Showing papers in "Annals of Operations Research in 1995"

Dynamic vehicle routing: Status and prospects

Abstract: Although most real-world vehicle routing problems are dynamic, the traditional methodological arsenal for this class of problems has been based on adaptations of static algorithms. Still, some important new methodological approaches have recently emerged. In addition, computer-based technologies such as electronic data interchange (EDI), geographic information systems (GIS), global positioning systems (GPS), and intelligent vehicle-highway systems (IVHS) have significantly enhanced the possibilities for efficient dynamic routing and have opened interesting directions for new research. This paper examines the main issues in this rapidly growing area, and surveys recent results and other advances. The assessment of possible impact of new technologies and the distinction of dynamic problems vis-a-vis their static counterparts are given emphasis.

Routing problems: A bibliography

Abstract: This bibliography contains 500 references on four classical routing problems: the Traveling Salesman Problem, the Vehicle Routing Problem, the Chinese Postman Problem, and the Rural Postman Problem. References are presented alphabetically under a number of subheadings.

A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives

Abstract: The paper describes a system for the solution of a static dial-a-ride routing and scheduling problem with time windows (DARPTW). The problem statement and initialization of the development project was made by the Copenhagen Fire-Fighting Service (CFFS). The CFFS needed a new system for scheduling elderly and disabled persons, involving about 50.000 requests per year. The problem is characterized by, among other things, multiple capacities and multiple objectives. The capacities refer to the fact that a vehicle may be equipped with e.g. normal seats, children seats or wheel chair places. The objectives relate to a number of concerns such as e.g. short driving time, high vehicle utilization or low costs. A solution algorithm REBUS based on an insertion heuristics was developed. The algorithm permits in a flexible way weighting of the various goals such that the solution reflects the user's preferences. The algorithm is implemented in a dynamic environment intended for on-line scheduling. Thus, a new request for service is treated in less than 1 second, permitting an interactive user interface.

System optimal and user equilibrium time-dependent traffic assignment in congested networks

Abstract: This paper formulates two dynamic network traffic assignment models in which O-D desires for the planning horizon are assumed known a priori: the system optimal (SO) and the user equilibrium (UE) time-dependent traffic assignment formulations. Solution algorithms developed and implemented for these models incorporate a traffic simulation model within an overall iterative search framework. Experiments conducted on a test network provide the basis for a comparative analysis of system performance under the SO and UE models.

An algorithm for large scale 0-1 integer programming with application to airline crew scheduling

Abstract: We present an approximation algorithm for solving large 0–1 integer programming problems whereA is 0–1 and whereb is integer. The method can be viewed as a dual coordinate search for solving the LP-relaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working together with this method. The approximation scheme works by adjusting the costs as little as possible so that the new problem has an integer solution. The degree of approximation is determined by a parameter, and for different levels of approximation the resulting algorithm can be interpreted in terms of linear programming, dynamic programming, and as a greedy algorithm. The algorithm is used in the CARMEN system for airline crew scheduling used by several major airlines, and we show that the algorithm performs well for large set covering problems, in comparison to the CPLEX system, in terms of both time and quality. We also present results on some well known difficult set covering problems that have appeared in the literature.

A review of Goal Programming and its applications

Abstract: This paper presents a review of the current literature on the branch of multi-criteria decision modelling known as Goal Programming (GP). The result of our indepth investigations of the two main GP methods, lexicographic and weighted GP together with their distinct application areas is reported. Some guidelines to the scope of GP as an application tool are given and methods of determining which problem areas are best suited to the different GP approaches are proposed. The correlation between the method of assigning weights and priorities and the standard of the results is also ascertained.

SOCRATES: A system for scheduling hydroelectric generation under uncertainty

Abstract: The Pacific Gas and Electric Company, the largest investor-owned energy utility in the United States, obtains a significant fraction of its electric energy and capacity from hydrogeneration. Although hydro provides valuable flexibility, it is subject to usage limits and must be carefully scheduled. In addition, the amount of energy available from hydro varies widely from year to year, depending on precipitation and streamflows. Optimal scheduling of hydrogeneration, in coordination with other energy sources, is a stochastic problem of practical significance to PG&E. SOCRATES is a system for the optimal scheduling of PG&E's various energy sources over a one- to two-year horizon. This paper concentrates on the component of SOCRATES that schedules hydro. The core is a stochastic optimization model, solved using Benders decomposition. Additional components are streamflow forecasting models and a database containing hydrological information. The stochastic hydro scheduling module of SOCRATES is undergoing testing in the user's environment, and we expect PG&E hydrologists and hydro schedulers to place progressively more reliance upon it.

A continuous day-to-day traffic assignment model and the existence of a continuous dynamic user equilibrium

Abstract: Suppose that a road network model is given, together with some given demand for travel by (say) car and that the demand for travel varies with time of day but not from day to day. Suppose that this demand is given in the form of specified total outflow rates from each origin headed towards each destination, for each origin-destination pair and for each time of day, and that some initial time-dependent routeinflow rates, meeting the given demand, are given. Finally, suppose that within-day time is represented by a continuous variable. This paper specifies a natural smooth day-to-day route-swapping procedure wherein drivers swap toward less expensive routes as day succeeds day, and shows that under reasonable conditions there is an equilibrium state of this dynamical system. If such a collection of route-inflows has arisen today, say, then there is no incentive for any route-inflow to change tomorrow, in the sense that at each moment of today each of today's route-inflows isalready on a route which today yielded the smallest travel cost. Such a set of “no-incentive-to-change” route-inflows is called adynamic equilibrium, or adynamic user-equilibrium, and may be regarded as a solution of the dynamic equilibrium traffic assignment problem. Thus, the paper introduces a smooth day-to-day dynamic assignment model and, using this model, shows that there is a dynamic user-equilibrium in a continuous time setting. The paper briefly considers the day-to-day stability of the route-swapping process, also in a continuous setting. Finally, the paper gives a simple dynamical example illustrating the stability of the route-swapping process in a simple two-route network when there is deterministic queueing at bottlenecks.

A projection technique for partitioning the nodes of a graph

Abstract: LetG=(N,E) be an undirected graph. We present several new techniques for partitioning the node setN intok disjoint subsets of specified sizes. These techniques involve eigenvalue bounds and tools from continuous optimization. Comparisons with examples taken from the literature show these techniques to be very successful.

Applying constraint satisfaction techniques to job shop scheduling

Abstract: In this paper, we investigate the applicability of a constraint satisfaction problem solving (CSP) model, recently developed for deadline scheduling, to more commonly studied problems of schedule optimization. Our hypothesis is twofold: (1) that CSP scheduling techniques provide a basis for developing high-performance approximate solution procedures in optimization contexts, and (2) that the representational assumptions underlying CSP models allow these procedures to naturally accommodate the idiosyncratic constraints that complicate most real-world applications. We focus specifically on the objective criterion of makespan minimization, which has received the most attention within the job shop scheduling literature. We define an extended solution procedure somewhat unconventionally by reformulating the makespan problem as one of solving a series of different but related deadline scheduling problems, and embedding a simple CSP procedure as the subproblem solver. We first present the results of an empirical evaluation of our procedure performed on a range of previously studied benchmark problems. Our procedure is found to provide strong costyperformance, producing solutions competitive with those obtained using recently reported shifting bottleneck search procedures at reduced computational expense. To demonstrate generality, we also consider application of our procedure to a more complicated, multi-product hoist scheduling problem. With only minor adjustments, our procedure is found to significantly outperform previously published procedures for solving this problem across a range of input assumptions.

A new branching strategy for time constrained routing problems with application to backhauling

Abstract: In this paper, we explore a new branching strategy for branch-and-bound approaches based on column generation for the vehicle routing problems with time windows. This strategy involves branching on resource variables (time or capacity) rather than on network flow variables. We also examine criteria for selecting network nodes for branching. To test the effectiveness of the branching strategy, we conduct computational experiments on time window constrained vehicle routing problems where backhauling is permitted only after all the shipments to clients have been made. The branching method proved very effective. In cases where time was the more binding constraint, time-based branching succeeded in decreasing the number of nodes explored by two thirds and the total computation time by more than half when compared to flow-based branching. The computational results also show that the overall algorithm was successful in optimally solving problems with up to 100 customers. It produced an average cost decrease of almost 7% when backhauling was permitted as compared to the cost involved when the client and the distributor routes were distinct.

Asset/liability management under uncertainty for fixed-income securities

Abstract: Short-sighted asset/liability strategies of the seventies left financial intermediaries — banks, insurance and pension fund companies, and government agencies — facing a severe mismatch between the two sides of their balance sheet. A more holistic view was introduced with a generation ofportfolio immunization techniques. These techniques have served the financial services community well over the last decade. However, increased interest rate volatilities, and the introduction of complex interest rate contingencies and asset-backed securities during the same period, brought to light the shortcomings of the immunization approach. This paper describes a series of (optimization) models that take a global view of the asset/liability management problem using interest rate contingencies. Portfolios containingmortgage-backed securities provide the typical example of the complexities faced by asset/liability managers in a volatile financial world. We use this class of instruments as examples for introducing the models. Empirical results are used to illustrate the effectiveness of the models, which become increasingly more complex but also afford the manager increasing flexibility.

A new exact algorithm for the vehicle routing problem based on q -paths and k -shortest paths relaxations

Abstract: We consider the basic Vehicle Routing Problem (VRP) in which a fleet ofM identical vehicles stationed at a central depot is to be optimally routed to supply customers with known demands subject only to vehicle capacity constraints. In this paper, we present an exact algorithm for solving the VRP that uses lower bounds obtained from a combination of two relaxations of the original problem which are based on the computation ofq-paths andk-shortest paths. A set of reduction tests derived from the computation of these bounds is applied to reduce the size of the problem and to improve the quality of the bounds. The resulting lower bounds are then embedded into a tree-search procedure to solve the problem optimally. Computational results are presented for a number of problems taken from the literature. The results demonstrate the effectiveness of the proposed method in solving problems involving up to about 50 customers and in providing tight lower bounds for problems up to about 150 customers.

Derivatives of probability functions and some applications

Abstract: Probability functions depending upon parameters are represented as integrals over sets given by inequalities. New derivative formulas for the intergrals over a volume are considered. Derivatives are presented as sums of integrals over a volume and over a surface. Two examples are discussed: probability functions with linear constraints (random right-hand sides), and a dynamical shut-down problem with sensors.

Using artificial neural networks to solve the orienteering problem

Abstract: In the orienteering problem, we are given a transportation network in which a start point and an end point are specified. Other points have associated scores. Given a fixed amount of time, the goal is to determine a path from start to end through a subset of locations in order to maximize the total path score. This problem has received a considerable amount of attention in the last ten years. The traveling salesman problem is a variant of the orienteering problem. This paper applies a modified, continuous Hopfield neural network to attack this NP-hard optimization problem. In it, we design an effective energy function and learning algorithm. Unlike some applications of neural networks to optimization problems, this approach is shown to perform quite well.

A robustness approach to international sourcing

Abstract: An important advantage of the use of international sourcing networks (i.e. selection of suppliers in various countries to support the demands of the firm's international factory network) is the resulting hedging power against real exchange rate changes in the international environment. Due to the uncertainty of future real exchange rate changes, the international manager wants to develop a sourcing network that is relatively insensitive (i.e. robust) to the potential changes of the macroeconomic parameters over a planning horizon. In our paper, we formally develop arobust approach to international sourcing. This approach develops the international supplier network in a way that adequately hedges the firm's performance against the worst contingency in terms of realizable real exchange rate shocks over a planning horizon. We present an algorithm to obtain theN best robust solutions (i.e. sourcing networks) to the international sourcing problem. Some computational results on the effectiveness of the approach are provided. We also demonstrate how the approach can be used to evaluate various sourcing strategies.

A computer assistant for vehicle dispatching with learning capabilities

Abstract: In this paper, we describe an expert consulting system for a dispatcher working in a courier service company. The system integrates interactive-graphic features and a learning module to support the dispatcher in his(her) task, and to suggest appropriate decisions when new requests come in. An experiment with a professional dispatcher is also reported.

A two-phase algorithm for the partial accessibility constrained vehicle routing problem

Abstract: In the partial accessibility constrained vehicle routing problem, a route can be covered by two types of vehicles, i.e. truck or truck + trailer. Some customers are accessible by both vehicle types, whereas others solely by trucks. After introducing an integer programming formulation for the problem, we describe a two-phase heuristic method which extends a classical vehicle routing algorithm. Since it is necessary to solve a combinatorial problem that has some similarities with the generalized assignment problem, we propose an enumerative procedure in which bounds are obtained from a Lagrangian relaxation. The routine provides very encouraging results on a set of test problems.

Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems

Abstract: Several exponential bounds are derived by means of the theory of large deviations for the convergence of approximate solutions of stochastic optimization problems. The basic results show that the solutions obtained by replacing the original distribution by an empirical distribution provides an effective tool for solving stochastic programming problems.

Sequencing inputs to multi-commodity pipelines

Abstract: This paper examines the problem of sequencing the input of commodities, e.g. petroleum products, to a pipeline so that a surrogate for pumping and maintenance costs is minimized. This problem is complicated by the need to impose a discrete framework which handles the sequencing choices on a continuous flow problem. By focusing on the discrete aspects of the problem, the proposed model allows decomposition of the sequencing problem into subproblems which can be easily priced out in a branch-and-bound algorithm. Computational results on data generated to mimic a large U.S. petroleum pipeline are presented. These results show that the branch-and-bound algorithm only explores a small region of the solution space within a reasonable amount of time, less than 2.5 minutes to optimally sequence deliveries to twenty-four destinations.

Lot streaming in the two-machine flow shop with setup times

Abstract: The lot streaming model can sometimes be analyzed as a variation of the basic flow shop model. In this paper, we consider the lot streaming model with setup times, transfer lots of size one, and makespan objective. We show how to harness existing theory for time lags and setup times in the two-machine flow shop to analyze the lot streaming case. Extensions to more than two machines are also discussed.

Discrimination Decisions for 100,000-Dimensional Spaces

Abstract: Discrimination decisions arise in many natural language processing tasks. Three classical tasks are discriminating texts by their authors (author identification), discriminating documents by their relevance to some query (information retrieval), and discriminating multi-meaning words by their meanings (sense discrimination). Many other discrimination tasks arise regularly, such as determining whether a particular proper noun represents a person or a place, or whether a given word from some teletype text would be capitalized if both cases had been used.

A simulated annealing approach to the nesting problem in the textile manufacturing industry

Abstract: The nesting problem in the textile industry is the problem of placing a set of irregularly shaped pieces (calledstencils) on a rectangularsurface, such that no stencils overlap and that thetrim loss produced when cutting out the stencils is minimized. Certain constraints may put restrictions on the positions and orientation of some stencils in the layout but, in general, the problem is unconstrained. In this paper, an algorithmic approach using simulated annealing is presented covering a wide variety of constraints which may occur in the industrial manufacturing process. The algorithm has high performance, is quite simple to use, is extensible with respect to the set of constraints to be met, and is easy to implement.

On the convex hull of the simple integer recourse objective function

Abstract: We consider the objective function of a simple integer recourse problem with fixed technology matrix. Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program. We present an algorithm to compute the convex hull of the expected value function in case of discrete right-hand side random variables. Allowing for restrictions on the first stage decision variables, this result is then extended to the convex hull of the objective function.

Determination of the number and locations of time points in transit schedule design — Case of a single run

Abstract: An analytical model for the determination of the number and locations of time points as well as the amount of slack times in transit schedule design is developed. The model considers a bus route with a special passenger demand pattern in which all boarding passengers coordinate their arrivals at each stop in such a way that they never miss their intended bus, and therefore designing the schedule separately a single run at a time, becomes possible. The model employs the dynamic programming method to deal with the trade-offs among various cost components associated with the schedule quantitatively, and yet is flexible enough to incorporate the existing rules of thumb as well as transit operators' policies. Numerical examples that illustrate the applications of the model are given. The model, although not quite applicable to bus routes with general passenger demand patterns, is useful in the analysis of the contributing factors to the design of an economical, reliable, and operational transit schedule, and is likely to be adaptable for more realistic cases.

Censored regression analysis of multiclass passenger demand data subject to joint capacity constraints

Abstract: In most passenger transportation systems, demand for seats is not recorded after all spaces for a particular trip have been sold out or after a booking limit has been reached. Thus historical booking data is comprised of ticketsales notdemand — a condition known as censorship of the data. Data censorship is particularly complex when there are multiple classes of demand since the demand in one class can influence the degree of censorship in another. This paper examines the problem of simultaneously estimating passenger demand models for two or more correlated classes of demand that are subject to a common capacity constraint. It is shown that theEM method of Dempster et al. [5] can be adapted to provide maximum likelihood estimates of the parameters of the demand model under these circumstances. The problem of modelling demand for airline flights is discussed as a typical example of this estimation problem. Numerical examples show that, with reasonable sample sizes, it is possible to obtain good estimates even when 75% or more of the data have been censored.

Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors

Abstract: In the classical scheduling theory, it is widely assumed that a task can be processed by only one processor at a time. With the rapid development of technology, this assumption is no longer valid. In this work we present a problem of scheduling tasks, each of which requires for its processing a set of processors simultaneously and which can be executed on several alternative sets of processors. Scheduling algorithms based on dynamic and linear programming are presented that construct minimum length non-preemptive and preemptive schedules, respectively. Results of computational experiments are also reported.

The nesting problem in the leather manufacturing industry

Abstract: The part-nesting problem is the problem of arranging a set of plane irregularly shapedparts on a plane irregularly shapedsurface, such that no parts overlap and as much of the surface is covered as possible. This problem occurs, e.g., in the textile and clothing industry, and one of the most challenging applications appears in the manufacturing of leather, e.g., in the furniture, car, clothing, and shoe industry. This application is characterized by a high degree of inhomogeneity of the surface as well as the parts and by severe restrictions on run time. We present an algorithmic method for computer-aided nesting in this context. The algorithm is characterized by selective data reduction, sequential part placement, a topological part fitting process, and a carefully tuned evaluation function for partial placements. Experiments show that the method is competitive with human nesters, for relatively nicely behaved part sets and surfaces.

Probabilist, possibilist and belief objects for knowledge analysis

Abstract: The main aim of the symbolic approach in data analysis is to extend problems, methods and algorithms used on classical data to more complex data called “symbolic objects” which are well adapted to representing knowledge and which are “generic” unlike usual observations which characterize “individual things”. We introduce several kinds of symbolic objects: Boolean, possibilist, probabilist and belief. We briefly present some of their qualities and properties; three theorems show how Probability, Possibility and Evidence theories may be extended on these objects. Finally, four kinds of data analysis problems including the symbolic extension are illustrated by several algorithms which induce knowledge from classical data or from a set of symbolic objects.

Histograms in symbolic data analysis

Abstract: We propose an extension of the notion of the histogram used for variables to describe a knowledge base where the knowledge is represented by a special kind of symbolic objects. Boolana assertion objects.