Showing papers on "Assignment problem published in 1982"

Comparative Models of the File Assignment Problem

Abstract: The optimal distribution of files among storage nodes is a major problem m computer system optimization. Differing design goals, varying system assumptions, and contrasting solution techniques yield a disparity of optimal file assignments. This paper views the differing file assignment models in a uniform manner Relative advantages and weaknesses of the various models become immediately apparent. This perspective exposes the further research which is necessary m order to provide a truly satisfactory solution to the file assignment problem

Introduction to Management Science

Abstract: 1. Management Science The Management Science Approach to Problem Solving Model Building: Break-Even Analysis Computer Solution Management Science Modeling Techniques Business Usage of Management Science Techniques Management Science Models in Descision Support Systems 2. Linear Programming: Model Formulation and Graphical Solution Model Formulation A Maximization Model Example Graphical Solutions of Linear Programming Methods A Minimization Model Example Irregular Types of Linear Programming Problems Characteristics of Linear Programming Problems 3. Linear Programming: Computer Solution and Sensitivity Analysis Computer Solution Sensitivity Analysis 4. Linear Programming: Modeling Examples A Product Mix Example A Diet Example An Investment Example A Marketing Example A Transportation Example A Blend Example A Multiperiod Scheduling Example A Data Envelopment Analysis Example 5. Integer Programming Integer Programming Models Integer Programming Graphical Solution Computer Solution of Integer Programming Problems with Excel and QM for Windows 0-1 Integer Programming Modeling Examples 6. Transportation, Transshipment, and Assignment Problems The Transportation Model Computer Solution of a Transportation Problem The Transshipment Model The Assignment Model Computer Solution of the Assignment Problem 7. Network Flow Models Network Components The Shortest Route Problem The Minimal Spanning Tree Problem The Maximal Flow Problem 8. Project Management The Elements of Project Management CPM/PERT Probabilistic Activity Times Microsoft Project Project Crashing and Time-Cost Trade-Off Formulating the CPM/PERT Network as a Linear Programming Model 9. Multicriteria Decision Making Goal Programming Graphical Interpretation of Goal Programming Computer Solution of Goal Programming Problems with QM for Windows and Excel The Analytical Hierarchy Process Scoring Model 10. Nonlinear Programming Nonlinear Profit Analysis Constrained Optimization Solution of Nonlinear Programming Problems with Excel A Nonlinear Programming Model with Multiple Constraints Nonlinear Model Examples 11. Probability and Statistics Types of Probability Fundamentals of Probability Statistical Independence and Dependence Expected Value The Normal Distribution 12. Decision Analysis Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility 13. Queuing Analysis Elements of Waiting Line Analysis The Single-Server Waiting Line System Undefined and Constant Service times Finite Queue Length Finite Calling Population The Multiple-Server Waiting Line Additional Types of Queuing Systems 14. Simulation The Monte Carlo Process Computer Simulation with Excel Spreadsheets Simulation of a Queuing System Continuous Probability Distributions Statistical Analysis of Simulation Results Crystal Ball Verification of the Simulation Model Areas of Simulation Application 15. Forecasting Forecasting Components Time Series Methods Forecast Accuracy Time Series Forecasting Using Excel Time Series Forecasting Using QM for Windows Regression Methods 16. Inventory Management Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models The Basic EOQ Model The EOQ Model with Noninstantaneous Receipt The EOQ Model with Shortages EOQ Analysis with QM for Windows EOQ Analysis with Excel and Excel QM Quantity Discounts Reorder Point Determining Safety Stocks Using Service Levels Order Quantity for a Periodic Inventory System Appendix A Normal Table Chi-Square Table Appendix B Setting Up and Editing a Spreadsheet Appendix C The Poisson and Exponential Distributions Solutions to Selected Odd-Numbered Problems Glossary Index Photo Credits CD-ROM Modules

An algorithm for the equilibrium assignment problem with random link times

Abstract: In this article we offer an equivalent minimization formulation for the traffic assignment problem when the link travel times are flow-dependent random variables. The paper shows the equivalency between the first-order conditions of this program and the stochastic equilibrium conditions as well as the uniqueness of the solution. The paper also describes an algorithmic approach to the solution of this program, including a proof of convergence. Finally, we conduct some limited numerical experiments on the rate of convergence of the algorithm and the merits of the stochastic equilibrium model, in general, as compared with deterministic approaches.

A Successive Shortest Path Algorithm for The Assignment Problem

Abstract: In this paper a new successive shortest path (SSP) algorithm for solving the assignment problem is introduced. A computer implementation of this algorithm has been developed and a discussion of the...

Exact pole assignment using direct or dynamic output feedback

Abstract: This note addresses the problem of the assignability of the eigenvalues of the matrix A + BPC by choice of the matrix P . This mathematical problem corresponds to pole assignment in the direct output feedback control problem, and by proper changes of variables it also represents the pole assignment problem with dynamic feedback controllers. The key to our solution is the introduction of the new concept of local complete assignability which in loose terms is the arbitrary perturbability, of the eigenvalues of A + BPC by perturbations of P . If n x is the order of the system, we show that if A + BP_{0}C has distinct eigenvalues, a necessary and sufficient condition for local complete assignability at P 0 is that the matrices C[A + BP_{0}C]^{i-1}B be linearly independent, for 1 \leq i \leq n_{x} . In special cases, this condition reduces to known criteria for controllability and observability. Although these latter properties are necessary conditions for assignability, we also address the question of the assignability of uncontrollable or unobservable systems both by direct output feedback and dynamic compensation. The main result of this note yields an algorithm that assigns the closed-loop poles to arbitrarily chosen values in the direct and in the dynamic output feedback control problems.

On Dynamic Traffic Assignment

Abstract: Traffic assignment is one of the most important steps in the mathematical theory of traffic flow and there is a lot of literature dealing with this subject (confer to Potts and Oliver (1972) or Florian (1976)). But almost all the papers have in common that only a static version of the assignment or the traffic equilibrium problem is treated. This means that there is always the assumption in the models that there are no changes in the structure of the network during the trip from an origin to a destination. Alternatively one can also say that there is no time dependancy for the trips considered. Relatively little attention has been paid to the solution of the assignment problem in a dynamic framework, which means that demand structure and trip costs are varying over time. There are basically two models which consider dynamic assignment problems. One is by Yagar (1976) which gives heuristic principles for a dynamic assignment by an “emulation technique”. This technique uses a dynamic demand structure, but there is no explicit dynamic flow model. The other model is by Merchant and Nemhauser (1978 a,b), who formulated a dynamic flow model and also presented an algorithm which obtains system- optimized flows. Perhaps one should mention in this context also the work of Maher and Akcelik (1977) about route control. Although there is no dynamic assignment model presented there the authors try to connect traffic assignment and dynamic flow structure by a combination of incremental loading and simulation in order to evaluate different strategies of traffic control. This is of interest because in urban networks traffic control strongly influences the flow dynamic and therefore also route choice as it is shown in an example given by Smith (1979).

Junction interactions and monotonicity in traffic assignment

Abstract: We consider the traffic equilibrium problem when the travel demand is inelastic and stationary in time. Junction interactions, which abound in urban road networks, are permitted. We prove that the set of equilibria (solutions to the assignment problem) is convex when certain monotonicity and continuity conditions are statisfied at each junction.

Simple Heuristics for the School Assignment Problem

Abstract: Several simple heuristic procedures are described for solving the pupils-school assignment problem. These methods have been applied to a real-life problem in Switzerland.

A generalized bottleneck assignment problem

Abstract: A solution procedure is presented for a generalization of the standard bottleneck assignment problem in which a secondary criterion is automatically provided. A partitioning problem is modeled by this bottleneck problem to provide an example of its application.

A parallel matching algorithm for convex bipartite graphs.

Abstract: Abstract An efficient parallel algorithm to obtain maximum matchings in convex bipartite graphs is developed. This algorithm can be used to obtain efficient parallel algorithms for several scheduling problems. Some examples are: job scheduling with release times and deadlines; scheduling to minimize maximum cost; and preemptive scheduling to minimize maximum completion time.

Application of graph theory to the solution of a nonlinear optimal assignment problem

Abstract: This paper poses an assignment problem with a nonlinear objective function. It is formulated as an integer programming problem and a graph model is used to determine its exact solution. Application of the problem in long-range homing in telephone networks is also discussed.

Some multicommodity transport problems reducible to a single-commodity problem☆

Abstract: THE CONNECTION between a multicommodity transport problem on a flow graph and the problem with arcs of unlimited handling capacity is studied. A method is outlined for seeking the integer-valued optimal plan of the initial problem. For the problem on a bipartite graph, sufficient conditions are established for an equivalent single-commodity transport problem to exist. An algorithm is given for reducing problems of a certain class to a single-commodity problem of small dimensionality.

An Extended Microcomputer-Based Network Optimization Package.

Abstract: : The capacitated generalized transshipment problem is the most general and universally applicable member of the class of network optimization models. This model subsumes, as specializations, the capacitated and uncapacitated transportation problem as well as the pure network specializations of these models, which include the personnel assignment problem, the maximum flow, and shortest path formulations. The generalized network problem, in turn, can be viewed as a specialization of a linear programming problem having at most two non-zero entries in each column of the constraint matrix. A detailed description is given of the implementation of an efficient algorithm and its supporting data structures, used to solve large-scale, minimum-cost generalized transshipment problems on an Apple II (64K) microcomputer. A suite of advanced techniques for managing minimum-cost network flow models and inherent data elements will also be discussed. (Author)

Geographic Decomposition of the Shortest Path Problem, with an Application to the Traffic Assignment Problem

Abstract: An algorithm, which can be applied to loosely connected networks, is given for geographically decomposing the shortest path problem. The algorithm is applicable to the traffic assignment problem when it is solved as a series of shortest path problems by the Frank-Wolfe algorithm. Numerical results for a large 1287 node, 3752 arc traffic assignment problem for Washington, D.C., indicate that using geographical decomposition can reduce computer memory storage requirements or program run time.

Braess' paradox in a transportation two-terminal network

Abstract: The sensitivity of a OD travel cost to changes in a flow through a new branch in the user optimizing assignment problem for a single commodity two-terminal transportation network is studied. The assignment problem and its dual are formulated as convex programming problems. Using these formulations, an intuitive characterization is derived for such paradoxical phenomenon that the creation of a new branch has the effect of increasing the OD travel cost.

Two False Endings to the Modified Assignment Problem: A Solution

Abstract: Dr. Bharath brings to light a point raised also in personal correspondence by Dieter Klein, Worcester Polytechnic Institute in the fall of 1980 about Stern's modification of the assignment algorithm to solve the transportation problem which resurfaces in Hesse/Woolsey. The condition described is indeed necessary but not sufficient and is analogous to a regular assignment problem having zeros in every row and column but still without a zero-cost allocation. In the modified method, when this happens, lines must be drawn again such that the total of the supplies and demands lined out are strictly less than the total supply (or demand).

Time minimizing flows in directed networks

Abstract: An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time-minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time-minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.

Computational Testing of Assignment Algorithms

Abstract: The methods used in an empirical evaluation of several recently proposed assignment algorithms are discussed. Brief descriptions of the algorithms tested are also included.