Knowledge that Transforms

The purpose of this study is to forecast the market shares of alternative home-heating units: oil-burners, gas-burners and electric-heating units for the United States. The forecasting method used ...

A list of working papers available in the Management Science offices, received from various institutions.

Wesolowsky [Wesolowsky, G. O. 1973. Dynamic facility location. Management Sci. 19 (11, July) 1241–1248.] has examined a dynamic version of the location problem for a single facility, obtained by allowing relocation of the facility over time to optimize a cost or benefit expression. This problem is essentially one of facility replacement, and may be expressed and solved through a simple network model as in deterministic equipment replacement situations ([Veinott, A. F., Jr., H. M. Wagner. 1962. Optimal capacity and scheduling—I. Oper. Res. 10 (4, July–August) 518–532 and Wagner, H. M. 1969. Principles of Operations Research. Prentice-Hall, Englewood Cliffs, New Jersey, pp. 180–181 and pp. 340–342.]).

A multi-pass heuristic scheduling procedure developed for job scheduling problems with deterministic processing times is tested with processing times that are random variables. The heuristic procedure, which uses expected processing times, typically generates a delay schedule (i.e., a schedule in which some operations are delayed while the machine to process these operations is kept idle awaiting the arrival of another operation). Simulation is employed to compare the performance of the schedule generated by the heuristic procedure, a nondelay transformation of that schedule, and the nondelay schedules obtained with four single-pass dispatching rules. The criteria employed are fraction of jobs tardy, mean tardiness, variance of tardiness, and maximum tardiness. The delay schedule produced by the heuristic procedure was found to be markedly superior under certain conditions. Under other conditions, the relative performance of the scheduling rules appears highly problem dependent. Implications of these results are discussed with respect to further research.

This part of the paper introduces some possible implementations of Self-Scaling Variable Metric algorithms based on the theory presented in Part I. These implementations are analyzed theoretically and discussed qualitatively. A special class of SSVM algorithms is introduced, which has the additional property of being invariant under scaling of the objective function or of the variables. Experimental results are provided for a particular case of this class. This case has been tested in comparison to the DFP algorithm on a variety of functions with up to 50 variables. The results indicate that the new method has substantial advantage for functions with a large number of variables.

David P. Rutenberg [Rutenberg, David P. 1970. Generalized networks, generalized upper bounding and decomposition of the convex simplex methods. Management Sci. 16 (5) 388–401.] provided a method to solve separable nonlinear objective functions with large-scale linear constraints by using W. I. Zangwill's Convex Simplex Method [Zangwill, W. L. 1967. The convex simplex method. Management Sci. 14 (3) 221–238.] However, there seem to be several errors in §4.3 [Rutenberg, David P. 1970. Generalized networks, generalized upper bounding and decomposition of the convex simplex methods. Management Sci. 16 (5) 397]. Two counterexamples to his conclusions are given in this paper. A revised definition of subproblem, therefore, an optimal criterion of the large-scaled program, is also given.