In this article, we address two network design problems for a responsive supply chain that consis... more In this article, we address two network design problems for a responsive supply chain that consists of make‐to‐order (make‐to‐assemble) facilities facing stochastic demand and service time. The response time to customer orders, critical to the success of the supply chain, is the sum of the flow time in the facility and the delivery time to the customers. The response time performance in our models is measured by the probability that the response time is shorter than a constant. This nonlinear performance measure makes the models less or not tractable. The objective of both problems is to minimize the expected network cost that consists of the cost of delivery to customers as a function of the time of delivery (or the mode of transportation), the fixed cost of locating facilities and the capacity cost as a linear function of the processing capacity. The main decision variables are the number and locations of facilities, the resources allocated to them and the delivery mode selected b...
In this paper we consider the weighted minimax (1-center) location problem in the plane when the ... more In this paper we consider the weighted minimax (1-center) location problem in the plane when the weights are not given but rather drawn from independent uniform distributions. The problem is formulated and analyzed. For certain parameters of the uniform distributions the objective function is proven to be convex and thus can be easily solved by standard software such as the
In this paper we develop a service network design model that explicitly takes into account the el... more In this paper we develop a service network design model that explicitly takes into account the elasticity of customer demand with respect to travel distance and congestion delays. The model incorporates a feedback loop between customer demand and congestion at the facilities. The problem is to determine the number of facilities, their locations, their service capacity, and the assignment of customers to facilities so as to maximize the overall profit of the system. Two versions of the problem are presented. In one, each facility is modeled as an M/M/1 queuing system where the service rate is a decision variable; in the other one, the facility is modeled as an M/M/k queuing model where the service rate is given, but the number k is a decision variable. An exact algorithm and heuristics are developed and tested via computational experiments. Although our model is of the “directed choice” type where the assignment of customers to facilities is controlled by the decision maker, computat...
The objective of this article was to find a location of a new facility on a network so that the t... more The objective of this article was to find a location of a new facility on a network so that the total number (weight) of nodes within a prespecified distance R is minimized. This problem is applicable when locating an obnoxious facility such as garbage dumps, nuclear reactors, prisons, and military installations. The paper includes an analysis of the problem, identification of special cases where the problem is easily solved, an algorithm to solve the problem in general, and a sensitivity analysis of R . 0 7996 John Wiley 8 Sons, Inc.
ABSTRACT A family of discrete cooperative covering problems is analysed in this paper. Each facil... more ABSTRACT A family of discrete cooperative covering problems is analysed in this paper. Each facility emits a signal that decays by the distance and each demand point observes the total signal emitted by all facilities. A demand point is covered if its cumulative signal exceeds a given threshold. We wish to maximize coverage by selecting locations for p facilities from a given set of potential sites. Two other problems that can be solved by the max-cover approach are the equivalents to set covering and p-centre problems. The problems are formulated, analysed and solved on networks. Optimal and heuristic algorithms are proposed and extensive computational experiments reported.
In this paper we consider the one-centre problem on a network when the speeds on links are stocha... more In this paper we consider the one-centre problem on a network when the speeds on links are stochastic rather than deterministic. Given a desirable time to reach customers residing at the nodes, the objective is to find the location for a facility such that the probability that all nodes are reached within this time threshold is maximized. The problem is formulated, analyzed and solved by using multivariate normal probabilities. The procedure is demonstrated on an example problem.
In this paper, we consider the location of a new obnoxious facility that serves only a certain pr... more In this paper, we consider the location of a new obnoxious facility that serves only a certain proportion of the demand. Each demand point can be bought by the developer at a given price. An expropriation budget is given. Demand points closest to the facility are expropriated within the given budget. The objective is to maximize the distance to the closest point not expropriated. The problem is formulated and polynomial algorithms are proposed for its solution both on the plane and on a network.
... We propose the following merging procedure between two parents S[ and S2. A similar merging p... more ... We propose the following merging procedure between two parents S[ and S2. A similar merging procedure is discussed in Alp et ai (2003), and a variant very similar to the one presented here is used in Erkut and Drezner (2003). ...
ABSTRACT A cooperative covering location problem anywhere on the networks is analysed. Each facil... more ABSTRACT A cooperative covering location problem anywhere on the networks is analysed. Each facility emits a signal that decays by the distance along the arcs of the network and each node observes the total signal emitted by all facilities. A node is covered if its cumulative signal exceeds a given threshold. The cooperative approach differs from traditional covering models where the signal from the closest facility determines whether or not a point is covered. The objective is to maximize coverage by the best location of facilities anywhere on the network. The problems are formulated and analysed. Optimal algorithms for one or two facilities are proposed. Heuristic algorithms are proposed for location of more than two facilities. Extensive computational experiments are reported.
In this paper we investigate the problem of locating a given number of facilities on a network. D... more In this paper we investigate the problem of locating a given number of facilities on a network. Demand generated at a node is distance dependent, i.e., it decreases with an increase in the distance. The facilities can serve no more than a given number of customers, thus they are capacitated and congested when they reach that limit. The objective function is to maximize the demand satisfied by the system given these constraints. An elegant solution is given for the location of one facility. The multiple facility problem is formulated and heuristic algorithms proposed for its solution. Computational experiments are reported.
ABSTRACT A cooperative-covering family of location problems is proposed in this paper. Each facil... more ABSTRACT A cooperative-covering family of location problems is proposed in this paper. Each facility emits a (possibly non-physical) “signal” which decays over the distance and each demand point observes the aggregate signal emitted by all facilities. It is assumed that a demand point is covered if its aggregate signal exceeds a given threshold; thus facilities cooperate to provide coverage, as opposed to the classical coverage location model where coverage is only provided by the closest facility. It is shown that this cooperative assumption is appropriate in a variety of applications. Moreover, ignoring the cooperative behavior (i.e., assuming the traditional individual coverage framework) leads to solutions that are significantly worse than the optimal cooperative cover solutions; this is illustrated with a case study of locating warning sirens in North Orange County, California. The problems are formulated, analyzed and solved in the plane for the Euclidean distance case. Optimal and heuristic algorithms are proposed and extensive computational experiments are reported.
This article presents the maximal covering problem on a network when some of the weights can be n... more This article presents the maximal covering problem on a network when some of the weights can be negative. Integer programming formulations are proposed and tested with ILOG CPLEX. Heuristic algorithms, an ascent algorithm, and simulated annealing are proposed and tested. The simulated annealing approach provides the best results for a data set comprising 40 problems.
In this article, we address two network design problems for a responsive supply chain that consis... more In this article, we address two network design problems for a responsive supply chain that consists of make‐to‐order (make‐to‐assemble) facilities facing stochastic demand and service time. The response time to customer orders, critical to the success of the supply chain, is the sum of the flow time in the facility and the delivery time to the customers. The response time performance in our models is measured by the probability that the response time is shorter than a constant. This nonlinear performance measure makes the models less or not tractable. The objective of both problems is to minimize the expected network cost that consists of the cost of delivery to customers as a function of the time of delivery (or the mode of transportation), the fixed cost of locating facilities and the capacity cost as a linear function of the processing capacity. The main decision variables are the number and locations of facilities, the resources allocated to them and the delivery mode selected b...
In this paper we consider the weighted minimax (1-center) location problem in the plane when the ... more In this paper we consider the weighted minimax (1-center) location problem in the plane when the weights are not given but rather drawn from independent uniform distributions. The problem is formulated and analyzed. For certain parameters of the uniform distributions the objective function is proven to be convex and thus can be easily solved by standard software such as the
In this paper we develop a service network design model that explicitly takes into account the el... more In this paper we develop a service network design model that explicitly takes into account the elasticity of customer demand with respect to travel distance and congestion delays. The model incorporates a feedback loop between customer demand and congestion at the facilities. The problem is to determine the number of facilities, their locations, their service capacity, and the assignment of customers to facilities so as to maximize the overall profit of the system. Two versions of the problem are presented. In one, each facility is modeled as an M/M/1 queuing system where the service rate is a decision variable; in the other one, the facility is modeled as an M/M/k queuing model where the service rate is given, but the number k is a decision variable. An exact algorithm and heuristics are developed and tested via computational experiments. Although our model is of the “directed choice” type where the assignment of customers to facilities is controlled by the decision maker, computat...
The objective of this article was to find a location of a new facility on a network so that the t... more The objective of this article was to find a location of a new facility on a network so that the total number (weight) of nodes within a prespecified distance R is minimized. This problem is applicable when locating an obnoxious facility such as garbage dumps, nuclear reactors, prisons, and military installations. The paper includes an analysis of the problem, identification of special cases where the problem is easily solved, an algorithm to solve the problem in general, and a sensitivity analysis of R . 0 7996 John Wiley 8 Sons, Inc.
ABSTRACT A family of discrete cooperative covering problems is analysed in this paper. Each facil... more ABSTRACT A family of discrete cooperative covering problems is analysed in this paper. Each facility emits a signal that decays by the distance and each demand point observes the total signal emitted by all facilities. A demand point is covered if its cumulative signal exceeds a given threshold. We wish to maximize coverage by selecting locations for p facilities from a given set of potential sites. Two other problems that can be solved by the max-cover approach are the equivalents to set covering and p-centre problems. The problems are formulated, analysed and solved on networks. Optimal and heuristic algorithms are proposed and extensive computational experiments reported.
In this paper we consider the one-centre problem on a network when the speeds on links are stocha... more In this paper we consider the one-centre problem on a network when the speeds on links are stochastic rather than deterministic. Given a desirable time to reach customers residing at the nodes, the objective is to find the location for a facility such that the probability that all nodes are reached within this time threshold is maximized. The problem is formulated, analyzed and solved by using multivariate normal probabilities. The procedure is demonstrated on an example problem.
In this paper, we consider the location of a new obnoxious facility that serves only a certain pr... more In this paper, we consider the location of a new obnoxious facility that serves only a certain proportion of the demand. Each demand point can be bought by the developer at a given price. An expropriation budget is given. Demand points closest to the facility are expropriated within the given budget. The objective is to maximize the distance to the closest point not expropriated. The problem is formulated and polynomial algorithms are proposed for its solution both on the plane and on a network.
... We propose the following merging procedure between two parents S[ and S2. A similar merging p... more ... We propose the following merging procedure between two parents S[ and S2. A similar merging procedure is discussed in Alp et ai (2003), and a variant very similar to the one presented here is used in Erkut and Drezner (2003). ...
ABSTRACT A cooperative covering location problem anywhere on the networks is analysed. Each facil... more ABSTRACT A cooperative covering location problem anywhere on the networks is analysed. Each facility emits a signal that decays by the distance along the arcs of the network and each node observes the total signal emitted by all facilities. A node is covered if its cumulative signal exceeds a given threshold. The cooperative approach differs from traditional covering models where the signal from the closest facility determines whether or not a point is covered. The objective is to maximize coverage by the best location of facilities anywhere on the network. The problems are formulated and analysed. Optimal algorithms for one or two facilities are proposed. Heuristic algorithms are proposed for location of more than two facilities. Extensive computational experiments are reported.
In this paper we investigate the problem of locating a given number of facilities on a network. D... more In this paper we investigate the problem of locating a given number of facilities on a network. Demand generated at a node is distance dependent, i.e., it decreases with an increase in the distance. The facilities can serve no more than a given number of customers, thus they are capacitated and congested when they reach that limit. The objective function is to maximize the demand satisfied by the system given these constraints. An elegant solution is given for the location of one facility. The multiple facility problem is formulated and heuristic algorithms proposed for its solution. Computational experiments are reported.
ABSTRACT A cooperative-covering family of location problems is proposed in this paper. Each facil... more ABSTRACT A cooperative-covering family of location problems is proposed in this paper. Each facility emits a (possibly non-physical) “signal” which decays over the distance and each demand point observes the aggregate signal emitted by all facilities. It is assumed that a demand point is covered if its aggregate signal exceeds a given threshold; thus facilities cooperate to provide coverage, as opposed to the classical coverage location model where coverage is only provided by the closest facility. It is shown that this cooperative assumption is appropriate in a variety of applications. Moreover, ignoring the cooperative behavior (i.e., assuming the traditional individual coverage framework) leads to solutions that are significantly worse than the optimal cooperative cover solutions; this is illustrated with a case study of locating warning sirens in North Orange County, California. The problems are formulated, analyzed and solved in the plane for the Euclidean distance case. Optimal and heuristic algorithms are proposed and extensive computational experiments are reported.
This article presents the maximal covering problem on a network when some of the weights can be n... more This article presents the maximal covering problem on a network when some of the weights can be negative. Integer programming formulations are proposed and tested with ILOG CPLEX. Heuristic algorithms, an ascent algorithm, and simulated annealing are proposed and tested. The simulated annealing approach provides the best results for a data set comprising 40 problems.
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Papers by Oded Berman