Knowledge that Transforms

The “Criss-cross” linear programming method formulated by Zionts (Zionts, Sanley. 1969. The criss-cross method for solving linear programming problems. Management Sci. 15 (7, March) 426–445.), although remarkably efficient for small problems (Zionts [Zionts, Sanley. 1972. Some empirical tests of the criss-cross method. Management Sci. 19 (4, December) 406–410.]), often requires an excessive number of iterations for problems of size 40 × 40 or larger. Garfinkel and Yu (Garfinkel, Robert S., P. L. Yu. 1974. The composite simplex algorithm. Paper MA10.4. Joint National ORSA/TIMS Meeting, Boston, 22 April.) reported 3 such problems for which it terminated short of solution after 1000 pivots. Fortunately, the algorithm can be salvaged. All that is needed is a minor pivot rule change.

Concrete criteria are needed for patient selection for scarce medical treatments and ranking of patient urgency for, or salvageability by, a given form of treatment. The mathematical theory of multi-attribute value functions is employed to rank order chronic renal failure patients with regard to therapeutic expectations. Order-2 mutual preferential independence was observed, thus an additive value function was justified. The paper demonstrates two different procedures for assessing a value function over a discrete attribute. The proposed approach yields a rank ordering (health status index) consistent with the physician's preferences and judgment. It can be employed for any medical decision process, even when only weaker preferential independence properties apply.

The optimal order size and reorder point are obtained for a simple perturbed demand inventory model having ordering and holding costs.

We consider open and closed queueing networks consisting of a set of controlled service centers. The controlled service center contains an exponential server, a queue of delayed customers and a control switch between them. The switch position is a function (control function) of the service center state which provides a means of controlling the service rate by admitting or not users into the server's queue. We give the stationary probability distribution for a broad class of control functions. An application of these results to the expected queue lengths and the expected waiting times in a two-server closed network is also considered.

This paper presents a model that develops a concise representation of a decision making task with a fixed number of alternatives. The methodology relies upon a conceptual information processing system analogous to that employed by a novice decision maker during the evolution of his decision paradigms. The model requires only the specification of relevant input stimuli and a sample of stimuli-response relationships in order to develop a representation of the task. The resulting representation is in a form which allows a predicted decision to be made given only the relevant stimuli. A mechanism is presented for efficiently operationalizing the task representation. An empirical study is presented which demonstrates the learning and performance capabilities of the model in the confines of an overdraft processing task.

We show in this paper the formal connection between brand switching models and multiperiod analysis of brand choice behavior. A formal, well-defined stochastic process is developed from stochastic choice premises which permits analysis of any event or combination of events in terms of subsets of the market. The formal connection between single-brand analysis and multi-brand analysis is demonstrated. The parameters of the stochastic process involve the market shares and a measure of the heterogeneity of the population. This information is sufficient to permit the estimation of aggregate brand switching on adjacent trials or brand penetration and multiple brand purchasing over sequences of purchase occasions.

This paper is concerned with developing long-range planning models of transportation systems to assist planners in assessing the impact of various levels of service in a transportation network. Railroad distribution networks are studied in particular, and emphasis is placed on the problem of determining optimal levels of service (improvements, degradations, abandonments) on each arc in the existing network. The problem is to optimally design a transportation system: the term “design” as used here, does not comprehend new networks, but more importantly, the optimization or “pruning” of existing transshipment networks. The model is formulated so that improvements to the shipping arcs are included as decision variables: The concave transshipment problem is extended to the case where coefficients of the shipping cost functions are treated as decision variables. Thus the model determines optimum movements of freight between nodes and optimum improvements/degradations to the network to minimize shipping costs plus maintenance costs on the shipping arcs. The result is a nonconvex, nonconcave transshipment problem which is then converted into a concave minimization problem for which global optimal solutions can be found. Several sample problems are solved.

A model is developed which allocates an available budget to research alternatives subject to budgetary constraints on both organizational and technical entities. The solution algorithm is based on the out-of-kilter minimum cost network flow algorithm and is programmed for use in a time-share, conversational mode. Although the model does not describe the decision processes observed empirically, its output is sufficiently similar to actual allocations that it can be viewed as predictive. Strengths and weaknesses of the model are detailed based on questionnaire and interview data provided by the potential users of the system. The decision information system is used to illustrate that experimentation concerned with better understanding of the adoption process can be used to facilitate model design and application.

This paper provides a computational technique for the evaluation of the net present value (NPV) of an investment, in which the cash inflows occur at random time points and which terminates after a fixed time interval. The initial cash outlay is deterministic and the magnitudes of the cash inflows are nonnegative random variables with known distributions. The lengths of the intervals between successive cash inflows are independently distributed and independent of the magnitude of the inflows. The Laplace transform of the distribution of the NPV is computed for both cases of mutual independence and perfect correlation of the inflows. It is argued that these distributions are indispensable in determining the accuracy of the manager's estimates and in evaluating actual versus expected performance of a project.

As the demand for natural resources intensifies so too the costs of further exploitation of these resources become enormous. These enormous costs in turn require the development of a given resource to be a cooperative venture among several participants, each of whom must be assured that the costs and benefits of the venture will be “fairly” distributed among them. It is at this point that the theory of cooperative games may offer guidelines as to what is fair or not fair to each participant or player in a given cost allocation. To illustrate an application of cooperative game theory in assigning “fair” costs and benefits to the participants in a cooperative venture we will consider a problem in water resource development.