# Dennis L. BrickerUniversity of Iowa | UI · Department of Industrial and Systems Engineering

Dennis L. Bricker

Ph.D. Industrial Engg, Northwestern U.

## About

60

Publications

6,784

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821

Citations

Introduction

**Skills and Expertise**

Additional affiliations

August 1974 - July 2004

## Publications

Publications (60)

This chapter presents a new mathematical formulation, which is based on multicommodity flow, for a classical capacitated minimum spanning tree problem. It also demonstrates the performance of Van Roy’s cross decomposition algorithm for solving the capacitated minimum spanning tree can be significantly improved by incorporating an edge exchange heur...

We examine computational solutions to all of the geometric programming problems published in a recent paper in the Journal of Optimization Theory and Applications. We employed three implementations of published algorithms interchangeably to obtain " perfect duality " for all of these problems. Perfect duality is taken to mean that a computed soluti...

This paper presents an optimization model and its application to a classical vehicle routing problem. The proposed model is exploited effectively by the hybrid Benders/genetic algorithm which is based on the solution framework of Benders’ decomposition algorithm, together with the use of genetic algorithm to effectively reduce the computational dif...

This paper presents an optimization model and its application to a generation expansion planning problem. The proposed model has a generalized network structure and is exploited effectively by Benders' decomposition algorithm, where a master problem generates trial expansion plans and a set of subproblems compute production cost and system reliabil...

In-vehicle information systems (IVISs) can enhance or compromise driving safety. Such systems present an array of messages that range from collision warnings and navigation instructions to tire pressure and e-mail alerts. If these messages are not properly managed, the IVIS might fail to provide the driver with critical information, which could und...

In-vehicle information systems (IVISs) can enhance or compromise driving safety. Such systems present an array of messages that range from collision warnings and navigation instructions to tire pressure and e-mail alerts. If these messages are not properly managed, the IVIS might fail to provide the driver with critical information, which could und...

Minimizing a nondecreasing separable concave cost function over a polyhedral set arises in capacity planning problems where economies of scale and fixed costs are significant, as well as production planning when a learning effect results in decreasing marginal costs. This is an NP-hard combinatorial problem in which the extreme points of the polyhe...

As computer communication networks become a prevalent part in our daily life, the importance of efficient design of those networks becomes more evident. One of the critical issues in the network design process is the topological design problem involved in establishing a centralized data communication network with best performance and low costs. It...

As computer communication networks becoming a prevalent part in our daily life, the importance of efficient design of those networks becomes more evident. One of the critical issues in the network design process is the topological design problem involved in establishing a centralized data communication network with best performance and low costs. I...

This paper presents two new algorithms for generating (n,2) de Bruijn sequences which possess certain properties. The sequences generated by the proposed algorithms may be useful for experimenters to systematically investigate intertrial repetition effects. Characteristics are compared with those of randomly sampled (n,2) de Bruijn sequences.

The degree-constrained minimal spanning tree (DCMST) problem with unreliable links and node outage costs consists of finding links in a network to connect a set of terminal nodes to a central node while minimizing the expected annual expenditure. The number of ports available on each terminal node limits the number of incident links (the degree con...

This paper presents two new algorithms for generating (n,2) de Bruijn sequences which possess certain properties. The sequences generated by the proposed algorithms may be useful for experimenters to systematically investigate intertrial repetition effects. Characteristics are compared with those of randomly sampled (n,2) de Bruijn sequences.

While improving performance and efficiency in educational production has been the concerned of educators, social scientists, and politicians for decades, questions such as how to improve and how to measure performance and efficiency still remain. Analysis of an educational production focusing on improving and controlling its performance and efficie...

An article entitled: “A Note on Modeling Multiple Choice Requirements for Simple Mixed Integer Programming Solvers” was published by W. A. Ogryczak [Comput. Oper. Res. 23, 199 (1996)]. In this article, Ogryczak proposed a reformulation technique called special ordered inequalities (SOI) to model the non-convex programming problems with special orde...

This paper revisits an efficient procedure for solving posynomial geometric programming (GP) problems, which was initially developed by Avriel et al. The procedure, which used the concept of condensation, was embedded within an algorithm for the more general (signomial) GP problem. It is shown here that a computationally equivalent dual-based algor...

This paper presents two new algorithms for generating (n,2) de Bruijn sequences which possess certain properties. The sequences generated by the proposed algorithms may be useful for experimenters to systematically investigate intertrial repetition effects. Characteristics are compared with those of randomly sampled (n,2) de Bruijn sequences. Keywo...

We present a new algorithm for the two-stage stochastic linear programming problem with complete recourse. This cross-decomposition algorithm employs the Benders (primal) subproblems as in the so-called L-shaped method but eliminates the Benders master problem for generating the next trial first-stage solution, relying instead upon Lagrangian (dual...

this paper, we shall briefly survey the existing theory of quasiconjugacy and surrogate duality as developed by Greenberg and Pierskalla ([2] and [3]) as it relates to nonconvex programming, interpreting it geometrically, and shall then add several extensions to this theory. QUASI-CONJUGATES A hyperplane in E n is a set, with parameters uE n , u0,...

Minimizing a nondecreasing separable concave cost function over a polyhedral set arises in capacity planning problems where economies of scale and fixed costs are significant, as well as production planning when a learning effect results in decreasing marginal costs. This is an NP-hard combinatorial problem in which the extreme points of the polyhe...

This paper combines the CCR output-oriented model of data envelopment analysis (DEA) and Factor Analysis (FA) to evaluate the performance of academic units of a university's graduate programs relative to their counterparts nationally. We propose DEA/FA as a means of increasing the utility of DEA for policy decisions when there is uncertainty about...

Stop-loss reinsurance is one type of reinsurance contract that has attracted recent attention. In the simplest form of this contract, a reinsurer agrees to pay all losses of the insurer in excess of an agreed limit. This paper concerns the computation of bounds on the stop--loss premium when the loss distribution is unknown, but information about p...

The Multiperiod Capacitated Minimal Spanning Tree (MCMST) Problem consists of scheduling the installation of links in a network so as to connect a set of terminal nodes S=[2,3,…,N] to a central node (node 1) with minimal present value of expenditures, where link capacities limit the number of terminal nodes sharing a link. Some of the terminal node...

Obstacle problems are typical problems in engineering and Physics. After finite approximation, the obstacle problem can be reduced to a QP problem with box constraints. In this paper, a new infeasible path-following algorithm, which follows a path on the complementarity surface, is proposed for solving obstacle problems. The sequence of iterates ge...

This paper studies the capacitated minimal spanning tree with unreliable links and node outage costs problem. Tree topologies appear in the design of centralized communication networks. In these topologies the number of nodes in a subtree rooted at the central node is limited to a predefined number due to polling, loading, and response time restric...

We develop and test a strong fractional cutting-plane algorithm for the classical non-preemptive precedence- and resource-constrained project scheduling problem. While our basic approach is to formulate the problem as a 0-1 IP and solve it by LP-based branch-and-bound, we enhance the algorithm considerably through (a) an improved IP reformulation,...

This paper presents genetic algorithms for solving various reliability design problems, which include series systems, series–parallel systems and complex (bridge) systems. The objective is to maximize the system reliability, while maintaining feasibility with respect to three nonlinear constraints, namely, cost and weight constraints, and constrain...

This paper describes a column generation algorithm for posynomial geometric programming that

This paper presents new Lagrangian Heuristics for the set covering problem (SCP). These heuristics are designed to be embedded within an algorithm (e.g., subgradient optimization) to search for optimal Lagrangian multipliers. A Lagrangian heuristic may adjust a (perhaps infeasible) solution of a Lagrangian relaxation and/or make use of information...

Stop-loss reinsurance contracts have attracted much attention recently. In its simplest form, the reinsurer agrees to pay all losses of the insurer in excess of an agreed-upon limit. This paper concerns the calculation of upper and lower bounds on the stop-loss premium, i.e. the expected payment by the reinsurer, when the claim distribution is unkn...

This paper describes procedures for generating trial sequences to balance out practice effects and intertrial repetition effects
in experiments consisting of repeated trials. In the sequences presented, each stimulus appears an equal number of times,
is preceded equally often by itself and by each other stimulus, and is distributed in a “balanced”...

This paper considers signomial geometric programming (GP) dual problems, a class of nonconvex nonlinear programming problems possessing multiple locally optimal solutions. The primary purpose of this paper is to investigate the quality of solutions found by use of a path-following algorithm. The path-following method may be applied to either the or...

This paper investigates the scheduling problems in which the job processing times do not remain constant but are increasing linear functions of their starting times. Two deteriorating scheduling models, Model 1 and Model 2, for multiple machines are considered, with the goal being to minimize the makespan. In this paper, we propose an efficient heu...

The problem of assigning cell probabilities to maximize a multinomial likelihood with order restrictions on the probabilies and/or restrictions on the local odds ratios is modeled as a posynomial geometric program (GP), a class of nonlinear optimization problems with a well-developed duality theory and collection of algorithms. (Local odds ratios p...

Machining economics problems usually contain highly non-linear equations which may present difficulties for some non-linear programming algorithms. An earlier article by Duffuaa et al. [1] compared the performance of several non-linear programming algorithms, including a geometric programming algorithm, applied to five machining economics problems....

While geometric programming is a useful computational approach for engineering design problems, it is often the case that some design variables specifying sizes must be rounded to readily available standard sizes, or variables specifying the number of component parts must be rounded to integers. To assist in deciding whether to round these variable...

We propose a new infeasible path-following algorithm for the convex linearly-constrained quadratic programming problem. This algorithm utilizes the monomial method rather than Newton's method for solving the KKT equations at each iteration. As a result, the sequence of iterates generated by this new algorithm is infeasible in the primal and dual li...

In this paper we review the theoretical background of two partitioning strategies, the Weighted-Mean-Method (WMM) and the Reformulation-and-Transformation-Technique (RTT), incorporated in the special ordered set branch-and-bound procedures leading to the global optimum in Multiple Choice Integer Programming (MCIP). Procedure flow is developed with...

Geometric programming problems in which several of the variables are restricted to assume either integer values or one of a set of standard sizes are known as Semi-Discrete Geometric Programming problems. In this paper several variations of Generalized Benders' Decomposition are described for these problems and some computational experience is pres...

A dual algorithm applied to a posynomial geometric programming problem generally terminates with a dual feasible solution which is only approximately optimal. The usual methods for recovering the primal solution then yields solutions with corresponding slight infeasibilities in the primal constraints. This paper demonstrates a linear programming pr...

Geometric programming problems in which several of the variables are restricted to assume either integer values or one of a set of standard sizes are known as Semi-Discrete Geometric Programming problems. In this paper several variations of Generalized Benders' Decomposition are described for these problems and some computational experience is pres...

The problem of sequencing inspection operations subject to errors in order to minimize the expected sum of inspection and penalty costs is formulated. Three basically different types of sequences (complete, fixed and variable) are defined. The paper presents methods for computing the optimal solution for each type, and a family of heuristics for th...

The dual of a geometric programming problem with negative degree of difficulty is often infeasible. It has been suggested that such problems be solved by finding a dual ‘approximate’ solution which minimizes a measure of the infeasibility, e.g., the summed squares of the infeasibilities in the dual constraints. We point out the shortcomings in that...

The authors present an informative application of Markov Chain Analysis to a multistage manufacturing problem. They also point out an error in the literature which has remained undetected for many years.Edward A. Silver, Department EditorAbsorption analysis is applied to a Markov chain model of a multistage manufacturing process with inspection and...

Unlike most other algorithms in optimization, such as the Simplex method in linear programming, dynamic programming is generally considered to be an approach to viewing an optimization problem rather than an algorithm which provides a step‐by‐step solution procedure converging to the optimum. This specificity of the dynamic programming technique of...

When a dual-based procedure is used to solve a geometric programming problem, the presence of inactive constraints at the primal optimum reduces the amount of information available about the relationship between the optimal primal and dual vectors. In certain situations one must resort to solving one or more subsidiary problems to recover solution...

This paper presents optimal and heuristic methods for finding the variable inspection policy that minimizes expected total cost per unit. These methods utilize a recursive function to compute the minimum remaining cost over all policies that begin with the given inspection sequence. The results of an exploratory experiment suggest that the best per...

The general solution approach leading to the global optimum for multiple choice integer programming uses the branch-and-bound procedure designed for special ordered sets. Incorporated in such a solution procedure, the partitioning strategy based on a weighted mean method is most often adopted to calculate the pseudo penalties on the partitioned sub...

Despite the importance and wide applicability of dynamic programming technique in optimization, the complexity and uniqueness of various dynamic programming models often make the comprehension of their solution procedures difficult, particularly for a novice. Although it can be argued that, unlike the Simplex method in linear programming, no genera...

This paper develops a wholly linear formulation of the posynomial geometric programming problem. It is shown that the primal geometric programming problem is equivalent to a semi-infinite linear program, and the dual problem is equivalent to a generalized linear program. Furthermore, the duality results that are available for the traditionally defi...

In recent years, nursing home care expenditures have approached one percent of GNP. Their growth is a major contributor to the escalating costs of health care. In this article, the authors analyze a sample of nursing homes from Wisconsin to determine the characteristics of the efficiently operated nursing homes. Data envelopment analysis is used to...

Several imperfect inspection operations are available in a discrete production environment. A decision regarding acceptance or rejection of the produced items needs to be made without exceeding specified limits for the probabilities of accepted units being non-conforming and rejected units conforming to quality specifications. A branch and bound ap...

We describe an algorithm for the geometric programming dual problem which uses an adaptation of the generalized LP algorithm, proposed by Dantzig et al. twenty-five years ago for the chemical equilibrium problem, and show the slack primal constraints pose no numerical difficulties for this algorithm as they do for previous dual-based algorithms.

We consider a class of problems of resource allocation under economies of scale, namely that of minimizing a lower semicontinuous, isotone, and explicitly quasiconcave cost function subject to linear constraints. An important class of algorithms for the linearly constrained minimization of nonconvex cost functions utilize the branch and bound appro...

While Lagrangian duality is quite well-known, surrogate duality remains relatively obscure, because computation of its solution is generally quite difficult. In this paper, we derive a surrogate dual for the simple (uncapacitated) plant location problem. Use of the lower bound provided by the surrogate dual value to fathom in a branch and bound alg...

Special Ordered Sets (SOSs) of variables of types 1 and 2 are used in mathematical programming for formulating both multiple choice problems and nonconvex separable programming problems, respectively. This paper suggests problem formulations which may be more efficiently solved by mixed-integer programming codes when special codes for handling SOSs...

A new infeasible path-following algorithm based on the monomial method, rather than Newton's method, is proposed to solve the convex quadratic programming problem. This algorithm generates a sequence of solutions which is exactly on the central trajectory. The different performances between the algorithms based on both Newton's and the monomial met...

## Projects

Project (1)