This paper derives the simple analytic solution to the special but important inventory problem in which the optimal policy is to reorder whenever units are demanded. The demand distribution can be any compound Poisson; the resupply distribution is arbitrary. Both the backorder case and the lost sales case are solved by generalizing a queueing theorem due to Palm. The steady state probabilities for the number of units in resupply (or repair) completely describe the item's long term behavior, and are simply the normalized values of the compound Poisson demand distribution based on the mean of the resupply distribution but not on the distribution itself. Knowledge of these state probabilities enables us to compute several measures of item supply performance as a function of the spare stock, s. Traditional inventory analysis can then be applied to minimize total cost based on estimates of holding cost and supply performance cost. The appendices contain a description of the algorithm and the computer program for calculating stuttering Poisson state probabilities and the measures of effectiveness for the backorder case. Numerical illustrations are also provided.

Past treatment of the single machine maintenance problem has shown that preventive maintenance may be desirable for equipment for which failures are caused at least partially by wear-out factors. In all previous treatment, however, the size of the maintenance-repair crew has been held constant and the optimal maintenance period has then been determined. This paper develops a simultaneous solution for the maintenance-repair crew size and the optimal maintenance period. The optimal maintenance period is seen to shift as the size of the maintenance-repair crew varies. For the multi-machine maintenance problem, the sharing of the maintenance-repair crew creates a queuing system. Because of its complexity, an analytical solution of this multi-machine maintenance queuing system is not feasible. A simulation model was used to develop a set of general rules for scheduling maintenance for the multi-machine case.

The purpose of this note is to point out that the proof in Appendix 1 of Feeney and Sherbrooke [Feeney, G. J., C. C. Sherbrooke. 1966. (s − 1, s) Inventory policy under compound poisson demand. Management Sci. 12(5, January) 391–411] can be adapted to generalize to arbitrary service a queueing formula known for exponential service [Saaty, T. L. 1961. Elements of Queueing Theory. McGraw-Hill, New York, 121.].

The time-sharing computer system now being operated in Phoenix by the Computer Department offers any Company executive willing to spend a few days learning to use the system an entirely new capability to explore and prepare business forecasts. The system does the arithmetic and prints the results in the privacy of the user's office in a few minutes. The planner can explore a range of assumptions and estimates impossible to handle by manual methods and difficult and time-consuming by more traditional computer methods. With the system, the planner can state his basic data and assumptions, observe the results, and then modify any of the assumptions he chooses and get new results within a few minutes. By following this procedure several times it is possible to explore the effects of a variety of environmental assumptions, such as market and price structure for a new product, and to find out what budget of costs for the new product must be realized to yield acceptable business results. This procedure, which requires many days of the time of several individuals by manual methods, can be completed in most cases by one man in less than one day, including the initial programming. An example from a recent new business study is given.

In a recent article [Teichroew, D., A. A. Robichek, M. Montalbano. 1965. An analysis of criteria for investment and financing decisions under certainty. Management Sci. 12(3, November) 151–179.] in this Journal, Daniel Teichroew, Alexander A. Robichek, and Michael Montalbano (TRM) investigated the decision-making procedures for accepting or rejecting investment alternatives available to the firm. There are, however, certain key ideas in their article which need either further clarification or simple modification. It is hoped that by suggesting these clarifications and modifications, this note will make more clear the full value of TRM's basic contributions.

A method is given for maximizing a linear function subject to a quadratic and a number of linear constraints. The method differs from general convex programming methods by terminating in a finite number of iterations and is actually an application of the Simplex and dual methods for quadratic programming to parametric quadratic programming problems. The method is shown to be useful for the solution of some chance-constrained programming problems. Detailed rules and a simple example of an application are given.

Models of situations in which individuals are faced with multiple activities among which they must allocate their effort are postulated. Optimal allocations are found for four assumed motivational structures—profit maximization and three involving performance goals in each of the activities. Heuristic approximations to the optimal allocations are developed. Also, the relationships between the various motivation structures are explored.

Funding of research projects is considered as encompassing three stages: (1) an initial short run plan for funding based upon projected regular demands and availability subject to random deviations; (2) adjustment of the initial plan to take into account the actual regular demands and availability and the funding of significant break-throughs which occur at random intervals preempting other demands; and (3) a plan for longer-run availability and demands which constitute a “posture” desired subsequent to the funding adjustments of (2). The essence of the distribution of the unexpected demands is multi-modality with low probability of occurrence but high resource demand when they do occur. This approach represents a substantial departure from the usual planning model development which produces only an optimal plan based on forecasted developments without provision for adjustment when the forecasted events actually materialize and additional unexpected demands are placed on resources. The adjustment process explored here—which provides the mechanism for optimal implementation of the original plan or control of resource allocation-enables optimal response to information received in “real-time” avoiding the frequently observed over- or under-response to receipt of such information without reference to the impact of the interim decision on future capabilities.

Correction to the article Feeney, G. J., C. C. Sherbrooke. 1966. (s − 1, s) Inventory policy under compound poisson demand. Management Sci. 12(5, January) 391–411.

The paper discusses forecasting peak load demand, one day in advance, for an electric utility, but its main purpose is to illustrate the combination of the exponential adaptation principle with modified rules-of-thumb being successfully used by the electric company. The results indicate that although the company is already doing a good forecasting job, the hybrid exponential model, in simplest form, does even better, although it uses only a portion of the data that is available and used by the company.