Showing papers on "Goal programming published in 1991"

Operations Research: Applications and Algorithms

Abstract: 1. INTRODUCTION TO MODEL BUILDING. An Introduction to Modeling. The Seven-Step Model-Building Process. Examples. 2. BASIC LINEAR ALGEBRA. Matrices and Vectors. Matrices and Systems of Linear Equations. The Gauss-Jordan Method for Solving Systems of Linear Equations. Linear Independence and Linear Dependence. The Inverse of a Matrix. Determinants. 3. INTRODUCTION TO LINEAR PROGRAMMING. What is a Linear Programming Problem? The Graphical Solution of Two-Variable Linear Programming Problems. Special Cases. A Diet Problem. A Work-Scheduling Problem. A Capital Budgeting Problem. Short-term Financial Planning. Blending Problems. Production Process Models. Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model. Multiperiod Financial Models. Multiperiod Work Scheduling. 4. THE SIMPLEX ALGORITHM AND GOAL PROGRAMMING. How to Convert an LP to Standard Form. Preview of the Simplex Algorithm. The Simplex Algorithm. Using the Simplex Algorithm to Solve Minimization Problems. Alternative Optimal Solutions. Unbounded LPs. The LINDO Computer Package. Matrix Generators, LINGO, and Scaling of LPs. Degeneracy and the Convergence of the Simplex Algorithm. The Big M Method. The Two-Phase Simplex Method. Unrestricted-in-Sign Variables. Karmarkar"s Method for Solving LPs. Multiattribute Decision-Making in the Absence of Uncertainty: Goal Programming. Solving LPs with Spreadsheets. 5. SENSITIVITY ANALYSIS: AN APPLIED APPROACH. A Graphical Introduction to Sensitivity Analysis. The Computer and Sensitivity Analysis. Managerial Use of Shadow Prices. What Happens to the Optimal z-value if the Current Basis is No Longer Optimal? 6. SENSITIVITY ANALYSIS AND DUALITY. A Graphical Introduction to Sensitivity Analysis. Some Important Formulas. Sensitivity Analysis. Sensitivity Analysis When More Than One Parameter is Changed: The 100% Rule. Finding the Dual of an LP. Economic Interpretation of the Dual Problem. The Dual Theorem and Its Consequences. Shadow Prices. Duality and Sensitivity Analysis. 7. TRANSPORTATION, ASSIGNMENT, AND TRANSSHIPMENT PROBLEMS. Formulating Transportation Problems. Finding Basic Feasible Solutions for Transportation Problems. The Transportation Simplex Method. Sensitivity Analysis for Transportation Problems. Assignment Problems. Transshipment Problems. 8. NETWORK MODELS. Basic Definitions. Shortest Path Problems. Maximum Flow Problems. CPM and PERT. Minimum Cost Network Flow Problems. Minimum Spanning Tree Problems. The Network Simplex Method. 9. INTEGER PROGRAMMING. Introduction to Integer Programming. Formulation Integer Programming Problems. The Branch-and-Bound Method for Solving Pure Integer Programming Problems. The Branch-and-Bound Method for Solving Mixed Integer Programming Problems. Solving Knapsack Problems by the Branch-and-Bound Method. Solving Combinatorial Optimization Problems by the Branch-and-Bound Method. Implicit Enumeration. The Cutting Plane Algorithm. 10. ADVANCED TOPICS IN LINEAR PROGRAMMING. The Revised Simplex Algorithm. The Product Form of the Inverse. Using Column Generation to Solve Large-Scale LPs. The Dantzig-Wolfe Decomposition Algorithm. The Simplex Methods for Upper-Bounded Variables. Karmarkar"s Method for Solving LPs. 11. NONLINEAR PROGRAMMING. Review of Differential Calculus. Introductory Concepts. Convex and Concave Functions. Solving NLPs with One Variable. Golden Section Search. Unconstrained Maximization and Minimization with Several Variables. The Method of Steepest Ascent. Lagrange Multiples. The Kuhn-Tucker Conditions. Quadratic Programming. Separable Programming. The Method of Feasible Directions. Pareto Optimality and Tradeoff Curves. 12. REVIEW OF CALCULUS AND PROBABILITY. Review of Integral Calculus. Differentiation of Integrals. Basic Rules of Probability. Bayes" Rule. Random Variables. Mean Variance and Covariance. The Normal Distribution. Z-Transforms. Review Problems. 13. DECISION MAKING UNDER UNCERTAINTY. Decision Criteria. Utility Theory. Flaws in Expected Utility Maximization: Prospect Theory and Framing Effects. Decision Trees. Bayes" Rule and Decision Trees. Decision Making with Multiple Objectives. The Analytic Hierarchy Process. Review Problems. 14. GAME THEORY. Two-Person Zero-Sum and Constant-Sum Games: Saddle Points. Two-Person Zero-Sum Games: Randomized Strategies, Domination, and Graphical Solution. Linear Programming and Zero-Sum Games. Two-Person Nonconstant-Sum Games. Introduction to n-Person Game Theory. The Core of an n-Person Game. The Shapley Value. 15. DETERMINISTIC EOQ INVENTORY MODELS. Introduction to Basic Inventory Models. The Basic Economic Order Quantity Model. Computing the Optimal Order Quantity When Quantity Discounts Are Allowed. The Continuous Rate EOQ Model. The EOQ Model with Back Orders Allowed. Multiple Product Economic Order Quantity Models. Review Problems. 16. PROBABILISTIC INVENTORY MODELS. Single Period Decision Models. The Concept of Marginal Analysis. The News Vendor Problem: Discrete Demand. The News Vendor Problem: Continuous Demand. Other One-Period Models. The EOQ with Uncertain Demand: the (r, q) and (s,S models). The EOQ with Uncertain Demand: the Service Level Approach to Determining Safety Stock Level. Periodic Review Policy. The ABC Inventory Classification System. Exchange Curves. Review Problems. 17. MARKOV CHAINS. What is a Stochastic Process. What is a Markov Chain? N-Step Transition Probabilities. Classification of States in a Markov Chain. Steady-State Probabilities and Mean First Passage Times. Absorbing Chains. Work-Force Planning Models. 18.DETERMINISTIC DYNAMIC PROGRAMMING. Two Puzzles. A Network Problem. An Inventory Problem. Resource Allocation Problems. Equipment Replacement Problems. Formulating Dynamic Programming Recursions. The Wagner-Whitin Algorithm and the Silver-Meal Heuristic. Forward Recursions. Using Spreadsheets to Solve Dynamic Programming Problems. Review Problems. 19. PROBABILISTIC DYNAMIC PROGRAMMING. When Current Stage Costs are Uncertain but the Next Period"s State is Certain. A Probabilistic Inventory Model. How to Maximize the Probability of a Favorable Event Occurring. Further Examples of Probabilistic Dynamic Programming Formulations. Markov Decision Processes. Review Problems. 20. QUEUING THEORY. Some Queuing Terminology. Modeling Arrival and Service Processes. Birth-Death Processes. M/M/1/GD/o/o Queuing System and the Queuing Formula L=o W, The M/M/1/GD/o Queuing System. The M/M/S/ GD/o/o Queuing System. The M/G/ o/GD/oo and GI/G/o/GD/o/oModels. The M/ G/1/GD/o/o Queuing System. Finite Source Models: The Machine Repair Model. Exponential Queues in Series and Opening Queuing Networks. How to Tell whether Inter-arrival Times and Service Times Are Exponential. The M/G/S/GD/S/o System (Blocked Customers Cleared). Closed Queuing Networks. An Approximation for the G/G/M Queuing System. Priority Queuing Models. Transient Behavior of Queuing Systems. Review Problems. 21.SIMULATION. Basic Terminology. An Example of a Discrete Event Simulation. Random Numbers and Monte Carlo Simulation. An Example of Monte Carlo Simulation. Simulations with Continuous Random Variables. An Example of a Stochastic Simulation. Statistical Analysis in Simulations. Simulation Languages. The Simulation Process. 22.SIMULATION WITH PROCESS MODEL. Simulating an M/M/1 Queuing System. Simulating an M/M/2 System. A Series System. Simulating Open Queuing Networks. Simulating Erlang Service Times. What Else Can Process Models Do? 23. SPREADSHEET SIMULATION WITH @RISK. Introduction to @RISK: The Newsperson Problem. Modeling Cash Flows From A New Product. Bidding Models. Reliability and Warranty Modeling. Risk General Function. Risk Cumulative Function. Risktrigen Function. Creating a Distribution Based on a Point Forecast. Forecasting Income of a Major Corporation. Using Data to Obtain Inputs For New Product Simulations. Playing Craps with @RISK. Project Management. Simulating the NBA Finals. 24. FORECASTING. Moving Average Forecasting Methods. Simple Exponential Smoothing. Holt"s Method: Exponential Smoothing with Trend. Winter"s Method: Exponential Smoothing with Seasonality. Ad Hoc Forecasting, Simple Linear Regression. Fitting Non-Linear Relationships. Multiple Regression. Answers to Selected Problems. Index.

Portfolio selection with skewness: A multiple-objective approach

Abstract: In the presence of skewness, the portfolio selection entails considering competing and conflicting objectives, such as maximizing both its expected returns and skewness, and minimizing its risk for decreasing absolute risk-aversion investors. Since it is unlikely that a portfolio can solve the multiple-objectives problem simultaneously, a portfolio selection must depend on the investor's preference among objectives. This article shows that investor preference can be incorporated into a polynomial goal programming problem from which a portfolio selection with skewness is determined. An inefficient mean-variance portfolio may be optimal in the mean-variance-skewness content. The features of applying polynomial goal programming in portfolio selection are 1) the existence of an optimal solution, 2) the flexibility of the incorporation of investor preference, and 3) the relative simplicity of computational requirements.

Linear Bi-level Programming Problems — A Review

Abstract: Multi-level programming is characterized as mathematical programming to solve decentralized planning problems. The decision variables are partitioned among ordered levels. A decision-maker at one level of the hierarchy may have his own objective function and decision space, but may be influenced by other levels.

Tour Scheduling and Task Assignment of a Heterogeneous Work Force: A Heuristic Approach

Abstract: The dual problem of work tour scheduling and task assignment involving workers who differ in their times of availability and task qualifications is examined in this paper. The problem is presented in the context of a fast food restaurant, but applies equally well to a diverse set of service operations. Developing a week-long labor schedule is a nontrivial problem, in terms of complexity and importance, which a manager spends as much as a full workday solving. The primary scheduling objective (the manager's concern) is the minimization of overstaffing in the face of significant hourly and daily fluctuations in minimum staffing requirements. The secondary objective (the workers’ concern) is the minimization of the sum of the squared differences between the number of work hours scheduled and the number targeted for each employee. Contributing to scheduling complexity are constraints on the structure of work tours, including minimum and maximum shift lengths and a maximum number of workdays. A goal programming formulation of a representative problem is shown to be too large, for all practical purposes, to be solved optimally. Existing heuristic procedures related to this research possess inherent limitations which render them inadequate for our purposes. Subsequently, we propose and demonstrate a computerized heuristic procedure capable of producing a labor schedule requiring at most minor refinement by a manager.

On the Origin and Persistence of Misconceptions in Goal Programming

Abstract: During the last two decades there has been wide application of goal programming. Despite this popularity, goal programming theories have been extensively criticized. Although some criticism may originate from the valid assessment of goal programming, large portions of the criticism seem to stem from confusions and misconceptions in underlying goal programming theories. In this paper, the origin of critical views on goal programming is uncovered and synthesized, to set the stage for a balanced discussion of the pros and cons of goal programming. Through such a discussion, the critical points are validated and, if necessary, some possible remedies for the weakness of goal programming are sought. Hence, the major intent of this paper is to provide a variety of future research ideas which, it is hoped, lend themselves to the further development and application of goal programming rather than provoking any controversies surrounding goal programming.

Multicriteria optimization of simulation models

Abstract: The authors suggest a framework for the multicriteria optimization of simulation models by first discussing the unique difficulties of this problem area along with important problem characteristics, and then discussing the way that these problem characteristics would affect the choice of a particular technique. The problem of manufacturing system optimization is addressed. Various techniques, along with their advantages and disadvantages, are discussed and categorized according to the timing of the articulation of the required preference (tradeoff) information with respect to the optimization. >

Estimation of Stochastic Frontier Cost Function Using Data Envelopment Analysis: an Application to the AT&T Divestiture

Abstract: This study develops a new use of data envelopment analysis for estimating a stochastic frontier cost function that is assumed to have two different error components: a one-sided disturbance (representing technical and allocative inefficiencies) and a two-sided disturbance (representing an observational error). The two error components are handled by data envelopment analysis in combination with goal programming/constrained regression. The approach proposed in this study can avoid several statistical assumptions used in conventional methods for estimating a stochastic frontier function. As an important application, this study uses the estimation technique to obtain an AT&T stochastic frontier cost function. As a result, this study measures technical and allocative efficiencies of AT&T production process and review its natural monopoly issue. The estimated stochastic frontier cost function is also compared with the other cost function models used for previous studies concerning the divestiture of the telephone industry.

A disaggregation model of a flexible nurse scheduling support system.

Abstract: A nurse scheduling support system is developed in which the demand profile and nurses' preferences are input to an expert-like capability designed to formulate linear and/or goal programming representations of the problem. Solutions of the alternative optimization models of this decision support system are then evaluated. An assignment model for disaggregating the optimum work patterns of individual nurses based on their desires and compatibilities is discussed in detail. A brief overview of one of the scheduling models and its extension is also presented along with discussion of the various uses of the assignment model.

Multiobjective linear programming: another DSS

Abstract: The paper presents an interactive menu driven decision support system for Multiobjective Linear Programming (MOLP) problems. The main contribution of the system lies in the ease of interaction between the decision maker (DM) and the system which is achieved, in contrast with other systems, by DM directed construction of a weak order on system variables and objectives. In the interactive stage the DM points out which objective functions are to be improved relative to the candidate solutions presented. No tradeoff evaluations are required from the DM. In addition, priorities/preferences of variables and objectives can be modified throughout the solution process.

A goal programming network for mixed integer linear programming: a case study for the job-shop scheduling problem

Abstract: Job-shop scheduling is an np-complete optimization problem subject to precedence and resource constraints. Recently, Foo and Takefuji have introduced a network-based solution procedure for solving job-shop problems formulated as mixed integer linear programming problems. To obtain the solution, the Tank and Hopfield linear programming network was repeatedly used. However, since such a network frequently produces constraint-violating solutions, the reliability of Foo and Takefuji’s approach is doubtful. In this article, it is shown that reliability of the network approach can be greatly improved, by guaranteeing constraint-satisfying solutions, if the original job-shop problem is reformulated as a goal programming problem, before it is mapped onto a goal programming network.

A goal programming network for linear programming

Abstract: Tank and Hopfield have shown that networks of analog neurons can be used to solve linear programming (LP) problems. We have re-examined their approach and found that their network model frequently computes solutions that are only suboptimal or that violate the LP problem's constraints. As their approach has proven unreliable, we have developed a new network model: the goal programming network. To this end, a network model was first developed for goal programming problems, a particular type of LP problems. From the manner the network operates on such problems, it was concluded that overconstrainedness, which is possibly present in an LP formulation, should be removed, and we have provided a simple procedure to accomplish this.

Structure/control design synthesis of active flutter suppression system by goal programming

Abstract: The simultaneous design of the structure and control for a typical wing section with a trailing control surface is considered. Since the original structure usually has inadequate dynamic characteristics for active control, design parameters must be optimally modified. Full-state feedback control gains are designed using the linear quadratic Gaussian regulator theory at the design airspeed; this is the only control design parameter. A typical wing section with a trailing control surface is examined as a design example, and then both structure and control design parameters are optimized in accordance with the following prioritized design requirements: 1) the flutter speed of an initial open-loop system is maintained, 2) the stability characteristics of a closed-loop system are obtained over a wide range of flight speed, 3) the control surface deflection angle is restrained, and 4) the degree of structural design changes is minimized. The sequential goal programming method is successfully applied to optimize these multidisciplinary design requirements.

Optimization of multipurpose reservoir system operation

Abstract: The goal programming approach for multipurpose reservoir operation has been proposed and applied to the Bhadra reservoir system, having irrigation and hydropower production as dual purposes, in India. The objective of the model is to satisfy sequentially a series of operating criteria. Two goal programming models, one with the objective function as minimizing the deviations from storage targets and the other with the objective function as minimizing the deviations from release targets, have been formulated and applied to the reservoir system under study. The results proved that the model with release targets is preferred over the model with storage targets for determining operational policies for multipurpose reservoir system.

A multiple objective selection methodology for strategic industry selection analysis

Abstract: An application of mathematical programming in the industry selection step of strategic acquisition analysis is presented. Specifically, the management information uses of multiple-objective programming in the strategic planning of organization acquisitions are described. The modeling approach has application to all forms of organization-acquisition analysis (i.e. acquisitions, mergers, joint ventures, etc.). An illustrative application of the modeling approach is presented using data from a regional conglomerate's actual acquisition study. The benefits of the use of the multiple-objective modeling approach include improvements in the efficacy and specificity of information on which acquisition decision making is based, and types of information that are not methodology. >

All-unit discounts, multi-item inventory model with stochastic demand, service level constraints and finite horizon

Abstract: Inventory systems are typically described as deterministic or stochastic, single, or multi-item, etc. The model reported in this research combines several such dichotomies, into a single model. It has the objective of deciding the optimal order quantities for a multi-item inventory system over a finite horizon. The demand is probabilistic with service level constraints, and there is an all-unit price break, for orders that exceed a given size. The solution approach uses a goal programming technique, in a mixed integer linear programming formulation. The model is analysed for sensitivity to deviations from the optimal policy, and inaccurate parameter estimation, including the demand distribution. In addition the optimal multi-item policy is compared to an optimal solution derived for each part type separately. Simulation experiments reveal that the model is not sensitive to inaccurate parameters nor to exact estimation of the demand distribution, thus aiding in reducing the control cost. It is als...

Goal programming for multiple land use planning at Mineral King, California.

Abstract: A primary benefit of planning through computer modeling is identifying data limitations, which may assist decision-makers to prioritize additional research or modify existing inventory procedures. With goal programming, additional benefits can be the inclusion of subjective estimates or desires as decision criteria, portrayal of several alternative potential solutions and tradeoff relationships, and identification of severe conflicts between certain goals that have an overriding influence on solutions. In this study, goal programming was used for multiple land use planning on 16,000 acres in the southern Sierra Nevada of California. The mountainous terrain contained coniferous forests, brush-fields, and meadows interspersed with streams, lakes, and rocky barrens. Land uses evaluated were outdoor recreation, timber and livestock production, and deer population management in conjunction with three alternative proposals for development of a winter-sports facility. The goal model assessed production tradeoffs for the various land uses associated with changing managerial priorities and indicated an optimal development strategy. Goal programming proved to be an effective, flexible technique for multiple land use planning.

Adapting Multi-criteria Planning to the Nigerian Economy

Abstract: Techniques of development planning involve physical and financial aspects. Financial planning refers to the allocation of monetary resources; in Nigeria the previous development plans and budgets, which had been based on the incremental approach, contained various shortcomings, resulting in the deliberate inflation of estimated expenditure, and consequently it has been associated with retarded growth and conflicts between ministries. In addition, the approach does not adequately relate national objectives to their priorities. Conventional mathematical programming models are unable to allocate resources effectively in a conflicting environment. This paper proposes a goal programming model for allocating a country's scarce resources among competing sectors during a planned period. The goal programming model is shown to be adequate for allocating resources under the conflicting conditions of national planning. The model can help to determine all the priorities for the goals.

Optimization of short-term operation of a single multipurpose reservoir — a goal programming approach

Abstract: The complex real-time reservoir operation model consists of flow forecasting, reservoir operations planning, and multiobjective modules. In the present paper the original reservoir operations planning module based on a linear programming (LP) formulation is substituted with a goal programming (GP) formulation. The advantage of applying goal programming instead of linear programming lies in the smaller input data requirement, and simpler model formulation. The LP approach requires two-dimensional information while the GP approach needs only one-dimensional information. The impact of change of the operations planning routine on the results of the complex model is observed and commented on a case study. The application of GP instead of LP is found viable, in certain cases even advantageous, giving a better overall objective function value. Key words: reservoir operation, optimization.

Goal Programming: the RPMS Network Approach

Abstract: This paper presents an application of the Resource Planning and Management Systems (RPMS) network approach to the goal programming (GP) problem as an alternative to several other approaches used in the GP process. The RPMS approach to solving the GP problem is illustrated through an example. Sensitivity analysis is also discussed.

Three Shortcomings of Goal Programming and their Solutions

Abstract: Despite its advantages as a multi-criteria decision making model, goal programming has a few practical drawbacks that may present serious problems This note identifies three such problems and gives a solution for each

An Introductory Overview of Goal Programming (GP) and some Related Multiple Criteria Decision Making (MCDM) Approaches

Abstract: This chapter discusses goal programming (GP) and some related multiple criteria decision making (MCDM) approaches, such as multiobjective (MOP) and compromise programming. Sales, profits, liquidity, and risk are examples of attributes in the decision making process of a large corporation. Objectives represent the maximization or the minimization of the mathematical functions corresponding to the attributes under consideration. Thus, maximizing profits, minimizing costs are examples of objectives. GP is the oldest approach within the field of MCDM. The first step in the formulation of a GP model is the establishment of a set of attributes to be considered in the problem situation. MOP is a MCDM approach valid for the analysis of decisions in environments surrounded by multiple objectives subjected to a set of constraints. MOP divides the feasible set of solutions into two subsets: (1) the subset of Paretian efficient solutions and (2) the subset of inferior solutions.

On Multiple-Objective Design Optimization by Goal Methods

Abstract: In the design of various engineering systems and, in lparticular, the integrated/simultaneous design of large space structures and their vibration control systems, there are more than one objectives for which the design must be optimized. Since the usefullness of the method of weighted sum for solving non-convex multiple-objective optimization problems is severely limited, the designer normally needs to find other methods, such as various goal methods, for general applications. The current goal methods, i.e., least deviations from the goals, goal programming, global criterion, and goal attainment, are found to have a common drawback. The "optimal" solutions thereby obtained may not even meet the basic multiple-objective optimality requirement that they be Pareto optimal, i.e., inferior to no other solution. Therefore, inferior solutions may be mistaken as the optimal solutions of the original multiple-objective problem.