Ram Gopalan

The Aircraft Maintenance Routing Problem

Federal aviation regulations require that all aircraft undergo maintenance after flying a certain number of hours. To ensure high aircraft utilization, maintenance is done at night, and these regulations translate into requiring aircraft to overnight at a maintenance station every three to four days (depending on the fleet type), and to visit a balance-check station periodically. After the schedule is fleeted, the aircraft are routed to satisfy these maintenance requirements. We give fast and simple polynomial-time algorithms for finding a routing of aircraft in a graph whose routings during the day are fixed, that satisfies both the three-day maintenance as well as the balance-check visit requirements under two different models: a static infinite-horizon model and a dynamic finite-horizon model. We discuss an implementation where we embed the static infinite-horizon model into a three-stage procedure for finding a maintenance routing of aircraft.

Mathematical models in airline schedule planning: A survey

The schedule is an airlines primary product, having the most influence (along with price) on a passengers choice of an airline. Once an airline decides (at least tentatively) on a schedule, a host of related problems have to be resolved before it can consider the schedule feasible, and can proceed to market the schedule. Among these problems are traffic forecasting and allocation that forecasts traffic on each flight leg for use in the fleet assignment model, fleet assignment that decides the fleet type of the aircraft flying the legs in the schedule, equipment swapping to change an assigned equipment type on a leg if and when necessary, through flight selection for determining which pairs of flights to market as one-stops (without any aircraft change), maintenance routing that develops aircraft rotations to provide adequate opportunities for overnight maintenance, and flight numbering to number flights as consistently as possible with a prior schedule. Considerable methodological and computational advances have been made in the recent past in developing models and solution methods for almost all of the problems mentioned above. In this paper we survey these various models and solution techniques.

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.

The equity constrained shortest path problem

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.

Dimensions of service quality in tourism – an Indian perspective

The purpose of this paper is to identify dimensions of service quality (SQ) and their corresponding measurement variables in the tourism industry by focusing on India, a South Asian destination. The dimensions and the measurement variables have been identified through a detailed review of literature and exploratory research. Service quality in tourism comprises 10 dimensions, namely core-tourism experience, information, hospitality, fairness of price, hygiene, amenities, value for money, logistics, food and security. This study aims to enrich the body of knowledge pertaining to similar work undertaken by researchers in other parts of the world. The growing importance of Asian destinations in the global tourism market in general and emergence of India as a prominent tourist destination in South Asia in particular marks the importance of this study. The proposed framework is expected to equip the tour operators in the western world to better understand the tourism industry in South-Asian destinations. It would also be useful to service-providers for managing other equally important tourist destinations in South Asia and Asia-Pacific regions, which are endowed with similar socio-cultural backgrounds.

An ant colony algorithm for cell-formation in cellular manufacturing systems

In this paper, we consider the problem of cell-formation in cellular manufacturing systems with the objective of maximising the grouping efficacy. We propose an Ant-Colony Optimisation (ACO) algorithm to obtain machine-cells and part-families. The Proposed ACO (PACO) algorithm is tested by using many benchmark data sets. The grouping efficacy obtained by the PACO algorithm for a given benchmark problem instance is compared with the grouping efficacies obtained by the existing approaches. The comparison shows that the PACO performs very well in maximising the grouping efficacy. [Received: 2 May 2007; Revised: 1 November 2007; Accepted: 3 December 2007]

FREIGHT TRAIN ROUTING AND SCHEDULING IN A PASSENGER RAIL NETWORK: COMPUTATIONAL COMPLEXITY AND THE STEPWISE DISPATCHING HEURISTIC

In many countries, freight trains have to share a rail network with passenger trains. In this paper, we consider a situation where passenger trains must adhere to a strict published schedule, whereas freight train movements can be inserted at any convenient time, without disrupting scheduled passenger trains. We propose an algorithm for the problem of routing and scheduling of a single freight train in a passenger rail network. However, the multiple freight train routing and scheduling problem is shown to be NP-complete, even for simplified instances. Specifically, we show that both routing and scheduling of freight trains are difficult, even when only two freight trains are considered. It is also difficult when freight train movements are restricted to reach their destinations with no idling permitted at intermediate stations. We have developed a Stepwise Dispatching Heuristic for routing and scheduling multiple freight trains in a passenger rail network. Computational results confirm the efficacy of our algorithm for single freight train routing and of the proposed Stepwise Dispatching Heuristic.

Locomotive assignment and freight train scheduling using genetic algorithms

This study considers the movement of freight trains through a passenger rail network, a common occurrence in many developing countries. Passenger trains run according to a fixed schedule while freight trains need to be accommodated and run on the same track, ensuring that they do not interfere with passenger train movements. Operationally, this requires the assignment of a locomotive to a freight rake and then creating a workable schedule. Accordingly, we propose to solve the problem in two phases. In the first phase, we assign locomotives with partial scheduling with the objectives of minimizing total deadheading time and total coupling delay. We use a genetic algorithm to find non-dominant locomotive assignment solutions and propose a method for evaluating its performance. The solutions are then ranked using two approaches, based on the decision makers preferences. In the second phase, we select a locomotive assignment solution based on the ranking and find the lower bound on the arrival time of freight trains at their destinations. We use a genetic algorithm again to schedule the freight trains in the passenger rail network, with prescribed locomotive assignment precedence constraints with the objective of minimizing total tardiness. Computational results confirm the efficacy of the proposed method.

A heuristic for routing and scheduling freight trains in a passenger rail network

This paper addresses the problem of routing and scheduling freight trains in a rail network where passenger trains must adhere to a strict schedule and freight train movements can be inserted at any time or as demands arise, without disrupting passenger trains. An exemplar of such a situation is the Indian Railway System. The problem is formulated as a 0–1 mixed integer programme to minimise the sum of travel times of the freight trains in a passenger rail network, for which a lower bound is developed. We propose a hierarchical permutation heuristic, which identifies the route and schedule for freight trains one at a time in a passenger rail network. A number of dispatching rules are proposed for identifying the best hierarchy in which trains must be scheduled. We report the computational experience for solving various problems based upon real data.

Analysis of algorithms for an online version of the convoy movement problem

In the convoy movement problem (CMP), a set of convoys must be routed from specified origins to destinations in a transportation network, represented by an undirected graph. Two convoys may not cross each other on the same edge while travelling in opposing directions, a restriction referred to as blocking. However, convoys are permitted to follow each other on the same edge, with a specified headway separating them, but no overtaking is permitted. Further, the convoys to be routed are distinguished based on their length. Particle convoys have zero length and are permitted to traverse an edge simultaneously, whereas convoys with non-zero length have to follow each other, observing a headway. The objective is to minimize the total time taken by convoys to travel from their origins to their destinations, given the travel constraints on the edges. We consider an online version of the CMP where convoy demands arise dynamically over time. For the special case of particle convoys, we present an algorithm that has a competitive ratio of 3 in the worst case and (5/2) on average. For the particle convoy problem, we also present an alternate, randomized algorithm that provides a competitive ratio of (√13−1). We then extend the results to the case of convoys with length, which leads to an algorithm with an O(T+CL) competitive ratio, where T={Maxet(e)}/{Minet(e)}, C is the maximum congestion (the number of distinct convoy origin–destination pairs that use any edge e) and L={MaxcL(c)}/{MincL(c)}; here L(c)>0 represents the time-headway to be observed by any convoy that follows c and t(e) represents the travel time for a convoy c on edge e.