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This report describes an interdisciplinary effort to apply the techniques of operations research and energy system modeling to a problem of concern to the nuclear-electric power system, namely, determination of cost-effective strategies for capacity expansion of the domestic nuclear fuel reprocessing industry for the 1975-2000 time period. The research also determines cost disadvantages associated with alternative strategies which may be attractive for political, social, or ecological reasons. The sensitivity of results to changes in cost assumptions is investigated at some length.

The authors give a method for strengthening cutting planes for pure and mixed integer programs. The method improves the coefficients of the integer-constrained variables, while leaving unchanged those of the continuous variables. The authors first state the general principle on which the method is based; then the authors apply it to the class of cuts that can be obtained from disjunctive constraints. Finally, simple procedures are given for calculating the improved coefficients of cuts in this class, and illustrate them on numerical examples.

This paper presents branch-and-bound linear mixed integer algorithms which employ nonbasic branching and/or a form of dual relaxation in order to attain the objective function change prescribed by a bound more rapidly than in the standard algorithm. The subproblems arising from the algorithms may at times be solved with no computation or their solution may result in simplex tableaus which are both primal and dual infeasible. Procedures to allow for recovery from dual infeasibility and branching criteria which guarantee optimality will be described. Sample problems will be solved and comparisons made between the specified algorithms.

This paper deals with experimental modifications to the mixed integer branch-and-bound algorithm of Beale and Tomlin. Their algorithm uses the multiple choice structure to dichotomize, not on an individual bivalent variable, but on a subset of variables in a multiple choice class. Partitioning in this manner has proven to be an effective method to obtain more balance penalties and accelerate convergence. The modifications proposed here involve deriving new penalties by enforcing the integer restriction on different combinations of variables and reordering variables within a multiple choice class in an attempt to force an integer solution.

Theory and methods are presented for analyzing sensitivity of the optimal value and optimal solution set to perturbations in problem data in nonlinear bounded optimization problems with discrete variables. Emphasis is given to studying behavior of the optimal value function. Theory is developed primarily for mixed integer programming (MIP) problems, where the domain is a subset of a Euclidean vector space., Personal Identifiable Information (PII) was redacted.

It is shown that the subadditive functions necessary for cutting-planes for mixed integer problems may be defined on all of (R sup n), rather than a submonoid., Sponsored in part by Office of Naval Research, Arlington, Va.

In an earlier report the concept of a mixed integer minimization model (MIMM) was defined and the utility of MIMM's as well as the relationship of MIMM's to classes of piecewise-linear functions of n variables was described. This report establishes necessary and sufficient conditions for bounded-integer MIMM representability for piecewise-linear functions of a single real variable.

OGRAMMING, Nonlinear programming, Linear programming, Optimization, Theorems*Integer programming, Mixed integer programmingIt is well-known that mixed-integer formulations can be used to model important classes of non-convex functions such as fixed-charge functions and linear economy-of-scale cost functions. The purpose of the paper is to formulate a rigorous definition of a mixed-integer model of a given function, and to study the properties of the functions that can be so modelled. An interesting by-product of this approach is the identification of a simple class of functions that cannot be modelled by computer-representable mixed-integer formulations, even though mixed-integer models based on the use of a single arbitrary irrational constant are available for this class. (Author)