Showing papers in "Operations Research in 1972"
TL;DR: The bond energy algorithm operates upon a raw input object-object or object-attribute data array by permuting its rows and columns in order to find informative variable groups and their interrelations.
Abstract: A new cluster-analysis method, the bond energy algorithm, has been developed recently; it operates upon a raw input object-object or object-attribute data array by permuting its rows and columns in order to find informative variable groups and their interrelations. This paper describes the algorithm and illustrates by several examples its use for both problem decomposition and data reorganization.
743 citations
TL;DR: This paper analyzes a queuing model consisting of a system of queues that are attended periodically in a given order by a single server and shows how the moments of these distributions can be calculated.
Abstract: This paper analyzes a queuing model consisting of a system of queues that are attended periodically in a given order by a single server. The server empties each queue before proceeding to the next queue in sequence. A changeover time is required whenever the server switches from one queue to another. For a stationary process expressions are obtained for the Laplace-Stieltjes transforms of the waiting-time and intervisit-time distributions at each queue. It is also shown how the moments of these distributions can be calculated.
259 citations
TL;DR: An algorithm is presented that will minimize the total processing time for a particular case of the n-job, m-machine scheduling problem by modeling it as a traveling-salesman problem and known solution techniques can be employed.
Abstract: This paper presents an algorithm that will minimize the total processing time for a particular case of the n-job, m-machine scheduling problem. In many industrial processes, jobs are processed by a given sequence of machines. Often, once the processing of a job commences, the job must proceed immediately from one machine to the next without encountering any delays en route. The machine sequence need not be the same for an jobs. Because of this processing constraint that prohibits intermediate queues, most normal scheduling techniques are not applicable. This paper obtains a solution to this constrained scheduling problem by modeling it as a traveling-salesman problem; known solution techniques can then be employed. The paper solves a sample problem and discusses computational considerations.
227 citations
TL;DR: The Dantzig property of transportation matrices is shown to hold for a more general class of matrices arising in connection with adjacent integer solutions to P′, and it is shown that, for every feasible integer basis toP′, there are at least as many adjacent feasible integer bases as there are nonbasic columns.
Abstract: This paper establishes some useful properties of the equality-constrained set-covering problem P and the associated linear program P′. First, the Dantzig property of transportation matrices is shown to hold for a more general class of matrices arising in connection with adjacent integer solutions to P′. Next, we show that, for every feasible integer basis to P′, there are at least as many adjacent feasible integer bases as there are nonbasic columns. Finally, given any two basic feasible integer solutions x1 and x2 to P′, x2 can be obtained from x1 by a sequence of p pivots (where p is the number of indices j ϵ N for which xj1 is nonbasic and xj2 = 1), such that each solution in the associated sequence is feasible and integer. Some of our results have been conjectured earlier by Andrew, Hoffmann, and Krabek in a paper presented to ORSA in 1968.
198 citations
TL;DR: This paper defines a problem type that can be considered a generalization of the Hitchcock transportation problem in which, in addition to seeking the amounts to be shipped from origins to destinations, it is also necessary to find the optimal locations of these sources with respect to a fixed and known set of destinations.
Abstract: This paper defines a problem type, called the transportation-location problem, that can be considered a generalization of the Hitchcock transportation problem in which, in addition to seeking the amounts to be shipped from origins to destinations, it is also necessary to find, at the same time, the optimal locations of these sources with respect to a fixed and known set of destinations. This new problem is characterized mathematically, and exact and approximate methods are presented for its solution.
196 citations
TL;DR: This paper gives a model in which two urban emergency service units such as fire engines or ambulances cooperate in responding to alarms or calls from the public in a specified region of a city.
Abstract: This paper gives a model in which two urban emergency service units such as fire engines or ambulances cooperate in responding to alarms or calls from the public in a specified region of a city. Given the home locations of the units and the spatial distribution of alarm rates, it is possible to specify which unit should respond to each alarm by defining a response area for each unit. The average response time to alarms and the workload of each unit are calculated as functions of the boundary that separates their response areas. The boundaries that minimize average response time and the ones that equalize workload are determined. Some boundaries can be dominated, in the sense that another boundary improves both workload balance and response time. The set of undominated boundaries is found.
173 citations
TL;DR: The queues formed by aircraft in stacks awaiting landing clearance have usually been treated either by machine simulation, or analytically as stochastic processes with time-independent transition probabilities, but the present paper regards the queue-developing process as strongly time-dependent, often with a diurnal (24-hour) periodicity.
Abstract: The queues formed by aircraft in stacks awaiting landing clearance have usually been treated either by machine simulation, or analytically as stochastic processes with time-independent transition probabilities (possessing stationary solutions). In contrast to such methods, the present paper regards the queue-developing process in question as strongly time-dependent, often with a diurnal (24-hour) periodicity. The formulation and treatment are entirely analytic and make use of machines only to solve the equations for the probabilities, by economical deterministic steps, using the coefficients as given in tabular form. Time-varying Poisson arrivals are assumed, and also an upper limit to queue length. Two laws of servicing are used: Poisson and fixed service time; these extremes are found to lead to numerically close results in the realistic case. This situation contrasts with the much cruder approximation of deterministic flow models. The stochastic equations belong to well studied types of differential or...
153 citations
TL;DR: This paper derives general results in the case where the income process is skip free to the right, and establishes the factorization formula and shows it to be closely connected with the probability of ruin.
Abstract: In this model the income process of a firm is assumed to be a homogeneous Markov process (discrete or continuous). One is interested in an optimal dividend strategy, i.e., a strategy that maximizes the expected sum of the discounted dividend payments. This paper derives general results in the case where the income process is skip free to the right; in particular, it establishes the factorization formula and shows it to be closely connected with the probability of ruin. The theory is illustrated by a numerical example.
137 citations
TL;DR: This paper considers one class of problems associated with urban service systems that dispatch vehicles from fixed facilities and suggests that redistricting and facility location based on rather crude assumptions and an awareness of some of the heuristic properties illustrated by simple analytical models may yield mean travel times very near the minimum possible.
Abstract: This paper considers one class of problems associated with urban service systems that dispatch vehicles from fixed facilities. Given the limited resources available, one important issue is the location of the facilities and the design of their response districts to minimize average response time in the face of spatially distributed demand patterns. Calculations with spatially homogeneous demands suggest that the mean travel time resulting from totally random distribution of facilities in the region served is reduced by only 25 per cent when the facilities are optimally distributed. This apparent insensitivity of mean travel time to facility location is pursued in detail by analyzing two classes of systems involving a pair of facilities. In the first case, a procedure is outlined for determining the optimal location of a second facility, given a position for the first facility, when no interfacility cooperation is allowed. In the second case, the same region is examined, but allowing a form of interfacility cooperation. These simple models suggest that, because of insensitivities, it may not be necessary to quantize geographical data finely and then to try laboriously to find the "optimal" solutions to redistricting and facility-location problems. Redistricting and facility location based on rather crude assumptions and an awareness of some of the heuristic properties illustrated by simple analytical models may yield mean travel times very near the minimum possible.
80 citations
TL;DR: This paper presents several fault-testing models for the k-out-of-n type k/n system, composed of n components that either work or fail, making the series n/n and parallel 1/n systems special cases.
Abstract: This paper presents several fault-testing models. Our system is composed of n components that either work or fail. The systems treated are the k-out-of-n type k/n. This system works if and only if k or more of its components work, making the series n/n and parallel 1/n systems special cases. Components can be individually tested and tests give perfect information. Each test has a time to complete it and testing procedures are judged by the expected cumulative testing time they require. In the first model, the components are assumed to function or fail independently of each other. A feasible test procedure must determine as if the system is working or has failed. This is solved for the series and parallel systems and, under a possibly restrictive hypothesis, for the general k/n system. In another model, the components are assumed to be nominally independent conditioned on the system being failed. Here a feasible test procedure must locate all failed components. This problem is solved for the general k/n system.
72 citations
TL;DR: The model characterizes the effects of center locations upon aggregate utilization and utilization of individual centers, and gives optimal locations of centers with respect to several alternative criteria.
Abstract: In planning for health services, the need arises to determine the location, capacity, and number of health centers for a geographically defined region. The present paper formulates this problem in a form convenient for solution and presents results from the model to clarify some important aspects of this allocation decision. The planning region is assumed to consist of geographically defined subareas or census blocks, of known location. The population is stratified in such a way that each stratum exhibits relatively homogeneous patterns of health-care utilization. The model characterizes the effects of center locations upon aggregate utilization and utilization of individual centers, and gives optimal locations of centers with respect to several alternative criteria. An example illustrating computational feasibility and the implications of various criteria for the location decision is presented.
TL;DR: The results show that the elimination of observations near the beginning of the simulation reduces bias, as intended, but increases the variance, sometimes significantly.
Abstract: This paper uses a first-order autoregressive scheme to investigate the effects of initial conditions in a simulation on the estimation of the population mean of a process of interest. The effects are measured by bias and variance. The results show that the elimination of observations near the beginning of the simulation reduces bias, as intended, but increases the variance, sometimes significantly.
TL;DR: This paper presents a generalization of results of Hakimi and Goldman on optimum locations of centers (warehouses) in a network leading to a proof of a stronger version of Goldman's conjecture.
Abstract: This paper presents a generalization of results of Hakimi and Goldman on optimum locations of centers (warehouses) in a network. This generalization is achieved by a conceptual simplification of the previous results leading to a proof of a stronger version of Goldman's conjecture.
TL;DR: 12. E. L. KELLER, Quadratic Optimization and Linear Complementarity, Doctoral Dissertation, University of Michigan, Ann Arbor, 1969.
Abstract: We construct a branch-and-bound algorithm for seeking the p-median, and make comparisons with the vertex-substitution method of Teitz and Bart [Opns. Res. 16, 955–961 (1968)]. We show how the vertex-substitution method can lead to a local optimum, and give a heuristic method for finding a good initial solution for this method.
TL;DR: A discounted analogue to L = λW is presented, together with an application to a queuing optimization problem, to construct a new proof of the classical (limiting average) version of L =λW, using as hypotheses only that the limiting averages of λ and W exist and are finite.
Abstract: This paper presents a discounted analogue to L = λW, together with an application to a queuing optimization problem. This discounted analogue is used to construct a new proof of the classical (limiting average) version of L = λW, using as hypotheses only that the limiting averages of λ and W exist and are finite.
TL;DR: Proofs of the convergence of these new algorithms are sketched and some computational experiences based on the modeling of the Great Lakes regulation systems are given.
Abstract: The difficulty in solving a Markovian decision problem with a large number of states by Howard's policy-iteration method is that one has to solve a large system of simultaneous linear equations. Procedures developed by D. J. White and J. MacQueen, which avoid this difficulty, have been widely used to handle large-scale Markovian decision problems. This paper extends these algorithms to the case where the Markovian decision process is periodic. Proofs of the convergence of these new algorithms are sketched. Some computational experiences based on the modeling of the Great Lakes regulation systems are also given.
TL;DR: A simulation model of the lengths of stay in the operating room and the recovery room is constructed by the Monte Carlo method, it is tested statistically and its results interpreted, and can facilitate planning, decision-making, and managerial control by providing management information.
Abstract: The purpose of this paper is to provide an insight into the increased need for operating-room and recovery-room facilities and space, based on an increased bed complement. The problem is formulated into three primary questions: (1) How many more surgical procedures will be performed because of the increased bed capacity? (2) How much operating-room time and space will the surgical procedures require? (3) How much recovery-room time and space will the surgical procedures require? To answer these questions, a simulation model of the lengths of stay in the operating room and the recovery room is constructed by the Monte Carlo method, it is tested statistically and its results interpreted. This simulation model can facilitate planning, decision-making, and managerial control by providing management information.
TL;DR: This paper specializes a more general formula, denoted by H = λG, in order to obtain relations between moments of L and W other than the first, and the basic queue considered is G/G/k with stationary input.
Abstract: The well known formula L = λW relates the time-average number in queue to the expected wait in queue of a customer. This paper specializes a more general formula, denoted by H = λG, in order to obtain relations between moments of L and W other than the first. The basic queue considered is G/G/k with stationary input. The special case where the arrival times form a renewal process and the more special case where they are a Poisson process are also discussed.
TL;DR: A tight lower bound to the travelling-salesman problem is found by an iterative procedure with guaranteed convergence and is shown to require a computation time only about 9 per cent greater than the time required to solve an equivalent assignment problem.
Abstract: This paper concerns finding a tight lower bound to the travelling-salesman problem, with the hope that all the different branch-and-bound algorithms for this problem can benefit from it. The bound is calculated by an iterative procedure with guaranteed convergence and is shown to require a computation time only about 9 per cent greater than the time required to solve an equivalent assignment problem. This new bound was tested on 14 sample problems and, on the average, found to be only 4.7 per cent below the optimum for symmetrical, and 3.8 per cent below the optimum for asymmetrical problems.
TL;DR: A procedure for assigning students to public schools optimally, given that a specified racial balance must be attained in each school, is developed as a minimum-cost flow problem in a single-commodity network.
Abstract: This paper is concerned with developing a procedure for assigning students to public schools optimally, given that a specified racial balance must be attained in each school. The criterion for optimality is to minimize the total number of miles traveled. The problem is formulated as a minimum-cost flow problem in a single-commodity network. A summary of the results achieved by the model for the Gainesville, Florida, school system is discussed.
TL;DR: A method for primal decomposition of large convex separable programs into a sequence of smaller subproblems is presented and is more efficient than the usual linear gradient approximation used in methods of feasible direction, but it is still made with a linear program.
Abstract: This paper presents a method for primal decomposition of large convex separable programs into a sequence of smaller subproblems. The main advantage of primal decomposition over Lagrange-multiplier or dual-decomposition methods is that a primal feasible solution is maintained during the course of the iterations. Feasibility is maintained by recasting the original convex separable program into a context of resource allocation. Then a direction-finding procedure for a method of feasible directions is developed for the derived resource-allocation problem. The direction-finding procedure utilizes the directional derivative to give a piecewise-linear approximation to the primal resource-allocation function. This approximation is more efficient than the usual linear gradient approximation used in methods of feasible direction, but it is still made with a linear program. The efficiency of the piecewise-linear approximation and the operation of the method of feasible directions are illustrated by a simple numerica...
TL;DR: Theoretical results are presented for a problem of optimally partitioning a given set of points in k-dimensional Euclidean space into n subsets, where each subset has a specified Lebesgue measure.
Abstract: Many problems in two-dimensional location analysis can be formulated as one of optimally dividing a given region into n subregions with specified areas. Examples are problems involving districting, facility design, warehouse layout, and urban planning. This paper contains a study of such a partitioning problem. Theoretical results are presented for a problem of optimally partitioning a given set of points in k-dimensional Euclidean space into n subsets, where each subset has a specified Lebesgue measure. The existence of an optimal solution is established, and necessary and sufficient optimality conditions are proved. Models are then formulated in terms of this partitioning problem for specific districting and warehouse-layout problems.
TL;DR: In this article, a branch-and-bound algorithm is proposed for scheduling jobs on a machine using various machine tools in which considerable changing of the tools is necessary, and the changeover time depends critically on the previous jobs.
Abstract: This note discusses a problem of scheduling jobs on a machine using various machine tools in which considerable changing of the tools is necessary, and the changeover time depends critically on the previous jobs. It derives a branch-and-bound algorithm, which has been shown to be computationally restrictive at the present time. Various heuristic methods have been tried and the computational results are very promising.
TL;DR: It is shown that strictly monotonic programs and positively homogeneous programs possess the closure property needed for stability and some necessary and sufficient conditions are presented for lower and upper semicontinuity of certain point-to-set mappings.
Abstract: This paper extends the results of Evans and Gould for stability in mathematical programming. In particular, it shows that their conditions apply to functional perturbation, to equality constraints, and to policy stability under certain conditions. Further, it shows that strictly monotonic programs and positively homogeneous programs possess the closure property needed for stability. Finally, some necessary and sufficient conditions are presented for lower and upper semicontinuity of certain point-to-set mappings.
TL;DR: The paper gives an algorithm that uses partial enumeration for what is essentially a mixed integer program and employs a maximum-flow computation as a check for feasibility with respect to available resources.
Abstract: This paper treats the problem of project (or machine) scheduling with resource constraints to achieve minimum total duration time as a disjunctive graph. The prospective advantage of this approach is the elimination of the need to consider individual time periods over the program horizon; a feasibility check determines whether the resource constraints can be met by any particular network representation of the project. The paper gives an algorithm that uses partial enumeration for what is essentially a mixed integer program. The algorithm employs a maximum-flow computation as a check for feasibility with respect to available resources.
TL;DR: An algorithm for solving an arborescence-structured production and inventory system to decompose the problem into single-stage problems at each lowest-echelon facility with special computational efficiency resulting when these costs are concave.
Abstract: This paper develops an algorithm for solving an arborescence-structured production and inventory system. Arborescence structures model multi-echelon production systems in which each facility requires input from a unique immediate predecessor. Assuming known demands, and no backlogging, the objective is to schedule production over a finite planning horizon to minimize production and holding costs. The algorithm is applicable to systems in which, at all facilities with followers in the system, the production costs consist of a set-up charge plus linear costs and holding costs are linear. General costs are permitted at the lowest-echelon facilities (those without followers) with special computational efficiency resulting when these costs are concave. The algorithm exploits the known results on the structure of optimal policies in arborescence systems to decompose the problem into single-stage problems at each lowest-echelon facility. This decomposition is achieved by enumerating implicitly the feasible produ...
TL;DR: In this paper, the authors describe and discuss the results of a national survey covering the activities of the operations-research department at the corporate level, including organizational structure of the department and its position in the corporation, budget and savings, use of services, and activities in the past, present, and future.
Abstract: This paper describes and discusses the results of a national survey covering the activities of the operations-research department at the corporate level. The major points considered are: 1 the organizational structure of the department and its position in the corporation, 2 the internal structure of the department, 3 budgets and savings, 4 use of services, and 5 a study of the activities in the past, present, and future.
TL;DR: This paper deals with a search model for allocating effort when there are many target objects of differing sizes present in a search area, gives the method of maximum likelihood estimation of the model parameters, and solves the sequential decision problem of when to terminate the search process.
Abstract: This paper deals with a search model for allocating effort when there are many target objects of differing sizes present in a search area. All target objects are initially present in the search area and remain at least until discovered; no new objects are generated during the search process. Targets are not moveable. The search process is characterized by the quantity of search effort. The model describes the distribution of the number and sizes of target objects present. The probability of discovery is assumed proportional to object size. The paper gives many results, including the probability distribution of the number and sizes of discovered objects, and the prior and posterior distributions of the number of objects remaining undiscovered. Then it gives the method of maximum likelihood estimation of the model parameters, and solves the sequential decision problem of when to terminate the search process.
TL;DR: A simple and intuitive procedure for determining the boundaries of the service districts, using the criterion that each facility serves all points to which it is closest in either distance or travel time is presented.
Abstract: A problem shared by many municipal agencies and many large industries is: Given n service facilities whose locations have been set in a region, how should that region best be apportioned among the facilities if each facility is to have primary responsibility for service in one district of the region? This paper presents a simple and intuitive procedure for determining the boundaries of the service districts, using the criterion that each facility serves all points to which it is closest in either distance or travel time. The procedure is designed to be computed rapidly, either by hand or on a computer.
TL;DR: A statistical technique for the control of the traffic intensity in single-server queuing systems with (i) Poisson arrivals and general service times and (ii) recurrent arrivals and exponential service times is presented.
Abstract: This paper presents a statistical technique for the control of the traffic intensity in single-server queuing systems with (i) Poisson arrivals and general service times and (ii) recurrent arrivals and exponential service times. The procedure is such that the system is readjusted only if the number of customers in the system either falls and stays beyond the upper control limit longer than a preassigned number of consecutive transitions or falls and stays below the lower control limit longer than a preassigned number of consecutive transitions. Methods are given to derive these two pairs of control limits using available transition probability tables, and tables of control limits have been provided for a selected number of parameter values in the queue with Poisson arrivals and general service times.