Showing papers in "Management Science in 1972"
TL;DR: An interactive mathematical programming approach to multi-criterion optimization is developed, and then illustrated by an application to the aggregated operating problem of an academic department.
Abstract: An interactive mathematical programming approach to multi-criterion optimization is developed, and then illustrated by an application to the aggregated operating problem of an academic department.
837 citations
TL;DR: The multilinear extension of an n-person game v is a function defined on the n-cube IN which is linear in each variable and which coincides with v at the conrners of the cube, satisfying f(x) = v(i ∣ xi = 1}).
Abstract: The multilinear extension of an n-person game v is a function defined on the n-cube IN which is linear in each variable and which coincides with v at the conrners of the cube, satisfying f(x) = v({i ∣ xi = 1}). Multilinear extensions are useful as a help in computing the values of large games, and give a generalization of the Shapley value.
624 citations
TL;DR: In this article, the authors extend Nash's theory of two-person bargaining games with fixed threats to bargaining situations with incomplete information, and define such bargaining situations, a formal bargainin...
Abstract: The paper extends Nash's theory of two-person bargaining games with fixed threats to bargaining situations with incomplete information. After defining such bargaining situations, a formal bargainin...
581 citations
TL;DR: In this paper, the authors considered the maximization of certain equivalent reward generated by a Markov decision process with constant risk sensitivity, and developed a policy iteration procedure to find the stationary policy with highest certain equivalent gain for the infinite duration case.
Abstract: This paper considers the maximization of certain equivalent reward generated by a Markov decision process with constant risk sensitivity. First, value iteration is used to optimize possibly time-varying processes of finite duration. Then a policy iteration procedure is developed to find the stationary policy with highest certain equivalent gain for the infinite duration case. A simple example demonstrates both procedures.
481 citations
TL;DR: It is shown how the K shortest (loopless) paths in an n-node network with positive and negative arcs can be computed with an amount of computation which is O(Kn 3 ).
Abstract: A general procedure is presented for computing the best, 2nd best,…, Kth best solutions to a given discrete optimization problem. If the number of computational steps required to find an optimal solution to a problem with n(0, 1) variables is c(n), then the amount of computation required to obtain the if best solutions is O(Knc(n)). The procedure specializes to published procedures of Murty and of Yen for the assignment problem and the shortest path problem, respectively. A method is presented for reducing the required amount of storage by a factor of n, compared with the algorithms of Murty and of Yen. It is shown how the K shortest (loopless) paths in an n-node network with positive and negative arcs can be computed with an amount of computation which is O(Kn3). This represents an improvement by a factor of n, compared with Yen's algorithm.
465 citations
TL;DR: A unifying framework is developed to facilitate the understanding of most known computational approaches to integer programming, and a number of currently operational algorithms are related to this framework.
Abstract: A unifying framework is developed to facilitate the understanding of most known computational approaches to integer programming. A number of currently operational algorithms are related to this framework, and prospects for future progress are assessed.
349 citations
TL;DR: The multilinear extension of an n-person game v is a function defined on the n-cube IN which is linear in each variable and which coincides with v at the conrners of the cube, satisfying fx = v{i ∣.
Abstract: The multilinear extension of an n-person game v is a function defined on the n-cube IN which is linear in each variable and which coincides with v at the conrners of the cube, satisfying fx = v{i ∣
296 citations
TL;DR: An efficient branch and bound algorithm for a special class of mixed integer programming problems called the warehouse location problem and an improved method of solving the linear programming problems at the nodes which substantially reduces the computations are introduced.
Abstract: This paper introduces an efficient branch and bound algorithm for a special class of mixed integer programming problems called the warehouse location problem. A set of branching decision rules is proposed for selecting warehouses to be constrained open and closed from any node of the branch and bound tree. These rules are tested for their efficiency in reducing computation times and storage requirements to reach optimal solutions. An improved method of solving the linear programming problems at the nodes which substantially reduces the computations is also introduced in this paper.
286 citations
TL;DR: The purpose of this paper is to present an effective method for finding all regions R i that cover K and do not overlap that uses an algorithm that finds all nodes of a finite connected graph.
Abstract: The multiparametric linear programming (MLP) problem for the right-hand sides (RHS) is to maximize z = cTx subject to Ax = b(λ), x ≧ 0, where b(λ) be expressed in the form \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$ b(\lambda) = b^\ast + F \lambda, $$ \end{document} where F is a matrix of constant coefficients, and λ is a vector-parameter. The multiparametric linear programming (MLP) problem for the prices or objective function coefficients (OFC) is to maximize z = cT(v)x subject to Ax = b, x ≧ 0, where c(I) can be expressed in the form c(v) = c* + Hv, and where H is a matrix of constant coefficients, and v a vector-parameter. Let Bi be an optimal basis to the MLP-RHS problem and Ri be a region assigned to Bi such that for all λ ϵ Ri the b...
250 citations
TL;DR: In this article, the problem is decomposed by a primal resource-directive approach into a multiple-choice programming master problem, with quadratic programming sub-problems, and a linear programming formulation, with a post-optimal feasibility search scheme, may be substituted for the multiplechoice master problem.
Abstract: The Nursing Personnel Scheduling Problem is defined as the identification of that staffing pattern which (1) specifies the number of nursing personnel of each skill class to be scheduled among the wards and nursing shifts of a scheduling period, (2) satisfies total nursing personnel capacity, integral assignment, and other relevant constraints, and (3) minimizes a “shortage cost” of nursing care services provided for the scheduling period. The problem is posed as a mixed-integer quadratic programming problem, which is decomposed by a primal resource-directive approach into a multiple-choice programming master problem, with quadratic programming sub-problems. Initial results suggest that a linear programming formulation, with a post-optimal feasibility search scheme, may be substituted for the multiple-choice master problem. The model is tested on six wards of a 600-bed general hospital, and results are presented.
224 citations
TL;DR: An algorithm which requires interaction with the relevant decision-maker in order to obtain certain information regarding his utility function defined over the permissible values of the criteria is presented.
Abstract: The use of goal programming for the solution of the multiple criteria problem is discussed. An extension of this use is presented in the form of an algorithm which requires interaction with the relevant decision-maker in order to obtain certain information regarding his utility function defined over the permissible values of the criteria. This algorithm provides a bridge between goal programming and recently suggested interactive strategies for the optimization of the multiple criteria problem.
TL;DR: In this paper, it was shown that the asymptotic rate of convergence of gradient projection methods is also given by a Kantorovich ratio, but with α and β being determined by the Lagrangian associated with the problem.
Abstract: The method of steepest descent for solving unconstrained minimization problems is well understood. It is known, for instance, that when applied to a smooth objective function f, and converging to a solution point x where the corresponding Hessian matrix F(x) is positive definite, the asymptotic rate of convergence is given by the Kantorovich ratio (β − α)2/(β + α)2, where α and β are respectively the smallest and largest eigenvalues of the Hessian matrix F(x). This result is one of the major sharp results on convergence of minimization algorithms. In this paper a corresponding result is given for the gradient projection method for solving constrained minimization problems. It is shown that the asymptotic rate of convergence of gradient projection methods is also given by a Kantorovich ratio, but with α and β being determined by the Lagrangian associated with the problem. Specifically, if L is the Hessian of the Lagrangian evaluated at the solution, α and β are the smallest and largest eigenvalues of L whe...
TL;DR: A finite decomposition algorithm, based on the Simplex method of quadratic programming, is developed for which computer storage requirements are independent of the number of points and computing time is approximately linear in the numberof points.
Abstract: The minimum covering sphere problem, with applications in location theory, is that of finding the sphere of smallest radius which encloses a set of points in En. For a finite set of points, it is shown that the Wolfe dual is equivalent to a particular quadratic programming problem and that converse duality holds. A finite decomposition algorithm, based on the Simplex method of quadratic programming, is developed for which computer storage requirements are independent of the number of points and computing time is approximately linear in the number of points.
TL;DR: In this paper, the authors presented a multiple period bond portfolio model and suggested a new approach for efficiently solving problems which are large enough to make use of as much information as portfolio managers can reasonably provide.
Abstract: The bond portfolio problem is viewed as a multistage decision problem in which buy, sell, and hold decisions are made at successive (discrete) points in time. Normative models of this decision problem tend to become very large, particularly when its dynamic structure and the uncertainty of future interest rates and cash flows are incorporated in the model. In this paper we present a multiple period bond portfolio model and suggest a new approach for efficiently solving problems which are large enough to make use of as much information as portfolio managers can reasonably provide. The procedure utilizes the decomposition algorithm of mathematical programming and an efficient technique developed for solving subproblems of the overall portfolio model. The key to the procedure is the definition of subproblems which are easily solved via a simple recursive relationship.
TL;DR: In this paper, the optimal issuing policies for some particular classes of perishable inventory problems are derived under several possible objective functions, and it is shown that the optimal policy is to issue the oldest unit which will satisfy the demand.
Abstract: Optimal issuing policies for some particular classes of perishable inventory problems are derived under several possible objective functions. The inventory considered is one in which stock is grouped into categories according to shelf age. Demand occurs for each of the categories, and may be satisfied by inventory units from that category or from any “younger” category. It is shown for most of the objective functions considered that the optimal policy is to issue the oldest unit which will satisfy the demand. A prime example of the classes of inventory problems considered in this paper is the issuance of whole blood from a hospital or central blood bank.
TL;DR: In this paper, operational assumptions about the decision maker's preferences for multi-attributed consequences are derived and functional forms of utility functions satisfying these assumptions are derived, and a procedure to verify the appropriateness of the necessary assumptions is included.
Abstract: One of the important methodological problems concerning the application of decision analysis to complex problems is the restrictiveness of existing techniques for systematically assessing multiattributed utility functions valid for decision making under uncertainty. This is the problem addressed in this paper. Operational assumptions are postulated about the decision maker's preferences for multiattributed consequences, and functional forms of utility functions satisfying these assumptions are derived. The results are a number of representation theorems which simplify the assessment of the utility function provided the requisite assumptions hold. A special case of these results is the well-known additive utility function. A procedure to verify the appropriateness of the necessary assumptions is included.
TL;DR: While the two mean performance measures attain their minimums at the same job sequence, it is shown that the sequence that minimizes the variance of flow-time is antithetical to the sequenceThat minimizesThe variance of waiting-time, and the minimum values of the two variance measures are equal.
Abstract: The variance of flow-time and variance of waiting-time performance measures are analyzed for the single machine sequencing problem. These measures are compared and contrasted to the performance measures of mean flow-time and mean waiting-time. In particular, while the two mean performance measures attain their minimums at the same job sequence, it is shown that the sequence that minimizes the variance of flow-time is antithetical to the sequence that minimizes the variance of waiting-time. However, the minimum values of the two variance measures are equal. Relationships are also derived for the special problems where either all the job processing-times are equal or all the job weights are equal.
TL;DR: In this article, the authors considered an n-period single-product inventory model with known requirements and separable concave production and storage costs and showed that if storage and production costs are respectively non-decreasing in order and nonincreasing in time, then an optimal schedule has the property that if in a given period, facility j produces, then facility j + 1 does also.
Abstract: We consider an n-period single-product inventory model with known requirements and separable concave production and storage costs. The model is a multi-echelon structure in which N facilities, labeled 1,…,N, are arranged in series. We show that if storage and production costs are respectively nondecreasing in order of facilities and nonincreasing in time, then an optimal schedule has the property that if in a given period, facility j produces, then facility j + 1 does also. This nested structure is exploited in an algorithm for finding an optimal schedule. The computational effort increases in proportion to the cube of the number of periods and linearly with the number of facilities. For the stationary infinite horizon case an algorithm yields a periodic optimal schedule.
TL;DR: In statistical decision theory, computations often involve the partial moments of a random variable as discussed by the authors, and several methods for determining partial moments are discussed, including direct calculation, the direct calculation and the...
Abstract: In statistical decision theory, computations often involve the partial moments of a random variable. Several methods for determining partial moments are discussed, including direct calculation, the...
TL;DR: The chromatic number problem as mentioned in this paper is a special case of the chromatic scheduling problem, which is defined as any problem in which the solution is a partition of a set of objects.
Abstract: The chromatic scheduling problem may be defined as any problem in which the solution is a partition of a set of objects. Since the partitions may not be distinct, redundant solutions can be generated when partial enumeration techniques are applied to chromatic scheduling problems. The necessary theory is developed to prevent redundant solutions in the application of partial enumeration techniques to chromatic scheduling problems with indistinguishable partitions and distinct objects. The chromatic number problem, which is the problem of finding the chromatic number of any graph, is a particular case of the chromatic scheduling problem. Two algorithms, basic and look-ahead, are developed for the chromatic number problem. Computational experience is given for each algorithm.
TL;DR: The balance problem is formulated, and some of the difficulties of achieving effective balances in practice are noted, and an estimate is made of the computer effort required to achieve a balance for a large-scale assembly operation.
Abstract: This paper considers the problem of mixed-model assembly-line balancing. First, the balance problem is formulated, and some of the difficulties of achieving effective balances in practice are noted...
TL;DR: In this paper, the authors examined the accuracy of forecasts produced by nine mechanical forecasting techniques and three groups of analysts, including exponential weighted moving averages, naive models, simple moving average, and regressions.
Abstract: This paper examines the accuracy of forecasts produced by mechanical forecasting techniques and three groups of analysts. The nine mechanical forecasting techniques are variations of exponentially weighted moving averages, naive models, simple moving averages, and regressions. One-, two-and three-year forecasts are used to evaluate these techniques.
The mechanical techniques exhibit statistically significant differences in their ability to forecast earnings per share, with the exponentially weighted moving averages producing the best forecasts. One-year forecasts produced by the best of the mechanical forecasting techniques were compared to the corresponding analysts' projections. No statistically significant difference could be discerned.
TL;DR: In this paper, a goal programming model for an optimum allocation of resources in an institution of higher learning is presented, where the goal is to maximize the amount of resources allocated to each student.
Abstract: The rapid rate of technological development and the growing complexity of society in recent years have brought renewed awareness of the importance of higher education. The rapid expansion of higher education, both in size and quality, requires systematic approaches and dynamic planning for efficient resource allocation on the part of the university administrators. This paper presents a goal programming model for an optimum allocation of resources in an institution of higher learning.
TL;DR: Following the equilibrium model which has been developed by Sharpe, Lintner and Treynor, several authors have developed one-parameter indexes as measures of performance as discussed by the authors.
Abstract: Following the equilibrium model which has been developed by Sharpe, Lintner and Treynor, several authors have developed one-parameter indexes as measures of performance. In this paper, it is shown ...
TL;DR: An algorithm is presented to find a feasible solution which tends to minimize the number of required routes and mileage and possible extensions of the approach to school location planning, bus fleets composition and timing conditions on particular bus stops.
Abstract: This paper reports on an application of computer technology to a significant and costly school administration problem: the transportation of students between home and school. The problem, as it is generally thought of, has been complicated by the consideration of attempting racial balance via busing. We present an algorithm to find a feasible solution which tends to minimize the number of required routes and mileage. After setting down the basic approach used and the results of an application, we will present possible extensions of the approach to school location planning, bus fleets composition and timing conditions on particular bus stops.
TL;DR: In this article, the authors derived the form of a minimal cost rate stationary operating policy for an M/M/I queueing system with K possible service rates, and characterized the optimal policy by if K − 1 numbers.
Abstract: This paper derives the form of a minimal cost rate stationary operating policy for an M/M/I queueing system with K possible service rates. The two costs of the system are a general cost rate dependent on the state of the system and a cost rate associated with each of the possible service rates. The optimal policy is completely characterized by if K − 1 numbers. The optimal service rate is shown to be nondecreasing in the state of the system.
TL;DR: The common characteristics and operational problems of urban emergency service systems are described and the various methods, both traditional and recently developed, which may be used for allocating their units are surveyed.
Abstract: An urban emergency service system provides mobile units vehicles to respond to requests for service which can occur at any time and any place throughout a city. This paper describes the common characteristics and operational problems of these systems and surveys the various methods, both traditional and recently developed, which may be used for allocating their units. Aspects of allocation policy discussed include 1 determining the number of units to have on duty, 2 locating the units, 3 designing their response areas or patrol areas, 4 relocating units, and 5 planning preventive-patrol patterns for police cars.
Typical policy changes which may be suggested by the use of quantitative allocation models include selective queuing of low priority calls, varying the number of units on duty and their locations by time of day, dispatching units other than the closest ones to certain incidents, relocating units as unavailabilities begin to develop, and assigning police cars to overlapping patrol sectors. As a result of making such changes, it is often possible to reduce queuing and travel time delays, improve the balance of workload among units, and enhance the amount of preventive patrol where needed.
TL;DR: In this article, the problem of warehouse denials is addressed by selecting the proper frequency and depth of inventory counts, together with modifications to a given stocking policy, to minimize the total cost per unit time, subject to the likelihood of a warehouse denial between inventory counts being below a prescribed level.
Abstract: An inventory stock record is in error when the stock record is not in agreement with the physical stock. Such discrepancies may be introduced due to time lags between flow of information and material, pilferage, incorrect unit of issue, inaccurate physical inventory counts, etc. The primary impact of these errors is that the system fails to order when it should, resulting in “warehouse denials,” i.e., the stock records show a balance sufficient to issue a given material release order, but for which insufficient units of stock can physically be found.
The object of this paper is to select the proper frequency and depth of inventory counts, together with modifications to a given stocking policy, so as to minimize the total cost per unit time, subject to the likelihood of a warehouse denial between inventory counts being below a prescribed level. The goal has been to obtain results easily implementable and leads to formulae comparable to those of the classical economic lot-size models. A numerical example is included to illustrate the procedure.
TL;DR: In this paper, an approximate cost model for a quality control procedure for two or more related variables is investigated, and a method is presented to determine the optimal sample size, interval between samples, and critical region parameter for the Hotelling T2 control chart.
Abstract: An approximate cost model for a quality control procedure for two or more related variables is investigated. A method is presented to determine the optimal sample size, interval between samples, and critical region parameter for the Hotelling T2 control chart. This model is a multivariate analog of several well-known models for the univariate XI-chart. It is assumed that only one assignable cause of variation exists and the time between occurrences is exponentially distributed. Numerical results are provided in a particular bivariate case for several values of the cost coefficients. The behavior of the model to variation of the model parameters is discussed.
TL;DR: A constructive existence proof for equilibria of polymatrix games is given in this paper, which is based on a generalization of the almost complementary paths used for the linear complementarity problem.
Abstract: A constructive existence proof is given for equilibria of polymatrix games. The construction is based on a generalization of the almost-complementary paths used for the linear complementarity problem.