Zvi Drezner - Academia.edu (original) (raw)

Papers by Zvi Drezner

arXiv (Cornell University), Apr 6, 2020

In this paper we propose the planar obnoxious facilities p-median problem. In the p-median proble... more In this paper we propose the planar obnoxious facilities p-median problem. In the p-median problem the objective is to find p locations for facilities that minimize the weighted sum of distances between demand points and their closest facility. In the obnoxious version we add constraints that each facility must be located at least a certain distance from a partial set of demand points because they generate nuisance affecting these demand points. The resulting problem is extremely non-convex and traditional non-linear solvers such as SNOPT are not efficient. An efficient solution method based on Voronoi diagrams is proposed and tested. We also constructed the efficient frontiers of the test problems to assist the planers in making location decisions.

Journal of The Operations Research Society of Japan, 2007

We investigate the location of one or more facilities anywhere in an area in which several cornpe... more We investigate the location of one or more facilities anywhere in an area in which several cornpeting facilities already exist. The attractiveness of each facility is modeled by a utility function. Each customer selects the facility with the greatest utility function value. The objective is to find the locations fbr. one er more facilities which attract the maxirnum buying power. We generate a set of candidate locations and solve the single facility problem by evaluating the buying power attracted to the new facility at each candidate location. We then solve the location of multiple facilities by converting the problem to a maximum covering preblem. The solution procedure is illustrated on an example problem with 100 demand points and seven existing facilities. As a case study we find the best locations of new convenience stores in the city of Seto, Japan.

Infor, Aug 1, 2011

... Tammy Drezner and Zvi Drezner Steven G. Mihaylo College of Business and Economics, California... more ... Tammy Drezner and Zvi Drezner Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA 92834, e-mail ... Berman and Wang (2006) solved the minimax problem on the network when the weights are uni-formly distributed. ...

Ima Journal of Management Mathematics, Aug 19, 2021

The clustering problem has many applications in machine learning, operations research and statist... more The clustering problem has many applications in machine learning, operations research and statistics. We propose three algorithms to create starting solutions for improvement algorithms for the minimum sum of squares clustering problem. We test the algorithms on 72 instances that were investigated in the literature. We found five new best known solutions and matched the best known solution for 66 of the remaining 67 instances. Thus, we are able to demonstrate that good starting solutions combined with a simple local search get results comparable with, and sometimes even better than, more sophisticated algorithms used in the literature.

Optimization Letters, Apr 8, 2021

Iise Transactions, Dec 1, 1980

Abstract We introduce the following problem in this paper. There are n points on the plane that a... more Abstract We introduce the following problem in this paper. There are n points on the plane that are to be observed from some point on a circle of given radius that encloses all of the points. We wish to find the observation point that has the best possible view of the n points in the sense that if we draw lines of sight from the observation point to the given points, the smallest angle between the lines is maximized. Applications could include the planning of photographs or displays. This is a “maximin problem” in which the function to be maximized has many local optima. We present two methods for solving the problem, one more efficient in computer time, and the other in storage. We also present a simplified procedure for the case where the observation point is “infinitely” distant from the given points.

Iie Transactions, Jun 1, 1995

We extend recent works by Tang and Tang dealing with the quality cost of a process that is screen... more We extend recent works by Tang and Tang dealing with the quality cost of a process that is screened with the use of correlated variables because the principal quality characteristic is difficult or expensive to measure. Our model includes a very flexible and general set of loss functions that can be used to model both traditional and contemporary ‘losses’ for deviation from target values or product specifications. We also give an analysis of the expected value of perfect information and sample information obtained from the screening variables. This facilitates the evaluation of the advisability of using screening variables.

European Journal of Operational Research, Nov 1, 1999

In this paper we ®nd the set of feasible solution points to the Weber location problem with squar... more In this paper we ®nd the set of feasible solution points to the Weber location problem with squared Euclidean distances when the weights can be at any point in a given set of intervals. We prove that this set is a convex polygon. The result is then used to solve the minimax regret objective when individual scenarios can be any set of weights in a given set of intervals.

Ima Journal of Management Mathematics, Oct 1, 2006

ABSTRACT

Journal of Regional Science, Aug 1, 1978

Communications in Statistics - Simulation and Computation, 1990

We propose a simple and efficient way to approximate multivariate normal probabilities using univ... more We propose a simple and efficient way to approximate multivariate normal probabilities using univariate and bivariate probabilities. The approximation is computationally tested for the trivariate and quadrivariate normal probabilities. A few problems of higher dimensions were also tested.

Bulletin of the Ecological Society of America, 2016

Ecological research often involves multiple statistical tests. It is common practice to employ th... more Ecological research often involves multiple statistical tests. It is common practice to employ the Bonferroni technique or its more advanced sequential variant for such multiple tests. Indeed, Moran (Oikos, 100, 2003, 403) found that 13% of ecological papers apply this technique. The seminal paper by Rice (Evolution, 43, 1989, 223) that introduced this technique to the ecological community, is cited to date over 12 000 times. However, these techniques are conservative and some null hypotheses that should be rejected are not. Using order statistics we find that significant results are correlated even when the data consist of independent events. The Bonferroni methods assume independent significant results which results in Type II error with their application. We propose a simple approach, which we term the correlated Bonferroni technique, to rectify this shortcoming, which reduces rejection of significant results. Ecologists may be able to confirm the significance of their results while they are unable to confirm it using the original Bonferroni technique. Researchers may revisit their projects and find that significant results were mistakenly ignored. We provide an Excel file (see supplement) that researchers can easily use. We illustrate the correlated Bonferroni technique with an example.

European Journal of Operational Research, Dec 1, 2010

This paper presents a solution procedure based on a gradient descent method for the k-centrum pro... more This paper presents a solution procedure based on a gradient descent method for the k-centrum problem in the plane. The particular framework of this problem for the Euclidean norm leads to bisector lines whose analytical expressions are easy to handle. This allows us to develop different solution procedures which are tested on different problems and compared with existing procedures in the literature of Location Analysis. The computational analysis reports that our procedures provide better results than the existing ones for the k-centrum problem.

The number of components grows ▪ More and more transistors used ▪ But also more racks, cabinets, ... more The number of components grows ▪ More and more transistors used ▪ But also more racks, cabinets, cables, power supplies, etc. ▪ Everything at a nearly constant reliability per part ▪ Things will fail! ▪ Wang et al., 2010: "Peta-scale systems: MTBF 1.25 hours" ▪ Brightwell et al., 2011: "Next generation systems must be designed to handle failures without interrupting the workloads on the system or crippling the efficiency of the resource." Checkpoint/restart will take longer MTBF! ▪ We need to enable applications to survive failures ▪ … to reach Petascale Exascale! ▪ Like they did for decades in distributed systems!

Communications in Statistics - Simulation and Computation, Nov 13, 2015

A generally applicable discretization method is proposed to approximate a continuous distribution... more A generally applicable discretization method is proposed to approximate a continuous distribution on a real line with a discrete one, supported by a finite set. The method adopts a criterion which is shown to be flexible in approximating higher order features of the underlying continuous distribution while automatically preserving mean and variance. To illustrate the effectiveness of the method, several examples covering a wide-range continuous distributions are analyzed. A computer implementation (using ) of the proposed procedure is provided.

Computational Statistics & Data Analysis, Mar 1, 1995

Abstract The concept of multirelation is defined to describe the closeness of a set of variables ... more Abstract The concept of multirelation is defined to describe the closeness of a set of variables to a linear relation. This concept extends the linear correlation between two variables to two or more variables. It provides a better measure of closeness to a linear relation than the widely used Kaiser measure. The multirelation is applied to the classification problem where a subset of a given set of variables with the highest relation is sought.

Kybernetes, Jun 6, 2016

Purpose – The purpose of this paper is to investigate a competitive location problem to determine... more Purpose – The purpose of this paper is to investigate a competitive location problem to determine how to allocate a budget to expand company’s chain by either adding new facilities, expanding existing facilities, or a combination of both actions. Solving large problems may exceed the computational resources currently available. The authors treat a special case when the market can be divided into mutually exclusive sub-markets. These can be markets in cities around the globe or markets far enough from each other so that it can be assumed that customers in one market do not patronize retail facilities in another market, or that cross-patronizing is negligible. The company has a given budget to invest in these markets. Three objectives are considered: maximizing profit, maximizing return on investment (ROI), and maximizing profit subject to a minimum ROI. An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time. Design/methodology/approach – Since the market can be partitioned into disjoint sub-markets, the profit at each market by investing any budget in this sub-market can be calculated. The best allocation of the budget among the sub-markets can be done by either solving an integer linear program or by dynamic programming. This way, intractabole large competitive location problems can be optimally solved. Findings – An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time. Such a problem cannot be optimally solved by existing methods. Originality/value – This model is new and was not done in previous papers.

Iie Transactions, Nov 1, 1997

An event may occur anywhere in a planar area or on a linear region such as a route. One or more d... more An event may occur anywhere in a planar area or on a linear region such as a route. One or more detectors are to be located within this region with the objective of maximizing the smallest probability of the detection of an event anywhere in the region. In other words, the minimum protection in the region is to be maximized. The probability that an event is detected by a detector is a decreasing function of the distance. For example, the probability may decrease with some power (say, 2) of distance, or this decrease could be approximately exponential with distance. Two solution procedures are proposed for the problem on a line segment: a mathematical programming model and a specially designed algorithm. The problem in an area is solved by a univariate search, a Demjanov-type algorithm, a mathematical programming model, and simulated annealing. Computational experience is reported.

Mathematical Methods of Operations Research, Jul 13, 2013

A model that combines an inventory and location decision is presented, analyzed and solved. In pa... more A model that combines an inventory and location decision is presented, analyzed and solved. In particular, we consider a single distribution center location that serves a finite number of sales outlets for a perishable product. The total cost to be minimized, consists of the transportation costs from the distribution center to the sales outlets as well as the inventory related costs at the sales outlets. The location of the distribution center affects the inventory policy. Very efficient solution approaches for the location problem in a planar environment are developed. Computational experiments demonstrate the efficiency of the proposed solution approaches.

Communications in Statistics - Simulation and Computation, 1990

We propose a simple and efficient way to approximate multivariate normal probabilities using univ... more We propose a simple and efficient way to approximate multivariate normal probabilities using univariate and bivariate probabilities. The approximation is computationally tested for the trivariate and quadrivariate normal probabilities. A few problems of higher dimensions were also tested.

arXiv (Cornell University), Apr 6, 2020

In this paper we propose the planar obnoxious facilities p-median problem. In the p-median proble... more In this paper we propose the planar obnoxious facilities p-median problem. In the p-median problem the objective is to find p locations for facilities that minimize the weighted sum of distances between demand points and their closest facility. In the obnoxious version we add constraints that each facility must be located at least a certain distance from a partial set of demand points because they generate nuisance affecting these demand points. The resulting problem is extremely non-convex and traditional non-linear solvers such as SNOPT are not efficient. An efficient solution method based on Voronoi diagrams is proposed and tested. We also constructed the efficient frontiers of the test problems to assist the planers in making location decisions.

Journal of The Operations Research Society of Japan, 2007

We investigate the location of one or more facilities anywhere in an area in which several cornpe... more We investigate the location of one or more facilities anywhere in an area in which several cornpeting facilities already exist. The attractiveness of each facility is modeled by a utility function. Each customer selects the facility with the greatest utility function value. The objective is to find the locations fbr. one er more facilities which attract the maxirnum buying power. We generate a set of candidate locations and solve the single facility problem by evaluating the buying power attracted to the new facility at each candidate location. We then solve the location of multiple facilities by converting the problem to a maximum covering preblem. The solution procedure is illustrated on an example problem with 100 demand points and seven existing facilities. As a case study we find the best locations of new convenience stores in the city of Seto, Japan.

Infor, Aug 1, 2011

... Tammy Drezner and Zvi Drezner Steven G. Mihaylo College of Business and Economics, California... more ... Tammy Drezner and Zvi Drezner Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA 92834, e-mail ... Berman and Wang (2006) solved the minimax problem on the network when the weights are uni-formly distributed. ...

Ima Journal of Management Mathematics, Aug 19, 2021

The clustering problem has many applications in machine learning, operations research and statist... more The clustering problem has many applications in machine learning, operations research and statistics. We propose three algorithms to create starting solutions for improvement algorithms for the minimum sum of squares clustering problem. We test the algorithms on 72 instances that were investigated in the literature. We found five new best known solutions and matched the best known solution for 66 of the remaining 67 instances. Thus, we are able to demonstrate that good starting solutions combined with a simple local search get results comparable with, and sometimes even better than, more sophisticated algorithms used in the literature.

Optimization Letters, Apr 8, 2021

Iise Transactions, Dec 1, 1980

Abstract We introduce the following problem in this paper. There are n points on the plane that a... more Abstract We introduce the following problem in this paper. There are n points on the plane that are to be observed from some point on a circle of given radius that encloses all of the points. We wish to find the observation point that has the best possible view of the n points in the sense that if we draw lines of sight from the observation point to the given points, the smallest angle between the lines is maximized. Applications could include the planning of photographs or displays. This is a “maximin problem” in which the function to be maximized has many local optima. We present two methods for solving the problem, one more efficient in computer time, and the other in storage. We also present a simplified procedure for the case where the observation point is “infinitely” distant from the given points.

Iie Transactions, Jun 1, 1995

We extend recent works by Tang and Tang dealing with the quality cost of a process that is screen... more We extend recent works by Tang and Tang dealing with the quality cost of a process that is screened with the use of correlated variables because the principal quality characteristic is difficult or expensive to measure. Our model includes a very flexible and general set of loss functions that can be used to model both traditional and contemporary ‘losses’ for deviation from target values or product specifications. We also give an analysis of the expected value of perfect information and sample information obtained from the screening variables. This facilitates the evaluation of the advisability of using screening variables.

European Journal of Operational Research, Nov 1, 1999

In this paper we ®nd the set of feasible solution points to the Weber location problem with squar... more In this paper we ®nd the set of feasible solution points to the Weber location problem with squared Euclidean distances when the weights can be at any point in a given set of intervals. We prove that this set is a convex polygon. The result is then used to solve the minimax regret objective when individual scenarios can be any set of weights in a given set of intervals.

Ima Journal of Management Mathematics, Oct 1, 2006

ABSTRACT

Journal of Regional Science, Aug 1, 1978

Communications in Statistics - Simulation and Computation, 1990

We propose a simple and efficient way to approximate multivariate normal probabilities using univ... more We propose a simple and efficient way to approximate multivariate normal probabilities using univariate and bivariate probabilities. The approximation is computationally tested for the trivariate and quadrivariate normal probabilities. A few problems of higher dimensions were also tested.

Bulletin of the Ecological Society of America, 2016

Ecological research often involves multiple statistical tests. It is common practice to employ th... more Ecological research often involves multiple statistical tests. It is common practice to employ the Bonferroni technique or its more advanced sequential variant for such multiple tests. Indeed, Moran (Oikos, 100, 2003, 403) found that 13% of ecological papers apply this technique. The seminal paper by Rice (Evolution, 43, 1989, 223) that introduced this technique to the ecological community, is cited to date over 12 000 times. However, these techniques are conservative and some null hypotheses that should be rejected are not. Using order statistics we find that significant results are correlated even when the data consist of independent events. The Bonferroni methods assume independent significant results which results in Type II error with their application. We propose a simple approach, which we term the correlated Bonferroni technique, to rectify this shortcoming, which reduces rejection of significant results. Ecologists may be able to confirm the significance of their results while they are unable to confirm it using the original Bonferroni technique. Researchers may revisit their projects and find that significant results were mistakenly ignored. We provide an Excel file (see supplement) that researchers can easily use. We illustrate the correlated Bonferroni technique with an example.

European Journal of Operational Research, Dec 1, 2010

This paper presents a solution procedure based on a gradient descent method for the k-centrum pro... more This paper presents a solution procedure based on a gradient descent method for the k-centrum problem in the plane. The particular framework of this problem for the Euclidean norm leads to bisector lines whose analytical expressions are easy to handle. This allows us to develop different solution procedures which are tested on different problems and compared with existing procedures in the literature of Location Analysis. The computational analysis reports that our procedures provide better results than the existing ones for the k-centrum problem.

The number of components grows ▪ More and more transistors used ▪ But also more racks, cabinets, ... more The number of components grows ▪ More and more transistors used ▪ But also more racks, cabinets, cables, power supplies, etc. ▪ Everything at a nearly constant reliability per part ▪ Things will fail! ▪ Wang et al., 2010: "Peta-scale systems: MTBF 1.25 hours" ▪ Brightwell et al., 2011: "Next generation systems must be designed to handle failures without interrupting the workloads on the system or crippling the efficiency of the resource." Checkpoint/restart will take longer MTBF! ▪ We need to enable applications to survive failures ▪ … to reach Petascale Exascale! ▪ Like they did for decades in distributed systems!

Communications in Statistics - Simulation and Computation, Nov 13, 2015

A generally applicable discretization method is proposed to approximate a continuous distribution... more A generally applicable discretization method is proposed to approximate a continuous distribution on a real line with a discrete one, supported by a finite set. The method adopts a criterion which is shown to be flexible in approximating higher order features of the underlying continuous distribution while automatically preserving mean and variance. To illustrate the effectiveness of the method, several examples covering a wide-range continuous distributions are analyzed. A computer implementation (using ) of the proposed procedure is provided.

Computational Statistics & Data Analysis, Mar 1, 1995

Abstract The concept of multirelation is defined to describe the closeness of a set of variables ... more Abstract The concept of multirelation is defined to describe the closeness of a set of variables to a linear relation. This concept extends the linear correlation between two variables to two or more variables. It provides a better measure of closeness to a linear relation than the widely used Kaiser measure. The multirelation is applied to the classification problem where a subset of a given set of variables with the highest relation is sought.

Kybernetes, Jun 6, 2016

Purpose – The purpose of this paper is to investigate a competitive location problem to determine... more Purpose – The purpose of this paper is to investigate a competitive location problem to determine how to allocate a budget to expand company’s chain by either adding new facilities, expanding existing facilities, or a combination of both actions. Solving large problems may exceed the computational resources currently available. The authors treat a special case when the market can be divided into mutually exclusive sub-markets. These can be markets in cities around the globe or markets far enough from each other so that it can be assumed that customers in one market do not patronize retail facilities in another market, or that cross-patronizing is negligible. The company has a given budget to invest in these markets. Three objectives are considered: maximizing profit, maximizing return on investment (ROI), and maximizing profit subject to a minimum ROI. An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time. Design/methodology/approach – Since the market can be partitioned into disjoint sub-markets, the profit at each market by investing any budget in this sub-market can be calculated. The best allocation of the budget among the sub-markets can be done by either solving an integer linear program or by dynamic programming. This way, intractabole large competitive location problems can be optimally solved. Findings – An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time. Such a problem cannot be optimally solved by existing methods. Originality/value – This model is new and was not done in previous papers.

Iie Transactions, Nov 1, 1997

An event may occur anywhere in a planar area or on a linear region such as a route. One or more d... more An event may occur anywhere in a planar area or on a linear region such as a route. One or more detectors are to be located within this region with the objective of maximizing the smallest probability of the detection of an event anywhere in the region. In other words, the minimum protection in the region is to be maximized. The probability that an event is detected by a detector is a decreasing function of the distance. For example, the probability may decrease with some power (say, 2) of distance, or this decrease could be approximately exponential with distance. Two solution procedures are proposed for the problem on a line segment: a mathematical programming model and a specially designed algorithm. The problem in an area is solved by a univariate search, a Demjanov-type algorithm, a mathematical programming model, and simulated annealing. Computational experience is reported.

Mathematical Methods of Operations Research, Jul 13, 2013

A model that combines an inventory and location decision is presented, analyzed and solved. In pa... more A model that combines an inventory and location decision is presented, analyzed and solved. In particular, we consider a single distribution center location that serves a finite number of sales outlets for a perishable product. The total cost to be minimized, consists of the transportation costs from the distribution center to the sales outlets as well as the inventory related costs at the sales outlets. The location of the distribution center affects the inventory policy. Very efficient solution approaches for the location problem in a planar environment are developed. Computational experiments demonstrate the efficiency of the proposed solution approaches.

Communications in Statistics - Simulation and Computation, 1990

We propose a simple and efficient way to approximate multivariate normal probabilities using univ... more We propose a simple and efficient way to approximate multivariate normal probabilities using univariate and bivariate probabilities. The approximation is computationally tested for the trivariate and quadrivariate normal probabilities. A few problems of higher dimensions were also tested.

We consider the problem of optimally locating a single facility anywhere in a network to serve bo... more We consider the problem of optimally locating a single facility anywhere in a network to serve both on-network and off-network demands. Off-network demands occur in a Euclidean plane, while on-network demands are restricted to a network embedded in the plane. On-network demand points are serviced using shortest-path distances through links of the network (e.g., on-road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst-case distance. We solve our formulations using the " Big Segment Small Segment " global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi-facility problems by solving a sequence of single-facility problems.