Rajan Batta - Profile on Academia.edu (original) (raw)

Papers by Rajan Batta

Socio-Economic Planning Sciences

We consider the School Bus Routing Problem (SBRP) for routing special education students based on... more We consider the School Bus Routing Problem (SBRP) for routing special education students based on our experience at a large suburban school district in Western New York, United States. We found the problem to be significantly different from that of routing regular students. The principle differences include the need to pick up special education student from their home, the need to configure buses appropriately for special education students, and the need to provide a higher level of service. Building upon prior work we developed a greedy heuristic coupled with a column generation approach to obtain approximate solutions for benchmark instances. Our findings demonstrated a 10 ∼ 20% cost reduction, which is particularly significant since special education transportation account for 40% of the transportation budget.

Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers

Annals of Operations Research, 2002

This paper studies a facility location problem with stochastic customer demand and immobile serve... more This paper studies a facility location problem with stochastic customer demand and immobile servers. Motivated by applications to locating bank automated teller machines (ATMs) or Internet mirror sites, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. Customers are assumed to visit the closest open facility. The objective of this problem is to minimize customers' total traveling cost and waiting cost. In addition, there is a restriction on the number of facilities that may be opened and an upper bound on the allowable expected waiting time at a facility. Three heuristic algorithms are developed, including a greedy-dropping procedure, a tabu search approach and an ε-optimal branch-and-bound method. These methods are compared computationally on a bank location data set from Amherst, New York.

Computers & Operations Research, 2002

This paper considers the problem of redistricting or redrawing police command boundaries. We mode... more This paper considers the problem of redistricting or redrawing police command boundaries. We model this problem as a constrained graph-partitioning problem involving the partitioning of a police jurisdiction into command districts subject to constraints of contiguity, compactness, convexity and size. Since the districting a ects urban emergency services, there also exist quality-of-service constraints, which limit the response time (queue time plus travel time) to calls for service. Confronted with the combinatorial challenge of the districting problem, we propose a simulated annealing algorithm to search for a "good" partitioning of the police jurisdiction. At each iteration of the algorithm, we employ a variant of the well-known PCAM model to optimally assign the patrol cars and assess the "goodness" of a particular district design with respect to some prescribed performance measures. This approach di ers from the well-known Hypercube queuing model, which simply evaluates the performance of a user-speciÿed district design and allocation. A computational case study using data from the Bu alo, New York, Police Department reveals the merits of this approach.

Budget constrained location problem with opening and closing of facilities

Computers & Operations Research, 2003

In this paper, we study a budget constrained location problem in which we simultaneously consider... more In this paper, we study a budget constrained location problem in which we simultaneously consider opening some new facilities and closing some existing facilities. Motivations for this problem stem from applications where, due to a change in the distribution of customer demand, the existing facility system no longer provides adequate service. The objective is to minimize the total weighted travel

On the use of genetic algorithms to solve location problems

Computers & Operations Research, 2002

... location models have been relatively few. In the two papers by Beasley and Chu [8] and Lorena... more ... location models have been relatively few. In the two papers by Beasley and Chu [8] and Lorena and de Souza-Lopez [9], the authors have focussed on the application of GAs to set covering problems. For location models as such ...

Spatial decision support system for hazardous material truck routing

Transportation Research Part C-emerging Technologies, 2000

Shipping hazardous material (hazmat) places the public at risk. People who live or work near road... more Shipping hazardous material (hazmat) places the public at risk. People who live or work near roads commonly traveled by hazmat trucks endure the greatest risk. Careful selection of roads used for a hazmat shipment can reduce the population at risk. On the other hand, ...

Operations Research Letters, 1993

While routing those hazardous materials that can be catastrophic when involved in an accident, it... more While routing those hazardous materials that can be catastrophic when involved in an accident, it sometimes can make more sense to minimize the risk given the occurrence of an accident, rather than the a priori risk. In this paper, we consider the concept of conditional risk, and propose two solution procedures. A model that minimizes the conditional risk, keeping the accident probability within a set threshold is also presented.

Dynamic Conflict-Free Routing of Automated Guided Vehicles

ABSTRACT This paper presents work performed to address design and operational control issues for ... more ABSTRACT This paper presents work performed to address design and operational control issues for an Automated Guided Vehicle (AGV) based material handling system. Various design issues connected with flow path design, such as traffic flow along the guide paths, location and representation of intersections, buffers, pickup and dropoff points, are outlined. A network representation of the AVG system (AGVS) is presented. Operational control factors, such as demand selection and assignment, route planning and traffic management, idle AGV positioning, and AGV characteristics, are addressed. In particular, the performance of six demand selection policies, four demand assignment policies, and two idle AGV positioning policies are outlined. A very effective route-generation technique that provides conflict-free routes for multiple AGVs with varying speeds is presented. A large-scale simulation of a dynamic batch type manufacturing system to test the feasibility of the proposed scheme for real time control of AGVs and to determine the effect of several factors on several performance measures is presented. Our findings indicate that performance is significantly affected by vehicle speed, number of vehicles, demand arrival interval, idle AGV positioning, and the demand selection and assignment policy in use.

When haste makes sense: Cracking down on street markets for illicit drugs

Socio-economic Planning Sciences, 1997

This paper presents an analytical approach to the tactical question: ‘What level of enforcement o... more This paper presents an analytical approach to the tactical question: ‘What level of enforcement over time allows one to eliminate a street market for illicit drugs while expanding the least possible total effort?’ The analysis is done in the context of Caulkins' model [6] which predicts the rate of change of dealers as a function of enforcement level and several

The Maximal Expected Covering Location Problem: Revisited

Transportation Science, 1989

ABSTRACT

The equity constrained shortest path problem

Computers & Operations Research, 1990

ABSTRACT This paper examines the problem of finding the shortest path on a network subject to “eq... more ABSTRACT This paper examines the problem of finding the shortest path on a network subject to “equity” constraints. A Lagrangean dual bounding approach is utilized, which relaxes the “complicating constraints” of the problem. After solving the Lagrangean dual, the duality gap is closed by finding the t shortest paths with respect to the Lagrangean function. Both looping and loopless paths are considered. A quick-and-dirty heuristic procedure is also suggested. We report a sampling of our computational experiences with the model.

Equitable Sequencing of a Given Set of Hazardous Materials Shipments

Transportation Science, 1991

ABSTRACT

European Journal of Operational Research, 1996

This paper presents an analytical approach for scheduling crackdowns on street{corner drug market... more This paper presents an analytical approach for scheduling crackdowns on street{corner drug markets. The crackdown scheduling problem is shown to be NP{Complete. A dynamic programming formulation is presented with an exponential time optimal algorithm. We then provide e cient optimal algorithms for several special cases and approximation algorithms for the general case. These results show that the optimal strategy is to give priority to markets that take longer to bring down and which require low levels of post-crackdown maintenance. The results are then extended to incorporate dealer displacement between drug markets.

Developing Conflict-Free Routes for Automated Guided Vehicles

Operations Research, 1993

ABSTRACT Automated guided vehicles (AGVs) are a highly sophisticated and increasingly popular typ... more ABSTRACT Automated guided vehicles (AGVs) are a highly sophisticated and increasingly popular type of material handling device in flexible manufacturing systems. This paper details solution methodologies for the static routing problem in which demand assignment of the AGVs are known; the focus is to obtain an implementable solution within a reasonable amount of computer time. The objective is to minimize the makespan, while routing AGVs on a bidirectional network in a conflict-free manner. This problem is solved via column generation. The master problem in this column generation procedure has the makespan and vehicle interference constraints. Columns in the master problem are routes iteratively generated for each AGV. The subproblem is a constrained shortest path problem with time-dependent costs on the edges. An improvement procedure is developed to better the solution obtained at the end of the master-subproblem interactions. Several methods of iterating between the master and subproblem are experimented with in-depth computational experiments. Our empirical results indicate that the procedure as a whole usually generates solutions that are within a few percent of a proposed bound, within reasonable computer time.

Modeling Equity of Risk in the Transportation of Hazardous Materials

Operations Research, 1990

In this paper, we develop and analyze a model to generate an equitable set of routes for hazardou... more In this paper, we develop and analyze a model to generate an equitable set of routes for hazardous material shipments. The objective is to determine a set of routes that will minimize the total risk of travel and spread the risk equitably among the zones of the ...

Socio-economic Planning Sciences, 1993

Local-level enforcement has been cited as an effective drug enforcement strategy by some policy m... more Local-level enforcement has been cited as an effective drug enforcement strategy by some policy makers and experts. A more intensive tactic, with focus on a specific target area and referred to as "crackdowns", has been implemented in some cities. In this paper, we analyze a mathematical model due to Caulkins, to study the effect of focussed enforcement on drug markets. Specifically, we consider both fixed and dynamic enforcement policies. Our analysis suggests that drug dealing can be effectively controlled only if enforcement resources exceed a certain threshold level, and that the success of a crackdown operation may be lost fairly quickly if care is not taken to prevent the market from returning. This should provide enforcement officials with analytically derived "rules of thumb" to help make improved policy decisions.

Single Server Queueing-Location Models with Rejection

Transportation Science, 1988

Socio-Economic Planning Sciences

We consider the School Bus Routing Problem (SBRP) for routing special education students based on... more We consider the School Bus Routing Problem (SBRP) for routing special education students based on our experience at a large suburban school district in Western New York, United States. We found the problem to be significantly different from that of routing regular students. The principle differences include the need to pick up special education student from their home, the need to configure buses appropriately for special education students, and the need to provide a higher level of service. Building upon prior work we developed a greedy heuristic coupled with a column generation approach to obtain approximate solutions for benchmark instances. Our findings demonstrated a 10 ∼ 20% cost reduction, which is particularly significant since special education transportation account for 40% of the transportation budget.

Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers

Annals of Operations Research, 2002

This paper studies a facility location problem with stochastic customer demand and immobile serve... more This paper studies a facility location problem with stochastic customer demand and immobile servers. Motivated by applications to locating bank automated teller machines (ATMs) or Internet mirror sites, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. Customers are assumed to visit the closest open facility. The objective of this problem is to minimize customers' total traveling cost and waiting cost. In addition, there is a restriction on the number of facilities that may be opened and an upper bound on the allowable expected waiting time at a facility. Three heuristic algorithms are developed, including a greedy-dropping procedure, a tabu search approach and an ε-optimal branch-and-bound method. These methods are compared computationally on a bank location data set from Amherst, New York.

Computers & Operations Research, 2002

This paper considers the problem of redistricting or redrawing police command boundaries. We mode... more This paper considers the problem of redistricting or redrawing police command boundaries. We model this problem as a constrained graph-partitioning problem involving the partitioning of a police jurisdiction into command districts subject to constraints of contiguity, compactness, convexity and size. Since the districting a ects urban emergency services, there also exist quality-of-service constraints, which limit the response time (queue time plus travel time) to calls for service. Confronted with the combinatorial challenge of the districting problem, we propose a simulated annealing algorithm to search for a "good" partitioning of the police jurisdiction. At each iteration of the algorithm, we employ a variant of the well-known PCAM model to optimally assign the patrol cars and assess the "goodness" of a particular district design with respect to some prescribed performance measures. This approach di ers from the well-known Hypercube queuing model, which simply evaluates the performance of a user-speciÿed district design and allocation. A computational case study using data from the Bu alo, New York, Police Department reveals the merits of this approach.

Budget constrained location problem with opening and closing of facilities

Computers & Operations Research, 2003

In this paper, we study a budget constrained location problem in which we simultaneously consider... more In this paper, we study a budget constrained location problem in which we simultaneously consider opening some new facilities and closing some existing facilities. Motivations for this problem stem from applications where, due to a change in the distribution of customer demand, the existing facility system no longer provides adequate service. The objective is to minimize the total weighted travel

On the use of genetic algorithms to solve location problems

Computers & Operations Research, 2002

... location models have been relatively few. In the two papers by Beasley and Chu [8] and Lorena... more ... location models have been relatively few. In the two papers by Beasley and Chu [8] and Lorena and de Souza-Lopez [9], the authors have focussed on the application of GAs to set covering problems. For location models as such ...

Spatial decision support system for hazardous material truck routing

Transportation Research Part C-emerging Technologies, 2000

Shipping hazardous material (hazmat) places the public at risk. People who live or work near road... more Shipping hazardous material (hazmat) places the public at risk. People who live or work near roads commonly traveled by hazmat trucks endure the greatest risk. Careful selection of roads used for a hazmat shipment can reduce the population at risk. On the other hand, ...

Operations Research Letters, 1993

While routing those hazardous materials that can be catastrophic when involved in an accident, it... more While routing those hazardous materials that can be catastrophic when involved in an accident, it sometimes can make more sense to minimize the risk given the occurrence of an accident, rather than the a priori risk. In this paper, we consider the concept of conditional risk, and propose two solution procedures. A model that minimizes the conditional risk, keeping the accident probability within a set threshold is also presented.

Dynamic Conflict-Free Routing of Automated Guided Vehicles

ABSTRACT This paper presents work performed to address design and operational control issues for ... more ABSTRACT This paper presents work performed to address design and operational control issues for an Automated Guided Vehicle (AGV) based material handling system. Various design issues connected with flow path design, such as traffic flow along the guide paths, location and representation of intersections, buffers, pickup and dropoff points, are outlined. A network representation of the AVG system (AGVS) is presented. Operational control factors, such as demand selection and assignment, route planning and traffic management, idle AGV positioning, and AGV characteristics, are addressed. In particular, the performance of six demand selection policies, four demand assignment policies, and two idle AGV positioning policies are outlined. A very effective route-generation technique that provides conflict-free routes for multiple AGVs with varying speeds is presented. A large-scale simulation of a dynamic batch type manufacturing system to test the feasibility of the proposed scheme for real time control of AGVs and to determine the effect of several factors on several performance measures is presented. Our findings indicate that performance is significantly affected by vehicle speed, number of vehicles, demand arrival interval, idle AGV positioning, and the demand selection and assignment policy in use.

When haste makes sense: Cracking down on street markets for illicit drugs

Socio-economic Planning Sciences, 1997

This paper presents an analytical approach to the tactical question: ‘What level of enforcement o... more This paper presents an analytical approach to the tactical question: ‘What level of enforcement over time allows one to eliminate a street market for illicit drugs while expanding the least possible total effort?’ The analysis is done in the context of Caulkins' model [6] which predicts the rate of change of dealers as a function of enforcement level and several

The Maximal Expected Covering Location Problem: Revisited

Transportation Science, 1989

ABSTRACT

The equity constrained shortest path problem

Computers & Operations Research, 1990

ABSTRACT This paper examines the problem of finding the shortest path on a network subject to “eq... more ABSTRACT This paper examines the problem of finding the shortest path on a network subject to “equity” constraints. A Lagrangean dual bounding approach is utilized, which relaxes the “complicating constraints” of the problem. After solving the Lagrangean dual, the duality gap is closed by finding the t shortest paths with respect to the Lagrangean function. Both looping and loopless paths are considered. A quick-and-dirty heuristic procedure is also suggested. We report a sampling of our computational experiences with the model.

Equitable Sequencing of a Given Set of Hazardous Materials Shipments

Transportation Science, 1991

ABSTRACT

European Journal of Operational Research, 1996

This paper presents an analytical approach for scheduling crackdowns on street{corner drug market... more This paper presents an analytical approach for scheduling crackdowns on street{corner drug markets. The crackdown scheduling problem is shown to be NP{Complete. A dynamic programming formulation is presented with an exponential time optimal algorithm. We then provide e cient optimal algorithms for several special cases and approximation algorithms for the general case. These results show that the optimal strategy is to give priority to markets that take longer to bring down and which require low levels of post-crackdown maintenance. The results are then extended to incorporate dealer displacement between drug markets.

Developing Conflict-Free Routes for Automated Guided Vehicles

Operations Research, 1993

ABSTRACT Automated guided vehicles (AGVs) are a highly sophisticated and increasingly popular typ... more ABSTRACT Automated guided vehicles (AGVs) are a highly sophisticated and increasingly popular type of material handling device in flexible manufacturing systems. This paper details solution methodologies for the static routing problem in which demand assignment of the AGVs are known; the focus is to obtain an implementable solution within a reasonable amount of computer time. The objective is to minimize the makespan, while routing AGVs on a bidirectional network in a conflict-free manner. This problem is solved via column generation. The master problem in this column generation procedure has the makespan and vehicle interference constraints. Columns in the master problem are routes iteratively generated for each AGV. The subproblem is a constrained shortest path problem with time-dependent costs on the edges. An improvement procedure is developed to better the solution obtained at the end of the master-subproblem interactions. Several methods of iterating between the master and subproblem are experimented with in-depth computational experiments. Our empirical results indicate that the procedure as a whole usually generates solutions that are within a few percent of a proposed bound, within reasonable computer time.

Modeling Equity of Risk in the Transportation of Hazardous Materials

Operations Research, 1990

In this paper, we develop and analyze a model to generate an equitable set of routes for hazardou... more In this paper, we develop and analyze a model to generate an equitable set of routes for hazardous material shipments. The objective is to determine a set of routes that will minimize the total risk of travel and spread the risk equitably among the zones of the ...

Socio-economic Planning Sciences, 1993

Local-level enforcement has been cited as an effective drug enforcement strategy by some policy m... more Local-level enforcement has been cited as an effective drug enforcement strategy by some policy makers and experts. A more intensive tactic, with focus on a specific target area and referred to as "crackdowns", has been implemented in some cities. In this paper, we analyze a mathematical model due to Caulkins, to study the effect of focussed enforcement on drug markets. Specifically, we consider both fixed and dynamic enforcement policies. Our analysis suggests that drug dealing can be effectively controlled only if enforcement resources exceed a certain threshold level, and that the success of a crackdown operation may be lost fairly quickly if care is not taken to prevent the market from returning. This should provide enforcement officials with analytically derived "rules of thumb" to help make improved policy decisions.

Single Server Queueing-Location Models with Rejection

Transportation Science, 1988