The fundamentals of the METRI approach to model-building are discussed. This approach may have applicability where the system to be modelled involves very large numbers of variables, ignorance, uncertainty, and hierarchical relationships, and where the decisions to be made involve enormous amounts of detail. Since the approach was developed in the context of the “allowance list” problem, the application of the approach to that problem is discussed in detail. The problem of “validation” is also discussed, since, as in some other cases, the payoff measure defined by the model has no close parallel in terms of independently available data. The paper is basically an account of certain aspects of a U.S. Navy project.
Non-defense Federal government departments and agencies are in the second year of program development and budgetary review in the context of a program packaging structure, in which activities with related objectives are grouped in common packages for analytical and budgetary purposes. One advantage in this approach is that activities can then be cost-benefit traded relative to a simplified objective structure. Where activities are complex and interrelated, it is particularly useful to develop a system concept as the framework for analysis. This paper seeks to introduce the concepts and methodology of systems analysis as applied to non-defense government operations. It places systems analysis in the context of an overall systems approach intended to develop and implement the best possible system configuration. A broad overview is presented of the problems of objectives, model building, quantification of system parameters, ambiguities in concepts of benefit, cost, and optimization. The organizational problem of integrating system analysis and program packaging concepts is discussed, particularly for an agency characterized by bottom up planning, extensive and detailed routine budgeting, including comments on control of suboptimization of systems analytical capability directly supporting top management and supporting analytical capability throughout the organization.
This paper presents a method, called the convex simplex method, for minimizing a convex objective function subject to linear inequality constraints. The method is a true generalization of Dantzig's linear simplex method both in spirit and in the fact that the same tableau and variable selection techniques are used. With a linear objective function the convex simplex method reduces to the linear simplex method. Moreover, the convex simplex method actually behaves like the linear simplex method whenever it encounters a linear portion of a convex objective function. Many of the sophisticated techniques designed to enhance the efficiency of the linear simplex method are applicable to the convex simplex method. In particular, as an example, a network transportation problem with a convex objective function is solved by using the standard transportation tableau and by only slightly modifying the usual procedure for a linear objective function.
In open-pit mining of lignite, production plans have to be set up for a period of about twenty to thirty years. This is partly due to the close interaction of production plans and investment plans and partly due to legal requirements for open-pit mining in Germany. The major uncertainties encountered in setting up a production plan stem from the geological structure of the pit. The total deposit of lignite in the field as well as the stratification of the layers of waste material and lignite can he considered as stochastic variables. The production plan is formulated as a chance-constrained programming problem. The model requires maximization of a linear form subject to linear and non-linear constraints. In order to facilitate computation of the large-scale problems encountered in practical applications the original model is changed into a straightforward linear programming model. An iteration procedure is derived by which the solution to the original non-linear problem is found. The production plan is computed for different levels of acceptable risk. The results form a risk-profit-surface from which management has to pick the optimum-optimorum plan according to its risk-preference function.
In this paper we study a model that minimizes the sum of production, employment smoothing, and inventory costs subject to a schedule of known demand requirements over a finite time horizon. The three instrumental variables are work force producing at regular-time, work force producing on overtime, and the total work force. Overtime is limited to be not more than a fixed multiple of regular time. The idle portion of the work force and the levels of inventory are resultant variables. We postulate the following shape characteristics for the cost functions production costs are convex-like, smoothing costs are V-shaped, and holding costs are increasing, both the production and holding cost functions need not be stationary. In this paper, we provide upper and lower bounds on the cumulative regular-time plus overtime work force for any sequence of demand requirements. We also give the form of an optimal policy when demands are monotone (either increasing or decreasing). Finally, we derive the asymptotic behavior of optimal policies when demands are monotone and the planning horizon becomes arbitrarily long. All of these results, which convey information about the numerical values of optimal policies, given specific demands and an initial level of inventory, depend only on the shape characteristics of the cost functions. Algorithmic techniques are discussed elsewhere [Lippman, S. A., A. J. Rolfe, H. M. Wagner, J. S. C. Yuan. Algorithms for optimal production scheduling and employment smoothing. Opns Res. To appear.], [Yuan, J. S. C. 1967. Algorithms and multi-product model in production scheduling and employment smoothing. Technical Report 22 (NSF GS-552), Stanford University, August.].
The model presented in this paper uses the method of linear programming to solve multi-plant, multi-product distribution networks constrained by plant production schedules and manufacturing combinations when the shipment of final goods is a function of the raw material input. This function connecting inbound material with outbound finished goods at a given production facility is described by the privilege of mill-in-transit granted by the material haulers. The model is developed under very general assumptions, and is able to solve the networks in terms of optimally applying transit billing, determining production schedules and combinations, and final distribution of product to customer while allowing for outside purchases of the same end products.
The organizational factors which can influence the “effectiveness” of a management science activity are discussed in this paper. The discussion is based on some preliminary findings from a series of studies, performed by Northwestern University, on the life histories of OR/MS groups in 66 large U.S. companies. Many companies could be observed having difficulties in absorbing their new management science functions. Such factors as the level of managerial support, client receptivity, organizational and technical capability of an OR/MS group (i.e., the type and quality of its personnel and leadership), the organizational location, group reputation, the relevance of projects performed, and other variables are noted as being significant in determining effectiveness. How well established a group was in the organization is identified as being a critical factor in how these variables would influence the potential for a group's success or failure. This level of “establishment” is defined in terms of four life-cycle phases, namely, Pre-birth, Introductory, Transitional and Maturity. A case study demonstrating the appearance of these phases is presented. Successful implementation of a group's output is discussed as a possible measure of effectiveness. Client “receptivity” is related to the freedom permitted to a group, by their clients, to select projects, gather data, and implement proposals.
Lee Smith's paper (Smith, L. H. 1967. Ranking procedures and subjective probability distributions. Management Sci. 14 (4, December) B-236–B-249.) is interesting as much for the questions he raises as for the answer he proposes. Those of us who have tried to elicit subjective probability distributions in the context of corporate systems can sympathize with his position that no “objective” way has yet been proposed. It is no wonder that the procedures which he cites as precursors to his proposal are ad hoc and, shall we say, “flexible.” The main issue, however, is whether the procedure advocated in his paper overcomes the limitations of previous devices. Related questions concern: (a) the compatability of probabilistic thinking with the culture of line management; and (b) the accuracy of the elicited judgments, using the “best” of methods.