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This paper considers "critical path" networks which are used for the planning and scheduling of projects that consist of well defined sequences of individual activities. When the number of activities is large, it becomes difficult to prepare a network for the project as one unit, and it may also be difficult to store the network in the high speed memory of a digital computer. Also, in the cases where there are two or more independent projects, which are weakly inter-related by common activities, the problem of efficient scheduling of all the projects becomes quite difficult. This paper presents a method to "tear" or "decompose" a project network into several subnetworks, schedule the subnetworks and then to put the subnetworks back together. A computational algorithm is first given for time-only networks; then two computational formulations are given for cost-time network of project subnetworks. The latter essentially generalize the algorithm due to Fulkerson, in order to handle piecewise linear, convex, cost-time curves for some or all of the activities. [ABSTRACT FROM AUTHOR]

This paper gives a detailed description of an algorithm for the solution of a specialized Linear Programming model, to be called the Machine Loading model. It is a generalization of the Transportation Problem, in that weighting factors are applied to the individual elements which form the row and column sums. For the Machine Loading model, the simplex method reduces to a specialized algorithm which generalizes the stepping stone method of the Transportation Problem [2], [3]. With the resulting generalized stepping stone method, it becomes practicable to solve many large-scale problems for which the direct application of the simplex method would be impracticable. The present paper is restricted to a discussion of the following topics: (I) the general characteristics of the model and its topological features; (ii) a detailed solution algorithm, including a consideration of degenerate cases and the use of a computer; (iii) a more restrictive capacitated model and the corresponding modifications to the solution algorithm; and (iv) the complete illustrative solution of a numerical example. The purpose is to aid interested readers in gaining familiarity with the algorithm and facility in the solution of numerical problems. No derivations or proofs will be included. [ABSTRACT FROM AUTHOR]

A mean-variance portfolio selection model suitable for the small investor is formulated as a sequence of quadratic integer programming problems. The special structure of these quadratic problems is exploited in a partial enumeration algorithm which uses cutting planes to accelerate convergence. Computational experience is reported on problems ranging in size from fifteen to fifty variables. [ABSTRACT FROM AUTHOR]

When all the fire companies in a region are engaged in fighting fires, protection against a future fire is considerably reduced. It is standard practice in many urban fire departments to protect the exposed region by relocating outside fire companies temporarily to some of the vacant houses. In New York City, situations requiring such relocations arise ten times a day on the average. The Fire Department of the City of New York (FDNY) currently makes its relocations according to a system of preplanned moves. This system was designed at a time when alarm rates were low and is based on the assumption that only one fire is in progress at a time. Because of the high alarm rates currently being experienced in parts of New York City, this assumption is no longer valid, and the preplanned relocation system breaks down at the times when it is needed most. This paper describes a computer-based method for determining relocations that overcomes the deficiencies of the existing method by utilizing the computer's ability to (1) store up-to-date information about the status of all fires in progress and the location and activity of all fire companies, (2) generate and compare many alternative relocation plans quickly. The method, which will become part of the FDNY's real-time Management Information and Control System (MICS), is designed to be fast and to require little computer memory. After giving some background of the problem and the objectives of relocation, we give the problem a mathematical programming formulation and then describe the heuristic algorithm to be used for generating relocations in the MICS. The remainder of the paper is devoted to a discussion of an example illustrating how the algorithm works, a rigorous test of the algorithm using a computer simulation model of Fire-Department operations, and a description of the current use of... [ABSTRACT FROM AUTHOR]

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Bounding techniques similar to those used with branch and bound procedures are used in this study in conjunction with zero-one programming to produce minimum duration schedules for the resource constrained, project scheduling problem, The algorithms developed consist of examining the feasibility of a series of zero-one programming problems rather than solving one zero-one problem optimally, Computational results demonstrate the advantage of this method over using zero-one programming without employing any form of bounding. A comparison with other exact procedures for solving the resource constrained, project scheduling problem is also given. [ABSTRACT FROM AUTHOR]

This paper considers an n-server queueing system with m customer classes distinguished by the reward associated with serving customers of that class. Our objective is to accept or reject customers so as to maximize the expected value of the rewards received over an infinite planning horizon. By making the assumptions of Poisson arrivals and a common exponential service time this problem can be formulated as an infinite horizon continuous time Markov decision problem. In §3 we customize the general algorithm for solving continuous time Markov decision problems to our queueing model. In §4 we obtain qualitative results about the form of the optimal policy. §6 reports the results of simulation tests which compare heuristic policies for our model when the service times associated with each customer class have arbitrary distributions. The ‘winning’ policy is based on a rather intricate theorem whose proof comprises §6. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology for determining suboptimum relative location patterns for physical facilities. It presents a computer program governed by an algorithm which determines how relative location patterns should be altered to obtain sequentially the most improved pattern with each change, commands their alteration, evaluates the results of alterations, and identifies the sub-optimum relative location patterns. The computer output yields a block diagramatic layout of the facility areas, and the areas need not be equal. A manufacturing plant layout example is used because the methodology is well illustrated by reference to some kind of example, and this one is commonly known. The methodology itself, however, is general in nature and not restricted to such applications. [ABSTRACT FROM AUTHOR]

This paper deals with the solution to a discrete optimization problem by decomposition. It develops a criterion for ranking the decomposition procedures, discusses the properties of the optimal decompositions, and gives an algorithm for finding the best decomposition in the case of no storage limitation. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimum allocation of redundant elements in a simple series system (maximizing system reliability subject to several linear cost constraints). Under the approximation that the components of the redundancy vector can be treated as continuous variables, the paper formulates this optimization problem as a geometric programming problem, describes techniques for obtaining numerical solutions in general, and obtains asymptotic closed-form solutions. A standard numerical example is used to illustrate that the asymptotic solution, when suitably rounded, compares favorably with the discrete optimal solution. [ABSTRACT FROM AUTHOR]

The article presents a list of papers published in the 1973 issue of the periodical. Some papers are "Announcements," "API Method Extended," "Airline Crew-Scheduling," "Air-Cargo Deployment Combat Personnel," "Aircraft Average Number Collisions," "Collision Probabilities," "Large Relative Velocity," "Special Cases, Velocity," "Air Fleet Evaluation Model (AFEM)," "Airports, Parallel Runways," "Air Routes, Potential Conflict," "Air-Route Network Planning," "Augmented Predecessor Indexing Method," "Books of Interest," "Brisbane City Council Transport Services, Note," "Broken Shifts, Bus Scheduling," "Bus Crew Scheduling," "Chesapeake Bay Bridge Traffic Control," "Column Generation Algorithm," "Combat Personnel, Equipment, Deployment," "Comparison, Steady-State and Simulation Methods," "Designing Transportation Networks," "Digital Simulation, Freeway Traffic, Long Island Expressway, New York," "Facility Location Algorithm," "Feeder Transit Lines," "Freeway Traffic, Digital Simulation," "General Networks Lemmas," "Generalized Network Problems," and "Generalized Transportation Problems."

The article presents a list of programs of sessions that would be organized during "The Institute of Management Sciences" XIX International Meeting. The topics of some of the programs are: The Social Costs of Reducing Social Cost; A Conceptual Model for Analyzing Environmental Systems; Institutional and Societal Obstacles to Effectively Managing the Future; Fuzzy Algorithms and Dynamic Programming; Team Theory, Information Structures, and Optimal Control; The Interactive Assessment of Complex Preference Functions; Evaluation Process Models, Objective and Subjective Comparisons; A Comparison of Aggregate Production Planning Rules Using a Corporate Simulation Model; Lot Sizing Procedures for Requirements Planning Systems: A Framework for Analysis; Business, Discretionary Power, and the Quality of Life; Predictive Models for Ambulatory Patient Service Time; Optimization of Interaction Process Between Psychiatric Setting and Community; and The Organization and Staffing of Evaluation Units in Limited Institutions.

A theory of equivalent integer programs is developed that shows that every all-integer integer programming problem is equivalent to infinitely many other integer programming problems. The equivalence is such that the solution to any one problem in the equivalence class determines the solution to every other problem in the class. Procedures to construct certain canonical problems in each equivalence class are described. The relationship of this theory to computational algorithms is discussed. [ABSTRACT FROM AUTHOR]

In this report, twenty-nine integer linear programming problems, ranging from very simple to apparently rather difficult, are introduced. The results of running these problems on four different computer codes, involving five distinct algorithms, are presented as both time and iteration data. A brief description of the codes used is also included. [ABSTRACT FROM AUTHOR]