We present a new disaggregated formulation of the Capacitated Concentrator Location Problem (CCLP) using the notion of cardinality of terminals assigned to a concentrator. This formulation consists of O(mnn) variables and constraints, where m denotes the number of concentrators and n the number of terminals, respectively. We prove that this extended formulation is stronger than the traditional one. We also present two classes of inequalities exploiting the cardinality effect of the extended formulation. The first class is a generalization of the well-known Cover and (1, k)-Configuration inequalities, which collectively are stronger than the original Cover and (1, k)-Configuration inequalities. The second class, called the 2-Facility Cardinality Matching Inequality, holds for the uncapacitated version of the Concentrator Location Problem and can be lifted to become a strong inequality for CCLP. We solve the LP relaxation of the extended formulation and use separation heuristics to identify and sequentially add the previous valid inequalities to improve the lower bound. This approach is embedded in a branch-and-bound and results in a branch-and-cut approach. We test our solution approach on a large set of benchmark problems. The experimentation shows that we can identify the optimal solution at the root node in most of the problem instances with up to 50 concentrators and 50 terminals. For larger sized test problems with up to 100 concentrators and 1000 terminals, the branch-and-cut procedure using the disaggregated formulation outperforms the branch-and-cut procedure applied to the traditional formulation both in terms of CPU and the required number of branch-and-bound nodes. (C) 2019 Elsevier B.V. All rights reserved.

We present a new extended formulation of the Generalized Assignment Problem (GAP), that is a disaggregation of the traditional formulation. The disaggregated formulation consists of O( mn2) variables and constraints, where m denotes the number of agents and n the number of jobs. In contrast, the traditional formulation consists of O(mn) variables and constraints. The extended formulation is stronger than the traditional formulation, as its linear programming relaxation provides tighter lower bounds. Furthermore, this new formulation provides additional opportunities to generalize the well-known Cover and (1, k)-Configuration inequalities to make them far more ubiquitous. In fact, we show that the generalizations of both these inequalities when added to the disaggregated formulation provided tighter bounds than when the original Cover and (1, k)-Configuration inequalities are added to the traditional formulation. We introduce two classes of inequalities involving multiple agents that are specific to the disaggregated formulation. One class of inequalities is called the Bar-and-Handle (1, pˆk) Inequality, which under certain restrictive conditions is a facet of the polytope defined by feasible solutions of GAP. The other important class of inequality is the 2-Agent Cardinality Matching Inequality involving two agents. Given the un-capacitated version of GAP in which each agent can process all jobs, we first show this inequality to be a facet of the polytope defined by the un-capacitated GAP. We then show how this inequality can be strengthened easily by lifting it to become a strong inequality for GAP. We also show that when m=2, this inequality, along with trivial facets completely describe the polytope associated with the un-capacitated version of GAP. Finally, through computational testing we demonstrate that by substantially reducing the number of sub-problems visited in the branch-and-bound tree, our extended formulation achieves significant computation gains.

Through recent technical advances, multiple resources can be connected to provide a computing grid for processing computationally intensive applications. We build on an approach, termed sequential grid computing, that takes advantage of idle processing power by routing jobs that require lengthy processing through a sequence of processors. We present two models that solve the static and dynamic versions of the sequential grid scheduling problem for a single job. In the static and dynamic versions, the model maximizes a reward function tied to the probability of completion within service-level agreement parameters. In the dynamic version, the static model is modified to accommodate real-time deviations from the plan. We then extend the static model to accommodate multiple jobs. Extensive computational experiments highlight situations (a) where the models provide improvements over scheduling the job on a single processor and (b) where certain factors affect the quality of solutions obtained.

Distribution of commodities such as power fuels to agricultural operations often involves trade-offs among competing criteria (for instance, minimization of delivery time versus maximization of volume delivered). The agricultural environment faces a number of market dynamics, including declining margins and more efficient farming methods such as 'no-till' farming, that affect the demand for power fuels. This dynamic environment requires farm managers to examine the supply chain for opportunities to obtain more efficient and effective delivery plans. We present an approach for distribution planning. It is comprised of three tightly-coupled stages with an underlying DSS system which we also applied to this single-commodity multiple-depot scenario of distributing agricultural power fuel to customers. The process facilitates (1) Problem characterization, (2) Model specification, and (3) Interactive distribution planning. A synthesis of the literature with our current study offers managers and academics a useful application scenario for integrating process components and viewing the major thrusts of past research. We present an illustrative case study which required a bicriteria model. Trade-offs are examined among non-dominated distribution plans.

In this paper, a model and a solution procedure is developed for the File Allocation and Join Site Selection Problem with 2-way Join [FAJSP-2], defined on a telecommunications network. This problem attempts to integrate the file allocation and query optimization aspects of a distributed computing system. By allowing for queries that require processing up to two file types, this problem is designed to determine simultaneously the number and location of file types and the location of join operations. This problem is modeled as a mixed-integer linear program, for which a fast dual-ascent approximation procedure is developed. Extensive computational results are presented which demonstrate that our dual-ascent procedure is able to solve even large-scale problems to near optimality quickly. © 1999 John Wiley & Sons, Inc. Networks 33: 109–124, 1999

Topological design of communication networks has been well examined in the literature. However, most of these studies focus on nonhierarchical networks where all nodes are considered equivalent from a routing perspective. It is well recognized, however, that hierarchical topologies offer several advantages for remote office internetworking. In this article, we provide a mixed integer programming formulation for designing hierarchical topologies. We also provide an interesting solution strategy that incorporates valid inequalities within a dual ascent framework to obtain tight lower bounds and feasible solutions to the problem. Computational experiments with a Fortran implementation of the procedure are also reported.

This paper considers a stochastic shortest path problem where the arc lengths are independent random variables following a normal distribution. In this problem, the optimal path is one that maximizes the expected utility, with the utility function being piecewise-linear and concave. Such a utility function can be used to approximate nonlinear utility functions that capture risk averse behaviour for a wide class of problems. The principal contribution of this paper is the development of exact algorithms to solve large problem instances. Two algorithms are developed and incorporated in labelling procedures. Computational testing is done to evaluate the performance of the algorithms. Overall, both algorithms are very effective in solving large problems quickly. The relative performance of the two algorithms is found to depend on the “curvature” of the piecewise linear utility function.

In this paper, the stochastic shortest path problem of determining a path that maximizes the expected utility is considered. The nature of the utility function used to evaluate paths is of a decreasing deadline type. The principal contribution of this paper is the development of exact algorithms that use two types of pruning techniques that are incorporated in labeling procedures. One type of pruning makes use of the concept of local preference relations while the other type makes use of relaxations. Specifically two algorithms are developed, each containing the same preference relation, but two different relaxations. Our extensive computational testing indicate that both these algorithms are able to solve even large size problems quickly. More importantly, even for large problems, both the algorithms solved them by enumerating a very small percentage of all paths.

We present a technique to construct efficient belief network structures for application areas where large amounts of data are available and information on the ordering of the variables can be obtained from domain experts. We identify classes of networks that are efficient for propagating beliefs. We formulate the problem as one of determining the belief network representation from a given class that best represents the data. We use the I-Divergence measure which is known to have certain desirable properties for evaluating different approximations. We present some theoretical findings that characterize the nature of solutions that are obtained. These theoretical results lead to an efficient solution procedure for finding the best network representation. We also discuss other information that may be reasonably obtained from experts, and show how such information leads to improving the efficiency of the technique to find the best network structure.

In this paper a form of the stochastic shortest path problem is considered where the optimal path is one that maximizes the expected utility which is concave and quadratic. The principal contribution of this paper is the development of a relaxation based pruning technique which is incorporated into a label setting procedure. The basic label setting procedure solves the problem by generating all Pareto-optimal paths. However, the number of such paths can grow exponentially with the size of the problem. The relaxation based pruning technique developed here is able to recognize and discard most of the Pareto-optimal paths that do not contribute to the optimal path. Our computational results show that the label setting procedure that incorporates the pruning technique consistently outperforms the basic label setting procedure, and is able to solve large problems very quickly.

This paper addresses the problem of constructing belief network based expert systems. We discuss a design tool that assists in the development of such expert systems by comparing alternative representations. The design tool uses information theoretic measures to compare alternative structures. Three important capabilities of the design tool are discussed: (i) evaluating alternative structures based on sample data; (ii) finding optimal networks with specified connectivity conditions; and (iii) eliminating weak dependencies from derived network structures. We have examined the performance of the design tool on many sets of simulated data, and show that the design tool can accurately recover the important dependencies across variables in a problem domain. We illustrate how this program can be used to design a belief network for evaluating the financial distress situation for banks.

The representation of uncertainty, and reasoning in the presence of uncertainty, has become an important area of research in expert systems. Belief networks have been found to provide an effective framework for the representation of uncertainty using probability calculus. Unfortunately, belief propagation techniques for general network structures are computationally intense. In this paper, we present belief network representations that approximate the underlying dependency structure in a problem domain in order to allow efficient propagation of beliefs. An important issue then is one of obtaining the ‘best’ approximate representation. A criterion is required to measure the closeness of the approximate to the actual. We examine desirable features of measures that compare approximate representations to the actual one. We identify two well-known measures, called the logarithm rule and the quadratic rule, as having special properties for evaluating approximations. We present a new result that shows the equivalence of using the logarithm rule to that of finding the maximum likelihood estimator. Next, we discuss the modeling implications of using the logarithm rule and the quadratic rule in terms of the nature of solutions that are obtained, and the computational effort required to obtain such solutions. Finally, we use a decision theoretic approach to compare such solutions using a common frame of reference. A simple decision problem is modelled as a belief network, and the comparison is performed over a wide range of probability distributions and cost functions. Our results suggest that the logarithm rule is very appropriate for evaluating approximate representations.

In this paper an interactive procedure is developed for the bicriterion shortest path problem. It is assumed that the decision maker's inherant utility function is quasi-concave and non-increasing, and that the network consists of non-negative, integer valued arc lengths. The proposed procedure uses the concept of domination cones, which it develops from pairwise comparisons of alternatives. These domination cones are used to fathom a large number of Pareto-optimal solutions. Extensive computational testing was performed on large grid networks, simulating the decision maker's response using polynomial utility functions. The results indicate that our proposed procedure is able to converge to the optimal solution in a reasonably small number of pairwise comparisons, even for those problems with a large number of Pareto-optimal solutions.

A major design issue facing the designer of a distributed computing system involves the determination of the number of file copies and their locations in the distributed environment. This problem is commonly referred to as the file allocation problem (FAP). In this paper, a FAP model is formulated that seeks to obtain the lowest cost file allocation strategy, that ensures the attainment of acceptable levels of response times during peak demand periods, for all on-line queries. Unlike previous FAP research, the proposed model treats response time on a query-by-query basis, and not as a single, system wide average delay constraint. A Laggrangian relaxation based solution procedure is proposed for the resulting 0/1 integer programming problem. Results of computational experiments with the proposed solution procedure are reported.

Rapid advances in computing and communications technology have made distributed computing an attractive alternative for geographically dispersed organizations. A telecommunication sub-network forms the backbone of these distributed systems. In general, this paper focuses on the assignment of communication channel capacities in the presence of time variant usage patterns. Specifically, we concentrate on long-range capacity planning for organizations that construct networks by leasing communication channels from telecommunication companies. We formulate the capacity assignment problem as a 0-1 integer program that seeks to minimize total leasing cost subject to communication delay restrictions. Unlike previous models that include a single-system wide-average delay constraint, our model allows the flexibility of specifying delay restrictions by communicating node pairs. We propose an efficient heuristic, and a Lagrangian relaxation based procedure to obtain performance guarantees on the solution obtained from the heuristic.

In this paper we consider the dynamic file allocation problem, where query and update costs vary from one time period to the next. We develop a mixed integer linear program to model this problem. The model incorporates startup costs which are incurred if a location maintains a file copy in a given time period, but did not maintain it the previous time period. We develop a branch-and-bound algorithm to solve this problem optimally. Our algorithm uses a new nested dual ascent procedure to solve the dual of the LP relaxation quickly and provide good feasible solutions. Our computational results show that the proposed solution procedure outperforms MPSX by many orders of magnitude and is able to solve large problems in a reasonable amount of time.

In this article we consider a multiperiod assignment problem where the assignment cost of assigning job i to machine j varies from one time period to the next. A start-up cost is incurred whenever the job processed by a machine in the current time period is different from the one processed in the previous time period. This problem is modeled as an integer programming problem for which a dual ascent approximate procedure is developed. Our computational results show that our procedure outperforms the more common Lagrangian-relaxation-based subgradient procedure by a significant margin. It is also found to be faster than MPSX/370 by many orders of magnitude.

In this article we consider the problem of determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it. This problem has a direct application in scheduling. It also has indirect applications in a class of routing problems and when considering multiobjective shortest-path problems. We present a label-correcting procedure for this problem. We also develop two pruning techniques, which, when incorporated in the label-correcting algorithm, recognize and discard many paths that are not part of the optimal path. Our computational results indicate that these techniques are able to speed up the label-correcting procedure by many orders of magnitude for hard problem instances, thereby enabling them to be solved in a reasonable time.

Due to the growing popularity of distributed computing systems and the increased level of modelling activity in most organizations, significant benefits can be realized through the implementation of distributed model management systems (DMMS). These systems can be defined as a collection of logically related modelling resources distributed over a computer network. In several ways, functions of DMMS are isomorphic to those of distributed database systems. In general, this paper examines issues viewed as central to the development of distributed model bases (DMB). Several criteria relevant to the overall DMB design problem are discussed. Specifically, this paper focuses on the problem of distributing decision models and tools (solvers), henceforth referred to as theModel Allocation Problem (MAP), to individual computing sites in a geographically dispersed organization. In this research, a 0/1 integer programming model is formulated for the MAP, and an efficient dual ascent heuristic is proposed. Our extensive computational study shows in most instances heuristic-generated solutions which are guaranteed to be within 1.5–7% of optimality. Further, even problems with 420 integer and 160,000 continuous variables took no more than 60 seconds on an IBM 3090-600E computer.

A major design issue facing the designer of a distributed computing system involves the determination of the number of file copies and their locations in the distributed environment. This problem is commonly referred to as the file allocation problem FAP. This paper considers two FAP models that seek to minimize operating costs i.e., the total cost of file storage and query/update communication. The first model ensures the attainment of acceptable levels of communication delay during peak network traffic periods worst-case scenario. The second model considers average communication delay. Unlike previous FAP research, the proposed models treat communication delay on a query-by-query basis, and not as a single, system-wide average delay constraint. For both models, a Lagrangian relaxation-based solution procedure is proposed for the resulting 0/1 integer programming problem. In the case of average delays, we utilize a hybrid model combining analytic and simulation procedures. The results of computational experiments with the proposed solution techniques are reported.