Pitu B. Mirchandani

Modeling and Analysis for Hazardous Materials Transportation: Risk Analysis, Routing/Scheduling and Facility Location

We survey research on hazardous materials transportation in the areas of risk analysis, routing/scheduling and facility location. Our focus is primarily on work done since 1980, and on research which is methodological rather than empirical. We also limit our focus to transport by land-based vehicles (truck and rail), excluding pipeline, air and maritime movements. The review traces the evolution of models from single-criterion optimizations to multiobjective analyses, and highlights the emerging direction of dealing explicitly with distributions of outcomes, rather than simply optimizing expected values. We also indicate examples of work which integrate risk analysis with routing, and routing with facility location. We conclude with a discussion of several aspects of hazardous materials transportation which offer important challenges for further research.

Shortest distance and reliability of probabilistic networks

Abstract When the “length” of a link is not deterministic and is governed by a stochastic process, the “shortest” path between two points in the network is not necessarily always composed of the same links and depends on the state of the network. For example, in communication and transportation networks, the travel time on a link is not deterministic and the fastest path between two points is not fixed. This paper presents an algorithm to compute the expected shortest travel time between two nodes in the network when the travel time on each link has a given independent discrete probability distribution. The algorithm assumes the knowledge of all the paths between two nodes and methods to determine the paths are referenced. In reliability (i.e. the probability that two given points are connected by a path) computations, associated with each link is a probability of “failure” and a probability of “success”. Since “failure” implies infinite travel time, the algorithm simultaneously computes reliability. The paper also discusses the algorithms capability to simultaneously compute some other performance measures which are useful in the analysis of emergency services operating on a network.

AN INTEGRATED NETWORK PLANAR MULTIOBJECTIVE MODEL FOR ROUTING AND SITING FOR HAZARDOUS MATERIALS AND WASTES

Dealing with hazardous materials and wastes has become a problem of major concern for countries throughout the world. This paper presents a model useful in making routing decision, for either material or waste shipments, and siting decisions for waste treatment facilities. Risk, cost, and risk equity are considered jointly in a multiobjective framework. Costs are treated as link attributes while risks, from both transport and treatment, are zonal attributes, pertaining to nonoverlapping geographic areas spread out over the plane. Risks accrue within these zones, due to shipments crossing nearby links or wastes being processed, stored or disposed of at nearby treatment facilities. Total risk is the sum of the zonal risks. Equity is measured as the maximum zonal risk per unit population. Shippers will find the model useful in optimizing their logistics plans. Government agencies will find it helpful in determining how regulations should be set to obtain publicly desirable routing and siting patterns. The model is described in detail and applied in simplified form to an illustrative problem.

Path Preferences and Optimal Paths in Probabilistic Networks

The classical shortest route problem in networks assumes deterministic link weights, and route evaluation by a utility (or cost) function that is linear over path weights. When the environment is stochastic and the “traveler’s” utility function for travel attributes is nonlinear, we define “optimal paths” that maximize the expected utility. In this setting, the concept of temporary and permanent preferences for route choices is introduced. It is shown that when the utility function is linear or exponential (constant risk averseness), permanent preferences prevail and an efficient Dijkstra-type algorithm can be used.

Optimal paths in probabilistic networks: a case with temporary preferences

Abstract The classical shortest route problem in networks assumes deterministic arc weights and a utility (or cost) function that is linear over path weights for route evaluation. When the environment is stochastic and the “travelers” utility function for travel attributes is nonlinear, we define “optimal paths” that maximize the expected utility. We review the concepts of temporary and permanent preferences for comparing a travelers preference for available subpaths. It has been shown before that when the utility function is linear or exponential, permanent preferences prevail and an efficient Dijkstra-type algorithm [3] is available that determines the optimal path. In this paper an exact procedure is developed for determining an optimal path when the utility function is quadratic—a case where permanent preferences do not always prevail. The algorithm uses subpath comparison rules to establish permanent preferences, when possible, among subpaths of the given network. Although in the worst case the algorithm implicitly enumerates all paths (the number of operations increasing exponentially with the size of the network), we find, from the computational experience reported, that the number of potentially optimal paths to evaluate is generally manageable.

‘Multidimensional’ extensions and a nested dual approach for the m-median problem

Abstract A general framework for modeling median type locational decisions, where (i) travel costs and demands may be stochastic, (ii) multiple services or commodities need to be considered, and/or (iii) multiple median type objectives might exist, is presented—using the concept of “ multidimensional networks ”. The classical m -median problem, the stochastic m -median problem, the multicommodity m -median problem and and multiobjective m -median problem are defined within this framework. By an appropriate transformation of variables, the multidimensional m -median problem simplifies to the classical m -median problem but with a K -fold increase in the number of nodes, where K is the number of dimensions of the network. A nested dual approach to solve the resulting classical m -median problem, that uses Erlenkotters facility location scheme as a subroutine, is presented. Computational results indicate that the procedure may perhaps be the best available one to solve the m -median problem exactly.

Localizing 2-medians on probabilistic and deterministic tree networks

Locating a single facility (the 1-median problem) on a deterministic tree network is very efficiently solved by Goldmans algorithm. This paper explores the possibility of efficiently solving the 2-median problem for both deterministic and probabilistic tree networks. Interesting properties (Theorems 1–4) are derived that relate the location of 1-median to the location of pairs of 2-medians. Two simple algorithms, the “Improved Link-Deletion” algorithm for the deterministic case and the “Selective Enumeration” algorithm for the probabilistic case, are presented which somewhat improve existing methods to determine 2-medians on tree networks.

Concurrent routing, sequencing, and setups for a two-machine flexible manufacturing cell

An approach that allows in-process machine-loading through magazine setups, and concurrently routes and sequences the jobs on the versatile machines, is presented. To illustrate the concurrent approach, a specific two-versatile-machine flowshop scheduling problem, referred to as 2-VFSP, is defined and studied in detail. Theoretical results show that the optimal schedule for 2-VFSP need not have more than two in-process magazine setups, giving rise to the three possible scheduling configurations. Further, it is proven that obtaining the optimal schedule is an NP-complete problem. A heuristic is developed and tested on sets of random joblists, with different setup times corresponding to varying degrees of machine versatility. Results indicate that schedules which incorporate in-process magazine setup(s) may be more desirable when the setup time is small. Thus the use of concurrent scheduling approach which allows in-process magazine setups may be especially useful for systems with very versatile machines. >

Spatial nodes in discrete location problems

Discrete location models often assume an underlying network where demands originate at point nodes. To apply these models to planar regions with continuously distributed demand, the region is usually partitioned into “zones” and the demand from each zone is assumed to originate at a point, usually the zone centroid. Thus, the point node in the underlying network represents a spatial zone with a finite area. This paper examines the effect of approximating these “spatial nodes” by point nodes. In some problem scenarios, the approximation does not affect the solution. However, especially when the locational criterion includes the consideration of intra-zonal travel cost variances (e.g. travel time variance) and demands may originate anywhere within zones of nonzero area, point nodes do not give an accurate evaluation of the performance of a locational design. To illustrate the application of the concept of spatial nodes, a model is formulated for locatingp (fire-fighting) units in a region having continuously distributed demand with the objective of minimizing a nonlinear function of arrival times of the first and second closest units to any (fire) incident. A heuristic “site-substitution” procedure is presented that solves the formulated model.

Generalized Hierarchical Facility Locations

This note presents an improved formulation of the hierarchical facility location-allocation problem. It is a generalized model in the sense that the rules for allocating demand types to facility types are general and the “successively inclusive,” “successively exclusive” and “locally inclusive-successively exclusive” allocations that have appeared in the literature are special cases of this model.