MATHEMATICAL ANALYSIS OF FACILITY-COMMODITY SCHEDULING PROBLEMS.

A number of operational situations exist in which certain facilities are available and where a number of commodities must be processed on some or all of these facilities. The paper describes an algorithm to generate schedules which are near optimal or optimal with respect to the total processing time of all the commodities, the idle time of facilities and production rate. Thus, these schedules are characterized by near minimal or minimal total processing time and idle time of facilities and near maximal or maximal production rate. Usually this algorithm does not result in the desired schedule after the first application; it is therefore proposed to generate a set "D" of schedules from which the desired schedule can be selected. A decision rule determines the optimal number of elements belonging to set D. In order to justify the concept of the algorithm for the determination of the schedules mentioned above, an analysis is given of the decision tree associated with the sequencing model in terms of the probabilities related to the nodes in the decision tree. [ABSTRACT FROM AUTHOR]