Chance-constrained programming methods are applied to examine some statistical properties of PERT networks. Using duality, the PERT method is shown to be equivalent to use of the crudest linear decision rule and the confidence (or lack thereof) in meeting constraints is explicitly presented. The distribution of completion times (= Tintner's stochastic programming) follows easily and may often be multimodal, contrasting with (erroneous) central limit theorem usages in the literature. Possible extensions and developments of PERT using more adequate chance-constrained models and techniques are suggested and will be presented elsewhere.

A new procedure for mixed integer programming is presented. It is applicable where the integer variables must be either zero or one, and where the integer variables are divided into sets such that the variables in each set sum to unity. Numerous practical applications fit this formulation. A justification for the algorithm is given, but proof of convergence is not known. The procedure has solved all test problems so far, and this computational experience is discussed along with some applications.

A solution to the feed-mix problem is presented that treats the problem as a part of a decision-making system. Three basic approaches are utilized to solve the problem of continual reformulation of many feeds in order to follow market price fluctuations. The resulting system can produce 20 to 30 new formulations in an hour on an IBM 650. Extension of the system to faster computers would make the system more flexible and responsive to grain market fluctuations.

The optimum routing of a fleet of trucks of varying capacities from a central depot to a number of delivery points may require a selection from a very large number of possible routes, if the number of delivery points is also large. This paper, after considering certain theoretical aspects of the problem, develops an iterative procedure that enables the rapid selection of an optimum or near-optimum route. It has been programmed for a digital computer but is also suitable for hand computation.