Zvi Drezner

California State University, Fullerton | CSUF · Department of Information Systems and Decision Sciences

This paper continues to develop and explore the impact of multipurpose trips on retail location. We develop a model for locating multiple facilities of a chain in an area where several other facilities, either competing or selling different products, are present. There may be some existing facilities of the same chain as well. A shopping trip may i...

In this note we propose an improved algorithm for the solution of the Weber problem which is the most fundamental problem in location analysis. It is used as a building block in many algorithms for solving more complicated location problems. The algorithm is very simple to implement and the idea behind it can inspire solution approaches to other op...

The most basic location problem is the Weber problem, that is a basis to many advanced location models. It is finding the location of a facility which minimizes the sum of weighted distances to a set of demand points. Solution approaches have convergence issues when the optimal solution is at a demand point because the derivatives of the objective...

In this paper we introduce a data analytics approach for specifying the gravity model as applied to competitive facility location. The gravity model is used primarily by marketers to estimate the market share attracted by competing retail facilities. Once the market share is computed, various solution techniques can be applied for finding the best...

In this paper we introduce a data analytics approach for specifying the gravity model as applied to competitive facility location. The gravity model is used primarily by marketers to estimate the market share attracted by competing retail facilities. Once the market share is computed, various solution techniques can be applied for finding the best...

Most competitive location models assume that as the distance increases, the patronage of a facility declines at the same rate regardless of the facility attractiveness. We observed that the rate at which patronage declines is slower for more attractive facilities. Customers are willing to drive long distances to patronize an attractive facility. Le...

In this paper we propose a new competitive location model that considers the possible negative impact generated by competing facilities (such as cannabis dispensaries) on surrounding communities. The facilities cannot be located too close to the communities. Therefore, when distances are Euclidean, the facilities must be located at a point outside...

We investigate the k-partitioning problem, in which a set of items is divided into mutually exclusive and collectively exhaustive non-empty groups (clusters). The number of groups is given, and the distances between items, which may include weights, are defined. The sum of the distances between all members of the same group is calculated for each g...

Most location models assume that the parameters are given and fixed. Demand for services is known, and the distance to the facility is given. Real-world parameters are not fixed but follow a probability distribution such as a normal distribution. Therefore, stochastic models estimate the results (cost, profit, cover) more accurately. In cover model...

In this paper we address the possibility that in a competitive facility location model, one of the existing competing facilities will go out of business. We find the best location for a new facility protecting against such a possibility. Four commonly used decision rules (optimistic, pessimistic, minimax regret, and expected value) are analyzed and...

Accepted by: Konstantinos Nikolopoulos We propose solving non-linear optimization problems by a trajectory method. A parameter is introduced into the optimization problem. For example, a variable in the original formulation is replaced by its squared value. The parameter is the power at which the variable is raised. For a particular value of the pa...

The inverse-square law states that the effect a source has on its surroundings is inversely proportional to the square of the Euclidean distance from that source. Its applicability spans multiple fields including physics, engineering, and computer science. We study the combined effect of multiple point sources surrounding a closed region in multidi...

In this paper we propose three models for locating multiple facilities anywhere in the plane. The facilities serve demand points and require raw materials from a list of available sources. Problem characteristic originally proposed in 1909 by Weber for manufacturing systems. Weber argued that optimal locations involve minimizing total transport cos...

Most competitive location models assume that as the distance increases, the patronage of a facility declines at the same rate regardless of the facility attractiveness. We observed that the rate at which patronage declines is slower for more attractive facilities. Customers are willing to drive long distances to patronize an attractive facility. Le...

The grey pattern problem is to select a pattern of p points in a square that is replicated in adjacent squares so that they are spread out as uniformly as possible. The goal is to cover a large area with many squares of the same pattern of p points. In the original formulation a special objective function is designed. In this paper we suggest the c...

The problem considered in this paper is the weighted obnoxious facility location in the convex hull of demand points. The objective function is to maximize the smallest weighted distance between a facility and a set of demand points. Three new global optimal solution approaches are proposed. Two variants of the “Big Triangle Small Triangle” global...

In this paper we propose a new competitive location model that considers the possible negative impact generated by competing facilities (such as cannabis dispensaries) on surrounding communities. The facilities cannot be located too close to the communities. Therefore, when distances are Euclidean, the facilities must be located at a point outside...

In this paper we address the possibility that in a competitive facility location model, one of the existing competing facilities will go out of business. We find the best location for a new facility protecting against such a possibility. Four commonly used decision rules (optimistic, pessimistic, minimax regret, and expected value) are analyzed and...

We locate a single competing facility in a particular retail category competing for customers who plan a visit to such a facility. Suppose that there is a probability that customers patronize in the same trip a second retail facility of a different category. In the standard competitive location model the probability of a multipurpose trip is zero....

The obnoxious facility location problem in three dimensions is optimally solved by an exact method based on Apollonius spheres, and in three or more dimensions by a modification of the Big-Cube-Small-Cube (BCSC, Schobel and Scholz in Comput Oper Res 37:115–122, 2010) global optimization method to within a pre-specified accuracy. In our implementati...

Previous work shows that individuals of the keystone cactus Carnegiea gigantea found in slower-growth, more arid populations live longer than those in wetter areas. This study follows by adding data for youth for these populations. The median age and the cut-off ages for the youngest deciles confirm that populations in wetter areas with faster grow...

The multiple obnoxious facilities location problem is an extremely non-convex optimization problem with millions of local optima. It is a very challenging problem. We improved the best known solution for 33 out of 76 test instances. We believe that the results of many instances reported here are still not optimal and thus better objective function...

One of the classics in the field of Location Science is the book on the theory of industrial location by Weber (1909). Weber used a simple construct comprised of a 3-point triangle to describe important issues, including where raw materials for manufacturing are sourced. Virtually all of the research conducted in the last 50 years related to Weber’...

The obnoxious facility location problem is to locate facilities that have a negative impact on communities (being “obnoxious”) and being farther from communities is preferred. For example, noisy or polluting factories, garbage dumps, airports, should not be located close to communities. Such facilities also serve the communities, otherwise they are...

We introduce a practically useful extension of the gravity model. When specifying the distance decay function, the basic gravity model and its variants use actual distance or travel time. But, in reality, travel time to a retail outlet is only a fraction of the time spent on shopping trips. Hence, ignoring “time spent in facilities” may bias market...

Premise: The point-intercept method is one of the most commonly used approaches to measure species cover in ecosystems worldwide. In this approach, multiple points are sampled for presence/absence of a species, and the number of present points divided by the total number of sampled points provides an estimate of percent cover. Our purpose is to ma...

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 sol...

In this paper we review research on the location of facilities that have a negative impact on surrounding communities which are defined in the literature, for example, as obnoxious, undesirable, noxious facilities. Overall, the literature on obnoxious facility location is quite large, and because of this we have even been somewhat selective in that...

In this paper we compare two new binary linear formulations to a standard quadratic binary program for the gray pattern problem and solved all three by the Gurobi solver. One formulation performed significantly better and obtained seven optimal solutions that were not proven optimal before. It is interesting that the formulation that performed best...

This paper examines the performance of improvement search as a function of the quality of the starting solution in the planar (or continuous) p-median problem. We show that using optimal solutions of the analogue discrete p-median problem as the starting solution for heuristic improvement algorithms, as recommended in the literature, can actually l...

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 communities and their closest facility. In the obnoxious version, we add constraints that each facility must be located at least a certain distanc...

In this paper, we present a hierarchicity-based (self-similar) hybrid genetic algorithm for the solution of the grey pattern quadratic assignment problem. This is a novel hybrid genetic search-based heuristic algorithm with the original, hierarchical architecture and it is in connection with what is known as self-similarity—this means that an objec...

Opuntia species express great intraspecific morphological variability. All reproductive structures, cladodes (stem segments), and spines respond to macroenvironmental and microenvironmental variation and all of these form from areoles (axillary buds). However, little is known about areole response to light and temperature differences. In this study...

The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed “direc...

In this paper we define and heuristically solve the multiple weighted obnoxious facilities location problem maximizing the minimum weighted distance between facilities and a given set of communities. Each community may have a different weight because different communities may be affected differently by a facility. The distance between pairs of faci...

In this paper we propose a simple general framework for obtaining facility dependent distance decay function in competitive location models. As the distance increases, the decay in patronage by more attractive facilities is slower than the decay by less attractive facilities. This implies that by using only the distribution patterns of neighborhood...

Opuntia cespitosa (Cactaceae, previously known under the synonym O. humifusa) is found over eastern North America, yet its populations are very sparse and small despite effective vegetative reproduction. Their edaphic preferences are poorly known, and may limit the distribution and success of the species. Soils were sampled for %O.M. (organic matte...

The problem considered in this paper is the weighted obnoxious facility location in the convex hull of demand points. The objective function is to maximize the smallest weighted distance between a facility and a set of demand points. Three new optimal solution approaches are proposed. Two variants of the "Big Triangle Small Triangle" global optimiz...

In this note, we analyze location problems where the distance (time) to get to the destination by air is affected by winds. We propose two models: the asymmetric Weber location problem and the round-trip Weber location problem. The problems are analyzed and solved.

Of critical importance to plants is the ability to secure adequate photosynthetically active radiation (PAR) for functioning, growth and reproduction. The Opuntia genus represents plants that produce new cladodes (=pads, the primary photosynthetic surface) annually and whose orientation is a response to PAR. Because of the great variability in orie...

A new gradual cover competitive facility location model is proposed and tested. In cover competitive models, it is assumed that up to a certain distance a demand point is attracted to a facility and beyond this distance it is not. The decline in attraction and cover is abrupt. It is either 0 or 1. We propose a gradual decline in attraction from 1 t...

In this paper we present two new approaches for finding good starting solutions to the planar p-median problem. Both methods rely on a discrete approximation of the continuous model that restricts the facility locations to the given set of demand points. The first method adapts the first phase of a greedy random construction algorithm proposed for...

A given number of communities exist in an area. Several obnoxious facilities, such as polluting factories, garbage dumps, need to be located in the area. The nuisance emitted by the facilities is cumulative. The objective is to minimize the nuisance inflicted on the most affected community. This problem is useful for planners who frequently face th...

The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed "direc...

In this paper we propose the planar obnoxious 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 pa...

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 this problem. We test the algorithms on 72 instances that were investigated in the literature. Forty eight of them are relatively easy to solve and we found th...

In this paper we suggest a new rule for parent selection in genetic algorithms inspired by natural evolutionary processes. The new rule is simple to implement in any genetic or hybrid genetic algorithm. We also review some biological principles that inspire genetic algorithms and their extensions. The new rule is tested on the planar p-median probl...

We investigate a new model for partitioning a set of items into groups (clusters). The number of groups is given and the distances between items are well defined. These distances may include weights. The sum of the distances between all members of the same group is calculated for each group, and the objective is to find the partition of the set of...

The objective of original cover location models is to cover demand within a given distance by facilities. Locating a given number of facilities to cover as much demand as possible is referred to as max-cover, and finding the minimum number of facilities required to cover all the demand is referred to as set covering. When the objective is to maximi...

In this paper we present two new approaches for finding good starting solutions to the planar p-median problem. Both methods rely on a discrete approximation of the continuous model that restricts the facility locations to the given set of demand points. The first method adapts the first phase of a greedy random construction algorithm proposed for...

Many Opuntia engage in nurse associations. Opuntia cespitosa is an endangered cactus species in Canada that is infrequent to rare in many parts of its US range. This study quantifies Opuntia cespitosa associations with other native and non-native plant species in its only substantial extant population in Canada, at Point Pelee National Park. Specie...

The aim of this research is to compile a database of vascular plants found in the Kingdom of Tonga in western Polynesia, a phyto‐geographic subregion of the South Pacific. The Tongan islands are spread over ~600,000 km² of the Pacific Ocean between 15–23° S latitude and 173–177° W longitude. The archipelago is comprised of 171 islands with an aggre...

The sequential linear programming (SLP) method for solving nonlinear problems was introduced in the 1960s. Many papers that attempted to use SLP reported poor performance and convergence issues. We found that nonlinear programs with reverse convex constraints, which are the most difficult nonlinear programs with many local optima, are solved (heuri...

We introduce a new bivariate exponential distribution that is analytically tractable and easily implementable. Some of its properties are discussed. Explicit expressions of the expected value of the larger and of the smaller of a pair of correlated exponentials are also provided. An application to tandem queues offers several interesting implicatio...

We proposed new techniques in statistics and in genetic algorithms. We used biological principles to innovate new approaches in genetic algorithms that yielded improved solutions to optimization problems, finding improved best known results for multiple instances. These mimicked patterns in the natural world, including female choice of mates, as we...

I started my career earning a BA in Mathematics in 1965 from the Technion, Israel Institute of Technology. I then served a mandatory service in the military for an extended period of time so I could serve at the newly established computer center as a computer programmer. The first computer, Philco 212, had a 32K memory and its machine language was...

In this paper we propose and solve a competitive facility location model when demand is continuously distributed in an area and each facility attracts customers within a given distance. This distance is a measure of the facility's attractiveness level which may be different for different facilities. The market share captured by each facility is cal...

We investigate the total covered area by multiple facilities applying the cooperative cover model. We found that the cooperative cover area is much larger than the one found by standard cover models. We also show that for a large number of facilities located in a symmetric grid, an hexagonal grid is best. We also investigate covering a given region...

This paper examines a special case of multi-facility location problems where the set of demand points is partitioned into a given number of subsets or clusters that can be treated as smaller independent sub-problems once the number of facilities allocated to each cluster is determined. A dynamic programming approach is developed to determine the op...

We propose to take advantage of symmetry that exists in some quadratic assignment instances when employing genetic or hybrid genetic algorithms to solve such instances. Such symmetry usually exists when the potential sites for the facilities are arranged in a rectangle. We designed a simple and effective approach to identify equivalent solutions if...

In this paper we propose a simple general framework for obtaining facility dependent distance decay function in competitive location models. As the distance increases, the decay in patronage by more attractive facilities is slower than the decay by less attractive facilities. This implies that by using only the distribution patterns of neighborhood...

We assessed the impact of fog on microclimate in a poorly understood fog desert under two common nurse plant species, at three sites: (1) foggy coast, (2) intermediate, and (3) above the main fog belt in the Atacama Desert (Peru). We quantify nurse plant modification of their understory that creates favorable microsites for other species. Datalogge...

We propose to apply a multi-start sequential linear programming (MSLP) algorithm for the solution of two multiple obnoxious facility problems on the plane. One problem (Max-Sum1) considers obnoxious facilities and the other (Max-Sum2) obnoxious demand points. The Max-Sum1 objective is maximizing the total distance between demand points and their cl...

We mimic alpha male social structure, which is common in many species of animals, for designing genetic algorithms. The population of solutions is partitioned into a number of social groups. One member of each is assigned alpha male status and the rest are reproductive females. A generation is defined as females producing one offspring each. Once a...

The objective of classic cover location models is for facilities to cover demand within a given distance. Locating a given number of facilities to cover as much demand as possible is referred to as max-cover. Finding the minimum number of facilities required to cover all the demand is the set covering problem. The gradual (or partial) cover replace...

As the extremity of Arctic climate lessens with global warming, the risk of invasion increases. We assess the presence of introduced plant species and their persistence (since the previous survey) in a Canadian subpolar site on the Hudson Bay with a history of human introductions from large-scale grain inputs. Widespread sampling was done to locate...

The multifacility collection depots problem is the location of one or more facilities among a given set of demand points and a given set of collection depots. Each service consists of a trip to the customer, collection of materials, dropping off the materials at one of the available collection depots, and returning to the facility to wait for the n...

Consider a situation where a given number of facilities must be located in a convex polygon with the objective of maximizing the minimum distance between facilities and a given set of communities subject to the facilities being farther than a certain distance from one another. This continuous multiple obnoxious facility location problem is very dif...

Opuntia mesacantha includes two subspecies, O. mesacantha subsp. mesacantha (tetraploid) and O. mesacantha subsp. lata (diploid), that are difficult to distinguish in the field. We show that (1) stomata length is effective for distinguishing the two subspecies, and (2) this can be visually assessed, reliably and non-destructively, using a microscop...

In this paper we propose the Weber obnoxious facility location problem. As in the classic Weber location problem, the objective is to minimize the weighted sum of distances between the facility and demand points. However, the facility location is required to be at least a given distance from demand points because it is “obnoxious” to them. A practi...

Covering location models assume that a demand point is either fully covered or not covered at all. Gradual cover models consider the possibility of partial cover. In this paper, we investigate the issue of joint partial coverage by several facilities in a multiple facilities location model. We establish theoretical foundations for the properties of...

In this short classroom note, we introduce a simple way to calculate the PERT/CPM algorithm in Excel. It can be used in an introductory Operations Management class when teaching PERT/CPM to avoid the laborious manual calculation involved in solving PERT/CPM. It can also be used as an interesting example for an advanced class in Excel. The user just...

Customers’ perception of a particular facility’s attractiveness is likely to be heterogeneous. However, existing competitive facility location models assume that facilities’ attractiveness levels are fixed. We extend the gravity model assuming randomly distributed facilities’ attractiveness. We propose two effective solution methods. One is based o...

Customers' attractiveness perception of a particular facility are likely to be heterogeneous due to their randomly varying levels of information about the facility. However, existing competitive facility location models (such as the gravity model) assume that attractiveness levels of facilities are fixed. This paper extends the gravity model by all...

Two efficient neighborhood reduction schemes are proposed for the solution of the p-median problem on the plane. Their integration into a local search significantly reduces the run time with an insignificant deterioration in the quality of the solution. For completeness this fast local search is also embedded into one of the most powerful metaheuri...

Facility location models deal, for the most part, with the location of plants, warehouses, distribution centers, retail facilities among others. In this chapter we review the game theoretical concept of the leader-follower in facility location models which addresses specific circumstances: (i) competitive location of two facilities anywhere on the...

Opuntia humifusa (eastern prickly pear cactus) is an endangered species in Canada, found principally in only one remaining location nationally, at Point Pelee National Park (PPNP). This study quantifies fruit and flower production in the population, the pad yellowing phenomenon that has been observed, overlying coverage and shade, and a variety of...

Deserts cover large areas of the globe, but their plant and animal life are not always well understood. This entry covers a variety of topics including the basics of primary production and food chains, and the seminal pulse‐reserve paradigm which has shaped our ideas about ecosystem function in arid lands. Also discussed are positive plant interact...

Hundreds of cactus species have evolved the rib and furrow morphology that aids in water storage and provides photosynthetic and thermal benefits. Limited work has been done on understanding rib spacing and furrow size in the context of a wide range of environmental variables. Data were collected in two Carnegiea gigantea Sonoran Desert (Northern H...

Age-size relationships of a species in any given population are variable due to local environmental and genetic variations across individuals. The aim of this study is to test an age-size model for the keystone Carnegiea gigantea (saguaro, Cactaceae), that establishes in cohorts, to assess its accuracy in reconstructing those cohorts. Monte Carlo s...

Opuntia cespitosa (until recent taxonomic splitting, identified as O. humifusa) is an endangered cactus in Canada, is found in only two populations nationwide after some local extirpations. The larger site is at Point Pelee National Park (PPNP-ON) at the northern edge of its range has little published data. Data were collected for plant size, overl...

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...