favorable direction when the level of information increases. The mathematical results are explained and illustrated by means of a numerical example involving barge transport. We also perform a sensitivity analysis and study the impact of erroneous information on efficiency and reliability based on a numerical analysis. [ABSTRACT FROM AUTHOR]

Railroad transportation of hazardous materials did not receive as much attention as highway transportation in the academic literature, although comparable volumes are shipped via these two transport modes in North America and Europe. In this paper, we present an optimization methodology for the railroad tactical planning problem with risk and cost objectives. We determine the routes to be used for each shipment, the yard activities, and the number of trains of different types needed in the network. The transport risk assessment component of our model incorporates the differentiating characteristics of railroad operations. We develop a memetic algorithm-based solution methodology, which combines genetic and local searches, to solve the biobjective model. The railroad infrastructure in the midwestern United States is used as a basis for generating problem instances of the size encountered in real life. Our analyses of the solutions of instances indicate that it is possible to achieve significant reductions in population exposure without incurring unacceptable increases in operational costs. [ABSTRACT FROM AUTHOR]

Designing multimodal freight transport networks can facilitate the economic development of regions and countries as well as help to reduce negative environmental impacts. It is therefore crucial that such be undertaken in areas where more priority is given on road-based freight transport systems. This paper proposes a model for strategic transport planning, particularly in freight terminal development and interregional freight transport network design. The model determines a suitable set of actions from a number of possible actions, such as improving the existing infrastructure or establishing new roads, railways, sea links, and freight terminals. Modelling is undertaken within the framework of bilevel programming, where a multimodal multiclass user traffic assignment technique is incorporated within the lower-level problem, whilst the upper-level problem determines the best combination of actions such that the freight-related benefit-cost ratio is maximised. The upper-level problem involves combinatorial optimisation, and a heuristic approach based on genetic local search is applied as a solution technique. Empirical results of the model as applied to an actual large-sized interregional intermodal freight transport network show that genetic local search could provide better performance as compared to other genetic algorithm-based, as well as tabu search-based, heuristics. The model is successfully applied to transport network planning in the Philippines, where the development of a freight transport network is necessary to increase the utilisation of other modes rather than road-based vehicles. [ABSTRACT FROM AUTHOR]

This paper presents a decision tree model for evaluating countermeasures to reduce vulnerabilities to terrorism in commercial truck crossings at United States southwestern land ports of entry. The model includes critical events in four phases of cargo movement: cargo transfer in Mexico, Mexican customs, U.S. customs, and the inland phase. Improvements in transportation security, inspections at Mexican ports, and at U.S. ports, are comparatively evaluated using parameterized variables. Costs and benefits of such improvements are analyzed to counter a radiological dispersion device (also known as a "dirty bomb") attack. The results suggest that security decisions depend primarily on the probability of attack and parameters that influence the overall cost of false alarms. Extensive exploratory analysis reveals that improving security at Mexican ports is not recommended, mainly due to the cost of false alarms. However, a high percentage and a high cost of false alarms may justify new radiation portal monitors at U.S. ports even when improvements in the capability to detect dangerous cargo are insignificant. Better transportation security is not recommended if the probability of attack is less than 0.15. When the probability of attack exceeds 0.15 and false-alarm related costs are high, the model recommends enhancing transportation security. In addition, the parameters modeling economic consequences of an attack in a populated area, the probability of discovering weapons after smuggling into the United States, the probability of detonation, as well as the probability of detection at U.S. ports of entry, have significant impact on the countermeasure decision. [ABSTRACT FROM AUTHOR]

In the global maritime transportation network, the on-time performance of cargo transportation depends largely on the service capacity and accessibility of seaports. When opportunities for infrastructure expansions are not available, seaport congestion mitigation may require effective scheduling of the vessel traffic in the port waters. Although existing works on vessel traffic scheduling focus on minimizing vessel delays, this paper studies a novel vessel traffic scheduling problem that aims to address the inter-shipping line equity issue. We develop a lexicographic optimization model that accounts for two conflicting performance measures: efficiency, which favors minimizing total vessel delay; and equity, which favors balancing the impacts of delays fairly among shipping lines. Our model allows the port operator to quantify the efficiency-equity tradeoff and make the best vessel traffic scheduling decisions. For solving the model, we develop an effective two-stage solution method in which the first stage solves two single-objective models to obtain the maximum system efficiency and equity, whereas the second stage trades between efficiency and equity and seeks the best compromise between the two conflicting objectives. We apply our model and solution method on instances generated from the operational data of the Port of Shanghai. Our computational results show that an efficiency-oriented model can lead to highly inequitable traffic plans, whereas inter-shipping line equity can be achieved at only mild losses in efficiency, indicating that the consideration of inter-shipping line equity can lead to satisfactory service at both the vessel level and the shipping line level. [ABSTRACT FROM AUTHOR]

Motivated by applications in freight handling and open-pit mining, Rhys, Balinski, and Picard studied the problems of selection and closure in papers published in Management Science in 1970 and 1976. They identified efficient algorithms based on linear programming and maximum-flow/minimum-cut procedures to solve these problems. This research has had major impact well beyond the initial applications, reaching across three decades and inspiring work on numerous applications and extensions. The extensions are nontrivial optimization problems that are of theoretical interest. The applications ranged from evolving technologies, image segmentation, revealed preferences, pricing, adjusting utilities for consistencies, just-in-time production, solving certain integer programs in polynomial time, and providing efficient 2-approximation algorithms for a wide variety of hard problems. A recent generalization to a convex objective function has even produced novel solutions to prediction and Bayesian estimation problems. This paper surveys the streams of research stimulated by these papers as an example of the impact of Management Science on the optimization field and an illustration of the far-reaching implications of good original research. [ABSTRACT FROM AUTHOR]

The fast development of transport activities and the introduction of shipment consolidation have considerably changed the logistics context over the last three decades. Consolidation terminals, also called transshipment centers (TC) or hubs, have justified their presence by improving the loading of trucks in terms of both volume and weight. In addition, the possibility of using external carriers, exclusively or in coordination with a private fleet, can reduce costs and increase customer service. The right combination of these strategies can dramatically impact the cost of transport. However, the complexity of the decisions has also increased and existing models have to be improved to tackle these new challenges. In this paper, after discussing the different formulations for distribution networks with transshipment centers existing in the literature, we present a new model and an efficient metaheuristic that determines the number and the location of TCs as well as the best transportation alternative --LTL, FTL, Parcel, or own fleet--on each segment accounting for both weight and volume metrics. The ability of our heuristic to solve this complex problem comes from a judicious combination of tabu search and variable neighborhood search. The performance of this approach is evaluated on several test data problems generated with real cost structures published by a U.S.carrier. The heuristic solutions are compared to optimal ones obtained by an exact method for small-sized instances of the simpler problems. Finally, we address issues in carrier price structure to achieve efficient shipment practices. [ABSTRACT FROM AUTHOR]

In this paper we formally introduce a generic real-time multi-vehicle truck-load pick-up and delivery problem. The problem includes the consideration of various costs associated with trucks' empty travel distances, jobs' delayed completion times, and job rejections. Although very simple, the problem captures most features of the operational problem of a real-world trucking fleet that dynamically moves truckloads between different sites according to customer requests that arrive continuously. We propose a mixed-integer programming formulation for the off-line version of the problem. We then con- sider and compare five rolling horizon strategies for the real-time version. Two of the policies are based on a repeated reoptimization of various instances of the off-line problem, while the others use simpler local (heuristic) rules. One of the reoptimization strategies is new, while the other strategies have recently been tested for similar real-time fleet management problems. The comparison of the policies is done under a general simulation framework. The analysis is systematic and considers varying traffic intensities, varying degrees of advance information, and varying degrees of flexibility for job-rejection decisions. The new reoptimization policy is shown to systematically outperform the others under all these conditions. [ABSTRACT FROM AUTHOR]

Less-than-truckload (LTL) carriers operate networks of consolidation terminals, and route each customer shipment through a sequence of transfer terminals. At each terminal stop, a shipment is unloaded from an inbound trailer and reloaded onto an outbound trailer. A load plan determines the specific path of terminals to be used to transfer freight moving between each origin and destination. The design of the load plan determines the line-haul transportation and handling costs required to serve customers. This paper develops an effective neighborhood search heuristic for solving a natural integer programming model for LTL load plan design. During each iteration of the heuristic, a modified version of the integer programming model is solved to find improving changes freight transfer paths for a subset of the origin-destination terminal pairs. Unlike existing approaches in the literature, the modified model solved here allows the simultaneous rerouting of freight destined for multiple terminals during each neighborhood search iteration, yet remains computationally practical. Computational experiments using data from a large U.S. carrier show substantial cost improvements generated by increased freight consolidation, in the order of 6%-7%, accounting for over $300,000 per week. [ABSTRACT FROM AUTHOR]

In this paper, we study a comprehensive model that addresses fleet deployment, speed optimization, and cargo allocation jointly, so as to maximize total profits at the strategic level. Our model considers a general fuel consumption function that depends on speed and load. To overcome intractability caused by nonlinear terms, we further separate fuel cost into two terms associated with ship speed and load to obtain a mixed integer linear programming formulation for approximation. Based on column generation techniques, we develop an iterative search algorithm that adaptively reorganizes the approximated formulation. We conduct extensive experiments using generated data sets from actual liner shipping services in different regions of the world to show the effectiveness of our approach as well as the significant impact of speed-load factors on fuel consumptions. Managerial insights are obtained by testing the model under different scenarios, which may greatly assist decision makers in the liner shipping industry. [ABSTRACT FROM AUTHOR]

We study a fundamental model of resource allocation in which a finite number of resources must be assigned in an online manner to a heterogeneous stream of customers. The customers arrive randomly over time according to known stochastic processes. Each customer requires a specific amount of capacity and has a specific preference for each of the resources with some resources being feasible for the customer and some not. The system must find a feasible assignment of each customer to a resource or must reject the customer. The aim is to maximize the total expected capacity utilization of the resources over the horizon. This model has application in services, freight transportation, and online advertising. We present online algorithms with bounded competitive ratios relative to an optimal off-line algorithm that knows all stochastic information. Our algorithms perform extremely well compared with common heuristics as demonstrated on a real data set from a large hospital system in New York City. This paper was accepted by Yinyu Ye, optimization. [ABSTRACT FROM AUTHOR]

For less-than-truckload (LTL) freight transportation carriers, as shipment sizes are small relative to trailer capacity, profitability is driven by the ability to load trailers with shipments from multiple customers. However, LTL carriers are facing increased pressure from customers to provide short delivery times, which limits their ability to hold freight, a critical tactic for consolidation. As consolidation requires the coordination of shipment paths in both space and time, shorter delivery times necessitate planning methods that can accurately estimate consolidation opportunities in time. This paper adapts and enhances the dynamic discretization discovery method designed for solving the scheduled service network design problem, defined on an arbitrarily fine discretization of time, to produce exact and heuristic methods for the LTL analog, the continuous time load plan design problem. With instances from the literature and based on data from a U.S. LTL carrier, we provide computational evidence that the algorithm can effectively solve this problem. With an analysis of high-quality solutions to the instances based on LTL carrier data, we derive insights into terminal staffing policies. [ABSTRACT FROM AUTHOR]

Driver fatigue is internationally recognized as a significant factor in approximately 15%-20% of commercial road transport crashes. In their efforts to increase road safety and improve working conditions of truck drivers, governments worldwide are enforcing stricter limits on the amount of working and driving time without rest. This paper describes an effective optimization algorithm for minimizing transportation costs for a fleet of vehicles considering business hours of customers and hours of service regulations. The algorithm combines the exploration capacities of population-based metaheuristics, the quick improvement abilities of local search, with forward labeling procedures for checking compliance with complex hours of service regulations. Several speedup techniques are proposed to achieve an overall efficient approach. The proposed approach is used to assess the impact of different hours of service regulations from a carrier-centric point of view. Extensive computational experiments for various sets of regulations in the United States, Canada, the European Union, and Australia are conducted to provide an international assessment of the impact of different rules on transportation costs and accident risks. Our experiments demonstrate that European Union rules lead to the highest safety, whereas Canadian regulations are the most competitive in terms of economic efficiency. Australian regulations appear to have unnecessarily high risk rates with respect to operating costs. The recent rule change in the United States reduces accident risk rates with a moderate increase in operating costs. [ABSTRACT FROM AUTHOR]

In seaport container terminals, berth allocation, quay crane assignment, and quay crane scheduling problems I are solved sequentially. However, this sequential way of planning the seaside operations often hinders obtaining a sufficient resource utilization and service quality at low cost. This paper provides a framework for aligning all decisions that have to be made in an integrative manner. The framework is laid down in three phases. Phase I estimates productivity rates for the cranes from the vessels' stowage plans. The productivity rates are used in Phase II to make berthing decisions and to assign crane capacity to vessels. Phase III determines detailed crane schedules and aligns the decisions made. The framework supports using well-known heuristics for solving the contained subproblems. Computational tests reveal that the integrated planning is computationally tractable for problem scenarios of realistic size. It is also demonstrated that the new approach balances the cost drivers of a terminal much better than the conventional way of operations planning does and that it enables significant cost reductions. [ABSTRACT FROM AUTHOR]

Although air carriers derive revenue from both passengers and cargo, the majority of the literature on airline management has focused on passengers. With the rapid growth in air freight, more studies are needed to examine the growing impact of air freight on air transportation. This paper addresses the optimal baggage-limit policy for airlines. Because much of the cargo is currently transported in the residual aircraft belly space after all of the passenger baggage has been enplaned, it is important for carriers to plan passenger and cargo levels together when setting passenger baggage limits. We formulate this problem as a variant of the price-dependent multi-item newsvendor model with weight-volume capacity constraints. The effects of baggage weight, prices, and costs on the number of passengers and amount of cargo carried are studied. Based on the model and carriers' existing practice, we develop several illustrative cases. Our findings suggest that airlines may be able to increase profits with significant reductions in passenger baggage limits for large aircraft. [ABSTRACT FROM AUTHOR]

A central element of the air cargo planning process is the generation of optimal flight schedules. A flight schedule simultaneously defines the market potential of an airline and allocates its resources. The schedule design process is a difficult and time-consuming task that involves and affects virtually all business units. Because of its complexity, the process is traditionally decomposed into several steps that are executed in a sequential manner. In this paper, we present novel model formulations and solution procedures which have been developed in the course of a feasibility study for a decision support system (DSS) for a pragmatic approach to "freighter network planning" at one of the top international cargo carriers. We formulate two integrated models that combine the three planning steps: flight selection, aircraft rotation planning, and cargo routing. The aim of the schedule optimization is to maximize the network-wide profit by determining the best combination from a list of mandatory and optional flights, assigning the selected flights to aircrafts and identifying optimal cargo flows. Both model formulations are embedded in a solution procedure that builds on the column generation technique with shortest path algorithms for solving the subproblems. The applicability of the models in a DSS is demonstrated on realistic problem instances that match the requirements specified in the feasibility study. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of determining the optimal integrations and consolidations of air cargo shipments. A freight forwarder arranges for the execution of many jobs (shipments) on behalf of several clients. Each job consists of a number of sequential activities, such as pickup, truck transportation, warehousing, and air transportation. Each activity can be performed by a number of processing units, such as trucking companies, warehouses, and airlines. If a number of consecutive activities of a job are integrated, i.e., performed by the same processing unit, then it typically costs less. If a number of similar activities of different jobs are consolidated, i.e., performed by the same processing unit, then it also typically costs less. Given a number of jobs and processing units, the sets of activities that can be integrated and consolidated, and the associated costs, the decision problem is to determine which processing unit should perform each activity of each job to minimize the total cost. This problem of assigning shipment activities to processing units is formulated as a linear 0-1 program. Principal properties of the model are established. Exploiting the special structure of this model, we design a solution procedure that includes heuristics and a branch-and-bound algorithm. [ABSTRACT FROM AUTHOR]

A game between two players acting on the same road transportation network is considered in this paper. The first player aims at minimizing the transportation costs, whereas the second player aims at maximizing her profit (or, in general, her utility) that is proportional to the flow passing through the arcs under her control. We introduce bilevel linear programming formulations for this problem. We derive conditions of existence and properties of the equilibrium points and propose an algorithm finding a local optimal solution. Finally, we present an application of the model to a real system involving trucks travelling through Europe from a Middle Eastern country. [ABSTRACT FROM AUTHOR]

This paper introduces a network design problem with a structure that is encountered in many transportation processes. The general organization of these systems is as follows. Freight has to be transported between a large number of origins and destinations. To consolidate the freight, it is first shipped to a terminal. Next, it is transported directly to a terminal where it is re-loaded and shipped to its destination. The task is to decide which terminals have to be used and how the freight is transported among the terminals. We describe an application where the terminals are airports and the freight is letter mail. Here, the transportation between terminals is by air, which is required due to temporal constraints. The economical impact of these decisions is huge because air transportation is costly and the process is repeated every night. We show how the problem can be modeled as a capacitated warehouse location problem with side constraints and propose a hybrid Tabu Search/Branch-and-Bound algorithm, which solves large real-world instances with acceptable computation times. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a survey of recent optimization models for the most commonly studied rail transportation problems. For each group of problems, we propose a classification of models and describe their important characteristics by focusing on model structure and algorithmic aspects. The review mainly concentrates on routing and scheduling problems since they represent the most important portion of the planning activities performed by railways. Routing models surveyed concern the operating policies for freight transportation and railcar fleet management, whereas scheduling models address the dispatching of trains and the assignment of locomotives and cars. A brief discussion of analytical yard and line models is also presented. The emphasis is on recent contributions, but several older yet important works are also cited. [ABSTRACT FROM AUTHOR]

In many business sectors such as airlines, hotels, trucking, and media advertising, customers' arrivals and willingness to pay are uncertain. Managers must decide whether to quote a price low enough to guarantee early sales, or to quote a higher price and risk that some units remain unsold. In allocating capacity, they face a trade-off between two types of potential losses; (1) Yield loss --selling at a low price, and losing a better price later, and (2) Spoilage loss-waiting in vain to sell at a high price, and losing the opportunity of an earlier low price offer. Yield loss means that consumers who value the product most do not get to use it, and spoilage loss means that valuable products are wasted because no consumers get to use them. Sellers typically hedge against the risk of spoilage loss by selling some units early at low prices, and against the risk of yield loss by blocking some units in hope of selling them later at a high price. In this paper we show that the use of overselling with opportunistic cancellations can increase expected profits and improve allocation efficiency. Under this strategy, the seller deliberately oversells capacity if high-paying consumers show up, even when capacity is already fully booked. The seller then cancels the sale to some low-paying customers while providing them with appropriate compensation. We derive a new rule to optimally allocate capacity to consumers when overselling is used, and show that overselling helps limit the potential yield and spoilage losses. Yield loss is reduced because the seller can capture more high-paying customers by compensating low-paying customers who give up their right to the product. Spoilage loss is reduced because the compensation decreases the price spread perceived by the seller, and as a result, the seller is less anxious to speculate and "block" units. Overselling with opportunistic cancellations assures that the product will be sold to consumers who value it most. This means that "everybody wins", and resources are allocated more efficiently than in conventional selling. [ABSTRACT FROM AUTHOR]

Any study of rail freight service or freight car utilization must eventually address the reliability of train connection performance. In a series of case studies over the past 10 years, the MIT Rail Group developed PMAKE analysis as an effective means of doing this. The PMAKE methodology has been used extensively in service planning by a number of railroads and has been used in two major rail network models. The Freight Car Utilization Program has supported two demonstration projects showing how to incorporate PMAKE analysis in railroad terminal control systems. The paper reviews three other major modeling approaches used in rail yard studies: simulation, queuing, and capacity planning. These approaches have had limited effectiveness in prediction train connection performance and in supporting management control systems. PMAKE analysis improves upon these approaches by making it easier to (a) calibrate models of yard performance and (b) incorporate analytic techniques within the operating control system. In short, PMAKE analysis builds a bridge between operations research technique and management control. The paper includes the parameters of PMAKE functions calibrated for various rail yards. It also includes the mathematical basis for PMAKE analysis and shows several means of calibrating PMAKE functions. This paper, therefore, provides a complete description of PMAKE analysis, including its development, its relation to other methods of terminal analysis and its use by the rail industry. [ABSTRACT FROM AUTHOR]

To remain competitive, manufacturers must seek transportation strategies that both reduce costs and maintain high levels of service. One approach is to consolidate inbound freight at transshipment points. This provides economies of scale and promotes capacity efficient mixes of high and low density items. When service level considerations are included via inventory holding costs, the approach yields a nonlinear network model with multiattribute multicommodity flows. The model is difficult to solve for global optimality in that the objective function is neither convex nor concave; therefore, a composite algorithm is proposed. The algorithm alternates between a linearization technique to find local optima and a heuristic search based on "adjacent concave flows" to provide local improvements. Computational results demonstrate the ability of the multiattribute approach to identify savings in overall transportation and inventory costs when compared to a single attribute approach. [ABSTRACT FROM AUTHOR]

This paper develops an analytic method for minimizing the cost of distributing freight by truck from a supplier to many customers. It derives formulas for transportation and inventory costs, and determines the optimal trade-off between these costs. The paper analyzes and compares two distribution strategies: direct shipping (i.e., shipping separate loads to each customer) and peddling (i.e., dispatching trucks that deliver items to more than one customer per load). The cost trade-off in each strategy depends on shipment size. Our results indicate that, for direct shipping, the optimal shipment size is given by the economic order quantity (EOQ) model, while for peddling, the optimal shipment size is a full truck. The peddling cost trade-off also depends on the number of customers included on a peddling route. This trade-off is evaluated analytically and graphically. The focus of this paper is on an analytic approach to solving distribution problems. Explicit formulas are obtained in terms of a few easily measurable parameters. These formulas require the spatial density of customers, rather than the precise locations of every customer. This approach simplifies distribution problems substantially while providing sufficient accuracy for practical applications. It allows cost trade-offs to be evaluated quickly using a hand calculator, avoiding the need for computer algorithms and mathematical programming techniques. It also facilitates sensitivity analyses that indicate how parameter value changes affect costs and operating strategies. [ABSTRACT FROM AUTHOR]

More than ever before, the airline industry must manage its operations very carefully if it is to adapt to the changes in its environment. One important planning problem is the scheduling of freight handling employees at air cargo terminals. Indeed, this area is particularly critical for achieving cost reductions while maintaining customer service levels. This paper presents a new model and an appropriate solution approach for the work-scheduling problem. In particular, a demand leveling procedure is introduced to take advantage of the flexibility that is often encountered in such problems. Experimental results obtained with actual data from a major airline are also presented. [ABSTRACT FROM AUTHOR]

Containerized liner trades have been growing steadily since the globalization of world economies intensified in the early 1990s. However, these trades are typically imbalanced in terms of the numbers of inbound and outbound containers. As a result, the relocation of empty containers has become one of the major problems faced by liner operators. In this paper, we consider the dynamic empty container allocation problem where we need to reposition empty containers and to determine the number of leased containers needed to meet customers' demand over time. We formulate this problem as a two-stage stochastic network: in stage one, the parameters such as supplies, demands, and ship capacities for empty containers are deterministic; whereas in stage two, these parameters are random variables. We need to make decisions in stage one such that the total of the stage one cost and the expected stage two cost is minimized. By taking advantage of the network structure, we show how a stochastic quasi-gradient method and a stochastic hybrid approximation procedure can be applied to solve the problem. In addition, we propose some new variations of these methods that seem to work faster in practice. We conduct numerical tests to evaluate the value of the two-stage stochastic model over a rolling horizon environment and to investigate the behavior of the solution methods with different implementations. [ABSTRACT FROM AUTHOR]

This paper considers the production-transportation problem of a firm with a finite number of production (supply) facilities of known location, facing demand distributed over a subset (market region) of K-dimensional Euclidean space. The demand for a single good is described by a demand density function which is continuous almost everywhere on the market region. Production cost functions exist at each production facility and transport cost functions refer to delivering the good from the production facility to the consumer The objective is to set production at each production facility and to select a supply policy such that total production and transportation costs are minimized. The problem is formulated in its entirety and later simplified through suboptimization. Necessary conditions for an optimal solution are derived and economic interpretations are provided. [ABSTRACT FROM AUTHOR]

Crew costs are a significant portion of rail operating expenses, and so effective deployment of train crews is an important priority for freight railroads. This paper proposes an optimization model and develops an effective solution approach to assign crews to trains and decide when to deadhead crew members in double-ended crew districts in U.S. freight railways. To solve this model quickly, we develop several modeling and methodological enhancements including methods to reduce the problem size, strengthen the model, and generate good heuristic solutions. Computational testing and validation using 140 real-life problem instances demonstrate that our algorithm can find optimal and implementable solutions very quickly (typically within one minute), making it well-suited for practical use to provide real-time decision support to crew planners. [ABSTRACT FROM AUTHOR]

Kara and Tansel (Management Science, Volume 47, 2001, 1408-1420) introduce the latest arrival hub location problem as a more realistic way of modeling cargo delivery. The key feature of the new model is that each link in the network is served by a single vehicle that makes exactly one trip. As a result, the traffic requiring a particular link may be forced to wait for all other traffic requiring the same link to arrive. Therefore, the travel time between a particular pair of nodes depends not just on travel times of the links on the path taken, but also on these forced "waiting times," which are called transient times in Kara and Tansel (2001). We show, however, that if the objective function depends only on the maximum travel time, this "new" model is essentially the same as the classical model that ignores the transient times. Our result implies that two of the three versions of the latest arrival hub location problem proposed by Kara and Tansel, including the one to which they devote most of their paper, are equivalent to their classical counterparts. [ABSTRACT FROM AUTHOR]

The traditionally studied hub location problems in the literature pay attention to flight times but not to transient times spent at hubs for unloading, loading, and sorting operations. The transient times may constitute a significant portion of the total delivery time for cargo delivery systems. We focus on the minimization of the arrival time of the last arrived item in cargo delivery systems and develop a model that correctly computes the arrival times by taking into account both the flight times and the transient times. Nonlinear and linear integer formulations are given and computational results are provided. The effects of delays on the system performance are analyzed. [ABSTRACT FROM AUTHOR]

We present in this paper a normative model for simulating freight flows of multiple products on a multimodal network. The multimodal aspects of the transportation system considered are accounted for in the network representation chosen. The multiproduct aspects of the model are exploited in the solution procedure, which is a Gauss-Seidel-Linear Approximation Algorithm. An important component of the solution algorithm is the computation of shortest paths with intermodal transfer costs. Computational results obtained with this algorithm on a network that corresponds to the Brazil transportation network are presented. Several applications of this model are reported as well. [ABSTRACT FROM AUTHOR]

Recently, we developed a multimode multiproduct network optimization model, that is the network assignment method implemented in an interactive-graphic system for the strategic analysis and planning of national freight transportation systems, called STAN. For STAN, we developed a modeling framework of the rail freight transportation system, its components, operations and goals, that is adapted for both the strategic objectives of the planning system and the representation of the other transportation modes that compose a national multimode transportation system. The objective of this paper is to present and analyze the rail component of this strategic model of a national freight transportation system. We show how the rail model is integrated into STAN, as well as how this modeling framework may be used to represent a number of realistic scenarios. [ABSTRACT FROM AUTHOR]

The transportation of freight, by any mode, usually generates a significant number of empty vehicle movements. Understanding and controlling this phenomenon is important for all levels of transportation and logistic system planning. In this paper, we propose a taxonomy of empty vehicle flow problems and models and review the existing literature on the subject. Major research trends and perspectives are identified and the advantages of a hierarchically integrated approach for the simultaneous management of empty and loaded freight vehicle movements are discussed. [ABSTRACT FROM AUTHOR]

This paper examines the problems of routing freight traffic, scheduling train services and allocating classification work between yards on a rail network. It describes a general optimization model which takes into account the interactions between these activities and develops global strategies for their management over a medium term planning horizon. A heuristic algorithm developed to solve this nonlinear, mixed-integer multicommodity flow problem is also presented with some computational results based on an example at the Canadian National Railroads. [ABSTRACT FROM AUTHOR]

Freight cars represent a substantial portion of total railroad investment, and the low utilization of this major capital resource is certainly a contributing factor in the poor financial health of many railroads. A key element in improving utilization is the process of empty car redistribution. This paper describes a dynamic network optimization model for distribution of empty freight cars. It incorporates information on potential revenues from loads available at various points in the network for each period over a specified planning horizon, the costs of not being able to satisfy these demands, the costs of holding empty cars in anticipation of demands, and the costs of moving empty cars over the system. The information on supplies of, and demands for, cars in future periods, as well as their travel times over the network, is represented stochastically to reflect the uncertainty inherent in forecasts of future conditions. [ABSTRACT FROM AUTHOR]

Recent developments in location systems technology for railroads provide a train dispatcher with the capability to improve the operations of a rail line by pacing trains over a territory; i.e., to permit trains to travel at less than maximum velocity to minimize fuel consumption while maintaining a given level of performance. Traditional railroad dispatching models assume that the velocities of the trains moving over a dispatcher's territory are fixed at their maximum value and, thus, are incapable of dealing with a pacing situation. This paper presents a mathematical programming model for the pacing problem and describes alternative solution procedures for this model. Analytical and numerical evidence are presented that confirm the applicability of a heuristic solution procedure for this problem, as well as providing evidence that a pacing approach versus the traditional dispatching approach is an efficient and potentially cost effective method for the control of train movements. [ABSTRACT FROM AUTHOR]

Conditional penalties are used to obtain lower bounds to subproblems in a branch-and-bound procedure that can be tighter than the LP relaxation of the subproblems. For the fixed charge transportation problem (FCTP), branch-and-bound algorithms have been implemented using conditional penalties proposed by Driebeek (1966), Cabot and Erenguc (1984), and Palekar et al. (1990). The last conditional penalties are referred to as the "modified" penalties. In this paper, we show that the modified penalties are not valid conditional penalties. In fact, in nearly a quarter of the test problems examined, the modified penalties prevented the branch-and-bound algorithm from properly identifying the optimal solution to the FCTP. A simple change, which corrects a subcase in the penalty calculation, restores the validity of the modified penalties while retaining their efficiency. Computational tests indicate that the "revised-modified" penalties continue to dominate the Driebeek and the Cabot and Erenguc penalties [ABSTRACT FROM AUTHOR]

Shippers and carriers are constantly in need of substantial amounts of transportation cost information: shippers are looking for the most economical means of moving freight; carriers need information to determine rates that attract or retain business. The model presented in this paper calculates the costs associated with shipping by barge via the Inland Waterways System. It does so with great improvements in time, money and accuracy over a previously used manual method. [ABSTRACT FROM AUTHOR]

Contracts in the for-hire trucking industry are unusual in that, although they establish prices for different services, there is typically no legally binding obligation or penalty for either party to offer or accept a load. When a load is rejected by all contract carriers, shippers must turn to the spot market, which can significantly increase supply chain costs. Because these transactions occur between private parties, data on load acceptances/rejections and contract/spot prices have not been available to academic researchers, leaving the freight rejection problem largely unexplored. We are able to examine this problem using a detailed transactional data set of a large national shipper. We estimate that spot prices for truckload services average about 62% higher than contract rates. We find key operational and economic factors to be drivers of freight rejection and the shipper-carrier relationship to be a deterrent to freight rejection. We also find that primary and secondary carriers respond differently to these operational and economic factors. We discuss how these insights could be used by a shipper to get better performance and lower cost from their carrier base. [ABSTRACT FROM AUTHOR]

Consolidation carriers transport shipments that are small relative to trailer capacity. To be cost effective, the carrier must consolidate shipments, which requires coordinating their paths in both space and time; i.e., the carrier must solve a service network design problem. Most service network design models rely on discretization of time-i.e., instead of determining the exact time at which a dispatch should occur, the model determines a time interval during which a dispatch should occur. While the use of time discretization is widespread in service network design models, a fundamental question related to its use has never been answered: Is it possible to produce an optimal continuous-time solution without explicitly modeling each point in time? We answer this question in the affirmative. We develop an iterative refinement algorithm using partially time-expanded networks that solves continuous-time service network design problems. An extensive computational study demonstrates that the algorithm not only is of theoretical interest but also performs well in practice. [ABSTRACT FROM AUTHOR]

We study a practical generalization of the classical stochastic dynamic inventory problem where privately owned trucks with limited cargo capacity are used to transport the replenishment quantity. The resulting replenishment cost function also includes the traditional fixed setup cost, and it is known as a multiple setup cost structure, which leads to complicated cost-to-go functions in the problem of interest. We introduce the concepts of non-(Δ, C)- decreasing and , and we develop a sophisticated replenishment policy called the policy. We examine the sufficient conditions under which the new policy is optimal. Our results offer a detailed characterization of optimal policies and generalize the existing theory on the concepts of K-convexity and non- K-decreasing. In doing so, we are able to investigate a traditional stochastic inventory problem which has remained open in the literature for more than four decades. The online appendix is available at . [ABSTRACT FROM AUTHOR]

We first present a new service network design model for freight consolidation carriers, one that selects services and routes both commodities and resources needed to support the services that transport them, while explicitly recognizing that there are limits on how many resources are available at each terminal. We next present a solution approach that combines column generation, meta-heuristic, and exact optimization techniques to produce high-quality solutions. We demonstrate the efficacy of the approach with an extensive computational study and benchmark its performance against both a leading commercial solver and a column generation-based heuristic. [ABSTRACT FROM AUTHOR]