Rajan Batta

On the use of genetic algorithms to solve location problems

This paper seeks to evaluate the performance of genetic algorithms (GA) as an alternative procedure for generating optimal or near-optimal solutions for location problems. The specific problems considered are the uncapacitated and capacitated fixed charge problems, the maximum covering problem, and competitive location models. We compare the performance of the GA-based heuristics developed against well-known heuristics from the literature, using a test base of publicly available data sets.

Review of recent developments in OR/MS research in disaster operations management

Potential consequences of disasters involve overwhelming economic losses, large affected populations and serious environmental damages. Given these devastating effects, there is an increasing interest in developing measures in order to diminish the possible impact of disasters, which gave rise to the field of disaster operations management (DOM). In this paper we review recent OR/MS research in DOM. Our work is a continuation of a previous review from Altay and Green (2006). Our purpose is to evaluate how OR/MS research in DOM has evolved in the last years and to what extent the gaps identified by Altay and Green (2006) have been covered. Our findings show no drastic changes or developments in the field of OR/MS in DOM since the publication of Altay and Green (2006). Additionally to our comparative analysis, we present an original evaluation about the most common assumptions in recent OR/MS literature in DOM. Based on our findings we provide future research directions in order to make improvements in the areas where lack of research is detected.

The Maximal Expected Covering Location Problem: Revisited

The Maximal Expected Coverage Location Problem (MEXCLP) addresses the problem of optimally locating servers so as to maximize the expected coverage of demand while taking into account the possibility of servers being unavailable when a call enters the service system. In this paper, an attempt is made to relax three of MEXCLPs assumptions: servers operate independently, servers have the same busy probabilities, and server busy probabilities are invariant with respect to their locations. We embed the hypercube queueing model in a single node substitution heuristic optimization procedure, to determine a set of server locations which “maximize” the expected coverage. Our empirical findings indicate that there is disagreement between the expected coverage predicted by the MEXCLP model and the hypercube optimization procedure. There is substantial agreement, however, between the locations generated by the two procedures. We also consider a simple “adjustment” to the MEXCLP model, based upon random sampling of servers without replacement; the same adjustment has been used previously to derive a hypercube approximation procedure. We discuss modifications and enhancements to the MEXCLPs heuristic solution procedure for this adjusted model. Our empirical findings indicate that there is better agreement between the expected coverage predicted by the adjusted model and the hypercube optimization procedure. The locations generated by the adjusted model, however, are of the same overall quality as those generated by the MEXCLP model. Readers should view the results of this paper in light of the fact that we are able to relax the MEXCLP by assuming that the operating characteristics of the service system fit the description of the hypercube queueing model, such as Poisson arrivals and exponential service times, which may not be strictly true in practice.

Optimal obnoxious paths on a network: transportation of hazardous materials

This paper considers the problem of determining optimal paths for routing an undesirable vehicle on a network embedded on an Euclidean plane. A typical application is the transporting of hazardous materials. Demand points, or population centers, are discretely distributed at nodes and continuously distributed on straight-line links of the network. The objective is to find, without incorporating the probability of accidental leakage of hazardous material, a path that minimizes the weighted sum of lengths over which this vehicle is within a threshold distance λ of population centers. By appropriately redefining link lengths, we can use a shortest-path algorithm to solve the problem. Special properties of the objective function allow us to efficiently calculate the modified link lengths. We discuss the properties of the optimal routing strategy and the objective value, and offer an economic interpretation of the case when λ varies. Operating within the framework of risk analysis, we integrate the probability...

On finding dissimilar paths

Abstract Given a transportation network, this paper considers the problem of finding a number of spatially dissimilar paths between an origin and a destination. A number of dissimilar paths can be useful in solving capacitated flow problems or in selecting routes for hazardous materials. A critical discussion of three existing methods for the generation of spatially dissimilar paths is offered, and computational experience using these methods is reported. As an alternative method, the generation of a large set of candidate paths, and the selection of a subset using a dispersion model which maximizes the minimum dissimilarity in the selected subset is proposed. Computational results with this method are encouraging.

Developing conflict-free routes for automated guided vehicles

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

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 geographical region in which the transportation network is embedded, when several trips are necessary from origin to destination. An integer programming formulation for the problem is proposed. We develop and test a heuristic that repeatedly solves single-trip problems: a Lagrangian dual approach with a gap-closing procedure is used to optimally solve single-trip problems. We report a sampling of our computational experience, based on a real-life routing scenario in the Albany district of New York State. Our findings indicate that one can achieve a high degree of equity by modestly increasing the total risk and by embarking on different routes to evenly spread the risk among the zones. Furthermore, it appears that our heuristic procedure is excellent in terms of computational requirements as well as solution quality. We also suggest some directions for future research.

Budget constrained location problem with opening and closing of facilities

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 distance for customers subject to a constraint on the budget for opening and/or closing facilities and a constraint on the total number of open facilities desired. For this problem, we develop a mathematical programming model and examine its theoretical properties. We then develop three heuristic algorithms (greedy interchange, tabu search and Lagrangian relaxation approximation) for this NP-hard problem. Computational testing of these algorithms includes an analysis of the sensitivity of the solution to the budget and the desired number of facilities. The intended application in this testing is that of locating/relocating bank branches in a large-size town such as in our data set from Amherst, New York. We also discuss the situation where operating costs are part of the objective function.

Locating Facilities on the Manhattan Metric with Arbitrarily Shaped Barriers and Convex Forbidden Regions

This paper considers two planar facility location problems while employing the Manhattan travel metric. We first consider the p -median problem in the presence of arbitrarily shaped barriers and convex forbidden regions. For this problem we establish that the search for an optimal solution can be restricted to a finite set of easily identifiable points. Next, we consider the stochastic queue median problem in the presence of arbitrarily shaped barriers. A procedure to obtain a global optimum solution for this problem is established. The results of the paper are illustrated via numerical examples. Finally, we comment on a connection between network location problems and planar location problems which use the Manhattan travel metric.

A branch-and-price approach for operational aircraft maintenance routing

Abstract In recent years, considerable effort in the field of operations research has been paid to optimizing airline operations, including the logistics of an airline’s fleet of aircraft. We focus on the problem of aircraft routing, which involves generating and selecting a particular route for each aircraft of a sub-fleet that is already assigned to a set of feasible sequences of flight legs. Similar studies typically focus on long-term route planning. However, stochastic events such as severe weather changes, equipment failures, variable maintenance times, or even new regulations mandated by the Federal Aviation Administration (FAA) play havoc on these long-term plans. In addition, these long-term plans ignore detailed maintenance requirements by considering only one or two of the primary maintenance checks that must be performed on a regular, long-term basis. As a result, these plans are often ignored by personnel in airline operations who are forced on a daily basis to develop quick, ad hoc methods to address these maintenance requirements and other irregular events. To address this problem, we develop an operational aircraft maintenance routing problem formulation that includes maintenance resource availability constraints. We propose a branch-and-price algorithm for solving this problem, which, due to the resource constraints, entails a modification of the branch-on, follow-on branching rule typically used for solving similar problems. Through computational testing, we explore the efficiency of this solution approach under a combination of heuristic choices for column (route) generation and selection.