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Full-Text Articles in Business Administration, Management, and Operations
Generalized Upper Bounding Methods In Production Scheduling And Distribution, Leon S. Lasdon
Generalized Upper Bounding Methods In Production Scheduling And Distribution, Leon S. Lasdon
Research Reports from the Department of Operations
Generalized Upper Bounding (GUB) is an efficient specialization of the Simplex Method for problems with disjoint rows of ones. The principles of the method are briefly reviewed, and an application to multi-item production scheduling is presented. A multifacility extension of the scheduling model is formulated and solved using GUB in conjunction with Bender's Partitioning algorithm. Application of GUB to integrated production and distribution problems is also discussed.
Nonlinear Optimization With Upper And Lower Bounds, Vaughn E. Huckfeldt
Nonlinear Optimization With Upper And Lower Bounds, Vaughn E. Huckfeldt
Research Reports from the Department of Operations
Many nonlinear programming problems containing only upper and lower bounds are currently solved as unconstrained problems using transformation, or penalty methods of optimization. In this thesis it is shown that (1) Goldfarb's conjugate gradient algorithm can be simplified for NLP problems containing only upper and lower bounds, (2) the simplified algorithm requires less computer storage, and fewer multiplications per iteration with no loss in accuracy, and (3) the simplified algorithm is superior to transformation, or penalty methods when tested on published nonlinear test problems. A FORTRAN code for the nonlinear algorithm for upper and lower bounds, including complete documentation, is …
An Efficient One-Dimensional Search Procedure For Barrier Function, Leon S. Lasdon, Richard L. Fox, Margery W. Ratner
An Efficient One-Dimensional Search Procedure For Barrier Function, Leon S. Lasdon, Richard L. Fox, Margery W. Ratner
Research Reports from the Department of Operations
Interior penalty functions are a popular approach for solving non-linear constrained optimization problems. Most current methods for minimizing such functions require a one-dimensional minimization along specified search directions, and this can be quite difficult, since the function approaches +∞ along the boundaries of the feasible set. A special purpose algorithm is described which alleviates this difficulty by using a simpler approximating function which also goes to infinity near the boundary. Numerical results are presented, showing that the number of function evaluations and computation time are reduced by factors of about three and two respectively. The ideas are easily extended to …
Algorithms For Stochastic Games: A Comparison Of Efficiency, Arvind Jain
Algorithms For Stochastic Games: A Comparison Of Efficiency, Arvind Jain
Research Reports from the Department of Operations
There are two convergent algorithms for the solution of two person zero sum nonterminating stochastic games. The first one is developed by Hoffman and Karp and the second one is recently developed by Nair, Rao and Chandrasekaran. This paper presents computer programs for the two algorithms and computational experiments for comparing the efficiency of the algorithms. The results show that the second algorithm requires fewer iterations and moreover, the computation time for each iteration in this is significantly lower. Further, the results show that the ratio of the computation of time of the first algorithms to that of the second …
A Pseudo Dual All-Integer Algorithm For The Set Covering Problem, Harvey M. Salkin, Ronald D. Koncal
A Pseudo Dual All-Integer Algorithm For The Set Covering Problem, Harvey M. Salkin, Ronald D. Koncal
Research Reports from the Department of Operations
A modified linear programming method for the inequality or equality set covering problem (i.e., minimize cx subject to Ex ≥ b or Ex = b, where E is a zero-one matrix, b is a column of ones, and c is a nonnegative integral row) is presented. The "almost unimodular" property of the (zero-one) constraint matrix suggested an algorithm in which one performs (dual) simplex interactions whenever unit pivots are available and adjoin Gomory all-integer cuts when they are not. Finiteness, time reducing criteria, the elimination of roundoff errors, and applications to enumerative schemes are discussed. Preliminary computational experience, being very …
Optimal Location Of A Single Service Center Of Certain Types, K.P. K. Nair
Optimal Location Of A Single Service Center Of Certain Types, K.P. K. Nair
Research Reports from the Department of Operations
Considering communities to be interconnected by road network, Hakimi provided a graph theoretic method for finding the optimal location of a single service center, such as hospital or police station, minimizing largest distance from the service center. The same problem is considered in this paper when the region to be served is represented by a convex polygon with finite number of corner points and the distance between any pair of points in the polygon is taken to be the straight path between the two points. This problem is shown to be exact in certain cases though in some other cases …
Non Iterative Algorithm Form Solving Special Types Of Transportation Problems, Benjamin Lev
Non Iterative Algorithm Form Solving Special Types Of Transportation Problems, Benjamin Lev
Research Reports from the Department of Operations
Many transportation problems are such that, when origins and destinations are suitably indexed, the cost matrix contains elements along the main diagonal, a band above it, and a band below it, while the other elements of the cost matrix are infinite. A procedure has been developed which yields optimal solution to such tridiagonal problems in n steps for a n-origin, n-destination problem. A second model has been solved for a tridiagonal and a coupling column of the cost matrix. A third model, a four-diagonal one, has been partially solved. We suggested and showed a method to solve any other model …
On The Resource Allocation Problem With S-Shaped Utility Functions, Fabio M. Vicentini
On The Resource Allocation Problem With S-Shaped Utility Functions, Fabio M. Vicentini
Research Reports from the Department of Operations
A given amount "a" of a resource is allocated among n activities. A return Fi(xi) is obtained as a result of using xi units of the resource in activity "i". The problem is to find an allocation which maximizes the total return, that is, max Σ Fi(xi) s.t. Σ xi = a, xi ≥ 0 . In this paper we examine this well known problem under the assumption that the Fi's are "s-shaped" functions. In an economic context this assumption means that small allocations lead to essentially zero returns while large ones have a saturation effect, the "law of diminishing …
A Generalized Upper Bounding Method For Doubly Coupled Linear Programs, James K. Hartman, Leon S. Lasdon
A Generalized Upper Bounding Method For Doubly Coupled Linear Programs, James K. Hartman, Leon S. Lasdon
Research Reports from the Department of Operations
The constraints of large linear programs can often be partitioned into independent subsets, except for relatively few coupling rows and coupling columns. The individual subsets may, for example, arise from constraints on the activity levels of subdivisions of a large corporation. Alternatively, such blocks may arise from activities in different time periods. The coupling rows may arise from limitations on shared resources or from combining the outputs of subdivisions to meet overall demands. The coupling columns arise from activities which involve different time periods (e.g storage), or which involve different subdivisions (e.g. transportation or assembly). The case with only coupling …
Some Manpower Planning Models Based On Educational Attainment, Warren L. Balinsky
Some Manpower Planning Models Based On Educational Attainment, Warren L. Balinsky
Research Reports from the Department of Operations
This paper is concerned with analytical solutions to manpower planning models. Dynamic feed-forward models are developed and analyzed. Optimal closed-form solutions minimizing given objective functions for the above models are developed. The models considered treat people as the only flow variable. The flow originates with some particular population of eligible persons and then traces them through the educational and economic sectors of the model. An objective function is developed, composed of educational costs and manpower "inventory" or penalty costs. The educational costs are for teacher and administrative salaries, investment in buildings and grounds, etc. The manpower penalty costs are for …
A Generalized Upper Bounding Algorithm For Multicommodity Network Flow Problems, James K. Hartman, Leon S. Lasdon
A Generalized Upper Bounding Algorithm For Multicommodity Network Flow Problems, James K. Hartman, Leon S. Lasdon
Research Reports from the Department of Operations
An algorithm for solving min cost or max flow multicommodity flow problems is described. It is a specialization of the simplex method, which takes advantage of the special structure of the multicommodity problem. The only non-graph or non-additive operations in a cycle involve the inverse of a working basis, whose dimension is the number of currently saturated arcs. Efficient relations for updating this inverse are derived.
Curriculums In The Operations Research Department At Case Western Reserve University, Patrice Breining
Curriculums In The Operations Research Department At Case Western Reserve University, Patrice Breining
Research Reports from the Department of Operations
The courses within the Operations Research Department were classified into one of four major fields (i.e., Optimization Theory, Stochastic Systems Behavior, Information Processing, and Research and Development). Courses within a field must usually be taken in a pre-defined order. However, since those in different categories are almost independent, and those in Research and Development (R&D) do not usually require specific prerequisites, one can consider three independent oriented networks. These are used to design the average schedule which draws from each course category. The programs of study of 50 randomly selected students registered in the Department between Fall 1967 and Fall …
A General Model For Investment Decisions; A Stochastic Extension, Arnold Reisman, Arza K. Rao
A General Model For Investment Decisions; A Stochastic Extension, Arnold Reisman, Arza K. Rao
Research Reports from the Department of Operations
In the general situation in which investments and/or equipment replacements have to be made at several points of time, Reisman and Buffa have developed a model which will reduce to their present worth all disbursements and receipts involved in the possession and operation of a succession of equipments. This paper deals with a stochastic variation of the above model. General expressions are derived for the expected values of the Purchase Prices, Salvage Values, Operating Expenses and Revenues. The model assumes that the lives of equipment are also stochastic in nature. The case when the rate of return is a function …
Enumerative Algorithms For Integer And Mixed Integer Programs, Harvey M. Salkin
Enumerative Algorithms For Integer And Mixed Integer Programs, Harvey M. Salkin
Research Reports from the Department of Operations
This thesis presents two flexible zero-one integer programming (single branch enumerative) algorithms. It is shown that the first method, applicable to the general program (i.e., min.(c'y: Ay<=b, y_j=0 or 1) ), has the ability, via a new dynamic origin technique, to adapt to the problem data. Other pioneering features, which assist in curtailing the length of the search, are linear programming, post optimization, and criteria for selecting branches from feasible nodes. Using this approach as a foundation, an extension for the mixed integer program (i.e., min.(c'y+d'x: Ay+Dx<=b, x>=0, y_j=0 or 1) ) is discussed. The second algorithm, applicable to the set covering problem (i.e., min.(c'y: Ry>=e, y>=0, y integer); where R is a matrix of 0's and 1's, and e is a vector of 1's), basically obtains upper and lower bounds on the integer problem from the associated linear program. It is shown, by certain proved facts, that one can always obtain two (and sometimes three) integer feasible …
Efficient Methods For Unconstrained Minimization, Leon S. Lasdon
Efficient Methods For Unconstrained Minimization, Leon S. Lasdon
Research Reports from the Department of Operations
It is now well known that the most efficient methods for unconstrained minimization which do not require second derivatives are those which, when applied to a quadratic, generate conjugate directions [1-4]. This insures that a quadratic in n variables is minimized in n steps or less. Since a general twice differentiable function behaves like a positive semidefinite quadratic in the neighborhood of its minimum, methods which will minimize it efficiently must work well on a quadratic. Conjugate direction methods meet this requirement, do not require second derivatives, and can be constructed so that the function is reduced at each step. …
Computer Time-Saving Applications In Economic Analysis: An Integrated Approach, Martin I. Taft, Arnold Reisman
Computer Time-Saving Applications In Economic Analysis: An Integrated Approach, Martin I. Taft, Arnold Reisman
Research Reports from the Department of Operations
A generalized evaluation program known as EVAL, and a general "present worth" program known as CEBS have been developed in the FORTRAN IV Computer language and are currently operational on a time-sharing or batch basis. The programs lead an individual or a group of people through a systematic step-by-step procedure for evaluating the relative value (utility including present worth) of each of a given set of alternatives with respect to explicitly stated goals and objectives. Applications in such areas as equipment design, selection, optimization and replacement; personnel administration; and allocation of resources are presented.
Allocation For Exploratory Development: Modifications In The Torque Model, Allan L. Service
Allocation For Exploratory Development: Modifications In The Torque Model, Allan L. Service
Research Reports from the Department of Operations
The Project TORQUE (Technology or Research Quantitative Utility Evaluation) methodology is examined in detail. A multi-level mathematical program model of the TORQUE procedure is developed. Two kinds of limitations are identified: one arising from procedural uncertainties and the other from process uncertainties. Various modifications in the formulation of the objective function are proposed to deal with these limitations. Directions for future work are indicated.
Programming In Markov Processes, Richard V. Evans
Programming In Markov Processes, Richard V. Evans
Research Reports from the Department of Operations
This paper is concerned with optimization problems which arise when one considers the design and control of systems whose basic behavior follows a Markov law. Of crucial importance is the elementary design problem which contrasted with the elementary control problem by examination of their linear programming formulations. Only linear programming formulations seem able to provide significant comparisons at the moment. Unfortunately the linear programming version of the design problem is not appealing from a computational point of view and alternative algorithms are badly needed.
Programming Problems And Changes In The Stable Behavior Of A Class Of Markov Chains, Richard V. Evans
Programming Problems And Changes In The Stable Behavior Of A Class Of Markov Chains, Richard V. Evans
Research Reports from the Department of Operations
This paper develops expressions for the derivatives with respect to a parameter u of the stable probabilities of a class of Markov Chains whose transition matrices are of the form Q + PW. These expressions lead to iterative schemes for calculation which in term suggest gradient algorithms for finding locally optimal chains.
Resource Allocation To Interrelated R & D Activities, Milton E.F. Schoeman
Resource Allocation To Interrelated R & D Activities, Milton E.F. Schoeman
Research Reports from the Department of Operations
The organizational problem of allocating resources to systems, components, and projects in an R&D network with interrelated elements is investigated. Four mathematical programming models are formulated and analyzed - two static and two dynamic. Essentially, the distinction between the models is based on the assumptions made concerning the nature of the network interrelationships and the form of the project cost-risk functions. Extensive use is made of concepts and developments in convex programming, integer linear programming and dynamic programming. Attention in each case is directed both towards a characterization of the optimal budgeting strategy and towards the construction of an algorithm …
Queueing Systems With Balking And Heterogeneous Servers, Vijendra P. Singh
Queueing Systems With Balking And Heterogeneous Servers, Vijendra P. Singh
Research Reports from the Department of Operations
A Markovian queueing system with balking and the heterogeneous servers, where the service rates are arranged in a decreasing sequence, is first studied. Conditions which show the efficiency of the heterogeneous systems and the optimal sequences of the service rates which yield the minimum values of the average characteristics of the heterogeneous system are found in two and three server cases. Various tables and graphs representing the average characteristics of both the homogeneous and the heterogeneous systems are given. The case where service depends upon queue length and there is a cost associated with both the servers and the waiting …
Primal Decomposition Of Mathematical Programs By Resource Allocation, Gary Jay Silverman
Primal Decomposition Of Mathematical Programs By Resource Allocation, Gary Jay Silverman
Research Reports from the Department of Operations
A new method to solve convex separable programs is developed; with the added consideration of having a feasible solution available at all times. This is done in a context of resource allocation where the optimal return from any given allocation is made a function of the amount of resource allocated. The main research problem involves the properties of this function, which is not generally differentiable, and its directional derivatives. These are explored and a method is constructed using their properties. A linear program called the reallocation problem provides either optimality conditions or a best direction in which to reallocate at …
Optimality Of (S,S) Policies When Setup Costs Vary, Richard V. Evans
Optimality Of (S,S) Policies When Setup Costs Vary, Richard V. Evans
Research Reports from the Department of Operations
This paper considers several analyses of the dynamic programming problem associated with an inventory system in which there is a setup cost which is a decreasing function of the inventory before ordering. Conditions are given under which the optimal policy is of the (s,S) form.
R & D Budgeting Allocation For New Product Development, Warren L. Balinsky, Melvin Brown, Donald C. Friedel, Milton E.F. Schoeman
R & D Budgeting Allocation For New Product Development, Warren L. Balinsky, Melvin Brown, Donald C. Friedel, Milton E.F. Schoeman
Research Reports from the Department of Operations
A brief study is made of the problem of budgeting for new product R & D, when a key budgeting decision is whether to perform the necessary research in-house or whether to acquire available research companies with the required capabilities. Three mathematical models are developed, of increasing complexity, and solution techniques are obtained. Several extensions are formulated, as possible suggestions for future studies.
Some Aspects Of Queueing Theory And Its Applications, U. Narayan Bhat
Some Aspects Of Queueing Theory And Its Applications, U. Narayan Bhat
Research Reports from the Department of Operations
This paper examines the state of queueing theory research, inspired by Saaty’s 1966 critique of the field’s lack of practical application despite substantial theoretical advancements. Acknowledging the limited progression in applied queueing solutions since Morse’s foundational work in 1958, the discussion attributes this gap to insufficient communication between theoretical researchers and applied scientists. The study organizes its review into three critical problem areas: behavioral, statistical, and optimization aspects of queueing systems. Each area is explored with historical context, highlighting trends, contributions, and deficiencies in the literature. Exceptions where optimization and simulation approaches have advanced practical applications are noted. The paper …
The Multidimensional Assignment Problem, William P. Pierskalla
The Multidimensional Assignment Problem, William P. Pierskalla
Research Reports from the Department of Operations
The multidimensional assignment problem is a higher dimensional version of the standard (two-dimensional) assignment problem in the literature. The higher dimensions can be thought of as time or space dimensions or both. An algorithm is proposed for the solution of the multi-index assignment problem. The algorithm is based on a tree search technique of the branch-and-bound variety. It uses dual subproblems to provide easily computed bounds for the primal assignment problem.
Optimality Of Full-Funding Strategies In R & D Allocation Problems, T. S. Chidambaram
Optimality Of Full-Funding Strategies In R & D Allocation Problems, T. S. Chidambaram
Research Reports from the Department of Operations
$C is to be allocated among n "approaches" such that the expected probability of successful completion of at least one of the n approaches is maximized. The ith approach involves a cost ci which is a random variable with probability density function $\i_ and has a probability P_i(c_i) of success. Faced with this uncertainty in cost, the R & D manager can either: a) Choose a large number of approaches to support but allocate to them small amount of money or b) Choose a small number of approaches to support but allocate to them large amount of money. This allocation …
Mathematical Programming With Increasing Constraint Functions, William P. Pierskalla
Mathematical Programming With Increasing Constraint Functions, William P. Pierskalla
Research Reports from the Department of Operations
The mathematical programming problem--find a non-negative n-vector x which maximizes f(x) subject to the constraints gᵢ(x) ≥ 0, i = 1,...,m — is investigated where f(x) is assumed to be concave or pseudo-concave and the gᵢ(x) are increasing functions. It is shown that under certain conditions on gᵢ(x), the Kuhn-Tucker-Lagrange conditions are necessary and sufficient for the optimality of x*. It is also shown that the gᵢ(x) are a useful class of functions since, among other properties, they are closed under non-negative addition, under the addition of any scalar, and under multiplication of non-negative members of the class. Examples of …
The Multi-Dimensional Assignment And Quadratic Assignment Problems, William P. Pierskalla
The Multi-Dimensional Assignment And Quadratic Assignment Problems, William P. Pierskalla
Research Reports from the Department of Operations
The multi-dimensional assignment problem is a higher dimensional version of the standard (two-dimensional) assignment problem in the literature. The higher dimensions can be though of as time or space dimensions or both. An algorithm is proposed for the solution of the multi-index assignment problem. The algorithm is based on a tree search technique of the branch and bound variety. It uses dual subproblems to provide easily computed bounds for the primal assignment problem. The same algorithm with appropriate modifications is used to find an optimal solution to the multi-dimensional quadratic assignment problem.
Project Selection Under Cost And Payoff Value Uncertainties, Burton V. Dean, T.S. Chidambaram, R.R. Palanki
Project Selection Under Cost And Payoff Value Uncertainties, Burton V. Dean, T.S. Chidambaram, R.R. Palanki
Research Reports from the Department of Operations
This paper considers a stochastic version of the project selection model (Model T in Dean and Hauser, "Advanced Material Systems Planning", IEEE Transactions on Engineering Management, March 1967), where $C has to be allocated among n technical approaches so that the probability of at least one approach being successfully completed is maximized. The cost of the ith approach, ci, is a random variable with distribution function, while the probability of success is, in general, a function P^(ct) of the cost. A dynamic programming formulation has been given to solve this problem assuming that the budget allocated to one approach cannot …